Texas Go Math

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Module 14 Quiz Answer Key.

Texas Go Math Grade 6 Module 14 Quiz Answer Key

Texas Go Math Grade 6 Module 14 Ready to Go On? Answer Key

14.1 Graphing on the Coordinate Plane

Graph each point on the coordinate plane.

Question 1.
A(-2, 4)
Answer:
Point A is 2 units left of the origin, and 4 units up. It has x-coordinate -2 and y-coordinate 4 written (-2, 4). It is located in Quadrant II.
A = (-2, 4) Final solution

Texas Go Math Grade 6 Answer Key Module 14 Review Quiz Question 2.
B(3, 5)
Answer:
Point B is 3 units right of the origin, and 5 units up. It has x-coordinate 3 and y-coordinate 5, written (3, 5). It is located in Quadrant I.
B = (3, 5) Final solution

Question 3.
C(6, -4)
Answer:
Point C is 6 units right of the origin, and 4 units down. It has x-coordinate 6 and y-coordinate -4 written (6, -4) It is located in Quadrant IV.
C = (6, -4) Final solution

Question 4.
D(-3, -5)
Answer:
Point D is 3 units left of the origin, and 5 units down. It has x-coordinate -3 and y-coordinate -5, written (-3, -5) It is located in Quadrant III.
D(-3, -5) Final solution

Module 14 Answer Key 6th Grade Go Math Question 5.
E(7, 2)
Answer:
Point E is 7 units right of the origin, and 2 units up It has x-coordinate 7 and y-coordinate 2, written (7, 2). It is located in Quadrant I.
E = (7, 2) Final solution

Question 6.
F(-4, 6)
Answer:
Point F is 4 units left of the origin, and 6 units up It has x-coordinate -4 and y-coordinate 6, written (-4, 6). It is located in Quadrant II.
F = (-4, 6) Fina solution

14.2 Independent and Dependent Variables in Tables and Graphs

Question 7.
Jon buys packages of pens for $5 each. Identify the dependent variables in the situation.
Answer:
The independent variable in this situation is the number of packages bought. The dependent variable in this situation is the total cost of the packages. The equation relating the 2 is y = 5x

14.3 Writing Equations from Tables

Write an equation that represents the data in the table.

Question 8.

Answer:
Compare the x- and y-values to find a pattern
Each y-value is 7 times the corresponding x-value
Use the pattern to write an equation expressing y in terms of x
y = 7x
y = 7x Final solution
y = 7x

Texas Go Math Module 14 Quiz Ready To Go On Answer Key Question 9.

Answer:
Compare the x- and y-values to find a pattern.
Each y-value is 12 more than the corresponding x-value.
Use the pattern to write an equation expressing y in terms of x.
y = x + 12
y = x + 12 Final solution
y = x + 12

14.4 Representing Algebraic Relationships in Tables and Graphs

Graph each equation.

Question 10.
y = x + 3

Answer:
Make a table of values. Choose some values for x and use the equation to find the corresponding values for y.
Plot the ordered pairs from the table.
Draw a line through the plotted points to represent all of the ordered pair solutions of the equation.

Question 11.
y = 5x

Answer:
Solution to this example is given below
y = 5x
Make a table of values. Choose some values for x and use the equation to find the corresponding values for y.
Plot the ordered pairs from the table.
Draw a line through the plotted points to represent all of the ordered pair solutions of the equation.

Essential Question

Module 14 Quiz Ready To Go On Answers 6th Grade Question 12.
How can you write an equation ¡n two variables to solve a problem?
Answer:
Any 2 quantity-based situation can be converted to an algebraic equation by identifying the independent and the dependent quantities and examining the relationship between them

Texas Go Math Grade 6 Module 14 Mixed Review Texas Test Prep Answer Key

Selected Response

Question 1.
What are the coordinates of point G on the coordinate grid below?

(A) (4, 3)
(B) (4, -3)
(C) (-4, 3)
(D) (-4, -3)
Answer:
(B) (4, -3)

Explanation:
Point G is 4 units right on the origin, and 3 units down It has x-coordinate 4 and y-coordinate -3, written (4, -3). It is located in Quadrant IV.
(G = 4, -3)
B This option is correct answer

Question 2.
A point is located in quadrant II of a coordinate plane. Which of the following could be the coordinates of that point?
(A) (-5, -7)
(B) (5, 7)
(C) (-5, 7)
(D) (5, -7)
Answer:
(C) (-5, 7)

Explanation:
A) Point A is 5 units Left of the origin, and 7 units down It has x-coordinate -5 and y-coordinate -7, written (-5, -7). It is located in Quadrant III.
Option A) is not correct answer
B)Point B is 5 units right of the origin, and 7 units up. It has x-coordinate 5 and y-coordinate 7, written (5, 7). It is located in Quadrant I.
Option B) is not correct answer
C)Point C is 5 units Left of the origin, and 7 units up. It has x-coordinate -5 and y-coordinate 7, written (-5, 7). It is located in Quadrant II.
Option C) is correct answer
D)Point D is 5 units right of the origin, and 7 units down. It has x-coordinate 5 and y-coordinate -7, written (5, -7). It is located in Quadrant IV.
Option D) is not correct answer
C This option is correct answer

Question 3.
Man had 5 library books. He checked 1 additional book out every week without returning any books. Which equation describes the number of books he has, y, after x weeks?
(A) y = 5x
(B) y = 5 – x
(C) y = 1 + 5x
(D) y = 5 + x
Answer:
(D) y = 5 + x

Explanation:
He had 5 books which increased at the rate of 1 book per week so he had y = x + 5 books in x weeks

Option D

Question 4.
Stewart is playing a video game. He earns the same number of points for each prize he captures. He earned 1,200 points for 6 prizes, 2,000 points for 10 prizes, and 2,600 points for 13 prizes. Which is the dependent variable in the situation?
(A) the number of prizes captured
(B) the number of points earned
(C) the number of hours
(D) the number of prizes available
Answer:
(B) the number of points earned

Explanation:
The number of points earned depends on the number of prizes captured, therefore the number of points earned is the dependent variable.

Option B.

Grade 6 Module 14 Quiz Answer Key Go Math Question 5.
Dwayne graphed the equation y = 10 + x. Which point does the graph not pass through?
(Â) (0, 10)
(B) (3, 13)
(C) (8, 2)
(D) (5, 15)
Answer:
(C) (8, 2)

Explanation:
We notice that through the point (8, 2) the graph does not pass.
Really if we substitute 8 for r in the equation, we get:
y = 10 + 8 = 18 ≠ 2
So, the conclusion is that correct answer is C

(C) (8, 2)

Question 6.
Amy gets paid by the hour. Her little sister helps. As shown below, Amy gives her sister part of her earnings. Which equation represents Amy’s pay when her sister’s pay is $13?

(A) y = \(\frac{13}{5}\)
(B) 13 = \(\frac{x}{5}\)
(C) 5y = 13
(D) 13 = 5x
Answer:
First, we need to find an equation which describes this situation:

so, we get the following equation
y = \(\frac{1}{5}\)x
Now, we will substitute 13 for y in previous equation and we wilL find the equation which represent Amy’s pay
13 = \(\frac{x}{5}\)x
So, correct answer is B.

Gridded Response

Question 7.
Betty earns $7.50 per hour at a part-time job. Let x be the number of hours and y be the amount she earns. Betty makes a graph to show how x and y are related. If she earns $60, how many hours did she work?

Answer:
According to informations in this task, we get the following equation which describes the relationship between hours and the amount Betty earns:
y = 7.50x
Now, we will graph previous equation:

Now, we wilt substitute 60 for y in the previous equation and calculate x on that way, which represent how many
hours she worked.
60 = 7.50x
x = 8
Betty worked 8 hours.

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 14.4 Answer Key Representing Algebraic Relationships in Tables and Graphs.

Texas Go Math Grade 6 Lesson 14.4 Answer Key Representing Algebraic Relationships in Tables and Graphs

Essential Question
How can you use verbal descriptions, tables, and graphs to represent algebraic relationships?

Texas Go Math Grade 6 Lesson 14.4 Explore Activity Answer Key

Explore Activity 1
Representing Algebraic Relationships
Angie’s walking speed is 5 kilometers per hour, and May’s is 4 kilometers per hour. Use tables and graphs to show how the distance each girl walks is related to time.

A. For each girl, make a table comparing time and distance.

B. For each girl, make a graph showing her distance y as it depends on time x. Plot points from the table and connect them with a line.

Reflect

Go Math Grade 6 Answers Pdf Algebraic Relationships Lesson 14.4 Question 1.
Analyze Relationships How can you use the tables to determine which girl is walking faster? How can you use the graphs?
Answer:
It can be seen from the table, that after 2 hours Angie has covered 10 miles while Mary has only covered 8 miles. This implies that Angie is walking faster than Mary.

The graph of Angie will be steeper than that of Mary’s indicating a greater rate of change of distance with respect
to time.

Explore Activity 2
Writing an Equation from a Graph
Cherise pays the entrance fee to visit a museum, then buys souvenirs at the gift shop. The graph shows the relationship between the total amount she spends at the museum and the amount she spends at the gift shop. Write an equation to represent the relationship.

A. Read the ordered pairs from the graph. Use them to complete a table comparing total spent y to amount spent at the gift shop x.

B. What is the pattern in the table?

C. Write an equation that expresses the total amount y in terms of the gift shop amount x.

Reflect

Question 2.
Identify the dependent and independent quantities in this situation.
Answer:
The money spent in the gift shop is the independent variable while the total amount depending on the gift shop amount is the independent variable.

Question 3.
Draw a line through the points in the graph. Find the point that represents Cherise spending $25 at the gift shop. Use this point to find the total she would spend if she spent $25 at the gift shop. Then use your equation from C to verify your answer.
Answer:
On the following picture there is a line through the given points in the graph.

From the graph, we can see that if she spent $25 at the gift shop, she would total spend $30.
Really, the equation from C is y = x + 5 where y represents the total amount and x represents the gift shop amount. We will Substitute 25 for x in this equation and get:
y = 25 + 5 = 30
So, we verified our answer.
$30

Texas Go Math Grade 6 Pdf Lesson 14.4 Practice Problems Answer Key Question 4.
Graph y = x + 2.5.

Answer:
Solution to this example is given below
y = x + 2.5
Make a table of values. Choose some values for x and use the equation to find the corresponding values for y.
Plot the ordered pairs from the table.
Draw a line through the plotted points to represent all of the ordered pair solutions of the equation.

Texas Go Math Grade 6 Lesson 14.4 Guided Practice Answer Key

Frank mows lawns in the summer to earn extra money. He can mow 3 lawns every hour he works. (Explore Activity 1 and Explore Activity 2)

Question 1.
Make a table to show the relationship between the number of hours. Frank works, x, and the number of lawns he mows, y. Graph the relationship and write an equation.

Answer:
Using given information we get the following table:

One way to determine relationship between the number of hours Frank works, x, and the number of lawns he mows, y is to find their quotient:
\(\frac{3}{1}\) = 3
\(\frac{6}{2}\) = 3
\(\frac{9}{3}\)3
So, required relationship is:
y = 3x
Now, we will graph previous equation.

y = 3x

Graph y = 1.5x. (Example 1)

Texas Go Math Grade 6 Graphing from Points and Tables Answer Key Question 2.
Make a table to show the relationship.


Answer:
Solution to this example is given below
y = 1.5x
Make a table of values. Choose some values or x and use the equation to find the corresponding values for y.

Question 3.
Plot the points and draw a line through them.
Answer:
Solution to this example is given below
y = 1.5x
Plot the ordered pairs from the table.
Draw a line through the plotted points to represent all of the ordered pair solutions of the equation.

Essential Check-in

Question 4.
How can a table represent an algebraic relationship between two variables?
Answer:
A table is a collection of ordered pairs which show a certain algebraic relationship between two variables. This can be a multiplicative one where y = or an additive one where y = x + k. The table enables the readers to determine this algebraic relationship using the ordered pairs in the table.

Texas Go Math Grade 6 Lesson 14.4 Independent Practice Answer Key

Students at Mills Middle School are required to work a certain number of community service hours. Students may work additional hours beyond the requirement.

Question 5.
Read the ordered pairs from the graph to make a table.


Answer:
x from the graph Corresponding value of y from the graph
0 20

5 25

10 30

15 35

20 40

Grade 6 Independent Practice Answer Key Texas Go Math Lesson 14.4 Question 6.
Write an equation that expresses the total hours in terms of the additional hours.
Answer:
From the study of the graph as well as the table, it can be seen that the total hours when additional hours is equal to 0 is 20, this implies that the total number of hours is the sum of 20 and additional hours, so the equation for the relation between additional hours z and total hours y, becomes: y = x + 20
y = x + 20.

Question 7.
Analyze Relationships How many community service hours are students required to work? Explain.
Answer:
The students are required to work 20 hours. This is seen when 0 additional hours are worked, the total is 20 hours.
The students are required to work 20 hours.

Beth is using a map. Let x represent a distance in centimeters on the map. To find an actual distance y in kilometers, Beth uses the equation y = 8x.

Question 8.
Make a table comparing a distance on the map to the actual distance.

Answer:
x y = 8x
0 y = 8(0) = O
1 y = 8(1) = 8
2 y = 8(2) = 16
3 y = 8(3) = 24
4 y = 8(4) = 32
5 y = 8(5) = 40

Question 9.
Make a graph that compares the map distance to the actual distance.
Answer:
On the following picture there is a graph that compares the map distance to the actual distance.

