Selected Answers
for
Core Connections Algebra
Lesson 3.1.1
3-6.
a:
d:
3-7.
1
h2
n8
b: x 7
c: 9k10
e: 8y 3
f: 28x 3 y 6
a: incorrect, x100
c: incorrect, 8m 6 n 45
b: correct
y
3-8.
x
3-9.
Let x = number of weeks. 150 + 10x
1
2
3-10. a: 9
b: –4
c: –1
d:
7
3-11. a: – 10
b: –2 23
c: 3 13
d: –3
b: 1
c:
3-21. a: x = 3
b: x = 6
c: x = 2
3-22. a: m = – 13
b: y = – 13 x – 2
Lesson 3.1.2
3-19. b, c, d, f
3-20. a:
1
4
1
52
=
1
25
d:
1
x2
d: x = 4
3-23. Let x = number of weeks. 1500 ! 35x = 915; x = 17 weeks
3-24.
2
y = 3x – 1
Core Connections Algebra
Lesson 3.2.1
3-33. a: 4x 2 + 6x + 13
b: 5y 2 + 8x + 19
c: 9x 2 + x + 44
d: 5y 2 + 6xy + 30
3-34. a: x = –8
b: x = 1
3-35. A pair of parallel lines.
3-36. Let x = the number of votes for candidate B, x + (x – 15,000) = 109,000. 62,000 votes
3-37. a: 1 19
3-38.
y=
1
2
3
b: –13 10
c: –14 17
20
d: –7 16
x +1
3-39. a: 4x + 2y + 6
c: 4y + 2x + 6
b: 2x + 4
d: 2y + 2x + 6
3-40. Possible equation: 2 + (!2x) ! (4 ! x) = 2 + (!3) ! (x ! 2) or
2 + (!2x) ! (!x) ! 4 = 2 + !3 ! x ! (!2)
3-41. a: x = 8
b:
x
y
–2
–5
0
–4
2
–3
4
–2
6
–1
8
0
10
1
c: It is the point where the lines intersects the x-axis
on the graph. It is the x-value when y = 0 in the table.
3-42. a: 16
b: 2
c: undefined
d: 0
b: 8x
c: 6x 2
d: 7x
y
x
3-43. B
3-44. a: 15x 2
Selected Answers
3
Lesson 3.2.2
3-48. 77 + 56 + 33 + 24 = 190 square units
3-49.
(2x + 4)(x + 2) = 2x 2 + 8x + 8
3-50. a: Multiply by 6.
b: x = 15
c: x = 4
3-51. a: m = 3
b: (0, –2)
c: y = 3x – 2
3-52. 10, 000 + 1500x = 18, 000 + 1300x , x = 40 months
y
3-53. The x-intercepts are (1.5, 0) and (–1, 0); the y-intercept is (0, –3).
x
y
–2
7
–1
0
0
–3
1
–2
2
3
3
12
x
Lesson 3.2.3
3-58. a: (x + 1)(x + 3) = x 2 + 4x + 3
b: (2x + 1)(x + 2) = 2x 2 + 5x + 2
3-59. a: 238 square units
b: 112 square units
3-60. a: x = 6
b: x = 16
c: x = 15
d: x = 8
b: –5 14
c: 17
d: –10 58
3-61. 30 ounces
3-62.
y=
2
3
x–3
1
3-63. a: –15 12
4
Core Connections Algebra
Lesson 3.2.4
3-70. a: 2x 2 + 17x + 30
b: 3m 2 – 4m – 15
c: 12x 3 + x 2 – 60x – 5
3-71.
d: 6 – 7y – 5y 2
y
y = –2x + 13
3-72. a: After 3 hours
b: 8
x
3-73. (–2, –1) See graph at right.
3-74. They are not. An odd number added to an odd number is an even number.
3-75. a: –15x
b: 64 p 6 q 3
c: 3m 8
b: –36x + 90xy
c: x 4 + 3x 3 + 3x 2 ! 6x ! 10
Lesson 3.3.1
3-81. a: –20xy – 32y 2
3-82. Yes, for even numbers. On a number line, if you start at any multiple of two and add a
multiple of two (an even number), you will always be stepping up the number line in
multiples of two; you will always land on an even number. No for odd numbers. For
example, 3 + 5 = 8; the sum of two odd numbers is not always odd.
3-83.
(x – 5)(x + 3) = x 2 – 2x – 15
3-84. a: x = 8 or x = –2
b: x = ±7
c: x = 1 or x = –3
d: no solution
3-85. a:
b:
c:
d:
–4
4
–1
–4
3
3-86. a: 12
Selected Answers
16
–4
–8
b: 59
c: 7
–33
–1
–3
11
7
6
8
d: 9
–7
e: –13
f: –5
5
Lesson 3.3.2
3-93. a: x = ±7
b: x = ±16
c: x = 3, –17
d: x = ±53.1
3-94. a: x = 6 + 23 y
b: y =
c: r =
d: r =
3-95. a: 5 59
b: –11 17
35
3-96. a: y = –11
b: y = –
3
2
x–9
3
4
d
t
c: 6 30
49
C
2!
d: 1 163
350
x + 21
y
3-97. See graph at right. (2, –5)
x
3-98. a:
x 4 y3
b: xy
c:
–6x 6
3-99. a: x = 10 or x = !16
b: x = 92 , ! 11
2
c: x = ! 13 or x = ! 13
d: no solution
d:
8x 3
3-100. a: 5x 2 – 30x
b: –54y + 27y 2
3-101. a: 2x(x + 5) = 2x 2 + 10x
b: (2x + 3)(x + 5) = 2x 2 + 13x + 15
3-102. a: x = 5
c: y = 0
b: x = 2
3-103. a: 4x 2 + 17x + 15
b: –6x 3 – 20x 2 – 16x
c: –3xy + 3y 2 8x – 8y
3-104. a: x =
6
y+5
2
d: x = 38
d: 3xy + 5y 2 – 22y – 12x + 8
b: w =
p–9
–3
c: m =
(4n+10)
2
d: y = –3x
Core Connections Algebra
Lesson 3.3.3
3-107. a: x = 0
b: x = 8
c: x = 1
d: x = –3, 13
3-108. y = 3x – 5
3-109. y =
1
5
x+7
3-110. a: – 19
24
b: 4
d: – 83 = –2 23
5
6
c:
7
e: –3 12
3-11. a: 6(13x – 21) = 78x – 126
Selected Answers
b: y
= 1 25
f: 2 27
b: (x + 3)(x – 5) = x 2 – 2x – 15
c: 4(4x 2 – 6x + 1) = 16x 2 – 24x + 4
3-112. a: 15x 3 y
7
5
c: x 5
d: (3x – 2)(x + 4) = 3x 2 + 10x – 8
d:
8
x3
7