Solution manual For College Algebra and Trigonometry 5e Young

,Solution manual For College Algebra and
Trigonometry 5e Young
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, CHAPTER 0
Section 0.1 Solutions --------------------------------------------------------------------------------

1. rational (integer/integer) 2. rational (integer/integer)

3. irrational (doesn’t repeat) 4. π = 3.14159... irrational (doesn’t
repeat)

5. rational (repeats) 6. rational (repeats)

7. 5 = 2.2360... irrational (doesn’t 8. 17 = 4.1231... irrational (doesn’t
repeat) repeat)

9. − 4 = −2 rational (integer) 10. − 9 = −3 rational (integer)

11. a. Rounding: 1 is less than 5, so 7 stays. 7.347 b. Truncating: 7.347 1 7.347

12. a. Rounding: 9 is greater than 5, so 4 rounds up to 5. 9.255 b. Truncating:
9.254 9 9.254

13. a. Rounding: 9 is greater than 5, so 4 rounds up to 5. 2.995
b. Truncating: 2.994 9 2.994

14. a. Rounding: 1 is less than 5, so 5 stays. 6.995
b. Truncating: 6.995 1 6.995

15. a. Rounding: 4 is less than 5, so 4 stays: 0.234
b. Truncating: 0.234 492 0.234

16. a. Rounding: 4 is less than 5, so 4 stays: 1.327
b. Truncating: 1.327 491 1.327

17. a. Rounding: 4 is less than 5, so 4 stays: 5.238
b. Truncating: 5.238 473 5.238

18. a. Rounding: 4 is less than 5, so 4 stays: 2.118
b. Truncating: 2.118 465 2.118


1

,Chapter 0


19. 20.
5 + 2
⋅3 − 7 8
3 π r3 units3
6

+6−7
5
11

11 − 7 = 4

21. 22.
8 − 3
⋅2 + 7 5 − 4
⋅ 4 − 12
6 16

−6+7
8 − 16 − 12
5
2 −11

2+7 =9 −11 − 12 = −23

23. 24.
2 ⋅3 + 2 6 ⋅1 + 4
2 + 3 ( −2 ) 7 + 3 ( −4 )
 6 6

2 ⋅3 + 2 6 ⋅1 + 4
2 + 3 ( −2 ) 7 + 3 ( −4 )
 
−6 −12

6+2 8 6+4 10
= = −2 = = −2
2 + ( −6 ) −4 7 + ( −12 ) −5

25. 26.
     
2 ⋅  5 + 7⋅ 4 − 20  −3 ⋅  2
+ 7  + 8 ⋅  7 − 2
⋅1 
 28   9   2 

   
2 ⋅  5+ 28 − 20  −3 ⋅ ( 9 ) + 8 ⋅  7 − 2
 33   5 
2 ⋅ ( 33 − 20 ) −3 ⋅ ( 9 ) + 8 ⋅ ( 5 )
2 ⋅13 = 26 −27 + 40 = 13




2

, Section 0.1


27. 28.
2 − 3 [ 4(2 ⋅ 3 + 5)] = 2 − 3 [ 4(11)] 4 ⋅ 6 (5 − 9 ) = 4 ⋅ 6(−4)
= 2 − 3(44) = 24( −4)
= −130 = −96

29. 8 − ( −2) + 7 = 10 + 7 = 17 30. −10 − ( −9) = −10 + 9 = −1

31. 2π r( 2r ) = 4π r 2 units 2 32. −5 + 2 − ( −3 ) = −5 + 2 + 3 = 0

33. −3 −1 = −3 (1) = −3 34. −5 −3 = −5 ( 3 ) = −15

35. 36.
3 9 9
= −1 =−
−3 −5 5

37. x − ( − y ) − z = x + y − z 38. −a + b − ( −c ) = −a + b + c

39. 1
2 ( 4π r ) = 2π r
2 2
units 2 40. − ( 4a − 2b ) = −4a + 2b

41. 42.
−3 −3 3 −12 −12
= = = = −1
(5 ) ( −1) −5 5 ( −3) ( −4 ) 12

43. 44.
−4 − 6 [(5 − 8)(4)] = −4 − 6 [(−3)(4)] −14 −14
= = −2
= −4 − 6(−12) 5 − ( −2) 7
= −4 + 72
= 68

