Core Connections, Course 3

Selected Answers
for
Core Connections, Course 3
Lesson 3.1.1
3-4.
a: Rule- Triple x and add 2; IN: 7, 100, OUT: 2, 6.5
b: Rule: Multiply x by 2.5; IN: –3, 11; OUT: 22.5, 0
c: Rule: Divide x by 2 and add 1; IN: 6, –7; OUT: 1.5, –4
3-5.
a: It subtracts 6 from the input value.
b: 71
3-6.
x + 5x + x + 35 = 385 , $50, $250, and $85
3-7.
x + 1! 2 ! (!x + 3) = 6 ! (1! 1) . x = 5
3-8.
a: Car B. Its line is steeper.
b: In 2 hours, both cars were 80 miles away from the game.
c: 160 miles
Lesson 3.1.2
3-13. a: Multiply x by 2 and add 1.
b: y = 2x + 1
3-14. a: x + 4 = 3x ! 2 ; x = 3
b: x + 2 = !x ! 1 ; x = ! 23
3-15. a: 31
b: 2
3-16. a: –13
b: 4
Selected Answers
c: 36
d: –4
e: 16
f: –3
1
Lesson 3.1.3
3-23. a: x = –5
b: x = –10
c: x = –15
d: x = –2
e: x = –10
f: x = 3 or –3
3-24. a: c = 2
3-25.
b: No solution.
x + 1! 2 ! (!x + 3) = 6 ! (!1+ 1) . x = 5
3-26. 1036 students
3-27. a: 26
b: 4
c: 2
3-28. a: Multiply x by –3.
b: y = !3x
3-29. a: x = 4
b: p = 0
3-30. a: 2x + 1! (!x ! 2) = 2 ! (!2x),!!x = !1
b: 0 = 0
d: 43
3-31. $1845.75. 32 games. $22.75.
3-32. a: 3x 2 + 2x + 8, 5x 2 + 2, 8x 2 + 2x + 10
b: 7x 2 ! 7x !17
c: 43 x + 23 x = 17
12 x
Lesson 3.1.4
3-37. Answers will vary.
3-38. a: x = 2
b: x = 2.5
3-39. a: 37
b: 5.5
3-40. a: ≈ 71.4 or 72 tomatoes
c: 3
d: 12
b: ≈ 81 people
3-41. 20 Schnauzers
2
Core Connections, Course 3
Lesson 3.1.5
3-46.
y= x+3
3-47. a:
x –2 –1 0 1 2 b:
y
y 11 9 7 5 3 x
3-48. a: left = –4, right = –7 (left is greater)
3-49. a:
8
15
x –2 –1 0 1 2 b:
or 0.53
3-50. a: x = 2
4
7
y
y –22 –11 0 11 22 x
b: left = –5, right = –1 (right is greater)
c: – 10
21
d:
16
15
1
or 1 15
b: x = 3.5
Lesson 3.1.6
y
3-56. Sample table and graph:
x
y
–3
11
–2
6
–1
3
0
2
1
3
2
6
3
11
x
y
3-57.
x
x
y
–3
6
–2
5
–1
4
0
3
1
2
2
1
3
0
3-58. Figure 0 will have 1 square, Figure 4 will have a 5-by-5 square with 8 tiles attached in a
row on the right, and Figure 100 will have a 101-by-101 square with 200 tiles attached in
a row on the right.
3-59.
2y + 4x + 2 , 2(7) + 4(3) + 2 = 28 units
3-60. a: 4x 2 + 5x ! 4y ! 3
c: !3y 2 + 34x ! 5y
Selected Answers
b: !6x 2 ! 2x + 8
d: 0
3
Lesson 3.1.7
y
3-65. a:
b: (–3, –2)
c: A parabola
d: (–3, –2)
should be
(–3, 5)
x
3-66. a:
x –2 –1 0 1 2 y
y 4 1 0 1 2 b:
x –2 –1 0 1 2 x
y
y –4 –1 0 –1 –2 x
c: The parabola in part (a) points upward, while the parabola in part (b) points downward.
d: ! ± 2.6
e: ! ± 3.2
3-67. a: $30
b: She earns $6 per hour, so after x hours, she earns 6x dollars.
c: See graph at right. It should be continuous assuming that
she is paid for partial hours.
