INT2 SA Ch5 - Ms. Harmony's Website of Mathematical Fabulousness

Lesson 5.1.1

5-4.

5-5.

a: x = 5

b: x = ¨C6

c: x = 5 or ¨C6

d: x = ¨C 14

e: x = 8

f: x = ¨C 14 or 8

Figure

#

1

2

3

4

a: See table at right. y = (x + 1)2 ? 2 = x2 + 2x ? 1

b: Method 1: 52 + 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 ¨C 2 = 34.

b: x = 6

5-6.

a: x = 10

5-7.

Jackie squared the binomials incorrectly. It should be: x2 + 8x + 16 ¨C 2x ¨C 5 = x2 ¨C 2x + 1,

6x + 11 = ¨C 2x + 1, 8x = ¨C 10, and x = ¨C1.25.

5-8.

a: Yes, AA ~.

b: No, side ratios not equal

12

64

c: x = 20¡ã

# of

tiles

2

7

14

23

d: x = 10¡ã

¡Ù 18

.

98

c: Cannot tell, not enough angle values given.

5-9.

LE = MS and LI = ES = MI

5-10. a: x = 4 or ¨C4

b: x = 4

c: x = 4 or ¨C4

d: x = 1

e: none

f: none

5-11. a: See possible area model at right.

b:

1

4

c:

1

9

5-12. tan

+ 16 + 16 + 14 =

25

36

parents

niece boyfriend

parents

niece

¡Ö 69%

boyfriend

( 4 ) ¡Ö 36.87?

¨C1 1

5-13. Possible response: Translate WXYZ to the left so that point W¡äcoincides with point A, then

rotate clockwise about W¡ä so that the corresponding angle sides coincide. Then dilate it

by a factor of 0.4 from point W¡ä. y = 7.5, z = 9.6

5-14. m¡ÏABC = 22¡ã, m¡ÏBAC = 68¡ã; acute; complementary

5-15. a: y =

5

2

Selected Answers

x?8

b: y =

3

2

x +1

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1

Lesson 5.1.2

5-20. This is a parabola. It is a continuous function. Vertex: (4, ¨C9),

x-intercepts: (1, 0) and (7, 0), y-intercept: (0, 7), opening upward,

line of symmetry x = 4

y

x

5-21. a: 3, ¨C7, 6, ¨C2

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. ¡Ö 26.9 feet

5-23. a: Graph 1

b: Graph 2

5-24. a: A¡ä(¨C3, ¨C3), B¡ä(9, ¨C3), C¡ä(¨C3, ¨C6)

b: A¡å(¨C3, 3), B¡å(¨C3, ¨C9), C¡å(¨C6, 3)

c: (9, 3)

5-25. ¡Ö 103.8 meters

2

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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 = ¨C2 or x = 1; ii: x = ? 12

5-33. a: x = 2 or x = ¨C8

b: x = 3 or x = 1

c: x = ¨C10 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, ¨C2)

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 ¡Ö 1.3448, effective rate is about 34.5% annually.

5-37. x = 7¡ã

Selected Answers

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3

Lesson 5.1.4

5-43. a: x-intercepts (3, 0), (¨C 5, 0), and (3, 0), y-intercept: (0, 16)

b: x-intercepts (1, 0) and (2.5, 0), y-intercept: (0, ¨C2.5)

c: x-intercept (8, 0) and y-intercept (0, ¨C 16). For part (b), y = ¨C(x ¨C 1)(x ¨C 2.5)

5-44. a: x = 3 or ? 23

d: x =

1

2

or ? 12

5-45. a: x = 8 or ¨C8

b: x = 2 or 5

c: x = ¨C3 or 2

e: x = ¨C3 or 3

f: x = 1

b: x = 7 or ¨C9

c: x = 7 or ¨C9

5-46. ¡Ö 61¡ã

5-47. x = (180? ¨C 28?) ¡Â 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? ¨C 76? = 104? because x and z form a

straight angle

18 + 12 ¨C P(long and lost), resulting in a probability of

5-48. Using the Addition Rule, 0.11 = 200

200

4% that the food took too long and the rider got lost.

Lesson 5.1.5

5-53. a: x = 1 or 7

b: x = 1 or 7

c: none

d: x = 1 or 7

e: x = 1 or 7

f: none

b: ¡Ö 7.24

c: ¡Ö ¨C4.24

5-54. a: ¨C1

5-55. Possible equations given below.

a: y = (x + 4)(x ¨C 2) = x2 + 2x ¨C 8

c: y = (x ¨C 0)(x ¨C 7) = x2 ¨C 7x

b: y = (x ¨C 3)(x ¨C 3) = x2 ¨C 6x + 9

d: y = ¨C(x + 5)(x ¨C 1) = ¨Cx2 ¨C 4x + 5

5-56. Parabola with vertex (1, ¨C9), x-intercepts (¨C2, 0) and (4, 0),

y-intercept (0, ¨C8), opening upward, line of symmetry x = 1.

y

x

5-57. a: ¡Ö 71.56¡ã

b: y = x + 3

c: (1, 4)

5-58. a: ¦¤SQR; HL ?

b: ¦¤GFE; alternate interior angles equal; ASA ?

c: ¦¤DEF; SSS ?

4

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Core Connections Integrated II

Lesson 5.2.1

5-65. The x-intercepts are at (?4 + 7, 0) and (?4 ? 7, 0) .

y

a: ¡Ö (¨C1.35, 0) and ¡Ö (¨C6.65, 0); See graph at right.

b: Irrational because 7 is not a perfect square.

x

c: The vertex is (¨C4, ¨C7). 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

5-69. a: sin(¦È) =

¦Â ¡Ö 38?

b: 90

6

9

; ¦È ¡Ö 42?

c: 4 5

b: cos(¦Á) =

5

7

; ¦Á ¡Ö 44?

c: tan(¦Â) =

7

9

;

!##"

!##"

5-70. a: It is a trapezoid. The slope of WZ equals the slope of XY .

b: ¡Ö 18.3 units

c: (¨C9, 1)

d: 2

Lesson 5.2.2

5-77. a: 25

b: 9

c: 121

5-78. a: 2

b: ¨C3

c: ¡Ö ¨C6.1

5-79. a: ¡Ö (¨C1.4, 0) and ¡Ö (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 (2) + 1 (3) + 1 (5) = 15 = 3.75 , so her

4

4

2

4

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

Segment is

? to itself

¦¤PQR ? ¦¤SRQ

SSS ?

¡ÏP ? ¡ÏS

Selected Answers

? ?s ¡ú ? parts

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