McDougal Littell · 2012-05-30 · 36. A hot air balloon rises 486 feet. It then descends 133 feet. Find the elevation of the hot air balloon, assuming its journey started at sea

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SUMMER STUDY PACKET ALGEBRA II

SUMMER 2012

Dear prospective Algebra II student,

This summer packet is designed to help you practice the concepts you learned in Algebra I and

Geometry so that you are prepared to study Algebra II this fall. The content and philosophy of this

summer packet is consistent with our departmental goals for all high school students:

(1) that they learn to value mathematics,

(2) that they become confident in their ability to do mathematics,

(3) that they become mathematical problem solvers,

(4) that they learn to communicate mathematically, and

(5) that they learn to reason mathematically.

The exercises were taken from the Test Generator that accompanies your Algebra I textbook. If

you do not know how to solve a problem you are expected to use the sources available to you (notes,

handouts, books, Internet, etc.) to figure it out independently. The best study routine during the

summer months is to constantly review topics and do a few problems each day, not attempt to do the

entire packet the day before school starts.

The publisher of your textbook, McDougal Littell, has developed a webpage to support your

textbook (http://www.classzone.com/books/algebra_1/index.cfm?state=CA). Help is available here on a

chapter‐by‐chapter basis. Other good resources for algebra can be found at: Khan Academy

(http://www.khanacademy.org) and Math is Fun (http://www.mathsisfun.com/algebra/index.html).

Unless specifically stated or unless you are to give a decimal approximation to a square root,

you should not use a calculator to do these exercises. You may, however, use your calculator to check

your answers. Use separate sheets as necessary to show your work in a neat and organized way. Do not

try to show all work on these worksheets; there isn’t enough room!

The topics covered in this packet are:

1. Connections to Algebra 2. Properties of real numbers 3. Solving linear equations 4. Graphing linear equations and functions 5. Writing linear equations 6. Solving and graphing linear inequalities 7. Systems of linear equations and inequalities 8. Exponents and exponential functions

2

9. Quadratic equations and functions 10. Polynomials and factoring 11. Rational equations and functions

This summer assignment will not be collected. You are responsible for knowing how to solve

every single problem, but this does not mean you need to do every single problem. To keep your total

summer time investment to a maximum of 10 hours, we suggest doing every third problem (e.g. 1, 4,

7, 10 …) so that your summer workload is manageable and you review some problems involving each

topic. Motivated students can work additional problems to gain confidence and familiarity with the

more difficult topics. For your convenience, the answers to all of the exercises are included at the end of

the document.

Important: You will have a test on this summer packet study material during your 2nd math class

of the year. The test will consist of approximately twenty (20) free‐response questions (no multiple

choice, matching, etc.); you will not be able to use a calculator on the test. This exam will not count

towards your math grade; however, those students who fail the exam will be obliged to attend remedial

sessions during lunch or after school until they pass a similar exam.

If you have any questions, please email [email protected] or [email protected]

Enjoy your summer and do your best!

Sincerely,

The ASFG Math Department

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1. Evaluate the expression 6 3 91. .x when x 9.

2. Evaluate 4j + 3k when j = 1 and k = 3. [A] 14 [B] 5 [C] 12 [D] 13 3. Evaluate the expression 2 163x when x 5.

4. Evaluate the expression 4 32

k mb g when k = 4 and m = 3.

[A] 337 [B] 49 [C] 625 [D] 25

5. Simplify: 3 + 2 4 22

b g

[A] 180 [B] 24 [C] 75 [D] 147 6. Evaluate 8 7 4 20 2 .

7. Evaluate (y + 3 )2 – 40 8 when y = 4.

8. Evaluate xy

x y when x 6 and y 11.

[A] 1 [B] 72

17 [C]

611

17 [D]

66

17

9. Complete the table.

Power Base Exponent Standard Form

25

3 4

1258r

10. Write a variable expression for “7 divided by the sum of x and 5.” 11. Write a variable expression for the volume of a cube whose side length is x. 12. Use a calculator to solve the problem. Laura Shawhan has a pumpkin patch with 13 rows of pumpkin plants. There are 2 rows with 88 pumpkins each and 11 rows with 105 pumpkins each. How many pumpkins does Laura have?

