Download Chapter 1 Real Numbers and Expressions Exercise Set 1.1

48. True
Chapter 1
Real Numbers and Expressions
4.
A finite set has a finite (countable) number of
elements; an infinite set does not.
^ˆ`
52. False
54. True
Exercise Set 1.1
2.
50. True
is not empty because the set contains one
56. False
58. False
60. True
element, the symbol ˆ .
62. False because 0 is neither positive nor negative.
6.
Because the absolute value of 0 is 0, and 0 is
neither positive nor negative.
64. 2.8
8.
{a, e, i, o, u}
66. 1
1
4
10. {April, June, September, November}
68. 0
12. {Washington, Wyoming, West Virginia,
Wisconsin}
70. 18
14. {2, 3, 5, 7}
16. {5, 10, 15,…}
18.
^ 2, 1, 0,1, 2`
22.
^ x x is a natural number`
24.
^ x x is a vowel of the English alphabet`
26.
28.
20. { } or ˆ
^ x x is a month`
^ x x is a natural-number multiple of 4`
30.
72. <
74. <
76. >
78. =
80. =
82. >
84. 4.7, 2.56, 5.4, 7
1
, 8.3
2
86. 1.3, 1, 0.05 , 0.4, π , 4
2
3
88. {2002, 2004, 2007}
32.
90. {2000, 2002, 2003, 2004, 2007}
92. {Musical, Anime, Westerns}
94. { } or ˆ
34.
96. {413, 497}
98. {Canada, Mexico, Saudi Arabia}
36.
38. True
40. False
Exercise Set 1.2
2.
The sum of 0 and a number is itself; the product of
1 and a number is itself.
4.
Multiplicative inverses are two numbers that have
a product of 1.
6.
To add two numbers that have different signs,
subtract the smaller absolute value from the greater
42. True
44. False
46. True
2
8.
Chapter 1 Real Numbers and Expressions
absolute value and keep the sign of the number
with the greater absolute value.
64. When multiplying or dividing two numbers with
different signs, the product or quotient is negative.
66. 13
10. Multiplicative inverse
12. Additive inverse
14. Multiplicative inverse
16. Additive identity
68. 9
70. 15
72. 4
74. 18. Additive identity
20. Multiplicative identity
22. 12 ,
1
12
24. 9 , 26. 1
9
7 2
,
2 7
28. , 2.5 2
5
7
8
1
6
76. 0
78. 3.34
80. 4.8
82. 10
84. 5
86. 2
3
88. 7
9
5
30. Commutative property of multiplication
90. 32. Commutative property of addition
92. 20
34. Associative property of addition
94. 24
36. Distributive property
96. 4.5
38. Commutative property of multiplication
98. 120
40. Associative property of multiplication
100.
42. 6
44. 20
46. 7
48. 16
50. 7
12
52. 23
20
54. 3.47
56. 16.96
58. 3
60. 4.2
62. 23
48
102. 256.5 273.15 16.65D C
104. $2197.75
106. 20 lb.
108. $1.365 million
110. a) Earth: 8726.2 lb.
The Moon: 1490.5 lb.
b) Mars: 3333.3 lb.
112. 1.875:
Puzzle Problem
When two books are placed back to back on a shelf, the
first page of one book and the last page of the other are
separated only by two covers, so the worm only travels
1
of an inch.
4
Collaborative Exercises
Instructor’s Solutions Manual
2.
40° at 35 mph; 35° at 20 mph
4.
2 – (–12) = 14; the answer is positive because it
“feels” like the temperature increases when the
wind speed drops.
6.
Between 10 and 15 mph
Exercise Set 1.3
2.
4.
6.
8.
A number’s square is a product resulting from
multiplying the number by itself. A number’s
square root is a number whose square is the given
number.
Work from the inside out: parentheses, then
brackets, and then braces.
Because a negative number raised to an odd power
is negative.
46.
1
2
48. not a real number
50. 5
52. 18
54. 54
56. 10
58. 63
60. 8
62. 15
64. 25.1
66. 11.999
2
5
base = 5; exponent = 2; five to the second power,
or five squared
10. 28
base = 2; exponent = 8; the additive inverse of two
raised to the eighth power.
12. 128
14. 49
16. 32
18. 81
20. 1
22.
3
1
81
24. 8
27
68. 21
70. 4
5
72. 2
74. undefined
76. The distributive property was applied instead of
adding 2 5 within the parentheses.
78. The commutative property of addition was used to
exchange –2 and 8 instead of adding –11 + 8 from
left to right.
80. Mistake: Subtracted before multiplied.
Correct: 246
82. Mistake: Raised the wrong base to the power 4.
Correct: 10
26. 0.0001
84. a) $201.5
b) Yes, as long as his usage remains the same in
2010.
28. 2.744
86. 167, 742
30. s9
88. 1360.024
32. s11
90. 2.69
5
34. s
6
92. 49 0.05 1258 1000 0.15 72
$72.70
36. No real-number roots exist.
94. 0.30 127 21.26 2 112.80 131.08
38. 10
96. ­«2 10.98 2 12.98 4 1.68¼º z 8
40. 3
98. 1500 499 4 12 0.20 68, 000 60, 000 =
42. 0.1
44. 4
$27,052.
$416.04
$6.83
4
Chapter 1 Real Numbers and Expressions
100. 216
58.
102. 3125
17
4
60. 132
104. 30, 000, 000
62. 14
64. a) 40
b) 12
Exercise Set 1.4
2.
from and less than
4.
To rewrite an expression, we apply mathematical
rules to write an expression that is equivalent to
the original. To evaluate an expression, we replace
all of the variables with numbers and then simplify
so that the result is a number.
6.
8.
To combine like terms, add or subtract the
coefficients and keep the variables and their
exponents the same.
8n
12. m – 7
16. 2n – m
10. 5n – 4
14.
y2
9
3
66. a) 13
b) 10
68. 0
70. 2
72. 2, 1
74.
3
5
76. 24 x 8
78. 16 x 56
80. 8k 18. x y
1
14
82. 8.82 x 21
20.
m 2
n 3
22. 4 7 n 9
84. 3 p
24.
y 6 4
26. 12 + 0.7n
86. 28.
c d a b
1
y
3
88. 9n 10m 7
30. Mistake: incorrect order
Correct: m 4
90. 0.6t 2 6.8
32. Mistake: incorrect order.
Correct: 7 z 2r 92.
34. 2l
38.
1
d
2
36. 4l 5
40. $ 2500 n
¨ 1·
42. © t ¸ hr.
ª 4¹
44. bh
46. 2π r r h
48.
50.
54.
1 2
at
2
52. mc 2
x2 x1 2 y2 y1 2
56. 4
4 3
πr
3
5 2
t 1.2t 8
12
94. 15 x 30
96. 6t 9
98. a) 5n 8 2n b) 7 n 8
c) 6.6