45. 46.
3 − 7 ( 2 + 6 ) − (12 − 3 )  2 − 6 (1 + 4 ) − ( 8 − 5 ) 
3 − 7 [8 − 9 ] 2 − 6 [ 5 − 3]
3 − 7 ( −1) 2 − 6 (2)
3 + 7 = 10 2 − 12 = −10


3

,Chapter 0


47. 48.
10 + 2 (16 ÷ 2 ⋅ 4 ) 7 + 3 ( 24 ÷ 4 ⋅3 )
10 + 2 ( 8 ⋅ 4 ) 7 + 3 ( 6 ⋅ 3)
10 + 2 ( 32 ) 7 + 3 (18 )
10 + 64 = 74 7 + 54 = 61

49. −3x + 6 + 4 = −3x + 10 50. −10x + 30 +12 = −10 x + 42

51. x − 3 y − xy + y = x − 2 y − xy 52. y − 7 x − xy + x = y − 6x − xy

53. 54.
−(6x − 4 y ) − (3x + 5y) = −6x + 4y − 3x − 5 y −4 x −4 x x
= = −
= −9x − y 6 − ( −2) 8 2

55. 56.
−(3 − 4 x ) − (4 x + 7) = −3 + 4 x − 4 x − 7 2 − 3 [(4 x − 5) − 3x − 7 ] = 2 − 3( x − 12)
= −10 = 2 − 3x + 36
= −3x + 38

57. 58.
−4(5) − 5 −20 − 5 −6(2x + 3 y ) − [3x − (2 − 5y)]
= = 5
−5 −5 = −6(2x + 3 y ) − [3x − 2 + 5 y ]
= −12x −18 y − 3x + 2 − 5 y
= −15x − 23 y + 2

59. 60.
1 5 1( 4 ) + 5 ( 3 ) 4 + 15 19 1 1 1( 5 ) −1( 2 ) 5 − 2 3
+ = = = − = = =
3 4 12 12 12 2 5 10 10 10

61. 62.
5 1 5 − 1⋅ ( 2 ) 5 − 2 3 1 7 1 7 ⋅ ( 2 ) − 1 14 −1 13
− = = = = − = = =
6 3 6 6 6 2 3 6 6 6 6




4

, Section 0.1


63. 3
2 + 152 = 12
18
+ 152 = 23
12 64. 1
3 + 95 = 93 + 59 = 8
9



65. 1
− 227 = 3
− 272 = 1 66. 4
3 + 72 = 28
21 + 216 = 34
21
9 27 27



67. 3
2 + 59 = 18
27
+ 10
18 = 18
37
68. 3
4 − 34 = 129 − 12
16
= − 127

69. 7
6 − 52 = 30
35
− 1302 = 30
23
70. 3
− ( −34 ) − 65 = 3(6 )+ 4(14 ) −5(7)
= 13
7 42 14



x x ⋅ (2) 3 ⋅ x + 2 ⋅ x 5 ⋅ x x y y y ⋅ (2) − y 2 ⋅ y − y y
71. + = = = 72. − = = =
5 15 15 15 3 3 6 6 6 6

73. x
3 − 27x = 7 x− 6 x
21 = x
21 74. y
10 − 15y = 3 y−302 y = y
30



75. 4y
15 − ( −34 y ) = 16 y +(3y
60
)(15)
= 61y
60
76. 6x
12 − 720x = x2 − 720x = 10x−7x
20 = 3x
20



77. 3
40 + 247 = 3(3)+5(7
120
)
= 11
30 78. − 103 − ( − 127 ) = − 103 + 127 = −3(6 ) + 7(5)
60 = 17
60



79. 80.
2 14 2 2 4 2 9 1 3 3
⋅ = ⋅ = ⋅ = ⋅ =
7 3 1 3 3 3 10 1 5 5

81. 82.

1 4 3 12
3 7 7 ⋅ =
⋅ = 7 13 91
5  12 20
4


83. 84.