4

13. Is x = 4 a solution of the equation 2 4 8x x ? 14. Solve and check: x2 16 [A] 8 [B] 8 [C] 14 [D] 4 15. Solve using mental math: x 13 = 25 [A] 38 [B] 12 [C] 37 [D] 13 16. Is x = 2 a solution of the inequality 7 3 7 2 x x ? 17. The members of a drama club are selling tickets to their next production. If their goal is to raise at least $140, the number of tickets they must sell at $3.10 each in order to meet their goal can be expressed by the inequality 310 140. .x Is 44 a solution of the inequality? 18. Write an expression to represent the following: “ the sum of 6 times and v w ” [A] (6 + )v w [B] 6 + v w [C] 6 + 6v w [D] 6( + )v w

19. Write a verbal phrase for the algebraic expression 104

x

.

20. Write the following sentence as a mathematical statement. The difference of d and 4 is greater than or equal to x. 21. Write an equation or inequality for the verbal statement “seven is equal to 4 times a number B.” 22. Write an equation or inequality for the verbal statement “seven is less than 4 times a number B.” 23. Using the bar graph below, determine how many students received a score of 90 or better on an algebra exam.

5

Number ofStudents

Exam Scores

50-59 60-69 70-79 80-89 90-100

2

4

6

8

10

[A] 21 [B] 14 [C] 7 [D] 1 24. Nutrition specialists often calculate calorie intake. The chart below shows calories for some common breakfast and luncheon foods. How many calories would a person consume if he or she had a lunch of a hot dog, french fries, and a glass of milk?

Food Calories

Banana 84

Cereal 120

Cola 73

Egg 81

French Fries 261

Hamburger 289

Hot Dog 136

Ice Cream 207

Milk (1 glass) 162

Milk Shake 275

Orange Juice 95

Toast 101

6

25.

0

–4

–8

–12

12 P.M.

Time of day

Tem

pera

ture

(°F

)4

P.M.8

P.M.12 A.M.

4 A.M.

8 A.M.

12 P.M.

The graph above shows the temperature in degrees Fahrenheit in a Minnesota city during a 24-hour period last winter. At what hour was the temperature about –12°F? 26. Does the input-output table represent a function? If it does represent a function, list the domain and range. If it does not represent a function, explain why.

Input

Output

2 3 4 5

13 15 17 19

27. Make an input-output table to represent the function. Use 1, 2, 3, 4, and 5 as the domain. f x xb g 5 6

28. Roman paid $150 to join a handball club. He pays an additional $15 every time he uses one of the club’s handball courts. Write an equation that describes Roman’s total cost for playing handball as a function of the number of times he plays. Let C = the total cost and n = the number of times he plays. 29. Graph –1, 4, –3, and 1 on a number line and determine the order of the numbers.

30. Write the numbers in increasing order. 3

210 0

2

3

5

41, , , , ,

31. What is the opposite of 15? 32. Evaluate the expression 12

[A] 11 [B] 12 [C] 12 [D] 11 33. Evaluate the sum 17.12 + (–5.23) + 172. .

34. Simplify the expression (–7) + 6 + [–(2 – 3)]. 35. Simplify the expression [ ( )].4 3

7

36. A hot air balloon rises 486 feet. It then descends 133 feet. Find the elevation of the hot air balloon, assuming its journey started at sea level. [A] 266 ft [B] 353 ft [C] 619 ft [D] –133 ft 37. Find the difference: (–10) (–3) 38. Simplify: – (–3) – (–7) + (–1) [A] 9 [B] 11 [C] –11 [D] –5 39. Evaluate the expression 17 – (–x) – 10 when x = 3.

40. The morning temperature was –3 . By noon, the temperature was 8 . How many degrees had the temperature risen?

41. Find the sum of the matrices

3 1

4 7

10 2

L

NMMM

O

QPPP

+

L

NMMM

O

QPPP

5 4

3 2

1 0

.

42. Find the difference of the matrices 9 3

4 8

LNMOQP –

2 7

8 4LNMOQP .

43. Mary asked the players on two hockey teams what new color each team uniform should be: red, blue, or green. She recorded the results in two matrices. Find the total for the two teams. R B GMales

Females

2 7 6

0 4 8

LNM

OQP P

R B GMales

Females

3 1 6

0 4 1

LNM

OQP Q

[A] 5 12 8

8 0 9

LNM

OQP [B]

12 8 5

9 8 0

LNM

OQP [C]

5 8 12

0 8 9

LNM

OQP [D]

9 8 0

12 8 5

LNM

OQP

44. Find the product: – (–8)4

45. Identify the product that will be negative. [A] 2 3 4 5b gb gb gb g [B] 2 3 4 5b gb gb gb g [C] 2 3 4 5b gb gb gb g [D] 2 3 4 5b gb gb gb g

8

46. What is the product of 3x yb gb gb g 4 5 ?

[A] 60xy [B] 12xy [C] – 60xy [D] 15xy

47. Which multiplication property illustrates the product 7 5 4 7 5 4 b g b g [A] property of opposite [B] associative [C] commutative [D] identity 48. Evaluate the expression when x 4.

