Selected Answers
for
Core Connections Algebra
Lesson 8.1.1
8-6.
(2x – 3)(x + 2y – 4) = 2x 2 + 4xy –11x – 6y +12
8-7.
a: 12x 2 +17x – 5
b: 4x 2 – 28x + 49
8-8.
a: t(n) = 500 +1500(n –1)
b: t(n) = 30 ×5n–1
8-9.
a:
b:
–80
10
–8
–3
2
c:
12
–4
7
–7
e:
d:
0
0
–81
9
7
–9
0
f:
2x
–7x
x
–6x
3x
5x
8-10. a: 4(x + 2)
b: 5(2x + 5y + 1)
c: 2x(x – 4)
d: 3x(3xy + 4 + y)
8-11. a: (0, –8); It is the constant in the equation.
b: (–2, 0) and (4, 0); Students may notice that the product of the x-intercepts equals the
constant term.
c: (1, –9); Its x-coordinate is midway between the x-intercepts.
8-12. a: –1
2
b: » 7.24
c: » –4.24
Core Connections Algebra
Lesson 8.1.2
8-17. a: (x –6)(x + 2)
c: (x – 5)(2x +1)
b: (2x +1)2
d: (x + 4)(3x – 2)
8-18. a: x-intercepts (–1, 0) and (3, 0), y-intercept: (0, –3)
b: x-intercept (2, 0), no y-intercept
c: x-intercepts (–3, 0), (–1, 0), and (1, 0), y-intercept (0, 2)
d: x-intercept (8, 0), y-intercept (0, –20)
8-19
a: t(n) = 12 ( 12 )n-1
8-20.
50(0.92)5 » $32.95
b: t(n) = -7.5 - 2(n -1)
8-21. a: (6, 9)
b: (0 2)
8-22. a: x = – 10
23
b: all real numbers
8-23.
c: c = 0
y = 14 x + 400
Selected Answers
3
Lesson 8.1.3
8-29. If x represents time traveled (in hours) and y represents distance between the two trains,
then 82x + 66x = y . When y = 111, x = 0.75 hours, which is 45 minutes. So, the time
when the trains are 111 miles apart is 4:10 p.m.
8-30. a: 9 units
b: 15 units
c:
10 units
8-31. a: (k – 2)(k –10)
b: (2x + 7)(3x – 2)
c: (x – 4)2
d: 121 square units
d: (3m +1)(3m –1)
e: The largest exponent in each expression is 2.
2
8-32. a: 3 125 = 25
b:
8-33. a: x = 5
b: x = –6
c: x = 5 or –6
e: x = 8
f: x = – 14 or 8
d: x = – 14
16 = 4
c:
1
16
=
1
4
d:
4 1
81
= 13
8-34. a: On average student backpacks get 0.55 pounds lighter with each quarter of high school
completed.
b: About 44% of the variation in student backpack weight can be explained by a linear
relationship with the length of time spent in high school.
c: The “largest” residual value is about 6.2 pounds and it belongs to the student who has
completed 3 quarters of high school.
d: 13.84 – 0.55(10) = 8.34 lbs
e: A different model would be better because it looks like there is a curved pattern in the
residual plot.
4
Core Connections Algebra
Lesson 8.1.4
b: (x – 3)(x + 2)
8-39. a: (2x + 5)(x –1)
c: (3x +1)(x + 4)
d: It is not factorable because no integers have a product of 14 and a sum of 5.
b: t(n) = -3+ 4(n -1) or an = -3+ 4(n -1)
8-40. a: explicit
d: t(n) = 3- 13 (n -1) or an = 3- 13 (n -1)
c: t(50) = a50 = 193
8-41. a: In 7 weeks
b: Joman will score more with 1170 points, while Jhalil will have 970.
8-42. a: Michelle is correct. One way to view this is graphically: The x-intercept always has a
y-coordinate of 0 because it lies on the x-axis.
b: (– 4, 0)
8-43. 45, 46, 47; x + (x +1) + (x + 2) = 138
8-44. a: 2
b: 3
c: 1
8-49. a: (x + 8)(x – 8)
b: (y – 3)2
c: (2x +1)2
8-50. a: 1
b: 20
x
c:
8-51. a: (–3, –7)
b: (5, –1)
Lesson 8.1.5
8-52. a: 4, 8,12,16; t(n) = 4 + 4(n -1)
5
t3
d: 5(x + 3)(x – 3)
d: x 2 y
b: 4, 8,16, 32; t(n) = 4(2)n-1
c: Answers will vary.