1 
2

3 12 3 7 7 5 3 5 22 10
÷ = ⋅ = ÷ = ⋅ =
10 7 10 
12 40 11 22 11 3 3
4 1




5

,Chapter 0


85. 86.
2 10 2 3 1 3 3 4 7 4 10 4 2 8
÷ = ⋅ = ⋅ = ÷ = ⋅ = ⋅ =
7 3 7 10 7 5 35 5 10 5 7 1 7 7

87. 88.
4b a 4b 27 12b 3a b 3a 21 3a 3 9a
÷ = ⋅ = ÷ = ⋅ = ⋅ =
9 27 9 a a 7 21 7 b 1 b b

89. 90.
3x 15 3 3 21 20 28
⋅ = = ⋅ =
10 6x 2 ⋅ 2 4 5 141 47

91. 92.
3x 9 3x 16y 4xy 14m 4
÷ = ⋅ = ⋅ = 4m
4 16y 4 9 3 2 7

93. 94.
6 x 28 8x 2 13 ⋅ 7 65 = 73 ⋅ 476 = 329
⋅ = 18
7 3y y

95. 2 ( −3 ) + 7 = 1 96. 3 ( −4 ) + 5 = −7

97. 4 1− 7 ( −2 )  = 4 (1 +14 ) = 4 (15 ) = 60 98. 3 2 − 5 ( −3 )  = 3 ( 2 +15 ) = 3 (17 ) = 51

99. 100.
−6 ( −1) − 3 5 + ( −1)  −4 ( −4 ) − 7 2 + ( −4 ) 
7 + 2 5 + ( −1)  12 + 4 2 + ( −4 ) 
6 − 3( 4) 6 − 12 −6 2 16 − 7 ( −2 ) 16 + 14 30 15
= = =− = = =
7 + 2 (4) 7 + 8 15 5 12 + 4 ( −2 ) 12 + ( −8 ) 4 2

101. 102. 2(5) + 2(10) = 30
( −4 ) 4 2
− = =
2(3) 6 3




6

, Section 0.1


103. 104.
3(4) 3⋅ 2 ⋅ 2 3 100 − 70 30
= = = = 2
10 2
10 ⋅10 25 15 15

105. $23,908,330,000,000 106. 329,459,000

107. 108.
23,908,330,373,765 23,908,330,373,765
≈ $72,568 ≈ $72,568.34
329,459,499 329,459,499

109. Only look to the right of the digit 110. Added incorrectly in very first
to round. 13.2749: the 4 is less than 5, step. Get an LCD. Should be
so 7 remains the same. Don’t round the 2(3) +1 7
= .
9 first. 13.27 9 9

111. 112. Forgot to distribute “−1” through
3 ⋅ ( x + 5 ) − 2 ⋅ ( 4 + y ) = 3 ⋅ x + 15 − 8 − 2 ⋅ y the 2nd term in (1 – y).
= 3 ⋅ x − 2 ⋅ y + 7.
Don’t forget to distribute the −2 to
both terms inside the parenthesis.

113. False. Not all student-athletes are 114. True. To be an active member in a
honors students. fraternity or sorority, you must also be
a student at the university.

115. True. 116. False.
integer
Every integer can be written as .
1

117. x ≠ 0 118. x ≠ 0

119.
−2 [3( x − 2 y ) + 7 ] + [3(2 − 5x ) + 10 ] − 7 [ −2( x − 3) + 5] =
−2 [3x − 6 y + 7 ] + [6 − 15x + 10 ] − 7 [ −2 x + 6 + 5] =
−6 x + 12 y − 14 + 6 − 15x + 10 + 14 x − 42 − 35 =
−7 x + 12 y − 75




7

, Chapter 0


120.
−2 {−5( y − x ) − 2 [3(2x − 5) + 7(2) − 4 ] + 3} + 7 =
−2 {−5( y − x ) − 2 [6x −15 +10 ] + 3} + 7 =
−2 {−5 y + 5x −12x +10 + 3} + 7 =
−2 {−7 x − 5 y +13} + 7 =
14x + 10 y − 19

121. 1260 = 35.4964787... irrational 122.
144 12
= rational
25 5

123. 67, so rational 124. 4.242640687, so appears irrational
at this point since no pattern seems to
emerge.




8