Graph y = 8x

Go Math Grade 6 Answer Key Equations, Tables and Graphs Worksheet Answers Question 10.
Critical Thinking The actual distance between Town A and Town B is 64 kilometers. What is the distance on Beth’s map? Did you use the graph or the equation to find the answer? Why?

Answer:
Use of the equation here is preferable because the graph plotted does not contain the point where y = 64, therefore given equation:
y = 8x
Substitute the value of y ¡n the given equation:
64 = 8x
Solve for x:
x = \(\frac{64}{8}\) = 8
Town A and Town B are 8 centimeters apart on the map.

Question 11.
Multistep The equation y = 9x represents the total cost y for x movie tickets.

a. Make a table and a graph to represent the relationship between x and y.


Answer:
On the following picture there is a graph of the equation y = 9x.

Also, there is the following table which represent the relationship between x and y:

b. Critical Thinking In this situation, which quantity is dependent and which is independent? Justify your answer.
Answer:
We can conclude that here dependent quantity is total, cost and independent quantity is number of tickets. We could conclude this because total cost depends of the number of tickets we bought

c. Multiple Representations Eight friends want to go see a movie. Would you prefer to use an equation, a table, or a graph to find the cost of 8 movie tickets? Explain how you would use your chosen method to find the cost.
Answer:
Here, the easiest way is to use an equation. We will substitute 8 for x in the equation and calculate y:
y = 9.8
y = 72
So, tickets for 8 movies will cost $72.

Texas Go Math Grade 6 Lesson 14.4 H.O.T. Focus On Higher Order Thinking Answer Key

6th Grade Go Math Graphs Algebraic Relationships Equations Question 12.
Critical Thinking Think about graphing the equations y = 5x and y = x + 500. Which line would be steeper? Why?
Answer:
The steepness of a graph depends on its coefficient of x, the greater the value of the coefficient, the more steep its graph is. Here 5 < 1 so the graph of y = 5x will be steeper than that of y = x + 500.

y = 5x will have a steeper graph.

Question 13.
Persevere in Problem Solving Marcus plotted the points (0, 0), (6, 2), (18, 6), and (21, 7) on a graph. He wrote an equation for the relationship. Find another ordered pair that could be a solution to Marcus’s equation. Justify your answer.
Answer:
From the given ordered pairs, it can be seen that the value of y is \(\frac{2}{6}\) = \(\frac{6}{18}\) = \(\frac{7}{21}\) = \(\frac{1}{3}\); times that of its corresponding value of x, therefore if z = 24, then y = \(\frac{24}{3}\) = 8 so the ordered pair (24, 8) must also lie on this graph.

Question 14.
Error Analysis The cost of a personal pizza is $4. A drink costs $1. Anna wrote the equation y = 4x + 1 to represent the relationship between the total cost y of buying x meals that include one personal pizza and one drink. Describe Anna’s error and write the correct equation.
Answer:
1 meal consists of a pizza for $4 and a drink for $1 so the total cost of 1 meal is $4 + $1 = $5. This implies that the cost of buying x meals will be y = 5x and not y = 4x + 1.

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Unit 5 Study Guide Review Answer Key.

Texas Go Math Grade 6 Unit 5 Study Guide Review Answer Key

Angles, Triangles, and Equations

Essential Question
How can you use angles, triangles, and equations to solve real-world problems?

Exercises

Tell whether a triangle can have sides with the given lengths. If it cannot, give an inequality that shows why not. (Lesson 15.1)

Question 1.
5 in., 12 in., 13 in.. ______
Answer:
Find the sum of the two sides of the triangLe then compare to the third side.

5 + 12 > 13 add the two sides and compare to the third side
17 > 13 the sum of the two sides is greater than the third side

5 + 13 > 12 add the two sides and compare to the third side
18 > 12 the sum of the two sides is greater than the third side

13 + 12 > 5 add the two sides and compare to the third side
25 > 5 the sum of the two sides is greater than the third side

The given sides can be the side lengths of a triangle because the sum of two sides is greater than the third side.

Grade 6 Unit 5 Angles and Triangles Unit Study Guide Texas Go Math Question 2.
4.5 ft, 5.5 ft, 11 ft. ______
Answer:
Find the sum of the two sides of the triangle then compare to the third side.
4.5 + 5.5 > 11 add the two sides and compare to the third side
10 ≯ 11 the sum of the two sides is NOT greater than the third side

4.5 + 11 > 5.5 add the two sides and compare to the third side
15.5 > 5.5 the sum of the two sides is greater than the third side

11 + 5.5 > 4.5 add the two sides and compare to the third side
16.5 > 4.5 the sum of the two sides is greater than the third side

The given side lengths cannot be used for a triangle because there are two sides with a sum lesser than the third side.

Find each missing angle measure. Classify each triangle as acute, obtuse, or right. (Lesson 15.2)

Question 3.

Answer:
Determine the unknown angle.
38° + 82° + x = 180° add all the angle measurements
120° + x = 180° sum of the given inner angle measurements
120° + x – 120° = 180° – 120° subtract 120° from both sides of the equation
x = 60° measure of the unknown angle

The value of x is 60°.

Question 4.

Answer:
Determine the unknown angle.
41°+ x + 49° = 180° add all the angle measurements
90° + x = 180° sum of the given inner angle measurements
90°+ x – 90°= 180° – 90° subtract 90° from both sides of the equation
x = 90° measure of the unknown angle
The value of x is 90°.

Match each side length with its correct measure. Classify each triangle as scalene, isosceles, or equilateral. (Lesson 15.3)

Question 5.
The side lengths of triangle ABC are 6.4 ft, 10 ft, and 6.4 ft.

Answer:
Determine the side length of the triangle.
AB = 6.4 ft opposite side of ∠C
BC = 10 ft opposite side of ∠À
AC = 6.4 ft opposite side of ∠B

The triangle is an isosceles triangle with the following side lengths:
AB = 6.4 ft,
BC = 10 ft,
AC = 6.4 ft.

Unit 5 Study Guide Answer Key Go Math Grade 6 Question 6.
The side length of ZX is 17 cm.

Answer:
Determine the side length of the triangle.
XY = 17 cm opposite side of ∠Z
YZ = 17 cm opposite side of ∠X

The triangle is an equilateral triangle with alt side lengths equal to 17 cm.

Area and Volume Equations

Essential Question
How can you use area and volume equations to solve real-world problems?

Exercises

Find the area of each figure. (Lessons 16.1, 16.2)

Question 1.

Answer:
b = 24
h = 12

Write equation of area of a parallelogram:
Area = b × h
Substitute values:
Area = 24 × 12
Evaluate:
Area = 288
Area of the parallelogram is 288 square inches

Question 2.

Answer:
Determine the area of the triangle.

The area of the triangle is 32 ft².

Find the missing measurement.

Grade 6 Angles and Triangles Unit Study Guide Answer Key Question 3.

Answer:
b₁ = 11, b₂ = 14
Area = 62.5

Height of the given trapezoid is 5 meters.

Question 4.

Answer:
Solution to this example is given below
b = ? mm h = 4mm A = 26 mm²
A = \(\frac{1}{2}\)bh
26 = \(\frac{1}{2}\)(b)(4 mm) Substitute
26 = (2)b Multiply
\(\frac{26}{2}\) = \(\frac{(2) b}{2}\) Divide both sides by 2
13 = b Simplify
b = 13 mm Final solution

Find the volume of each rectangular prism.

Question 5.

Answer:
l = 20
w = 6
h = 8
Write equation of volume of a rectangular prism:
Volume = l × w × h
Substitute values:
Volume = 20 × 6 × 8
Evaluate:
Volume = 960
Volume of the given rectangular prism is equal to 960 cubic inches.

Grade 6 Unit 5 Test Study Guide Relationships in Triangles Question 6.
A rectangular prism with a width of 7 units, a length of 8 units, and a height of 2 units ______________________
Answer:
l = 8
w = 7
h = 2
Write equation of volume of a rectangular prism:
Volume = l × w × h
Substitute values:
Volume = 8 × 7 × 2
Evaluate:
Volume = 112
Volume of the given rectangular prism is equal to 112 cubic inches.

Question 7.
Jelani is ordering a piece of glass in the shape of a trapezoid to create a patio table top. Each square foot of glass costs $25. The trapezoid has base lengths of 5 feet and 3 feet and a height of 4 feet. Find the cost of the glass. (Lesson 16.1)
Answer:
Determine the area of the glass and the cost

The glass costs $400

Texas Go Math Grade 6 Unit 5 Performance Tasks Answer Key

Question 1.
CAREERS IN MATH Theater Set Construction Ahmed and Karina are building scenery of the Egyptian pyramids out of plywood for a community play. The pyramids are represented by triangles on a rectangular base. The diagram shows the measurements of the piece of scenery.

a. They have one sheet of plywood, 3 ft by 6 ft. Will they be able to make the piece using this one sheet? Explain.
Answer:
A = 3 6 area of the plywood
A= 18 ft²
Determine the area of the scenery.

Yes, they will be able to make the piece using only one sheet because the plywood is enough.

Determine the area of the completed piece.

b. How many square feet of plywood is in the completed piece? Show your work.
Answer:
Determine the area of the completed piece

c. The pyramids (the triangles) will be painted gray, and the base (the rectangle) will be painted black. How much of each paint color will they use, if one quart covers 45 square feet? Only one side of the model needs to be painted, but two coats of paint will be needed. Show your work. Round to the nearest hundredth of a square foot.
Answer:
Determine the area of the rectangular base.
A = 5 0.75 area of the rectangular base
A = 3.75 . 2multiply by 2 for the paint needed
A = 7.5 ft² area covered by the black paint
Determine the area of the triangles.

A = 0.75 + 1.5 + 0.375 simplify
A = 2.625 . 2 multiply by 2 for the paint needed
A = 5.25 ft² area covered by the gray paint

Determine the amount of paint to be used for the model

Geometry Unit 5 Test Answer Key Grade 6 Texas Go Math Question 2.
Cassandra is making a design for a logo. One part of the design is a triangle with two congruent sides. She must draw the triangle with at least one side with length 6 centimeters, and at least one side with a length of 4 centimeters. Sketch two possible figures that Cassandra could use. Label the side lengths in both figures.
Answer:
Figure that Cassandra could use.

Figure that Cassandra could use.

The figure is an isosceles triangle with side lengths 6 cm – 6 cm – 4 cm or 4 cm – 4 cm – 6 cm.

Texas Go Math Grade 6 Unit 5 Mixed Review Texas Test Prep Answer Key

Selected Response

Question 1.
Part of a large wooden art project will be a triangle formed by joining three boards together. The artist has four boards that measure 16 feet, 11 feet, 7 feet, and 3 feet. Which board could not be used with two of the others to form a triangle?
(A) the 3-foot board
(B) the 7-foot board
(C) the 11-foot board
(D) the 16-foot board
Answer:
(A) the 3-foot board

Explanation:
Find the sum of the two sides of the triangle then compare to the third side.
16 + 11 > 7 add the two sides and compare to the third side
27 > 7 the sum of the two sides is greater than the third side
16 + 7 > 11 add the two sides and compare to the third side
23 > 11 the sum of the two sides is greater than the third side
7 + 11 > 16 add the two sides and compare to the third side
17 > 16 the sum of the two sides is greater than the third side

The board that could not be used to form a triangle is A. the 3-foot board.

Question 2.
Which of these could be the value of x in the triangle below?

(A) 5
(B) 6
(C) 8
(D) 10
Answer:
(B) 6

Explanation:
Determine the opposite side length of the midsize angle.
a. 5x = 5 . 5 substitute for the given value of x
= 25
b. 5x = 5 . 6 substitute for the given value of x
= 30 opposite side length of the midsize angle
c. 5x = 5 8 substitute for the given value of x
= 40
d. 5x = 5 . 10 substitute for the given value of x
= 50
The value of x that will satisfy the given side lengths is B. 6.

Question 3.
What is the area of a trapezoid that has bases measuring 19 centimeters and 23 centimeters, and a height of 14 centimeters?
(A) 105 square centimeters
(B) 266 square centimeters
(C) 294 square centimeters
(D) 322 square centimeters
Answer:
(C) 294 square centimeters

Explanation:
Solution to this example is given beLow
b₁ = 19 b₂ = 23 h = 14
Use the formula for area of a trapezoid
A = \(\frac{1}{2} h\left(b_{1}+b_{2}\right)\)
= \(\frac{1}{2} \cdot 14(19+23)\) Substitute
= \(\frac{1}{2} \cdot 14(42)\) Add inside the parentheses
= 7 . 42 Multiply \(\frac{1}{2}\) and 14
= 294 square centimeters Multiply
C. This option is correct answer

Question 4.
What is the area of the triangle shown below?

(A) 110.5 square inches
(B) 221 square inches
(C) 442 square inches
(D) 884 square inches
Answer:
(B) 221 square inches

Explanation:
Find the area of the triangle.
b = 26 inches h = 17 inches
A = \(\frac{1}{2} b h\)
= \(\frac{1}{2}(26 \text { inches })(17 \text { inches })\) Substitute
= 221 square inches Multiply
Area of the triangle is 221 square inches
B This option is correct answer

Question 5.
The trapezoid below has an area of 475 square meters.

