Selected Answers
© 2006 - 2016 CPM Educational Program.
All rights reserved.
1
Lesson 5.1.1
5-4.
a:
x
= 5
b:
x
= –6
c:
x
= 5 or –6
d:
x
= –
1
4
e:
x
= 8
f:
x
= –
1
4
or 8
5-5.
a:
See table at right.
y
= (
x
+ 1)
2
−
2 =
x
2
+ 2
x
−
1
b:
Method 1: 5
2
+ 2(5)
−
1 = 34 tiles;
Method 2: The next term in
the pattern is 34 because the terms of the sequence (2, 7, 14, 23)
increase by consecutive odd numbers. Method 3: Figure 5 is a
6-by-6 square minus two corner squares, so (6)
2
– 2 = 34.
5-6.
a:
x
= 10
b:
x
= 6
c:
x
= 20
°
d:
x
= 10
°
5-7.
Jackie squared the binomials incorrectly.
It should be:
x
2
+ 8
x
+ 16 – 2
x
– 5 =
x
2
– 2
x
+ 1,
6
x
+ 11 = – 2
x
+ 1, 8
x
= – 10, and
x
= –1.25.
5-8.
a:
Yes, AA ~.
b:
No, side ratios not equal
12
64
≠
18
98
.
c:
Cannot tell, not enough angle values given.
5-9.
LE
=
MS
and
LI
=
ES
=
MI
5-10.
a:
x
= 4 or –4
b:
x
= 4
c:
x
= 4 or –4
d:
x
= 1
e:
none
f:
none
5-11. a:
See possible area model at right.
b:
1
4
c:
1
9
+
1
6
+
1
6
+
1
4
=
25
36
≈
69%
5-12.
tan
–1
3
4
(
)
≈
36.87º
5-13.
Possible response: Translate
WXYZ
to the left so that point
W
′
coincides with point
A
, then
rotate clockwise about
W
′
so that the corresponding angle sides coincide.
Then dilate it
by a factor of 0.4 from point
W
′
.
y
=
7.5,
z
= 9.6
5-14.
m
∠
ABC
= 22°,
m
∠
BAC
= 68°;
acute;
complementary
5-15. a:
y
=
5
2
x
−
8
b:
y
=
3
2
x
+
1
Figure
#
# of
tiles
1
2
2
7
3
14
4
23
parents
niece
boyfriend
parents
niece
boyfriend

2
© 2006 - 2016 CPM Educational Program.
All rights reserved.
Core Connections Integrated II
Lesson 5.1.2
5-20.
This is a parabola.
It is a continuous function.
Vertex: (4, –9),
x
-intercepts: (1, 0) and (7, 0),
y
-intercept: (0, 7), opening upward,
line of symmetry
x
= 4
5-21.
a:
3,
–7, 6, –2
b:
…it does not change the value of the number.
c:
It tells us that
a
= 0.
d:
0, 0, 0, 0
e:
…the result is always zero.
f:
It tells us that at least one of the numbers must be zero.
5-22.
≈
26.9 feet
5-23.
a:
Graph 1
b:
Graph 2
5-24.
a:
A
′
(–3, –3),
B
′
(9, –3),
C
′
(–3, –6)
b:
A
″
(–3, 3),
B
″
(–3, –9),
C
″
(–6, 3)
c:
(9, 3)
5-25.
≈
103.8 meters
x
y

Selected Answers
© 2006 - 2016 CPM Educational Program.
All rights reserved.
3
Lesson 5.1.3
5-32.
a:
Both are expressions equal to 0.
One is a product and the other is a sum.
b:
i
:
x
= –2 or
x
= 1
ii
:
x
=
−
1
2
5-33.
a:
x
= 2 or
x
= –8
b:
x
= 3 or
x
= 1
c:
x
= –10 or
x
= 2.5
d:
x
= 7
5-34.
a:
4;
Since the vertex lies on the line of symmetry, it must lie halfway between the
x
-intercepts.
b:
(4, –2)
5-35.
a:
3
8
b:
1
8
c:
3
8
d:
1
8
; The sum must be equal to 1.
5-36.
a:
2.5%
b:
f
(
t
) = 500(1.025)
t
where
t
represents time in months.
c:
$579.85
d:
(1.025)
12
≈
1.3448, effective rate is about 34.5% annually.
5-37.
x
= 7º

4
© 2006 - 2016 CPM Educational Program.
All rights reserved.
Core Connections Integrated II
Lesson 5.1.4
5-43.
a:
x
-intercepts (3, 0), (–
5, 0), and (3, 0),
y
-intercept: (0, 16)
b:
x
-intercepts (1, 0) and (2.5, 0),
y
-intercept: (0, –2.5)
c:
x
-intercept (8, 0) and
y
-intercept (0, –
16).
For part (b),
y
= –(
x
– 1)(
x
– 2.5)
5-44.
a:
x
= 3 or
−
2
3
b:
x
= 2 or 5
c:
x
= –3 or 2
d:
x
=
1
2
or
−
1
2
e:
x
= –3 or 3
f:
x
= 1
5-45.
a:
x
= 8 or –8
b:
x
= 7 or –9
c:
x
= 7 or –9
5-46.
≈
61°
5-47.
x
= (180º – 28º) ÷ 2 = 76º because of the Triangle Angle Sum Theorem and because the
base angles of an isosceles triangle are congruent;
y
= 76º because corresponding angles
are congruent when lines are parallel;
z
= 180º – 76º = 104º
because
x
and
z
form a
straight angle
5-48.
Using the Addition Rule, 0.11 =
18
200
+
12
200
–
P
(long and lost), resulting in a probability of
4% that the food took too long and the rider got lost.

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- Winter '16
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- Pythagorean Theorem, triangle, 20a3b