Selected Answers for

Core Connections, Course 3

Selected Answers 1

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 = ! 3

2 3-15. a: 31 b: 2 3-16. a: –13 b: 4 c: 36 d: –4 e: 16 f: –3

2 Core Connections, Course 3

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 b: No solution. 3-25. x +1! 2 ! (!x + 3) = 6 ! (!1+1) . x = 5 3-26. 1036 students 3-27. a: 26 b: 4 c: 2 d: 43 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 3-31. $1845.75. 32 games. $22.75. 3-32. a: 3x2 + 2x + 8, 5x2 + 2, 8x2 + 2x +10

b: 7x2 ! 7x !17

c: 34 x +23 x =

1712 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 c: 3 d: 12 3-40. a: ≈ 71.4 or 72 tomatoes b: ≈ 81 people 3-41. 20 Schnauzers

Selected Answers 3

Lesson 3.1.5 3-46. y = x + 3 3-47. a: b: 3-48. a: left = –4, right = –7 (left is greater) b: left = –5, right = –1 (right is greater) 3-49. a: 815 or 0.53 b: 47 c: – 1021 d: 1615 or 1 115 3-50. a: x = 2 b: x = 3.5

Lesson 3.1.6 3-56. Sample table and graph: 3-57. 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: 4x2 + 5x ! 4y ! 3 b: !6x2 ! 2x + 8

c: !3y2 + 34x ! 5y d: 0

x

y

x

y x   y  –2   –22  –1   –11  0   0  1   11  2   22  

x

y

x

y

x   y  –2   11  –1   9  0   7  1   5  2   3  

x –3 –2 –1 0 1 2 3 y 11 6 3 2 3 6 11

x –3 –2 –1 0 1 2 3 y 6 5 4 3 2 1 0

4 Core Connections, Course 3

Lesson 3.1.7 3-65. a: b: (–3, –2) c: A parabola d: (–3, –2)

should be (–3, 5)

3-66. a: b: 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:

x

y

x   y  –2   4  –1   1  0   0  1   1  2   2  

x

y x   y  –2   –4  –1   –1  0   0  1   –1  2   –2  

x

y

4

–28 7 – 4

3

56 –7 – 8

–15

10

7 2 5

Selected Answers 5

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 b: No c: No d: Yes 3-76. a: See graph at right. b: It is a slanted line that decreases as x increases. 3-77. a: 2x + 6 b: 4x + 6 c: 4x + 4y d: 6y ! 2x + 4 3-78. a: $68.75 b: 20 pounds

Lesson 3.2.2 3-84. a: y = 2x + 2 b: (5, 12) 3-85. a: b: y = 2x !1

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 c: x = 4 d: p = –10 3-88. a: # of Books—12, 73 b: Minutes—0, 14 c: Miles—420, 350 Days—15, 1 Blocks—2.5, 50, 75 Gallons—1, 5, 50

x

y

y-intercept: (0, 1)

x-intercept: (0.5, 0) (2, –3)

Figure 0 Figure 4

x   y  0   2  1   4  2   6  3   8  4   10  

x

y

IN (x) – 4 –3 –2 –1 0 1 2 3 4 OUT (y) 9 7 5 3 1 –1 –3 –5 –7

6 Core Connections, Course 3

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

a: See graph at right. b: A parabola opening upward. 3-98. a: 207 = 2 67 b: – 50

143 c: – 189220 d: 1445 = 485 = 9 35

Lesson 3.2.4 3-102. a: b: c: d: 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

x

y

1 0.5 2

2.5

10 2 5

7

5 –2.5 –2

– 4.5

– 48 8 –6

2

Selected Answers 7

Lesson 3.2.5 3-113. a: x = 2 b: x = –7 3-114. a: 2x2 +12x ! 8 b: 8y2 !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 b: 0.6 g

cm c: ! $3.50

d: $11.88 e: ! 169 shots f: 3 13 teaspoons