Which equation could you solve to find the height of the trapezoid?
(A) 23h = 475
(B) 252h = 475
(C) 46h = 475
(D) 504h = 475
Answer:
(A) 23h = 475

Explanation:
Data:
b₁ = 18, b₂ = 28
Area = 475

Write equation of area of a trapezoid:
Area = \(\frac{1}{2} \times\left(b_{1}+b_{2}\right) \times h\)
Substitute values:
475 = \(\frac{1}{2} \times(18+28) \times h\)
Simplify:
475 = 23h

Unit 5 Go Math Test 6th Grade Answer Key Question 6.
A rectangular prism has a volume of 1,500 cubic centimeters. It has a length of 34 centimeters and a width of 22 centimeters. Which equation could be solved to find the height of the rectangular prism?
(A) 374h = 1,500
(B) 28h = 1,500
(C) 748h = 1,500
(D) 56h = 1,500
Answer:
(C) 748h = 1,500

Explanation:
Data:
l = 34, w = 22
volume = 1500

Write equation of volume of a rectangular prism:
Volume = l × w × h
Substitute values:
1500 = 34 × 22 × h
Simplify:
1500 = 748h
Option C.

Question 7.
Which expression represents the sum of 59 and x?
(A) 59 + x
(B) 59 ÷ x
(C) 59x
(D) 59 – x
Answer:
(A) 59 + x

Explanation:
Sum implies addition so the given statement is given by the expression: 59 + x.
Option A

Question 8.
Which number has more than two factors?
(A) 19
(B) 23
(C) 25
(D) 29
Answer:
(C) 25

Explanation:
The number 25 has more than 2 factors. They are 1.5 and 25. The rest 3 numbers are prime in nature with only 1 and themselves as their factors.

Option C.

Question 9.
Which of the following statements about rational numbers is not correct?
(A) All whole numbers are also rational numbers.
(B) All integers are also rational numbers.
(C) All rational numbers can be written in the form \(\frac{a}{b}\) where b ≠ 0.
(D) Rational numbers cannot be negative.
Answer:
(D) Rational numbers cannot be negative.

Explanation:
Rational numbers are whole numbers, integers, and fractions in which positive and negative numbers included.
The incorrect statement is D. Rational numbers cannot be negative.

Gridded Response

Question 10.
What is the measure of the missing angle in a triangle that contains angle measures of 37° and 59°?

Answer:
Determine the unknown angle by adding the given angles and subtracting the result from 180°.
37° + 59° + x = 180° substitute for the sum of angle measures in triangle
96° + z = 180° sum of the two angles
96° + x – 96° = 180° – 96° subtract 96° from both sides of the equation
x = 84° measure of the unknown angle

The gridded response is 84.00°.

Hot Tip!
It is helpful to draw or redraw a figure. Answers to geometry problems may become clearer as you redraw the figure.

Geometry Unit 5 Review Answer Key Go Math Test 6th Grade Question 11.
What is the measure, in degrees, of the missing angle in the triangle below?

Answer:
Determine the unknown angle by adding the given angles and subtracting the result from 180°.
39 + 66° + x = 180° substitute for the sum of angle measures in triangle
105° + x = 180° sum of the two angles
105° + x – 105° = 180° – 105° subtract 105° from both sides of the equation
x = 75 measure of the unknown angle

The gridded response is 75.00

Question 12.
Janice wants to buy carpet for a trapezoid shaped room. The bases of the trapezoid are 12 feet and 14 feet, and the height is 15 feet. If the carpet she likes is $5.50 per square foot, how much will new carpet for the room cost in dollars?

Answer:
Determine the area of the room and the cost

Cost = 195 • $5.50 multiply the area by the cost per square foot
= $1,072.50 cost of the carpet for the room

The gridded response is $1,072.50 which represents the cost of the carpet for the room.

Vocabulary Review

Use puzzle to preview key vocabulary from this unit. Unscramble the circled letters within found words to answer the riddle at the bottom of the page.

• A triangle that has three congruent sides and three congruent angles. (Lesson 15-2)
• A triangle that has two congruent sides. (Lesson 15-3)
• A triangle that contains a right angle. (Lesson 15-2)
• A triangle that has no congruent sides. (Lesson 15-3)
• A quadrilateral where opposite sides are congruent and parallel. (Lesson 16-1)
• A quadrilateral in which all sides are congruent and opposite sides are parallel. (Lesson 16-1)

Q: Where does a mathematician go when she commits a crime?
A: __ __ __ __ ___!

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 14.2 Answer Key Independent and Dependent Variables in Tables and Graphs.

Texas Go Math Grade 6 Lesson 14.2 Answer Key Independent and Dependent Variables in Tables and Graphs

Essential Question
How can you identify independent and dependent quantities from tables and graphs?

Texas Go Math Grade 6 Lesson 14.2 Explore Activity Answer Key

Explore Activity 1
Identifying independent and Dependent Quantities from a Table

Many real-world situations involve two variable quantities in which one quantity depends on the other. The quantity that depends on the other quantity is called the dependent variable, and the quantity it depends on is called the independent variable.

A freight train moves at a constant speed. The distance y in miles that the train has traveled afterx hours is shown in the table.

A. What are the two quantities in this situation?

Which of these quantities depends on the other?

What is the independent variable? _____________________

What is the dependent variable? ______________________

B. How far does the train travel each hour? ________________
The relationship between the distance traveled by the train and the time in hours can be represented by an equation in two variables.

Reflect

Question 1.
Analyze Relationships Describe how the value of the independent variable is related to the value of the dependent variable. Is the relationship additive or multiplicative?
Answer:
It can be seen that when the independent variable is 0 the dependent variable is 0 and then the dependent variable is proportional to the independent variable by ×50. Therefore, it can be said that the y = 50x. The relation is multiplicative.

Independent and Dependent Variables Worksheet with Answer Key Pdf Question 2.
What are the units of the independent variable and of the dependent variable?
Answer:
The independent variable here is time in hours while the dependent variable is distance traveled in miles. The constant of proportionality is the speed of the train in miles per hour.

Question 3.
A rate is used in the equation. What is the rate?
Answer:
The constant of proportionality or the rate of change of y with respect to x, is the speed of the train in miles per hour. It is 50 miles per hour.

Explore Activity 2
Identifying independent and Dependent Variables from a Graph

In Explore Activity 1, you used a table to represent a relationship between an independent variable (time) and a dependent variable (distance).You can also use a graph to show a relationship of this sort.

An art teacher has 20 pounds of clay but wants to buy more clay for her class. The amount of clay x purchased by the teacher and the amount of clay y available for the class are shown on the graph.
A. If the teacher buys 10 more pounds of clay, how many pounds will be available for the art class? _____________lb

If the art class has a total of 50 pounds of clay available, how many pounds of clay did the teacher buy?
How can you use the graph to find this information?

B. What are the two quantities in this situation?

Which of these quantities depends on the other?

What is the independent variable? ____________

What is the dependent variable? ______________

C. The relationship between the amount of clay purchased by the teacher and the amount of clay available to the class can be represented by an equation in two variables.

D. Describe in words how the value of the independent variable is related to the value of the dependent variable.

Reflect

Question 4.
In this situation, the same units are used for the independent and dependent variables. How is this different from the situation involving the train in the first Explore?
Answer:
In this situation, the same units are used for the independent and dependent variables. This is different from the situation involving the train in the first Explore as in that the units of the independent and dependent variables were different from each other.

6th Grade Go Math Lesson 14.2 Independent Practice Answer Key Question 5.
Analyze Relationships Tell whether the relationship between the independent variable and the dependent variable is a multiplicative or an additive relationship.
Answer:
The relationship between the independent variable and the dependent variable is an additive relationship because the coefficient of x or the independent variable is 1 and 20 is being added to ¡t

Question 6.
What are the units of the independent variable, and what are the units of the dependent variable?
independent variable: ___ ; dependent variable: ____
Answer:
The unit of the independent variable and the unit of the dependent variabLe here is pounds.

Pounds.

Example 1.
A. The table shows a relationship between two variables, x and y. Describe a possible situation the table could represent. Describe the independent and dependent variables in the situation.

As x increases by 1, y increases by 1. The relationship is additive. The value of y is always 10 units greater than the value of x.
The table could represent Jina’s savings if she starts with $10 and adds $1 to her savings every day.
The independent variable, x, is the number of days she has been adding money to her savings.
The dependent variable, y, is her savings after x days.

B. The graph shows a relationship between two variables.
Describe a possible situation that the graph could represent. Describe the independent and dependent variables.
As x increases 1y 1, y increases L’y 1 2. The relationship is multiplicative. The value of y is always 12 times the value of x.
The graph could represent the number of eggs in cartons that each hold 12 eggs.
The independent variable, x, is the number of cartons.
The dependent variable, y, is the total number of eggs.

Reflect

Question 7.
What are other possible situations that the table and graph in Example 1 could represent?
Answer:
A real world example of the table can be a $10 membership of a books club, where the registration costs $10 and then it is $1 per hook. Here the number of books burrowed is the independent variable; x and the cost to be paid is the dependent variable; y,

Your Turn

Describe a real-world situation that the variables could represent. Describe the relationship between the independent and dependent variables.

Question 8.

Answer:
The table represents an additive relation between the independent and the dependent variable, given by the equation y = x + 15. A real-world example to model the relationship can be the amount of money earned per week by Sam if his weekly pocket is $15 and he gets $1 for every errand that he runs for his parents.

Independent and Dependent Variables in Tables and Graphs Grade 6 Answer Key Question 9.

Answer:
The table represents a multiplicative relation between the independent and the dependent variable, given by the equation y = 16x. A real world example to model the relationship can be the cost of attending a movie and lunch per person. Here the independent variable is the number of people and the dependent variable is the cost

Question 10.

Answer:
The graph represents a multiplicative relation between the independent and the dependent variable because the graph passes through the origin and is given by the equation y = 3x. A real world example to model the relationship can be the cost of sandwiches. Here the independent variable is the number of sandwiches bought and the dependent variable is the cost.

Texas Go Math Grade 6 Lesson 14.2 Guided Practice Answer Key

Identify the coordinates of each point in the coordinate plane. Name the quadrant where each point is located. (Example 1)

Question 1.
A boat rental shop rents paddleboats for a fee plus an additional cost per hour. The cost of renting for different numbers of hours is shown in the table.

What is the independent variable, and what is the dependent variable?
How do you know? (Explore Activity )
Answer:
The independent variable is the time in hours for which the boat is rented for.

The dependent variable is the amount of rent in dollars; y for renting a boat for x hours.

Texas Go Math Grade 6 Answer Key Pdf Independent and Dependent Graphs Question 2.
A car travels at a constant rate of 60 miles per hour. (Explore Activity 1)

a. Complete the table.
Answer:
Table: Each value of x is multiplied with 60 to evaluate the value of y:

b. What is the independent variable, and what is the dependent variable?
Answer:
The independent variable is time in hours and the dependent variable is distance traveled in mites.

c. Describe how the value of the dependent variable is related to the value of the independent variable.
Answer:
The independent variable x and the dependent variable y are related by the equation y = 60x

Use the graph to answer the questions.

Question 3.
Describe in words how the value of the dependent variable is related to the value of the independent variable. (Explore Activity 2)
Answer:
It can be seen that each value of y is 5 times that of x so it can be said that they are related by the equation: y = 5x

Question 4.
Describe a real-world situation that the graph could represent. (Example 1)
Answer:
The graph represents a multiplicative relation between the independent and the dependent variable because the graph passes through the origin and is given by the equation y = 5x. A real world example to model the relationship can be the cost of sandwich meals. Here the independent variable is the number of sandwich meals bought and the dependent variable is the cost.

Essential Question Check-In

Question 5.
How can you identify the dependent and independent variables in a real-world situation modeled by a graph?
Answer:
According to a graphing convention, the independent variabLe is aLways plotted on the x-axis while the dependent variable is always plotted on the y-axis, so from the graph the quantity on the x-axis is the independent variable and that on the y-axis is the dependent variable.

Texas Go Math Grade 6 Lesson 14.2 Independent Practice Answer Key

6th Grade Go Math Independent and Dependent Variables Answer Key Question 6.
The graph shows the relationship between the hours a soccer team practiced after the season started and their total practice time for the year.

a. How many hours did the soccer team practice before the season began?
Answer:
From the graph, we can see that the soccer team practiced 6 hours before the season began.

b. What are the two quantities in this situation?
Answer:
In this situation, there are two quantities: the first one is practice time during the season in hours and the second one is total practice time for a year, also in hours.

c. What are the dependent and independent variables?
Answer:
Here the dependent variable is total practice time for year and independent variable is practice time during the season.

d. Analyze Relationships Describe the relationship between the quantities in words.
Answer:
We can notice that as x increase by 1, y increases by 1

e. Is the relationship between the variables additive or multiplicative? Explain.
Answer:
We can conclude that this relationship is additive because the value of dependent variable is always 6 units greater than the value of independent variable.

Question 7.
Multistep Teresa is buying glitter markers to put in gift bags. The table shows the relationship between the number of gift. Number of marker bags and the number of glitter markers she needs to buy.

a. What is the dependent variable? ______________________
Answer:
Here, the dependent variable is number of markers, y.

b. What is the independent variable? _____________________
Answer:
Here, the independent variable is number of gift bags, x.

c. Describe the relationship between the quantities in words.
Answer:
As x increases by 1, y increases by 5.

d. Is the relationship additive or multiplicative? Explain.
Answer:
We can notice that the relationship is multiplicative because the value of y is always 5 times the value of x.