8-53. a: x = 1.5y + 5
b: x = 24
c: x = 2.5
d: x = 0 or 3
8-54. a: Answers will vary.
b: The “largest” residual value is about 17ºF and it belongs to the day after the 69.8ºF
day.
c: 13.17 + 0.85(55) = 60.0ºF
d: The upper bound is given by y = 30.17 + 0.85x , and the lower bound is given by
y = -3.83 + 0.85x . Mitchell predicts tomorrow’s temperature will fall between 42.9ºF
and 76.9ºF. Despite the strong relationship between the variables, Mitchell’s model is
not very useful.
Selected Answers
5
Lesson 8.2.1
8-58. Vertex: (4, –9), x-intercepts: (1, 0) and (7, 0), y-intercept: (0, 7)
8-59. a: 3; –7; 6; –2
c: It tells us that a = 0.
b: …it does not change the value of the number
d: All equal 0.
e: …the result is always 0.
8-60. a: x-intercepts (2, 0), (– 4, 0), and (3, 0), y-intercept: (0, 18);
b: x-intercepts (3, 0) and (8, 0), y-intercept: (0, –3)
95
c: x-intercept (1, 0) and y-intercept (0, – 4)
b: There is a weak to moderate positive linear
association between Diego’s run time and
the strokes taken for each match. There
looks to be an outlier at 92 minutes.
90
Strookes
8-61. a: See scatterplot at right.
45 minutes + 77 strokes = 122
c: See graph shown below right.
d: Every minute of improvement in time reduces
the number of strokes by 0.7 on average.
85
80
75
40 50 60 70 80 90 100
Time (minutes)
e: Answers will vary.
8-62. a: no solution
b: (7, 2)
8-63. a: The symbol “≥” represents “greater than or
equal to” and the symbol “>” represents “greater than.”
b: 5 > 3
c: x ≤ 9
d: –2 is less than 7.
6
Core Connections Algebra
Lesson 8.2.2
8-69. This parabola should have x-intercepts (–3, 0) and (2, 0) and y-intercept (0, –6).
8-70. a: One is a product and the other is a sum.
b: first: x = –2 or x = 1; second: x = – 12
8-71. a: x = 2 or x = –8
c: x = –10 or x = 2.5
b: x = 3 or x = 1
d: x = 7
8-72. a: The line x = 0 is the y-axis, so this system is actually finding where the line
5x – 2y = 4 crosses the y-axis.
b: (0, –2)
8-73. a: 4; Since the vertex lies on the line of symmetry, it must lie halfway between the
x-intercepts.
b: (4, –2)
8-74. a: 2(x – 2)(x +1)
b: 4(x – 3)2
8-75. a: (3x)3/2
b: 811/x
c: 17 x/3
b: x = 0 or –6
c: x = –5 or 23
Lesson 8.2.3
8-83. a: x = 1 or 43
8-84. The result must be the original expression because multiplying and factoring are opposite
processes; 65x 2 + 212x –133.
8-85. a: x = 3 or – 23
c: x = –3 or 2
b: x = 2 or 5
d: x = 12 or – 12
8-86. See graphs at right.
8-87. a: true
b: false
c: true
d: true
e: false
f: false
b: » 1.6
c: –3
8-88. a: –1
Selected Answers
7
Lesson 8.2.4
8-92. a: y = x 2 + 2x – 8
b: y = x 2 – 6x + 9
d: –x 2 – 4x + 5
c: y = x 2 – 7x
8-93. m = 12 , (0, 4)
8-94. a: » –1.4 and » 0.3
b: The quadratic is not factorable.
8-95. a: x = 4 or –10
b: x = –8 or 1.5
8-96. a: 4
b: –10
8-97. a: (1, –1)
b: –2, 12
(
c: –8
d: 1.5
)
Lesson 8.2.5
8-106. a: y = (x + 3)2 + 6, (–3, 6)
c: y = (x + 4)2 –16, (–4, –16)
(
8-107. a: 4, –
1
2
)
b: (–2, –3)
b: y = (x – 2)2 + 5, (2, 5)
d: y = (x + 2.5)2 – 8.25, (–2.5, –8.25)
( )
c: 0, 52
d: (0, –4)
8-108. » 1.088; 8.8% monthly increase
8-109. x-intercepts: (–1, 0) and (–2, 0),
y-intercept: (0, 4), solution graph shown at right.
8-110. a: m = 43 , b = 29
4
b: Yes, it makes the equation a true statement.
8-111. a: p = 3.97v +109.61, where p is power (watts) and v is VO2max (ml/kg/min).
b: 280 watts. The measurements are rounded to the nearest whole number.
c: 293 – 280 = 13 watts
d: r = 0.51. The linear association is positive and weak.
e: There is a weak positive linear association between power and VO2max, with no
apparent outliers. An increase of one ml/kg/min in VO2max is predicted to increase
power by 3.97 watts. 26.7% of the variability in the power can be explained by a
linear relationship with VO2max.
8
Core Connections Algebra