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Pg61: Quuestions 56 &64

Pg68&69 Questions 58,62,66

Pg77&78 Questions 12, 34, 46, 50, 60, 64

Just in Time Exercises

1. Multiply: (2 + 3.x) ( -3 + x)

2. Multiply: (x + 2)(x – 2)

3. Multiply: G + V2) G-V3) 4. Multiply: (x + 2)(x – 3y)

In Exercises 5-8, use the quadratic formula to solve the equation.

5.x – 3×08. x2 + 4x – 2-0 7. 2×1-x=1 8.x = x+1

Skills

15. 2

In Exercises 9-M, write the number as a pure imaginary Pumber

9. V-16

10. V-64

11. V-12

12. V-24

4

13.

14.

25

In Exercises 15-22. find the real and imaginary parts of the complex number

18.-3

17.-

18. V3

19. 1 +V5 20. V7 – 1 21. 1 + V-5 22. V-7-1

In Exercises 23-30, find the complex conjugate of each number

23.-2

24.-5

25. 1-1

28.-21 + 4

27. 3+VE

28. 9-V3 29.

30.

In Exercises 31-42, find x + x – x xy, and

31. x – 3y – 2 –

32. –

25+ i

33. * -3 + 5ty 2 – 31

34. = 2 – = -4+61

35. – 4-5y 3+21

38. x-2-7 y 11 + 21

1

37. *

38. X=

1

26 y

2

30. –

*=+1V2:y- +IV2

40. X

+10535=-3-2115

—3+hy-1+

41. -3+y

42. x= -2- by 1+2

In Exercises 43-48, use the definition of i to solve the equation.

43.-16

44.-25

46. – 12

47. 3×2-30

45. -*-18

48. 5-60

Paying Attention to Instructions: Exercises 49-50 are intended to give you practice reading and paying

attention to the instructions that accompany the problems you are working

49. Consider the equation x+x+1 -0.

.. Find the real solutions of this equation, if any.

. Find all solutions of this equation.

50. Consider the equation 2x +x+1=0.

a. Find the real solutions of this equation, if any.

. Find all solutions of this equation.

77

Chap 1 fustions and inte

53. – 3x + 2x – 4-0

50.-7x + 2x-10

50-3×2 + 8x 16

Inris 51-66. fed all solutions of the guidati quo

81. x + 2x + 3-0

52.-2+x-5-0

5.-22 + 3x – 1-0

53.5 – 2x + 3-0

57. -2-3

48. –*-1

60. 2018-

61.

—

2

03.

64.

-x-2

3

6. x – 2)

2-16

62. -6+21 –

65. (x + 1) = -25

22+ = -1

Objectiv

As E 67-70, we the following demon. A complex amber of is often det

|ಆಯಿದು..

Se

ration

dive

radice

Solve

VIC

letter. It conjuge, – is then denoted by Z

67. Show that: +7 – 2a and that – 206

6a. Show that +++

show that the real part of z is equal to?

2

70. Show that the imaginary part of is equal to

28

In Exercises 71-76. refer to the equation ar? + 2x + 1 = 0, where a is a real rumber

71. Find the discriminant bi-4dc.

72. For what value(s) of a will the equation have two solutions?

73. For what value(s) of a will the equation have one solution?

74. For what value(s) of a will the equation have no solution?

In Exercises 75-78 solve the quadratic equation by entering the quadratic formula in the home some

of your graphing utility See the Using Technology sidebar next to Example 11.

75 -0.25 + 1.14x – 2.50

76. 0.621 – 1.29 + 1.5 = 0

77. 3 + V19 = 21

78. 2x + V11 –

Concepts

70. In this problem, you will explore factoring a quadratic expression over the complex number

Multiply (x + 1)(x – 1).

D. Using your answer to part(a) as a guide, how would you factor x? +9?

c. Using your answers to parts (a) and (b) as a guide, how would you factor x2 + 2, where

a positive real number?