Independent and Dependent Variables 6th Grade Go Math Answer Key Question 8.
Ty borrowed $500 from his parents. The graph shows how much he owes them each month if he pays back a certain amount each month.

a. Describe the relationship between the number of months and the amount Ty owes. Identify an independent and dependent variable and explain 200 your thinking.
Answer:
The independent variable here is time in months and the dependent variable is the amount of money left to be returned in dollars. As the time in months increases, this amount of debt decreases as he will pay back at a rate of $50 per month.

b. How long will it take Ty to pay back his parents?
Answer:
Locate the value of x when y = 0. Here that point is (10, 0) and implies that after tile luth payment, he will owe $o to his parents.

Texas Go Math Grade 6 Lesson 14.2 H.O.T. Focus On Higher Order Thinking Answer Key

Question 9.
Error Analysis A discount store has a special: 8 cans of juice for a dollar. A shopper decides that since the number of cans purchased is 8 times the number of dollars spent, the cost is the independent variable and the number of cans is the dependent variable. Do you agree? Explain.
Answer:
No, the cost is the dependent variable and the number of cans is the independent variable because the cost or money obtained depends on the sale of cans.

Question 10.
Analyze Relationships Provide an example of a real-world relationship where there is no clear independent or dependent variable. Explain.
Answer:
A real-world relationship when there is no clear independent or dependent value could be when there is no value in the independent and dependent variable at all, or when the independent and dependent variable have the same value. Therefore, the variables will be indiscernible since their values will be exactly alike.

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 16.4 Answer Key Solving Volume Equations.

Texas Go Math Grade 6 Lesson 16.4 Answer Key Solving Volume Equations

Example 1

A rectangular swimming pool is 25 meters long and 17\(\frac{1}{2}\) meters wide. It has an average depth of 1\(\frac{1}{2}\) meters. What is the volume of the pool?

Label the rectangular prism to represent the pool.
l = 25 meters; w = 17\(\frac{1}{2}\) meters; h = 1\(\frac{1}{2}\) meters
Use the formula to write an equation.
v = lwh

Your Turn

Texas Go Math Grade 6 Lesson 16.4 Question 1.
Miguel has a toolbox that measures 18\(\frac{1}{2}\) inches by 12\(\frac{1}{2}\) inches by 4 inches. What is the volume of the toolbox?
V = _________ cubic inches
Answer:
Determine the volume of the toolbox.
V = 18\(\frac{1}{2}\) ∙ 12\(\frac{1}{2}\) ∙ 4 substitute for the given values
V = \(\frac{37}{2}\) ∙ \(\frac{25}{2}\) ∙ 4 write mixed numbers as fractions
V = \(\frac{3,700}{4}\) simplify
V = 925 cubic inches volume of the toolbox
The volume of the toolbox is 925 cubic inches

Example 2

Samuel has an ant farm with a volume of 375 cubic inches. The width of the ant farm is 2.5 inches and the length is 15 inches. What is the height of Samuel’s ant farm?

The height of the ant farm is 10 inches.

Reflect

Question 2.
Communicate Mathematical Ideas Explain how you would find the solution to Example 2 using the formula V = 8h.
Answer:
Here B = l × w can be evaluated and then the given volume can be divided by B to evaluate h.

Your Turn

Question 3.
Find the height of this shape, which has a volume of \(\frac{15}{16}\) cubic feet.

Answer:
Data:
l = \(\frac{3}{4}\) = 0.75
w = \(\frac{1}{2}\) = 0.5
Volume = \(\frac{15}{16}\) = 0.9375
Write equation of volume of a rectangular prism:
VoLume = l × w × h
Solve for h:
h = \(\frac{\text { Volume }}{l \times w}\)
Substitute values:
h = \(\frac{0.9375}{0.75 \times 0.5}\)
Evaluate:
h = 2.5
Height of the given rectangular prism is equal to 2.5 = 2\(\frac{1}{2}\) feet.

Example 3

The classroom aquarium holds 30 gallons of water. It is 0.8 feet wide and has a height of 2 feet. Find the length of the aquarium.

Reflect

Go Math 6th Grade Answer Key Lesson 16.4 Question 4.
Persevere in Problem Solving Flow much does the water in the classroom aquarium weigh? Explain.
Answer:
The volume of the classroom aquarium is 4 cubic feet and the equivalent of 1 cubic foot is approximately 62.43 pounds. Therefore, multiply the volume by the estimated weight.
62.43 × 4 = 249.72 pounds
The water in the aquarium weighs about 249.72 pounds.

Your Turn

Question 5.
An aquarium holds 33.75 gallons of water. It has a length of 2 feet and a height of 1.5 feet. What is the volume of the aquarium? What is the width of the aquarium? Explain.
Answer:
Determine the volume and width of the aquarium.
V = \(\frac{33.75}{7.5}\) volume of the aquarium in cubic feet
V = 4.5 cubic feet
V = lwh formula for the volume of the aquarium
4.5 = 2 ∙ w ∙ 1.5 substitute for the given values
4.5 = 3w simplify
\(\frac{4.5}{3}=\frac{3 w}{3}\) divide both sides of the equation by 3
1.5 = w width of the aquarium
The volume of the aquarium is 4.5 cubic feet and the width is 1.5 feet.

Texas Go Math Grade 6 Lesson 16.4 Guided Practice Answer Key

Question 1.
Find the volume of this rectangular prism. (Example 1)

The volume of the rectangular prism is _________ cubic inches.
Answer:
Determine the volume.

The volume of the rectangular prism is 15\(\frac{3}{4}\) cubic inches.

Question 2.
Write an equation to find the width of the rectangular prism. Show your work. (Example 2)

Answer:
Determine the width of the rectangular prism
V = lwh formula for the volume of the rectangular prism
w = \(\frac{V}{l h}\) equation for the width of the prism
w = \(\frac{6,336 \mathrm{~cm}^{3}}{16 \mathrm{~cm} \cdot 18 \mathrm{~cm}}\) substitute for the given values
w = \(\frac{6,336 \mathrm{~cm}^{3}}{288 \mathrm{~cm}^{2}}\) simplify
w = 22 cm width of the rectangular prism
The width of the rectangular prism is 22 cm.

Lesson 16.4 Go Math Grade 6 Answers Pdf Question 3.
One red clay brick weighs 5.76 pounds. The brick is 8 inches long and 2 inches wide. If the clay weighs 0.08 pounds per cubic inch, what is the volume of the brick? Write an equation to find the height of the brick. Show your work. (Example 3)
Answer:
Determine the volume and height of the brick.
V = \(\frac{5.76}{0.08}\) volume of the brick in cubic inches
V = 72 cubic inches
V = lwh formula for the volume of the brick
72 = 8 ∙ 2.25 ∙ h substitute for the given values
72 = 18h simplify
\(\frac{72}{18}=\frac{18 h}{18}\) divide both sides of the equation by 18
4 inches = h height of the brick
The bricks is 4 inches in height.

Essential Question Check-In

Question 4.
How do you solve problems about volume of right rectangular prisms?
Answer:
Solving problems involving the volume of right rectangular prisms, identify the length, width, and height of the rectangular prism then get its product.

Texas Go Math Grade 6 Lesson 16.4 Independent Practice Answer Key

Question 5.
Jala has an aquarium in the shape of a rectangular prism with the dimensions shown. What is the height of the aquarium?

Height = ___________
Answer:
Solution to this example is given beLow
l = 24.25 inches; w = 12.5 inches; h = ? ; V = 3758.75 in³
V = lwh Write the formula.
3758.75 = 24.25 × 12.5 × h Use the formula to write an equation
3758.75 = (303.125)h Multiply
\(\frac{3758.75}{303.125}=\frac{303.125 h}{303.125}\) Divide both sides of the equation by 303125.
12.4 = h
Height of the given aquarium is 12.4 inches

Question 6.
Find the volume of a juice box that is 3 in. by 1\(\frac{1}{2}\) in. by 4 in.
Volume = ______________
Answer:
Determine the voLume of the juice box.
V = 3 ∙ 1.5 ∙ 4 substitute for the given values
V = 18 in³ volume of the juice box
The volume of the juice box is 18 cubic inches.

Question 7.
Find the width of a cereal box that has a volume of 3,600 cm³ and is 20 cm long and 30 cm high.
Width = ____________
Answer:
Determine the width of the box.
V = lwh formula for the volume of box
3, 600 = 20 ∙ w ∙ 30 substitute for the given values
3,600 = 600w simplify
\(\frac{3,600}{600}=\frac{600 w}{600}\) divide both sides of the equation by 600
6 cm = w width of the cereal box
The width of the cereal box is 6 cm.

Question 8.
Bill has a box of markers that has a base of 8 cm by 20 cm and a height of 6 cm. Martin’s pencil box has a height of 4 cm and a base that is 15 cm by 16 cm. Bill says his marker box has the same volume as Martin’s pencil box. Is Bill right? Explain.
Answer:
Determine the volume of both objects then compare.
V = 8 ∙ 20 ∙ 6 substitute for the dimensions of the box of markers
V = 960 cm³ volume of the box of markers
V = 4 ∙ 15 ∙ 16 substitute for the dimensions of the pencil box
V = 960 cm³ volume of the pencil box
Yes, Bill is right with his conjecture because the volume of the box of marker and pencil box are both the same.

Question 9.
Physical Science A small bar of gold measures 40 mm by 25 mm by 2 mm. One cubic millimeter of gold weighs about 0.0005 ounces. Find the volume in cubic millimeters and the weight in ounces of this small bar of gold.
Answer:
Data:
Density = 0.0005
l = 40
w = 25
h = 2
Write equation of volume of a rectangular prism:
VoLume = l × w × h
Substitute vaLues:
Volume = 40 × 25 × 2
Evaluate:
Volume = 2000
Volume of the bLock is 2000 cubic millimeters.

Write equation of density of a substance:
Density = \(\frac{\text { mass }}{\text { Volume }}\)
Solve for mass:
mass = Density × Volume
Substitute values:
mass = 0.0005 × 2000
Evaluate:
mass = 1
Mass of this block is 1 ounce.

6th Grade Go Math Answer Key Lesson 16.4 Question 10.
History The average stone on the lowest level of the Great Pyramid in Egypt was a rectangular prism 5 feet long by 5 feet high by 6 feet deep and weighed 15 tons. What was the volume of the average stone? How much did one cubic foot of this stone weigh?
Answer:
Data:
mass = 15
l = 5
w = 5
h = 6
Write equation of volume of a rectangular prism:
Volume = l × w × h
Substitute values:
VoLume = 5 × 5 × 6
Evaluate:
Volume = 150
Volume of the block is 150 cubic feet.

Write equation of density of a substance:
Density = \(\frac{\text { mass }}{\text { Volume }}\)
Substitute values:
Density = \(\frac{15}{150}\)
Evaluate:
Density = 0.1
Density of this block is 0.1 ton per cubic feet.

Question 11.
A freshwater fish is healthiest when there is at least one gallon of water for every inch of its body length. Roshel wants to put a goldfish that is about 2\(\frac{1}{2}\) inches long in her tank. Roshel’s tank is 7 inches long, 5 inches wide, and 7 inches high. The volume of 1 gallon of water is about 231 cubic inches.
a. How many gallons of water would Roshel need for the fish?
Answer:
a. According to the given information, the amount of water needed by the goldfish is 2\(\frac{1}{2}\) × 1 = 2\(\frac{1}{2}\) = 2.5 gallons of water. This is equal to 2.5 × 231 = 577.5 cubic inches.

b. What is the volume of Roshel’s tank?
Answer:
Volume of the tank is 7 × 5 × 7 = 245 cubic inches.

c. Is her fish tank large enough for the fish? Explain.
Answer:
Since the volume of water required is 577.5 > 245, her tank is not large enough to store the amount of water required by the fish.

Question 12.
A box of crackers is a rectangular box with the dimensions shown. The box is one-fourth full. What is the volume of crackers in the box? _______________________________

Answer:
Determine the volume of the crackers in the box.
V = 8 ∙ 4 ∙ 4 substitute for the given values
V = 128 in³ volume of the box
V = \(\frac{128}{4}\) divide the volume by 4
V = 32 in³ volume of the crackers in the box
The volume of the crackers in the box is 32 cubic inches.

H.O.T. Focus on Higher Order Thinking

Question 13.
Multistep Larry has a clay brick that is 7 inches long, 3.5 inches wide, and 1.75 inches thick, the same size as the gold stored in Ft. Knox in the form of gold bars. Find the volume of this brick. If the weight of the clay in the brick is 0.1 pound per cubic inch and the weight of the gold is 0.7 pounds per cubic inch, find the weight of the brick and the gold bar. Round all answers the nearest tenth.
Volume of the brick or bar = __________ cubic inches
Weight of the brick = __________ pounds
Weight of the gold bar = __________ pounds
Answer:
VoLume of the brick or bar is 7 × 3.5 × 1.75 = 42.875 cubic inches.
Weight of the brick in pounds is the product of its given density and its volume, therefore its weight is 42.875 × 0.1 = 4.2875 pounds.
Weight of the bar in pounds is the product of its given density and its voLume, therefore its weight is 42.875 × 0.7 = 30.0125 pounds.