3-68. Left Expression: –2x + 4 , x ; Right Expression: 3 + 1 , 0;
Explanation: Flip the tiles from “–”region to “+” region, Take 4 away from both sides
3-69. a:
b:
c:
d:
–28
7
4
4
56
–4
3
–7
10
–8
–15
2
5
7
Core Connections, Course 3
Lesson 3.2.1
3-74. a: x = –2
b: x = 1
c: !(x ! 3) represents the opposite of x ! 3 , which is !x + 3 .
3-75. a: Yes
3-76.
b: No
c: No
d: Yes
IN (x)
–4
–3
–2
–1
0
1
2
3
4
OUT (y)
9
7
5
3
1
–1
–3
–5
–7
a: See graph at right.
y
b: It is a slanted line that decreases as x increases.
3-77. a: 2x + 6
y-intercept:
(0, 1)
b: 4x + 6
c: 4x + 4y
d: 6y ! 2x + 4
3-78. a: $68.75
x
x-intercept:
(0.5, 0)
b: 20 pounds
(2, –3)
Lesson 3.2.2
3-84.
a:
Figure 0
Figure 4
x 0 1 2 3 4 y = 2x + 2
y 2 4 6 8 10 y
x
b: (5, 12)
b: y = 2x ! 1
3-85. a:
IN (x)
–1
0
1
2
3
OUT (y)
–3
–1
1
3
5
3-86. Area ! 176.7 , circumference ! 47.1
3-87. a: Any number
b: m = 9
3-88. a: # of Books—12, 73
Days—15, 1
b: Minutes—0, 14
Blocks—2.5, 50, 75
Selected Answers
c: x = 4
d: p = –10
c: Miles—420, 350
Gallons—1, 5, 50
5
Lesson 3.2.3
3-94. a: No solution
b: x = 3.5
c: Any number
d: x = 0
3-95. a: 42
b: 3
c: 12
d: 3
3-96. Let x represent the width of the rectangle, 2x + 2(2x + 3) = 78 , 27 cm and 12 cm
3-97.
IN (x)
–3
–2
–1
0
1
2
3
OUT (y)
–5
0
3
4
3
0
–5
y
x
a: See graph at right.
b: A parabola opening upward.
3-98. a:
20
7
= 2 67
50
b: – 143
c: – 189
220
d:
144
5
=
48
5
= 9 53
Lesson 3.2.4
3-102. a:
b:
c:
1
0.5
2
10
5
7
–2.5 –2
– 4.5
2
2.5
5
d:
– 48
8
–6
2
3-103. They are downloading at the same rate, 0.8 songs/min.
3-104. a: x = 2
b: x = –1
c: All numbers
d: x = 1.5
3-105. IN—4; OUT—8, 3, 1, 24 ÷ x
a: Answers will vary. Sample response: The product of x and y is always 24.
b: xy = 24 or y = 24
x
c: See graph at right.
3-106. a: Three less than five times x
b: Twice the sum of x and y
c: Three decreased by the sum of x and 5
6
Core Connections, Course 3
Lesson 3.2.5
3-113. a: x = 2
b: x = –7
3-114. a: 2x 2 + 12x ! 8
b: 8y 2 ! 10y + 1
c: 30xy + 4y ! 4x
d: 0.8x
3-115. median = 61, upper quartile = 97, lower quartile = 48
3-116. A ! 31.78 sq m, P ! 23.31 m
3-117. a:
$0.84
pound
d: $11.88
Selected Answers
g
b: 0.6 cm
c: ! $3.50
e: ! 169 shots
f: 3 13 teaspoons
7

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