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

? 2015 CPM Educational Program. All rights reserved.

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

? 2015 CPM Educational Program. All rights reserved.

5

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download