Question 14.
Represent Real-World Problems Luisa’s toaster oven, which is in the shape of a rectangular prism, has a base that is 55 cm long by 40 cm wide. It is 30 cm high. Luisa wants to buy a different oven with the same volume but a smaller length, so it will fit better on her kitchen counter. What is a possible set of dimensions for this different oven?
Answer:
VoLume of this toaster is 55 × 40 × 30 = 66000 cubic centimeters.
The volume of the new toaster must be same but with different dimensions provided that l < 55 centimeters, therefore:
Volume = 66000 = 48 × 42 × 32.74
Note that the length of the new toaster is less than 55 but to maintain the same volume, the width and height of the toaster has increased.

Lesson 16.4 Go Math Answer Key 6th Grade Question 15.
Multiple Representations Use the formula V = Bh to write a different version of this formula that you could use to find the area of the base B of a rectangular prism if you know the height h and the volume V. Explain what you did to find this equation.
Answer:
Write equation of volume of a rectangular prism in terms of base Area B:
Volume = B × h
Divide both sides of this equation with h to solve for B:

This is the equation of the same formula for B.

Question 16.
Communicate Mathematical Ideas Explain how you could find the volume of a cube that has an edge of e.
Answer:
Determine the volume of cube.
V = e ∙ e ∙ e multiply the edge of the cube by itself three times
V = e³ volume of the cube
Tne volume of the cube is e³.

Question 17.
Justify Reasoning Mariel says that a jewelry box that is 3 inches high, 4\(\frac{1}{2}\) inches wide, and 5 inches long has a volume of 67\(\frac{1}{2}\) inches. Katy says that answer is not quite correct. What is the error in Mariel’s answer?
Answer:
Determine the volume of the jewelry box.
V = 3 ∙ 4.5 ∙ 5 substitute for the given values
V = 67.5 in³ volume of the jewelry box
The answer of Mariel is not correct because of the indicated unit. It should be cubic inches for volume and not inches only.f

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 14.1 Answer Key Graphing on the Coordinate Plane.

Texas Go Math Grade 6 Lesson 14.1 Answer Key Graphing on the Coordinate Plane

Essential Question
How do you locate and name points in the coordinate plane?

Reflect

Question 1.
If both coordinates of a point are negative, in which quadrant is the point located?
Answer:
If both coordinates of a point are negative, then this implies that the point lies in the third quadrant.

Third quadrant.

Question 2.
Describe the coordinates of all points in Quadrant 1.
Answer:
Both the x and y coordinates of all the points of Quadrant 1 are positive.

Go Math Grade 6 Lesson 14.1 The Coordinate Plane Answer Key Question 3.
Communicate Mathematical Ideas Explain why (-3, 5) represents a different location than (3, 5).
Answer:
(-3, 5) lies in the 2nd quadrant while (3, 5) lies in the 1st quadrant. They are a mirror image of one another in the y-axis.

Your Turn

Identify the coordinates of each point. Name the quadrant where each point is located.

Question 4.
G ______
E _______
Answer:
Solution to this example is given below
Point G is 4 units right of the origin, and 4 units down. It has x-coordinate 4 and y-coordinate -4, written (4, -4). It is located in Quadrant IV
Point E is 2 units Left of the origin, and 4 units up. It has x-coordinate -2 and y-coordinate 4, ‘written (-2, 4). It is located in Quadrant II
G = (4, -4) : E = (2, -4) Final solution
G = (4, -4) : E = (2, -4)

Question 5.
F _____
H _____
Answer:
Solution to this example is given below
Point F is 3 units right of the origin, and 2 units up. It has x-coordinate 3 and y-coordinate 2, written (3, 2). It is located in Quadrant I.
Point H is 1 units left of the origin, and 3 units down It has x-coordinate -1 and y-coordinate -3, written (-1, -3). It is located in Quadrant III.
F = (3, 2) : H = (-1, -3) Final solution
F = (3, 2) : H = (-1, -3)

Your Turn

Graph and label each point on the coordinate plane.

Question 6.
P(-4, 2)
Answer:
Solution to this example is given below
Point P is 4 units left of the origin, and 2 units up. It has x-coordinate -4 and y-coordinate 2, written (-4, 2). It is located in Quadrant II.
P = (-4, 2) Final solution

P = (-4, 2)

Texas Go Math Grade 6 Answer Key Pdf Lesson 14.1 Question 7.
Q(3, 2.5)
Answer:
Solution to this example is given below
Point Q is 3 units right of the origin, and 2.5 units up It has x-coordinate 3 and y-coordinate 2.5, written (3, 2.5). It is located in Quadrant I.
Q = (3, 2.5) Final solution

Q = (3, 2.5)

Question 8.
R(-4.5, -5)
Answer:
Solution to this example is given below. Point R is 4.5 units left of the origin, and 5 units down It has x-coordinate -4.5 and y-coordinate -5, written (-4.5, -5). It is located in Quadrant III
R = (-4.5, -5) Final solution

R(-4.5, -5)

Question 9.
S(4, -5)
Answer:
Solution to This example is given below. Point S is 4 units right of the origin, and 5 units down. It has x-coordinate 4 and y-coordinate -5, written (4, -5). It is located in Quadrant IV.
S = (4, -5) Final solution

S(4, -5)

Texas Go Math Grade 6 Answer Key Coordinate Plane Question 10.
T(-2.5, 0)
Answer:
Solution to this example is given below.
Point T is 2.5 units left of the origin, and 0 units down/up. It has an x-coordinate -2.5 and y-coordinate 0, written (-25, 0). It is located in Quadrant II.
T= (-2.5, 0) Final solution

T(-2.5, 0)

Your Turn

Use the graph in the Example.

Question 11.
Ted lives 20 miles south and 20 miles west of the city represented on the graph in Example 3. His brother Ned lives 50 miles north of Ted’s house. Give the coordinates of each brother’s house.
Answer:
Ted lives 20 miles south and 20 miles west of the city represented on the graph, then the point of Teds location is given by (-20, -20). Note that the negative signs are chosen because of the given directions. If Ned’s house is 50 miles north of Ted, then add 50 to the y-coordinate of Teds location to determine Ned’s location, therefore (-20, -20 + 50) = (-20, 30).

Texas Go Math Grade 6 Lesson 14.1 Guided Practice Answer Key

Identify the coordinates of each point in the coordinate plane. Name the quadrant where each point is located. (Example 1)

Question 1.
Point A is 5 units ____ of the origin and 1 unit ___ from the origin. Its coordinates are ___. It is in quadrant ___.
Answer:
Solution to this example is given below. Point A is 5 units Left of the origin, and 1 units up. It has x-coordinate -5 and y-coordinate 1, written (-5, 1). It is located in Quadrant II
A = (-5, 1) Final solution
A = (-5, 1)

Question 2.
Point B is ____ units right of the origin and ___ units down from the origin. Its coordinates are ____. It is in quadrant ____.
Answer:
Solution to this example is given below. Point B is 2 units right of the origin, and 3 units down. It has x-coordinate 2 and y-coordinate -3. written (2, -3). It is located in Quadrant IV
B = (2, -3) Final solution
B = (2, -3)

Graph and label each point on the coordinate plane above. (Example 2)

Question 3.
Point C at (-3.5, 3)
Answer:
Solution to this example is given below. Point C is 3.5 units left of the origin, and 3 units up. It has x-coordinate -3.5 and y-coordinate 3, written (-3.5, 3). It is located in Quadrant II.
C = (-3.5, 3) Final solution

C(-3.5, 3)

6th Grade Graphing Texas Go Math Lesson 14.1 Question 4.
Point D at (5, 0)
Answer:
Solution to this example is given below. Point D is 5 units right of the origin, and 0 units down/up It has x-coordinate 5 and y-coordinate 0, written (5, 0). It is located in Quadrant I.
D = (5, 0) Final solution

D(5, 0)

For 5-7, use the coordinate plane shown. (Example 3)

Question 5.
Describe the scale of the graph.
Answer:
Study the graph to determine the size represented by 1 grid. It can be seen that for both x and y-axes, 2 grids represent 1 unit so this means that each grid represents 0.5 units on each axes.

Question 6.
Plot point A at (-\(\frac{1}{2}\), 2).
Answer:
Solution to this example is given below
–\(\frac{1}{2}\) = -0.5 Convert to decimal number
Point A is 0.5 units left of the origin, and 2 units up. It has x-coordinate -0.5 and y-coordinate 2, written (-0.5, 2). It is located in Quadrant II.
A = (-0.5, 2) Final solution

A = (0.5, 2)

Lesson 14.1 Answer Key 6th Grade Graphs Go Math Question 7.
Plot point 6 at (2\(\frac{1}{2}\), -2).
Answer:
Solution to this example is given below
2\(\frac{1}{2}\) = \(\frac{2 \times 2+1}{2}\) = 2.5 Convert to decimal number
Point B is 2.5 units right of the origin, and 2 units down. It has x-coordinate 2.5 and y-coordinate -2, written (2.5, -2). It is located in Quadrant IV.
B = (2.5, -2) Final solution

B = (2.5, -2)

Question 8.
Vocabulary Describe how an ordered pair represents a point on a coordinate plane. Include the terms x-coordinate, y-coordinate, and origin in your answer.
Answer:
The ordered pair represented by (x, y) = (a, b) means that the ordered pair is a units towards the right of the origin along the positive x-axis. If it is -a then the negative sign implies the left side of the origin on the negative x-axis. It also means that the ordered pair is b units above the origin along the positive y-axis. If it is -b then the negative sign implies along the negative y-axis.

Essential Question Check-In

Question 9.
Give the coordinates of a point that could be in each of the four quadrants, a point on the x-axis, and an point on the y-axis.
Answer:
Described point only could be point (0, 0) because it is the only point which is in each of the four quadrants.

Point (0, 0)

Texas Go Math Grade 6 Lesson 14.1 Independent Practice Answer Key

For 10-13, use the coordinate plane shown. Each unit represents 1 kilometer.

Question 10.
Write the ordered pairs that represent the location of Sam and the theater.
Answer:
Solution to this example is given below.
Sam is located 4 units right of the origin, and 2 units up. It has x-coordinate 4 and y-coordinate 4, written (4, 2). It is located in Quadrant I.

Theater is located 3 units left of the origin, and 5 units up. It has x-coordinate -3 and y-coordinate 5, written (-3, 5). It is located in Quadrant II.
Sam:(4 , 2): Theate(-3, 5) solution
Sam = (4, 2): Theater: (3, 5)

Question 11.
Describe Sam’s location relative to the theater.
Answer:
Evaluate the difference between the coordinates of Sam and the theater Therefore: 4 – (-3) = 7 and 2 – 5 = -3. This implies that Sam is 7 units on the right and 3 units south of the theater.

Go Math Answer Key Grade 6 Graphing on Coordinate Plane Question 12.
Sam wants to meet his friend Beth at a restaurant before they go to the theater. The restaurant is 9 km south of the theater. Plot and label a point representing the restaurant. What are the coordinates of the point?
Answer:
The solution to this example is given below
The restaurant is located 3 units left of the origin, and 4 units down. It has x-coordinate -3 and y-coordinate -4 written (-3, -4). It is located in Quadrant III.
Restaurant (-3, -4) Final solution

Restaurant ( -3, -4)

Question 13.
Beth describes her current location: “I’m directly south of the theater, halfway to the restaurant.” Plot and label a point representing Beth’s location. What are the coordinates of the point?
Answer:
Solution to this example is given below
Beth is located 3 units left of the origin, and 0.5 units up. It has x-coordinate -3 and y-coordinate 0.5, written (-3, 0.5) It is located in Quadrant II.
Beth (-3, 0.5) Final solution

Beth (-3, 0.5)

For 14-15, use the coordinate plane shown.

Question 14.
Find the coordinates of points T, U, and V.
Answer:
Solution to this example is given below
Point T is 0.75 units right of the origin, and 1 units down. It has x-coordinate 0.75 and y-coordinate -1, written (0.75, -1). It is located in Quadrant IV.
Point U is 0.75 units right of the origin, and 1.25 units up. It has x-coordinate 0.75 and y-coordinate 1.25, written (0.75, 1.25) It is located in Quadrant I.
Point V is 0.75 units Left of the origin, and 1.25 units up. It has x-coordinate -0.75 and y-coordinate 1.25, written (-0.75, 1.25). It is located in Quadrant II.
T = (0.75, -1): U = (0.75, 1.25) : V = (-0.75, 1.25) Final solution

Question 15.
Points T, U, and V are the vertices of a rectangle. Point W is the fourth vertex. Plot point W and give its coordinates.
Answer:
Solution to this example is given below
Point W is 0.75 units left of the origin, and 1 unit down. It has x-coordinate -015 and y-coordinate -1, written (-0.75, -1). It is located in Quadrant III.
w = (-0.75, -1) Final solution

Grade 6 Lesson 14.1 The Coordinate Plane Answer Key Question 16.
Explain the Error Janine tells her friend that ordered pairs that have an x-coordinate of 0 lie on the x-axis. She uses the origin as an example. Describe Janine’s error. Use a counterexample to explain why Janine’s statement is false.
Answer:
A point lies on the x-axis when its y-coordinate is equal to 0, like the point (5, 0). The origin or (0, 0) represents the point where both x and y are 0. Another example is that of the point (0, 9). Its x-coordinate is equal to 0 but it does not lie on the x-axis but on the y-axis

Texas Go Math Grade 6 Lesson 14.1 H.O.T. Focus On Higher Order Thinking Answer Key

Question 17.
Critical Thinking Choose scales for the coordinate plane shown so that you can graph the points J(2, 40), K(3, 10), L(3, -40), M(-4, 50), and N(-5, -50). Explain why you chose the scale for each axis.