80. We know that A –1, but is there a complex number z such that A We answer

question in this exercise.

a. Calculate

(a+(

3) 2 (1+0)

2. Use your answer in part (a) to find a complex number z such that ? – i.

81. Isk possible for a quadratic equation with real values of a, b and to have one real solution

one nonreal solution? Explain. (Hint: Fixamine the quadratic formula.)

1.2 Ex

Applications

37. Physies: Ball Height The height of a ball after being dropped from a point 100 feet above the

ground is given by –161 +100, where is the time in seconds since the ball was dropped

and A is in feet.

.. When will the ball be 60 feet above the ground?

b. When will the ball reach the ground!

c. For what values of does this problem make sense (from a physical standpoint)?

58. Phales The height of a ball after being dropped from the roof of a 200-foot tall building is given

by h – 1612 + 200, where is the time in seconds since the ball was dropped, and his in feet.

a. When will the ball be 100 feet above the ground?

6. When will the ball reach the ground?

e. For what values of does this problem make sense (from a physical standpoint)?

9. Performing Arts Revenue from Broadway shows in New York can be modeled by

p=0.0489 -0.78154 + 10.31, where is the number of years since 1981 and p is in millions

of dollars. The model is based on data for the years 1981-2000. When will the revenue be

$12 million?

(Source: The League of American Theaters and Producers, Inc.)

60. Leisure The average amount of money spent on books and magazines per household in the

United States can be modeled by -0.28371 +5.547 + 136.7. Here, is in dollars and is

the number of years since 1985. The model is based on data for the years 1985-2000. According

to this model, in what year(s) was the average expenditure per household for books and

magazines equal to $160?

(Source:US. Bureau of Labor Statistica)

01. Construction A rectangular sandbox is to be enclosed with a fence on three of its sides and a

brick wall on the fourth side. If 24 feet of fencing material is available, what dimensions will yield

an enclosed region with an area of 70 square feet?

62. Landscaping A rectangular plot situated along a river is to be fenced in. The side of the plot

bordering the river will not need fencing. If the builder has 96 feet of fencing available, what

dimensions will yield an enclosed region with an area of 1,080 square feet?

63. Number Puzzle The product of a positive number and another that is three greater than that

number is 270. What the two numbers?

64. Number Puzzle The product of two consecutive, positive odd integers is 399. What are the

two numbers?

65. Business The profit, pin dollars), for q units produced is given by the equation

p=-0.0172 +409 – 5000

a. What is the profit obtained when 1000 units are produced?

5. How many units must be produced to obtain a profit of $35,000?

66. Business The profit, pin dollars), for q units produced is given by the equation

-0.01 +509 – 6000

a. What is the profit obtained when 800 units are produced?

D. How many units must be produced to obtain a profit of $56,500

Exercises 1.2

Skills

IN Eris 1-20 quad core

2. – 16-0

42-A-21-O

& -5 + 450

2.5-7-6-0

10. 9+1=-

12 – Tor + 8 -32

14.- + 4-0

16. x + + 4-0

18. -*-20

20. – 31+ 101 – 8-0

22. -67

24. &6

28.-3

1.-25 – 0

1.- 7x + 120

5.-3x+120

7. 6-x-2

+ 1 – 4

11, 2+3

13. -90

15 – 21 +1 -0

17. 2x + 5x – 3-0

10.-2+ ++30

In Exercises 27-28. solve the quadrare equation by completing the square.

21. x + 4-3

23. – 2x – 4

25. x + x2

28. 3 – 6x + 20

27. 2 + 8x-1-0

In Exercises 22-42, solve the quadratic equations using the quadratic formula. Find only real soluta

29. + 2x – 1-0

30 +*-50

31.-22 + 2x + 1 – 0

32. 27+ 4- 5-0

33. 3-x-X0

34. -2+ + 0

35. 2x + x + 2 – 0

36.-3x + 2x – 1-0

37. -+ 40 = 100

38.- + 50x – 300

39.

