INT2 SA Ch5 - Ms. Harmony's Website of Mathematical Fabulousness
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 = x2 + 2x - 1
Figure # of
#
tiles
b: Method 1: 52 + 2(5) - 1 = 34 tiles; Method 2: The next term in
1
2
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.
2 3 4
7 14 23
5-6. a: x = 10
b: x = 6
c: x = 20?
d: x = 10?
5-7. Jackie squared the binomials incorrectly. It should be: x2 + 8x + 16 ? 2x ? 5 = x2 ? 2x + 1, 6x + 11 = ? 2x + 1, 8x = ? 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
parents niece boyfriend
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
1 4
36.87?
parents niece boyfriend
5-13. Possible response: Translate WXYZ to the left so that point Wcoincides 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. mABC = 22?, mBAC = 68?; acute; complementary
5-15.
a:
y=
5 2
x-8
b:
y
=
3 2
x +1
Selected Answers
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1
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
y x
2
? 2015 CPM Educational Program. All rights reserved.
Core Connections Integrated II
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 c: x = ?10 or x = 2.5
b: x = 3 or x = 1 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 = 7?
Selected Answers
? 2015 CPM Educational Program. All rights reserved.
3
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
d: x =
1 2
or
-
1 2
5-45. a: x = 8 or ?8
b: x = 2 or 5 e: x = ?3 or 3
b: x = 7 or ?9
c: x = ?3 or 2 f: x = 1
c: x = 7 or ?9
5-46. 61?
5-47.
x = (180? ? 28?) ? 2 = 76? because of the Triangle Angle Sum Theorem and because the base angles of an isosceles triangle are congruent; y = 76? because corresponding angles are congruent when lines are parallel; z = 180? ? 76? = 104? 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.
Lesson 5.1.5
5-53. a: x = 1 or 7 d: x = 1 or 7
b: x = 1 or 7 e: x = 1 or 7
c: none f: none
5-54. a: ?1
b: 7.24
c: ?4.24
5-55. Possible equations given below. a: y = (x + 4)(x ? 2) = x2 + 2x ? 8 c: y = (x ? 0)(x ? 7) = x2 ? 7x
b: y = (x ? 3)(x ? 3) = x2 ? 6x + 9 d: y = ?(x + 5)(x ? 1) = ?x2 ? 4x + 5
5-56. Parabola with vertex (1, ?9), x-intercepts (?2, 0) and (4, 0), y-intercept (0, ?8), opening upward, line of symmetry x = 1.
5-57. a: 71.56?
b: y = x + 3
c: (1, 4)
y x
5-58.
4
a: SQR; HL b: GFE; alternate interior angles equal; ASA c: DEF; SSS
? 2015 CPM Educational Program. All rights reserved.
Core Connections Integrated II
Lesson 5.2.1
5-65. The x-intercepts are at (-4 + 7, 0) and (-4 - 7, 0) . a: (?1.35, 0) and (?6.65, 0); See graph at right. b: Irrational because 7 is not a perfect square. c: The vertex is (?4, ?7). It is exact.
5-66. He needs to buy 15 more small square tiles to complete the design.
5-67. 6" < ML < 14"
5-68. a: 3 2
b: 90
c: 4 5
5-69. 5-70.
a: sin() = 38?
6 9
;
42?
b: cos() =
5 7
;
44?
!##"
!##"
a: It is a trapezoid. The slope of WZ equals the slope of XY .
b: 18.3 units
c: (?9, 1)
d: 2
y x
c: tan() =
7 9
;
Lesson 5.2.2
5-77. a: 25
b: 9
c: 121
5-78. a: 2
b: ?3
c: ?6.1
5-79. a: (?1.4, 0) and (0.4, 0)
b: The quadratic is not factorable.
5-80. no a: The parabola should have its vertex on the x-axis. b: Answers vary, but the parabola should not cross the x-axis.
5-81. See sample flowchart at right.
5-82.
The expected value per throw is
1 4
(2)
+
1 4
(3)
+
1 2
(5)
=
15 4
=
3.75
,
so
her
expected winnings over 3 games are
3(3.75) = 11.25; so she is likely to win
enough tickets to get the panda bear.
Given
Given
PQR SRQ SSS
Segment is to itself
Selected Answers
P S
s parts
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