Answer:
Study the x-coordinates of the given points. The most negative one is -5 and the largest is 3, so 1 grid is equal to 1 unit on the x-axis.

Study the y-coordinates of the given points. The most negative one is -50 and the largest is 50, so 1 grid is equal to 10 units on the y-axis.

Question 18.
Communicate Mathematical Ideas Edgar wants to plot the ordered pair (1.8, -1.2) on a coordinate plane. On each axis, one grid square equals 0.1. Starting at the origin, how can Edgar find (1.8, -1.2)?
Answer:
1.8
Divide the coordinate by the scale to determine the number of grids to be moved across. Here \(\frac{1.8}{0.1}\) = 18 implies that from the origin, he will have to move 18 grids to the right and then \(\frac{1.2}{0.1}\) = 12 grids perpendicularly downwards to reach the point (1.8, -1.2).

Question 19.
Represent Real-World Problems Zach graphs some ordered pairs in the coordinate plane. The x-values of the ordered pairs represent the number of hours since noon, and the y-values represent the temperature at that time.

a. In which quadrants could Zach graph points? Explain your thinking.
Answer:
Zach’s points will lie either in the first quadrant if both the quantities are positive or in the fourth quadrant if the temperature noted is negative.

b. In what part of the world and at what time of year might Zach collect data so that the points he plots are in Quadrant IV?
Answer:
He should note down these readings somewhere in Alaska in December to have all his points in the fourth quadrant.

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 14.3 Answer Key Writing Equations from Tables.

Texas Go Math Grade 6 Lesson 14.3 Answer Key Writing Equations from Tables

Essential Question
How can you use an equation to show a relationship between two variables?

Texas Go Math Grade 6 Lesson 14.3 Explore Activity Answer Key

Explore Activity
Writing an Equation to Represent a Real-World Relationship
Many real-world situations involve two variable quantities in which one quantity depends on the other. This type of relationship can be represented by a table. You can also use an equation to model the relationship.

The table shows how much Amanda earns for walking 1,2, or 3 dogs. Use the table to determine how much Amanda earns per dog. Then write an equation that models the relationship between number of dogs walked and earnings. Use your equation to complete the table.

A. For each column, compare the number of dogs walked and earnings. What is the pattern?

B. Based on the pattern, Amanda earns $ ___ for each dog she walks.

C. Write an equation that relates the number of dogs Amanda walks to the amount she earns. Let e represent earnings and d represent dogs.

D. Use your equation to complete the table for 5,10, and 20 walked dogs.

E. Amanda’s earnings depend on ____.

Reflect

Lesson 14.3 Writing Equations from Tables Grade 6 Question 1.
What If? If Amanda changed the amount earned per dog to $11, what equation could you write to model the relationship between the number of dogs walked and earnings?_____
Answer:
If Amanda changed the amount earned per dog to $11 then her total earning y is given by the equation; y = 11x.

y = 11x

Your Turn

For each table, write an equation that expresses y in terms of x.

Question 2.

Answer:
Compare the x- and y-values to find a pattern.
Each y-value is 2 less than the corresponding x-value.
Use the pattern to write an equation expressing y in terms of x.
y = x – 2
y = x – 2 Final solution
y = x – 2

Question 3.

Answer:
Compare the x- and y-values to find a pattern.
Each x-value is 2.5 times the corresponding y-value.
Use the pattern to write an equation expressing y in terms of x.
y = 2.5x
y = 2.5x Final solution
y = 2.5x

Question 4.

Answer:
Compare the x- and y-values to find a pattern.
Each y-value is 5 more than the corresponding x-value.
Use the pattern to write an equation expressing y in terms of x.
y = x + 5
y = x + 5 Final solution
y = x + 5

Grade 6 Writing Equations to Model Relationships Lesson 14.3 Question 5.

Answer:
Compare the x- and y-values to find a pattern.
Each x-value is 2 times the corresponding y-value.
Use the pattern to write an equation expressing y in terms of x.
y = 2x
y = 2x Final solution
y = 2x

Your Turn

Question 6.
When Ryan is 10, his brother Kyle is 15. When Ryan is 16, Kyle will be 21. When Ryan is 21, Kyle will be 26. Complete the table for Ryan and Kyle. Write and solve an equation to find Kyle’s age when Ryan is 52.

Answer:
Using all given informations for Ryan’s and Kyle’s ages. we get the following

First we need to find What is relationship betWeeti Ryan’s and Kyle’s ages, let x₁ be 10 and ₂ be 16, because of this, y₁ will be 15 and y₂ will be 21.
We will use equation of line through those two points and get:

So, when Ryan is 52, that means y = 52. We will substitute it in previous equation where s represent ages of Kyle.
52 = x + 5
x = 47
So, Kyle will be at the age of 47 when Ryan is 52.
47

Texas Go Math Grade 6 Lesson 14.3 Guided Practice Answer Key

Write an equation to express y in terms of x.

Question 1.

Answer:
Compare the x- and y-values to find a pattern.
Each y-value is 4 less than the corresponding x-value.
Use the pattern to write an equation expressing y in terms of x.
y = x – 4
y = x – 4 Final solution

Question 2.

Answer:
Compare the x- and y-values to find a pattern.
Each y-value is 4 times less than the corresponding x-value.
Use the pattern to write an equation expressing y in terms of x.
y = 4x
y = 4x Final solution

Question 3.

Answer:
Compare the x- and y-values to find a pattern.
Each y-value is 3 more than the corresponding x-value.
Use the pattern to write an equation expressing y in terms of x.
y = x + 3
y = x + 3 Final solution

Question 4.

Answer:
Compare the x- and y-values to find a pattern.
Each y-value is 6 times less than the corresponding x-value.
Use the pattern to write an equation expressing y in terms of x.
y = \(\frac{x}{6}\)
y = \(\frac{x}{6}\) = Final solution

Question 5.
Jameson downloaded one digital song for $1.35, two digital songs for $2.70, and 5 digital songs for $6.75. Complete the table. Write and solve an equation to find the cost to download 25 digital songs. (Example 2)

Number of songs = n; Cost = ____
The total cost of 25 songs is _____
Answer:
We have the following table:

One way to determine realitonship between downloaded songs and total cost is to find their quotient:
\(\frac{1.35}{1}\) = 1.35
\(\frac{2.70}{2}\) = 1.35
\(\frac{6.75}{5}\) = 1.35
Let n represent number of songs and let p represent cost in $. According to previous result, we have the following relationship:\p1.35n\
Now, we will find the total cost of 25 songs using previous result and subtracting 25 for n:
p = 1.35 . 25
p = 33.75
So, the total cost of 25 songs is $ 33.75.
So, equation is correct.

p = 1.35n, p = 33.75

Essential Question Check-In

Question 6.
Explain how to use a table to write an equation that represents the relationship in the table,
Answer:
The ordered pairs in a table can be used to determine the equation of the relationship between the 2 variables.

Case 1: Check if each value of y is proportional to the corresponding value of x. If its true, then the equation is given by: y = kx where k is evaluated using the equation k = \(\frac{y}{x}\) using the ordered pairs.

Case 2: Check if each value of y is a units bigger (or smaller) than the corresponding value of x. If its true, then the equation is given by: y = x + a where a is evaluated using the equation a = y – x using the ordered pairs.

Texas Go Math Grade 6 Lesson 14.3 Independent Practice Answer Key

Question 7.
Vocabulary What does it mean for an equation to express y in terms of x?
Answer:
An equation to express y in terms of x means that the quantity y depends on the quantity x.

Question 8.
The length of a rectangle is 2 inches more than twice its width. Write an equation relating the length l of the rectangle to its width w.
Answer:
If the length of a rectangle is 2 inches more than twice its width, then the equation for the length of the rectangle is l = 2w + 2.

l = 2w + 2.

Lesson 14.3 Dependent and Independent Variables Answer Key Question 9.
Look for a Pattern Compare the y-values in the table to the corresponding x-values. What pattern do you see? How is this pattern used to write an equation that represents the relationship between the x- and y-values?

Answer:
Compare the x- and y-values to find a pattern.
Each y-value is 4 times less than the corresponding x-value
Use the pattern to write an equation expressing y in terms of x.
y = \(\frac{x}{4}\)
y = \(\frac{x}{4}\) Final solution

Question 10.
Explain the Error A student modeled the relationship in the table with the equation x = 4y. Explain the student’s error. Write an equation that correctly models the relationship.

Answer:
Compare the x- and y-values to find a pattern.
Each y-value is 4 times the corresponding x-value.
Use the pattern to write an equation expressing y in terms of x.
y = 4x
y = 4x Final solution

Question 11.
Multistep Marvin earns $8.25 per hour at his summer job. He wants to buy a video game system that costs $206.25.

a. Write an equation to model the relationship between number of hours worked h and amount earned e.
Answer:
Marvin earns $8.25 per hour at his summer job. This implies that after working for h hours, he will earn e = 8.25h.

b. Solve your equation to find the number of hours Marvin needs to work in order to afford the video game system.
Answer:
He needs to raise S206.25 so substitute e = 206.25 and solve for h:
206.25 = 8.25h
Solve for h:
h = \(\frac{206.25}{8.25}\) = 25
Marvin needs to work for 25 hours to buy the video game.

Question 12.
Communicate Mathematical Ideas For every hour that Noah studies, his test score goes up 3 points. Explain which is the independent variable and which is the dependent variable. Write an equation modeling the relationship between hours studied h and the increase in Noah’s test score s.
Answer:
The independent variable here is the number of hours studied and the dependent variable here is the increase in test score. The 2 are related with the equation: S = h + 3

s = h + 3

Texas Go Math Grade 6 Lesson 14.3 H.O.T. Focus On Higher Order Thinking Answer Key

Question 13.
Make a Conjecture Compare the y-values in the table to the corresponding x-values. Determine whether there is an additive relationship or a multiplicative relationship between x and y. If possible, write an equation modeling the relationship. If not, explain why.

Answer:
No clear pattern is visible between the 2 variables shown. The value of y 2 more than the value of x in the first case but this pattern does not continue and the values of y are neither a multiple of x and a constant so the relationship shown can not be expressed by an equation.

No pattern exists between x and y.

Question 14.
Represent Real-World Problems Describe a real-world situation in which there is an additive or multiplicative relationship between two quantities. Make a table that includes at least three pairs of values. Then write an equation that models the relationship between the quantities.

Answer:
Case 1: The total cost y of x sandwiches if each sandwich costs $4 is a case of a multiplicative relationship which is given by the equation: y = 4x. Therefore, the ordered pairs are: (0, 0), (1, 4), (2, 8), (3, 12), (4, 16)… and so on.

Case 2: The total cost y of a boat rental for x hours if the rent of 1 hour is $1 plus a fixed cost of $15 is a case of a additive relationship which is given by the equation: y = x + 13. Therefore, the ordered pairs are: (0, 10), (1, 16), (2, 17), (3, 18), (4, 19)… and so on.

Question 15.
Critical Thinking Georgia knows that there is either an additive or multiplicative relationship between x and y. She only knows a single pair of data values. Explain whether Georgia has enough information to write an equation that models the relationship between x and y.
Answer:
A single pair of data values is not sufficient to determine the relation between x and y. At least 2 pairs of data values are required.

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Module 14 Answer Key Relationships in Two Variables.

Texas Go Math Grade 6 Module 14 Answer Key Relationships in Two Variables

Essential Question
How can you use relationships in two variables to solve real-world problems?

Texas Go Math Grade 6 Module 14 Are You Ready? Answer Key

Complete these exercises to review skills you will need for this chapter.

Multiply.

Question 1.
7 × 6 ____
Answer:
Solution to this example is given below
7 × 6 =? Use a related fact you know.
6 × 6 = 36.
Think:7 × 6 = (6 × 6) + 6
= 36 + 6
= 42
Final solution
42

Go Math Grade 6 Module 14 Answer Key Question 2.
10 × 9 ____
Answer:
Solution to this example is given below
10 × 9 = 7 Use a related fact you know.
9 × 9 = 81.
Think: 10 × 9 = (9 × 9) + 9
= 81 + 9
= 90
Final solution
90

Question 3.
13 × 12 ____
Answer:
Solution to this example is given below
13 × 12 =? Use a related fact you know.
12 × 12 = 144.
Think: 13 × 12 = (12 × 12) + 12
= 144 + 12
= 156
Final solution
156

Question 4.
8 × 9 ____
Answer:
Solution to this example is given below
8 × 9 =? Use a related fact you know.
8 × 8 = 64.
Think: 8 × 9 = (8 × 8) + 8
= 64 + 8
= 72
Final solution
72

Write the rule for each table.

Question 5.

Answer:
Compare the x- and y-values to find a pattern.
Each x-value is 7 times the corresponding y-value
Use the pattern to write an equation expressing y in terms of x
y = 7x
y = 7x Final solution
y = 7x

Texas Go Math Grade 6 Answer Key Pdf Module 14 Question 6.