( )–5 FHGIKJx

2

3

49. At 50 km/h, how far can you travel in 9 h? Use unit analysis to check your answer. 50. Use the distributive property to simplify the expression 6 2 4( )x y .

[A] 12 24x y [B] 12 24x y [C] 12 4x y [D] 2 4x y

51. Remove parentheses by applying the Distributive Property. 20x(3 – 2x) 52. Simplify the expression 3(2 – x) –2(3 – x). 53. Simplify: 4 5 2 4x x [A] 6 1x [B] 2 9x [C] 6 9x [D] 2 1x

54. Find the quotient 1249

.

[A] 1

27 [B]

9

4 [C]

3

9 [D] 27

55. Divide: –12 3

56. Simplify the expression 201

5r .

57. Simplify the expression 40 15

5

d .

9

58. Evaluate x

y if x = –48 and y = 12.

59. Simplify the quotient

42 18

6

x.

60. The yearly profit or losses for a restaurant are shown for a period of three years. Use a calculator to determine the restaurant’s overall profit or loss in the three years.

1995

1996

1997

$22,500.15

$1227.34

$7989.91

61. A box contains 7 green, 4 yellow, and 6 purple balls. Find the probability of obtaining a yellow or a purple ball in a single draw. 62. A bag has 4 blue blocks and 5 white blocks. Sonya takes a block out of the bag, records the color, then replaces the block in the bag. She does this 90 times. Which answer shows the results she is most likely to have? [A] 50 blue and 40 white [B] 45 blue and 45 white [C] 40 blue and 50 white [D] 89 blue and 1 white 63. After the introduction of a new soft drink, a taste test is conducted to see how it is being received. Of those who participated, 56 said they preferred the new soft drink, 108 preferred the old soft drink, and 36 could not tell any difference. What is the probability that a person in this survey preferred the new soft drink?

[A] 7

25 [B]

14

41 [C]

14

27 [D]

7

18

64. A bag contains three red marbles and one blue marble. The marbles are randomly selected one at a time. What are the odds of picking the blue marble on the first selection? 65. Solve: 21 6 m

66. If the sum of the two angles is 90 degrees, use an addition equation to solve for .x

10

x27°

Solve: 67. 25 = 5y

68. 2

770x

69. x

2 = 6

[A] –3 [B] 12 [C] 3 [D] –12 70. 2 10 4n n = 18 Solve the equation: 71. 5 2 2n n– ( – ) –11

72. 3 2

47

y

73. The Fahrenheit and Celsius scales are related by the equation F C 9

532 . What

temperature Celsius would give the body temperature of 98 6. F ? 74. Solve: x x 7 3 5

75. Solve the equation: 3 17 5 12 6 3x x x – – ( )

Solve the equation. Round your result to two decimal places. 76. 18 3 7 6 8 4 14 6. . . .y y

77. –1.9x + 3.9 = 4.4 [A] –4.37 [B] 2.40 [C] –0.79 [D] –0.26 78. The simple interest I on an investment of P dollars at an interest rate r for t years is given by I = Prt. Find the time it would take to earn $1600 in interest on an investment of $17,000 at a

11

rate of 6.6%. 79. The temperature was x F . It rose 14 F and is now –11 F . What was the original temperature? Write a linear model of the situation. 80. You played tennis for 35 minutes and burned 190 calories. How many calories did you burn per minute? [A] 6.42857 calories per minute [B] 225 calories per minute [C] 5.42857 calories per minute [D] 225.053 calories per minute 81. You have recorded your car mileage and gasoline use for 5 weeks. Estimate the number of miles you can drive on a full 18-gallon tank of gasoline.

Number of miles

Number of gallons

120 261 144 154 138

5 9 6 7 6

82. The two rectangles are similar. Find the width of the smaller rectangle.

w

7 m

10.62 m

12.6 m

83. One video rental club charges $25 to become a member and $2.50 to rent each video. Another charges no membership fee, but charges $3.25 to rent each video. How many videos must you rent to make the first club more economical?

