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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!