12

– 4 – 3 – 0

40. -* – 3x +90

3

41. -0.75x + 2 – 2x

42. 0.25% – 0.5×1

In Exercise 43-52, solve the quadratic equations using any method.

43. – 4-0

44-9=0

45.- + 2x=1

48. x – 4x = -4

47. -2x – 1 – 3x

48.-3? – 27x

40. – 2x – 9

51. (x – 1)x+2) = 1

50. – – 3x 1

82. (x + 1)(x – 2) – 2

For each of the equations in Exercises 53-56. find the discriminant – ac, and use it to determ

the number of real solutions to the equation. You need not solve the equation.

53. – 2x-10

54.-+*+ 3 = 0

65. + 2x = -3

5.- + 4x = 4

1.1 Exercises

61

51. Commerce The profit, in dollars, from selling x units of Blu-rwy players is given by 40x – 200

of $800.

Set up and solve an equation to find out how many Blu-ray players must be sold to obtain a profit

52. Consumer finance The cost of owning a cell phone for months is given by C – 200 + 351. Set up

and solve an equation to find out how many months a cell phone was owned if the cost was $795.

of a side of the square

53. Construction A contractor builds a square fence with 50 feet of fencing material. Find the length

54. Art A rectangular frame for a painting has a perimeter of 96 inches. If the length of the frame is

30 inches, find the width of the frame.

55. Law enforcement The total amount of spending for law enforcement by the federal state, and local

governments in the United States in 2005 was $311 billion. Since then, it has increased by $9.44

billion annually. In what year will the total amount spent on law enforcement equal $358.2 billion

(Source using)

56. Sociology The number of young adults, ages 25-34, living at home was 4.25 million in 2005. The

number has been increasing by 225.000 each year. In what year will the number of young adults

living at home reach 6,05 million? (Source facts.org)

57. Geometry An extra large, rectangular chocolate bar is three inches longer than its width. The

perimeter of the bar is 14 inches. Find the length and width of the chocolate bar.

5. Printing The perimeter of one rectangular page from an original Gutenberg Bible is 1504 mm.

The height of the page is 138 mm longer than the width. Find the dimensions of the page.

59. Finance An amount of $3000 was borrowed and repaid four years later, with simple interest. The

amount repaid was $3720. Find the annual simple interest rate.

50. Finance An amount of S4000 was borrowed at 5% simple interest and repaid later, with simple

interest. The amount repaid was $5200. Find the duration of the loan, in years.

61. Online Services in 2015, online streaming service Hulu generated $1.3 billion in revenue. This is

3.5 times what their revenue was in 2011. How much revenue did Hulu generate in 2011, to the

nearest million?

(Source Whirl.com/hule statistics)

62. Commerce In 2016, Nike sold 121,000,000 pairs of athletics footwear. This represents 31% of

the global athletic footwear market. What is the total number of pairs of athletic footwear sold

globally, to the nearest million?

(Source: www.statisticbrain.com/ike-company-stic

83. Measurement Find the height of a right circular cylinder whose radius is 3 inches and whose

volume is 54 cubic inches. The volume of a right circular cylinder is given by the formula

V = , where is the radius and is the height

84. Measurement Find the height of a rectangular box with a length of 8 inches, a width which is

double the length, and a volume of 144 cubic inches. The volume of a rectangular box is given by

Vlw, where is the length, w is the width and his the height

85. Finance Acash-back rewards credit card costs $85 annually and gives a rebate of 2% on all

purchases charged to the card.

a. If $4500 is charged on the credit card, what is the rebate amount?

b. What is the amount that can be charged on the credit card to receive a rebate of $60?

c. What is the amount that can be charged on the credit card so that the rebate equals the

amount of the annual fee?

86. Finance A membership department store gives a 4% discount on all purchases, but charges

$55 annually

a. If a shopper spends $600 a year at the store, what is the dollar amount of the discount they

receive?

. What is the amount a shopper has to spend if they want to receive a discount of $100?

c. How much should a shopper spend annually so that the dollar amount of the discount equals

the amount of the annual fee!