McGraw Hill Math Grade 7 Unit Test Lessons 16–17 Answer Key

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McGraw-Hill Math Grade 7 Unit Test Lessons 16–17 Answer Key

Restate in exponential form then calculate.

Question 1.
8 × 8 × 2 + 3 × 3 × 3
Answer:
155
Explanation:
8 × 8 × 2 + 3 × 3 × 3
= 8²× 2 + 3³
= 155
Question 2.
2 × 2 × 4 × 4 – 3 × 3 × 3
Answer:
37
Explanation:
2 × 2 × 4 × 4 – 3 × 3 × 3
= 2² × 4² – 3³
= 2² x 2² × 2² – 3³
= 2⁶ – 3³
= 64 – 27
=37
Question 3.
5 × 25 × 2 × 2 × 4 × 4 + 7 × 7 – 5 × 5
Answer:
8024
Explanation:
5 × 25 × 2 × 2 × 4 × 4 + 7 × 7 – 5 × 5
=5³ × 2² x 4² x 7² – 5²
=125 x 4 x 16 x 49 – 25
= 8024

Restate using scientific notation.

Question 4.
13,654,764.011
Answer:
1.3654764011 x 10⁷
Explanation:
The proper format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10.
b is the power of 10 required so that the scientific notation is mathematically equivalent to the original number.
1.3654764011 x 10⁷

Question 5.
28,397.01
Answer:
2.839701 x 10⁴
Explanation:
The proper format for scientific notation is a x 10^b where a is a number or decimal number.
Such that the absolute value of a is greater than or equal to one and less than ten or,
1 ≤ |a| < 10.
b is the power of 10 required,
so that the scientific notation is mathematically equivalent to the original number.

Question 6.
.100745
Answer:
1.00745 x 10^-1
Explanation:
The proper format for scientific notation is a x 10^b where a is a number or decimal number.
Such that the absolute value of a is greater than or equal to one and less than ten or,
1 ≤ |a| < 10.
b is the power of 10 required,
so that the scientific notation is mathematically equivalent to the original number.

Question 7.
21,194,668,041.1
Answer:
2.11946680411 x 10¹⁰
Explanation:
The proper format for scientific notation is a x 10^b where a is a number or decimal number.
Such that the absolute value of a is greater than or equal to one and less than ten or,
1 ≤ |a| < 10.
b is the power of 10 required,
so that the scientific notation is mathematically equivalent to the original number.

Question 8.
813.056
Answer:
8.13056 x 10²
Explanation:
The proper format for scientific notation is a x 10^b where a is a number or decimal number.
Such that the absolute value of a is greater than or equal to one and less than ten or,
1 ≤ |a| < 10.
b is the power of 10 required,
so that the scientific notation is mathematically equivalent to the original number.

Calculate.

Question 9.
3³
Answer:
aⁿ = a x a x a ….a(n times)
3³ = 3 x 3 x 3
= 27
Question 10.
8⁴
Answer:
4096
Explanation:
aⁿ = a x a x a ….a(n times)
8⁴ = 8 x 8 x 8 x 8
= 4096

Question 11.
2³ × 2^-2
Answer:
2
Explanation:
a^m + aⁿ = a^m+n
2³ × 2^-2
= 2^3-2
= 2
Question 12.
10^-8 ÷ 10^-9
Answer:
Explanation:
10^-8 ÷ 10^-9
a^m ÷ aⁿ = a^m-n
10^-8 ÷ 10^-9
= 10^-8 × 10⁹
= 10^{9 – 8}
= 10

Question 13.
15¹¹ × 15^-11
Answer:
Explanation:
a^m + aⁿ = a^m+n
15¹¹ × 15^-11
= 15^{11 – 11}
= 15⁰
= 1  (a⁰ = 1)

Question 14.
\(\sqrt{49}\)
Answer:
7
Explanation:
\(\sqrt{49}\)
= \(\sqrt{7 X 7}\)
= 7

Question 15.
\(\sqrt{64}\)
Answer:
8
Explanation:
\(\sqrt{64}\)
= \(\sqrt{8 X 8}\)
= 8

Question 16.
\(\sqrt{16}\)
Answer:
4
Explanation:
\(\sqrt{16}\)
= \(\sqrt{4 X 4}\)
= 4

Question 17.
\(\sqrt{1}\)
Answer:
1
Explanation:
\(\sqrt{1}\)
= \(\sqrt{1 X 1}\)
= 1

Question 18.
\(\sqrt{25}\)
Answer:
5
Explanation:
\(\sqrt{25}\)
= \(\sqrt{5 X 5}\)
= 5

Solve for x.

Question 19.
x – 15 ≤ 23
Answer:
x ≤ 38
Explanation:
x – 15 ≤ 23
x ≤ 23 + 15
x ≤ 38

Question 20.
3 + x ≥ 4
Answer:
x ≥ 1
Explanation:
3 + x ≥ 4
x ≥ 4 – 3
x ≥ 1

Question 21.
5x < 650
Answer:
x < 130
Explanation:
5x < 650
x < 650/5
x < 130

Question 22.
3x – 6 > 36
Answer:
x > 14
Explanation:
3x – 6 > 36
3x > 36 + 6
3x > 42
x >42 / 3
x > 14

Question 23.
\(\frac{x}{4}\) ≤ 8
Answer:
x ≤ 32
Explanation:
\(\frac{x}{4}\) ≤ 8
x ≤ 8 x 4
x ≤ 32

Question 24.
6 + x = 13
Answer:
x = 7
Explanation:
6 + x = 13
x = 13 – 6
x = 7

Question 25.
x – 15 = 22
Answer:
x = 7
Explanation:
x – 15 = 22
x = 22 – 15
x = 7

Question 26.
39 – x = 25
Answer:
x = 14
Explanation:
39 – x = 25
39 – 25 = x
x = 14

Question 27.
x + 60 = 90
Answer:
x = 30
Explanation:
x + 60 = 90
x = 90 – 60
x = 30

Question 28.
6x + 3 = 33
Answer:
x = 5
Explanation:
6x + 3 = 33
6x = 33 – 3
6x = 30
x = 30/6
x = 5

Question 29.
4x – 5 = 19
Answer:
x = 6
Explanation:
4x – 5 = 19
4x = 19 + 5
4x = 24
x = 24/4
x = 6

Question 30.
6x + 3 = 45
Answer:
x = 7
Explanation:
6x + 3 = 45
6x = 45 – 3
6x = 42
x = 42/6
x = 7

Question 31.
2x + 14 = 42
Answer:
14
Explanation:
2x + 14 = 42
2x = 42 – 14
2x = 28
x = 28/2
x = 14

Question 32.
4 – 4x = -48
Answer:
x = 13
Explanation:
4 – 4x = -48
– 4x = -48 – 4
– 4x = -52
x = 52/4
x = 13

Question 33.
\(\frac{x}{6}\) + 3 = 12
Answer:
x = 54
Explanation:
\(\frac{x}{6}\) + 3 = 12
\(\frac{x}{6}\) = 12 – 3
x = 9 x 6
x = 54

Question 34.
\(\frac{x}{2}\) – 5 = 30
Answer:
x = 70
Explanation:
\(\frac{x}{2}\) – 5 = 30
\(\frac{x}{2}\) = 30 + 5
\(\frac{x}{2}\) = 35
x = 35 x 2
x = 70

Question 35.
\(\frac{1}{3}\)x – 4 = 16
Answer:
x = 60
Explanation:
\(\frac{1}{3}\)x – 4 = 16
\(\frac{1}{3}\)x = 16 + 4
\(\frac{1}{3}\)x = 20
x = 60