Answer:
Compare the x- and y-values to find a pattern.
Each x-value is 6 more than the corresponding y-value
Use the pattern to write an equation expressing y in terms of x
y = x + 6
y = x + 6 Final solution
y = x + 6

Question 7.

Answer:
For example let x₁ be 1 and x₂ be 3 and because of this y₁ will be -5 and y₂ will be -15. We will use equation of a line through those two points and get:
y – y₁ = \(\frac{y_{2} \cdot y_{1}}{x_{2}-x_{1}}\)(x – x₁)
y + 5 = \(\frac{-15+5}{3-1}\)(x – 1)
y + 5 = -5(x – 1)
y = -5x + 5 – 5
y = -5x
So,
required rute is y = -5x.
y = -5x

Question 8.

Answer:
Compare the x- and y-values to find a pattern.
Each x-value is 0.5 times the corresponding y-value
Use the pattern to write an equation expressing y in terms of x
y = 0.5x
y = 0.5x Final solution
y = 0.5x

Graph each point on the coordinate grid above.

Texas Go Math Answer Key Grade 6 Module 14 Question 9.
B (0, 8)
Answer:
Solution to this example is given below
Start at the origin.
Move 0 units right
Then move 8 units up.
Graph point B( 0, 8).

Question 10.
C (2, 3)
Answer:
Solution to this example is gin below
Start at the origin
Move 2 units right
Then move 3 units up.
Graph point C( 2, 3).

Question 11.
D (6, 7)
Answer:
Solution to this example is given below
Start at the origin.
Move 6 units right
Then move 7 units up.
Graph point D( 6, 7).

Module 14 Texas Go Math Grade 6 Answer Key Question 12.
E (5, 0)
Answer:
Solution to this example is given below
Start at the origin.
Move 5 units right
Then move 0 units up.
Graph point E( 5, 0).

Texas Go Math Grade 6 Module 14 Reading Start-Up Answer Key

Visualize Vocabulary
Use the ✓ words to complete the chart.

Understand Vocabulary

Complete the sentences using the preview words.

Question 1.
The numbers in an ordered pair are _____
Answer:
The numbers in an ordered pair are coordinates
We know that coordinates are ordered pairs formed of numbers so, the missing word is coordinates.

Module 14 Answer Key Grade 6 Go Math Question 2.
A ________________________ is formed by two number lines that intersect at right angles.
Answer:
A coordinate plane is formed by two number lines that intersect at right angles.

The coordinate plane is actually made of two number lines that intersect at right angles, so, the missing word is the coordinate plane.

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 13.2 Answer Key Addition and Subtraction Inequalities.

Texas Go Math Grade 6 Lesson 13.2 Answer Key Addition and Subtraction Inequalities

Texas Go Math Grade 6 Lesson 13.2 Explore Activity Answer Key

Modeling One-Step Inequalities

You can use algebra tiles to model an inequality involving addition.

On a day in January in Watertown, NY, the temperature was 5 °F at dawn. By noon it was at least 8 °F. By how many degrees did the temperature increase?

A. Let x represent the increase in temperature. Write an inequality.

B. The model shows 5 + x ≥ 8. How many tiles must you remove from each side to isolate x on one side of the inequality? :
Circle these tiles. _________

C. What values of x make this inequality true? Graph the solution of the inequality on the number line.
x ≥ ____________

Reflect

Question 1.
Analyze Relationships How is solving the inequality 5 + x ≥ 8 like solving the equation 5 + x = 8? How is it different?
Answer:
Solving the equation, we get exactly one solution, but in solving the inequality, we get usually more values than one which is solutions.

Your Turn

Solve each inequality. Graph and check the solution.

Subtraction of Inequalities Lesson 13.2 Answer Key Question 2.
y – 5 ≥ -7

Answer:
We will add 5 to both sides and get:
y ≥ 2
Now, we will graph the solution.

The next thing we will do is to check the solution.
We will substitute a solution from the shaded part of our number line into the original inequality.
So, we will substitute 0 for y into y – 5 ≥ -7 and get:
0 – 5 ≥ 7
5 ≥ -7
So, the inequality is true.

Question 3.
21 > 12 + x

Answer:
We will subtract 12 from both sides and get:
9 > x
Now, we will graph the solution:

The next thing we will do is to check the solution.
So, we will substitute 3 for x into 21 > 12 + x:
21 > 12 + 3
21 > 15
So, the inequality is true

Reflect

Question 4.
If you were to graph the solution, would all points on the graph make sense for the situation?
Answer:
Not all, of the points on the graph make sense for the situation, for example, in the previous example, June’s dog will never weigh 1 pound, but – 1 is a solution of inequality from that task.

Your Turn

Question 5.
Write a real-world problem that can be modeled by x – 13> 20. Solve your problem and tell what values make sense for the situation.
Answer:
Today’s temperature decreased by 13°C compared to yesterday’s temperature, but it is not greater than 20°.
For example, this situation can be described using the model in the task and its solution is x > 26
But, values greater than 40°C do not make sense for this situation.

Texas Go Math Grade 6 Lesson 13.2 Guided Practice Answer Key

Question 1.
Write the inequality shown on the model. Circle the tiles you would remove from each side and give the solution. (Explore Activity)

Inequality: ______________
Solution: ______________
Answer:

Solve each inequality. Graph and check the solution. (Example 1)

Question 2.
x + 4 ≥ 9 ______________

Answer:
First, we will subtract 4 from both sides and get:
x ≥ 5
Now, we will graph the solution:

Now we will check our solution substituting a solution from the shaded part of our number line into the original inequality.
We will substitute 6 for x into x + 4 ≥ 9 and get:
6 + 4 ≥ 9
10 ≥ 9
So, the inequality is true

Go Math Grade 6 Lesson 13.2 Answer Key Question 3.
5 > z – 3 ______________

Answer:
We will add 3 to both sides and get:
8 > z
Now, we will graph the solution:

Now we will check our solution substituting a solution from the shaded part of our number line into the original inequality.
We will substitute 2 for z into 5 > z – 3 and get:
5 > 2 -3
5 > -1
So, the inequality is true.
z < 8

Question 4.
t + 5 > 12 ______________

Answer:
We will subtract 5 from both sides and get:
t > 7
Now, we will graph the solution.

Now we will check our solution substituting a soLution from the shaded part of our number line into the original inequality.
We will substitute 10 for t into t + 5 > 12 and get:
10 + 5 > 12
15 > 12
So, the inequality is true.
t > 7

Question 5.
y – 4 < 2 ______________

Answer:
We will add 4 to both sides and get:
y < 6
Now, we will graph the solution:

Now we will check our solution substituting a solution from the shaded part of our number line into the original inequality.
We will substitute 3 for y into y – 4 < 2 and get:
3 – 4 < 2
-1 < 2
So, the inequality is true.
y < 6

Go Math Grade 6 Answer Key Lesson 13.2 Question 6.
Write a real-world problem that can be represented by the inequality y – 4 < 2. Solve the inequality and tell whether all values in the solution make sense for the situation. (Example 2)
Answer:
Sara has apples and when she gave 4 of them to her sister, she left less than 2.
How many apples Sara could have?
We will use the Addition Property of Inequality, we will add 4 to both sides and get:
y < 6 So, Sara has less than 6 apples, but this real-world situation makes sense only for the following values of y : 5.4, where y represents a number of apples Sara had.

Essential Question Check-In

Question 7.
Explain how to solve 7 + x ≥ 12. Tell what property of inequality you would use.
Answer:
We will use the Subtraction Property of Inequality in order to solve this inequality, subtracting 7 from both sides and get: x ≥ 5

Texas Go Math Grade 6 Lesson 13.2 Independent Practice Answer Key

Solve each inequality. Graph and check the solution.

Question 8.
x – 35 > 15 _______________

Answer:
We will, use Addition Property of inequality, we will add 35 to both sides and get:
x > 50
Now, we will graph the solution.

Now we will check our solution substituting a solution from the shaded part of our number line into the original inequality.
We will substitute 60 for x into x – 35 > 15 and get:
60 – 35 >15
25 > 15
So, the inequality is true.
x > 50

Question 9.
193 + y ≥ 201 _______________

Answer:
We will use Subtraction Property of Inequality in order to solve this inequality, we will subtract 193 from both sides and get:
y ≥ 8
Now, we will graph the solution.

Now we will check our solution substituting a solution from the shaded part of our number line into the original inequality.
We will substitute 10 for y into 193 + y ≥ 201 and get:
193 + 10 ≥ 201
203 ≥ 201
So, the inequality is true
y ≥ 8

Go Math Answer Key Grade 6 Addition and Subtraction Inequalities Question 10.
y – 5 ≥ -15 ________________

Answer:
We will use the Addition Property of Inequality, we will add 5 to both sides and get:
y ≥ -10
Now, we will graph the solution.

Now we will check our solution substituting a solution from the shaded part of our number line into the original inequality.
We will substitute -8 for y into y – 5 ≥ – 15 and get:
8 – 5 ≥ -15
12 ≥ -15
So, the inequality is true.
y ≥ -10

Question 11.
15 ≥ z + 26 ________________

Answer:
We will first use first Subtraction Property of Inequality.
We will subtract 26 from both sides and get:
-11 ≥ z
Now, we will graph the solution:

Now we will check our solution substituting a solution from the shaded part of our number line into the original inequality.
We will substitute 15 for z into 15 ≥ z + 26 and get:
15 ≥ -15 + 26
15 ≥ 11
The inequality is true
z ≤ -11

Write an inequality to solve each problem.

Question 12.
The water level in the aquarium’s shark tank is always greater than 25 feet. If the water level decreased by 6 feet during cleaning, what was the water level before the cleaners took out any water?
Answer:
Let x be the water level before the cleaners book out any water. We have the following inequality according to information given in task:
x – 6 > 25
We will use Addition Property of Inequality adding 6 to both sides in order to solve this inequation and get:
x > 31
So, before the cleaners took water, the water level was greater than 31.

Question 13.
Danny has at least $15 more than his big brother. Danny’s big brother has $72. How much money does Danny have?
Answer:
Let x be sum of money Danny has. According to given informations in this task, we have the following inequality:
x – 72 ≥ 15
We will use Addition Property of Inequality adding 72 to both sides and get:
x ≥ 87
So, conclusion is that Danny has at least $87.

Question 14.
The vet says that Ray’s puppy will grow to be at most 28 inches tall. Ray’s puppy is currently 1 foot tall. How much more will the puppy grow?
Answer:
First, we will convert 1 foot to inches, it is 12 inches.
Let x be how much more will, the puppy grow.
According to informations given in this task, we will have the following inequality:
12 – x ≤ 28
We will use Subtraction Property of Inequality and subtract 12 from both sides and get:
x ≤ 16
So, the puppy will grow for 16 inches at most.

Question 15.
Pierre’s parents ordered some pizzas for a party. 4.5 pizzas were eaten at the party. There were at least 5\(\frac{1}{2}\) whole pizzas left over. How many pizzas did Pierre’s parents order?
Answer:
Let x be number of pizzas Pierres parents ordered. According to informations given in this task, we will have the following inequality:
x – 4.5 ≥ 5\(\frac{1}{2}\)
We will first convert decimals into fraction:
5\(\frac{1}{2}\) = \(\frac{11}{2}\)
Now, we will use Adding Property of Inequality, we will add \(\frac{9}{2}\) to both sides and get:
x ≥ \(\frac{11}{2}\) + \(\frac{9}{2}\)
x ≥ \(\frac{20}{2}\)
x ≥ 10
So, Pierre’s parents ordered at least 10 pizza’s.

Question 16.
To get a free meal at his favorite restaurant, Tom needs to spend $50 or more at the restaurant. He has already spent $30.25. How much more does Tom need to spent to get his free meal?
Answer:
Let x be the sum of money Tom needs to spend to get his free meal.
According to information given in this task, we will have the following inequality:
30.25 + x ≥ 50
In order to solve this inequality, we will use the Subtraction Property of Inequality, we will subtract 30.25 from both sides and get:
x ≥ 19.75
So, Tom needs to spend $19.75 or more to get his free meal.

Lesson 13.2 Subtraction Property of Inequality Grade 6 Answer Key Question 17.
Multistep The table shows Marco’s checking account activity for the first week of June.

a. Marco wants his total deposits for the month of June to exceed $1,500. Write and solve an inequality to find how much more he needs to deposit to meet this goal.
Answer:
Let x be deposit needed to Marco which he add to $520.45 to exceed $1,500.
Using informations in t his task, we have the following inequality.
520.45 + x > 1,500
We will use Subtraction Property of Inequalities and subtract 520.15 from both sides and get:
x > 979.55
So, Marco will need more than $979.55 to exceed $1,500.

b. Marco wants his total purchases for the month to be less Write and solve an inequality to find how much more he and still meet this goal.
Answer:
Marco’s total purchases for the first week of June is:
16.50 + 24.00 + 22.82 = 93.32
Let t be the sum of money Marco can spend over $ 93.32 in order to his total purchase be less than $ 450.
According to all informations given in task, we have the following:
93.32 + x < 450
We will use Subtracting Property of inequalities and subtract 93.32 from both sides and get:
x < 356.68
So, his purchases need to he less than $ 356.68 to meet his goal.

c. There are three weeks left in June. If Marco spends the same amount in each of these weeks that he spent during the first week, will he meet his goal of spending less than $450 for the entire month? Justify your answer.
Answer:
Marco spent 93.32 in first week of June. We will multiply this result by 3 because there are 3 more weeks left in June and get: 3 ∙ 93.32 = 279.96 We got that for the whole month he will spend $ 279.96 which is less than $450. so. he will meet his goal.

H.O.T. Focus on Higher Order Thinking

Question 18.
Critique Reasoning Kim solved y – 8 ≤ 10 and got y ≤ 2. What might Kim have done wrong?
Answer:
She did not use proper Property of Inequalities. Here, instead of Adding Property, she used Subtracting Property and got the wrong result.
So, using Adding Property and adding 8 to both sides, we get: y ≤ 18

Question 19.
Critical Thinking Jose solved the inequality 3 > x + 4 and got x < 1. Then, to check his solution, he substituted -2 into the original inequality to check his solution. Since his check worked, he believes that his answer is correct. Describe another check Jose could perform that will show his solution is not correct. Then explain how to solve the inequality.
Answer:
For, example, if he substitute 0 for x into inequality, we will get: 3 > 0 + 4
3 > 4
So, we can notice that this inequality is incorrect.
So, the right way to solve this inequality is to use the Subtracting Property of Inequalities and subtract 4 from both sides and get:
-1 > x
So, the solution is x < -1

Question 20.
Look for a Pattern Solve x + 1 > 10, x + 11 > 20, and x + 21 > 30. Describe a pattern. Then use the pattern to predict the solution of x + 9, 991 > 10,000.
Answer:
First, we will solve x + 1 > 10 using the Subtracting Property of Inequalities subtract 1 from both sides and get:
x > 9
Now, we will solve x + 11 > 20 using the Subtracting Property of Inequalities subtract 11 from both sides, and get:
x > 9
We can notice that the solution of all previous inequalities is x > 9.
So, according to the previous, the solution of x + 9,991 > 10,000 is supposed to be also x > 9.

Refer to our Texas Go Math Grade 6 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 6 Lesson 13.1 Answer Key Writing Inequalities.

Texas Go Math Grade 6 Lesson 13.1 Answer Key Writing Inequalities

Texas Go Math Grade 6 Lesson 13.1 Explore Activity Answer Key

Using inequalities to Describe Quantities

You can use inequality symbols with variables to describe quantities that can have many values.

A. The lowest temperature ever recorded in Florida was -2°F. Graph this temperature on the number line.

B. The temperatures 0°F, 3°F, 6°F, 5°F, and -1°F have also been recorded in Florida. Graph these temperatures on the number line.
C. How do the temperatures in B compare to -2? How can you see this relationship on the number line?
D. How many other numbers have the same relationship to -2 as the temperatures in B ? Give some examples.
E. Suppose you could graph all of the possible answers to D on a number line. What would the graph look like?
F. Let x represent all the possible answers to D.
Complete this inequality: x ________ – 2

Example 1

Graph the solutions of each inequality. Check the solutions.

Reflect

Question 1.
How is x < 5 different from x ≤ 5?
Answer:
x < 5 means that x can be any number less than 5 while x ≤ 5 means that x can be 5 and any number less than 5. The number 5 is a solution of x ≤ 5 but is not a solution of x < 5.

Your Turn

Texas Go Math Grade 6 Divide Multi Digit Numbers Lesson 13.1 Answer Key Question 2.
Graph the solution of the inequality t ≤ —4.

Answer:
Draw a solid circle at -4 to show that -4 is a solution.
Shade the number line to the left of -4 to show that numbers Less than -4 are solutions.
Check your solution.
Choose a number that is on the shaded section of the number line, such as -5. Substitute -5 for t.
-5≤ 4 : -5 Less than -4, so -5 is a solution
Graph the solution on a number line.

Example 2

A. Write an inequality that represents the phrase the sum of y and 2 is greater than 5. Draw a graph to represent the inequality.

B. To test the temperature rating of a coat, a scientist keeps the temperature below 5 °C. Write and graph an inequality to represent this situation.

Your Turn

Question 3.
Write an inequality that represents the phrase the sum of 1 and y is greater than or equal to 3. Check to see if y = 1 is a solution.
Answer:

Write and graph an inequality to represent each situation.

Question 4.
The highest temperature in February was 6°F. _________________

Answer:
Let t represent the temperature of a garter snake’s body during hibernation. Its temperature is greater than 3° C, so, required inequality is:
t > 3
Now, we will graph this situation.

Go Math Grade 6 Answer Key How to Write an Inequality Question 5.
Each package must weigh more than 2 ounces. _______________________

Answer:
Write the inequality. Let w represent the package.
w > 2 The package must weigh more than 2 ounces.
Graph the inequality.

Texas Go Math Grade 6 Lesson 13.1 Guided Practice Answer Key

Question 1.
Graph 1 ≤ x. Use the graph to determine which of these numbers are solutions of the inequality: -1, 3, 0, 1 (Explore Activity and Example 1)

Answer:
Graph of 1 ≤ x

It can be seen that the points -1 and 0 do not lie on the graph of 1 ≤ x so they are not the solutions of the given inequality. It can also be seen that the points 1 and 3 lie on the graph of 1 ≤ x so they are the solutions of the given inequality.

Question 2.
Graph -3 > z. Check the graph using substitution. (Example 1)
Answer:
Draw a solid circle at -3 to show that -3 is not a solution.
Shade the number line to the left of -3 to show that numbers less than -3 are solutions.
Check your answer.
Substitute -4 for z.
3 > – 4 : -3 ¡s greater than -4, so -4 is a solution
Graph the solution on a number line

Question 3.
Write an inequality that represents the phrase the sum of 4 and x is less than 6.” Draw a graph that represents the inequality, and check your solution. (Example 2)
Answer:
Write the inequality.
The sum of x and 4 is greater than 6
x + 4 > 6.
Graph the solution
For x + 4 to have a value greater than 6.
x must be a number greater than 2

Go Math Answer Key Grade 6 Lesson 13.1 Question 4.
During hibernation, a garter snake’s body temperature never goes below 3°C. Write and graph an inequality that represents this situation. (Example 2)
Answer:
Write the inequality. Let t represent the temperature in the snake’s body.
t ≥ 3° F
The temperature must be greater than or equal to 3°
Graph the inequality.

Essential Question Check-In

Question 5.
Write an inequality to represent this situation: Nina wants to take at least $15 to the movies. How did you decide which inequality symbol to use?
Answer:
The words at least imply that the minimum amount Lina want to take to the movies is 815, so the inequality becomes: m ≥ 15. where m is money in dollars.

Texas Go Math Grade 6 Lesson 13.1 Independent Practice Answer Key

Question 6.
Which of the following numbers are solutions to x ≥ 0? -5, 0.03, -1, 0, 1.5, -6,
Answer:
The inequality x ≥ 0 implies that the solution will contain x and all numbers greater than 0, therefore 0, \(\frac{1}{2}\) and 1.5 are solutions of the given inequality. Note that these are all positive numbers.

Graph each inequality.

Question 7.
t ≤ 8

Answer:
Draw a solid circle at 8 to show that 8 is a solution
Shade the number line to the left of 8 to show that numbers less than 8 are solutions.
Check your solution.
Choose a number that is on the shaded section of the number line, such as 7. Substitute 7 for t.
7 ≤ 8 : 7 Less than 8, so 7 is a solution
Graph the solution on a number line.

Question 8.
-7 < h

Answer:
Draw a solid circle at -7 to show that – 7 is not a solution.
Shade the number line to the right of -7 to show that numbers greater than -7 are solutions.
Check your answer.
Substitute -6 for 4.
-7 < -6 : -7 is less than -6, so -6 ¡s a solution
Graph the solution on a number line.

Question 9.
x ≥ -9

Answer:
Draw a solid circle at -9 to show that -9 is a solution.
Shade the number line to the right of -9 to show that numbers greater than -9 are solutions.
Check your solutions
Choose a number that is on the shaded section of the number line, such as -8. Substitute -8 for x.
-8 ≥ 9 : -8 greater than -9, so -8 is a solution
Graph the solution on a number line.

Go Math Grade 6 Answers How to Write an Inequality Question 10.
n > 2.5

Answer:
Draw a solid circle at 25 to show that 25 is not a solution.
Shade the number line to the right of 2.5 to show that numbers greater than 25 are solutions.
Check your answer.
Substitute 3 for n.
3 > 2.5 : 3 is greater than 2.5, so 3 is a solution
Graph the solution on a number line.

Question 11.
-4\(\frac{1}{2}\) > x

Answer:
-4\(\frac{1}{2}\) = \(-\frac{4 \times 2+1}{2}=-\frac{9}{2}\) = -4.5 Convert to decimal number
Draw a solid circle at-45 to show that -4.5 is not a solution.
Shade the number line to the left of -4.5 to show that numbers less than -4.5 are solutions.
Check your answer.
Substitute -5 for x.
-4.5 > 5 : -5 is less than -4.5, so -5 is a solution
Graph the solution on a number line.

Write an inequality that matches the number line model.

Question 12.

Answer:
Draw an empty circle at 6 to show that 6 is not a solution.
Shade the number line to the right of 6 to show that numbers greater than 6 are solutions.
Check your answer
Substitute 7 for x.
7 > 6: 7 greater than 6, so 7 is a solution
x > 6

Question 13.

Answer:
Draw a solid circle at -3 to show that -3 is a solution.
Shade the number line to the left of -3 to show that numbers less than -3 are solutions.
Check your solution.
Choose a number that is on the shaded section of the number line, such as -4. Substitute -4 for x.
– 4 ≤ -3 : -4 less than -3, so -4 is a solution
x ≤ -3

6th Grade Math Answer Key Lesson 13.1 Question 14.

Answer:
Draw an empty circle at 1.5 to show that 1.5 is not a solution.
Shade the number line to the left of 1.5 to show that numbers less than 15 are solutions.
Check your answer.
Substitute 1 for x.
1 < 1.5 : 1 less than 1.5, so 1 is a solution
x < 1.5

Question 15.

Answer:
Draw a solid circle at -3.5 to show that -3.5 is a solution.
Shade the number Line to the right of -35 to show that numbers greater than -3.5 are solutions.
Check your solution.
Choose a number that is on the shaded section of the number line, such as -3. Substitute -3 for x.
-3 ≥ -3.5 : -3 greater than -3.5, so -3 is a solution
x ≥ -3.5

Question 16.
A child must be at least 48 inches tall to ride a roller coaster.
a. Write and graph an inequality to represent this situation.

Answer:
The word at least imp[y that the minimum height required for riding the roller coaster is 48 inches. The inequality to represent this situation is h ≥ 48, therefore its graph is:

b. Can a child who is 46 inches tall ride the roller coaster? Explain.
Answer:
A child 46 inches tall will not be able to ride the roller coaster as the minimum height requirement is 48 inches. It can also be seen that the point 46 does not lie on the graph of the inequality.

Write and graph an inequality to represent each situation.

Question 17.
The stock is worth at least $ 14.50.

Answer:
Draw a solid circle at 14.5 to show that 145 is a solution.
Shade the number line to the right of 14.5 to show that numbers greater than 14.5 are solutions.
Check your solution.
Choose a number that is on the shaded section of the number line, such as 15. Substitute 15 for x.
15 ≥ 14.5 : 15 greater than 14.5, so 15 is a solution
Graph the solution on a number line.

Lesson 13.1 Go Math Grade 6 Answer Key Pdf Question 18.
The temperature is less than 3.5 °F.

Answer:
Write the inequality. Let t represent the temperature.
t < 3.5° F
The temperature must be less than 3.5°
Graph the inequality.

Question 19.
The goal of the fundraiser is to make more than $ 150.

Answer:
Draw a solid circle at 150 to show that 150 is not a solution.
Shade the number Line to the right of 150 to show that numbers greater than 150 are solutions.
Check your answer.
Substitute 200 for x.
200 > 150: 200 is greater than 150, so 200 is a solution
Graph the solution on a number line.

H.O.T. Focus on Higher Order Thinking

Question 20.
Communicate Mathematical Ideas Explain how to graph the inequality 8 ≥ y.
Answer:
The inequality 8 ≥ y is read as 8 is greater than or equal to y. This implies that the maximum value of y is 8 and than the inequality holds true for all values of y less than 8. The symbol: ≥ implies that there will be a closed dot on 8 and that 8 is the solution of the given inequality.
Therefore the graph of the given inequality will be:

Question 21.
Represent Real-World Problems The number line shows an inequality. Describe a real-world situation that the inequality could represent.

Answer:
Note that the open dot implies that the inequality can be represented by < or>.
The graph of the inequality shows values greater than 2.75 and an open dot on 2.75, this implies that the given graph can be represented by the inequality: x > 2.75.

Real-world example: John is preparing for his exam and wants to spend more than 2.75 hours on his studies each day.

Lesson 13.1 6th Grade Go Math Homework Answer Key Question 22.
Critique Reasoning Natasha is trying to represent the following situation with a number line model: There are fewer than 5 students in the cafeteria. She has come up with two possible representations, shown below. Which is the better representation, and why?

Answer:
The second model is a better representation of the given situation because of 2 reasons. The first reason is that the number of students in the cafeteria can never be less than 0, therefore all the negative values of students do not make sense in this context The second reason is that the number of students is discrete. What that means is that the number of students can never be 1.5, as this number has to be a whole number so decimal numbers do not make sense in this context.