84. A page of pictures for a yearbook is 91

2 inches wide by 12

1

2 inches tall. The top margin is

1

2 inches and the bottom margin is 1 inch. The space between each picture is

4

16 inches at

least. How many 1-inch-tall pictures can fit on the page in a column? Use a diagram to help you solve the problem. 85. Suzy can run 4 m/sec and Tim can run 7 m/sec. How far ahead of Tim must Suzy be to not to fall behind Tim in the first 10 seconds of running? Use a graph to check your answer.

12

86. The sales tax rate in a certain state is 5%. Find the total price paid for a pair of shoes that costs $59. 87. Write 3 2 6x y = as a function of y.

88. Name the coordinates of the points A, B, C, and D.

x

y

–10 10

–10

10

A B

CD

89. Plot the points (4, 0), (–2, –3), (3, 1), and (–2, 2).

90. The weights of ten Holstein calves of different ages are given in the table. Sketch a scatter plot of the data. Then describe any pattern that you see in the scatter plot.

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Age Weight

(months) (pounds)

2 240

3 350

3 370

4 510

6 690

6 700

7 800

8 940

8 980

10 1250

12 1300

91. Which point, 5

23, FHGIKJ or 3

220, FHGIKJ , is on the graph of 2

2

33x y ?

92. Complete the table and graph the function.

x

y x

3 1 0 2 41

24

93. Sketch the graphs of x = –3 and y = 4. Find the point at which the two graphs intersect.

94. State the x- and y-intercepts of y x 8 7 .

14

[A] x-intercept: 7; y-intercept: 7

8 [B] x-intercept: 8; y-intercept: 7

[C] x-intercept: 7; y-intercept: 8 [D] x-intercept: 7

8; y-intercept: 7

95. Graph the linear equation by finding x- and y-intercepts. 3 3x y =

[A]

x

y

[B]

x

y

[C]

x

y

[D]

x

y

96. For 1980 through 1990, Brentwood Middle School’s enrollment, y, was related to the year, t, by the equation y = 240 + 20t, where t = 0 represents 1980. Sketch the graph of this equation.

t

y

2

100

4

200

6

300

8

400

97. Plot the points and find the slope of the line passing through the points (–4, 2) and (4, –3).

15

98. Find the slope of the line that contains (–4, 5) and (5, 5). 99. At 6:21 P.M., a parachutist is 6200 feet above the ground. At 6:25 P.M., the parachutist is 2300 feet above the ground. Find the average rate of change in feet per minute. 100. Write the variation and find the quantity indicated. x varies directly with y. If x is 171 when y is 190, find x when y is 110. 101. Tell whether the data show direct variation. If so, give the constant of variation and write the equation.

Days

Growth (cm)

7 9 13 15

8 75 1125 16 25 18 75. . . .

102. The volume of a sample of gas increases with an increase in the temperature of the gas. Write a direct variation equation that models the relationship between volume and temperature for the data collected.

V ml

T K

b gb g

10 20 30 40

91 182 273 364

103. Find the slope and y-intercept of the line 4 2 24x y = .

104. Write in slope-intercept form and sketch the line. 3 2 0x y

16

105. Find the slope and y-intercept of the line y x 8 9 . Is the line parallel to y x 8 9 ?

106. The following situation can be modeled by the equation y x 8 25 .

Graph the equation. A music club membership costs $25.00 and $8.00 per CD. 107. Solve, then check algebraically and graphically: 2x + 1 = 9 [A] 4 [B] 8 [C] 10 [D] 20 108. Find the solution to the equation graphically. 5x – 5 = x + 2 109. Decide whether the information defines a function. If it does, state the domain of the function.

input

output

0 1 2 3 4

1 2 3 2 1

110. Erik pays $392 in advance on his account at the athletic club. Each time he uses the club, $6 is deducted from the account. Find a linear function that models the value remaining in his account after x visits to the club. Find the value remaining in the account after 18 visits. 111. An employee who receives a weekly salary of $250 and a 10% commission is paid according to the formula p s s( ) . 01 250 , where s represents the total weekly sales. Make a

function table to show an employee’s weekly salary for weekly sales of $3,700, $2,460, and $5,670.

112. Write an equation of the line with slope 3

2 and y-intercept –5.

113. Write an equation of the line shown in slope-intercept form.

17

x

y

–10 10

–10

10

114. The cost of a school banquet is $80 plus $13 for each person attending. Determine the linear equation that models this problem. What is the cost for 41 people? [A] y = 13x + 80; $613 [B] y = 13x – 80; $453 [C] y = 80x – 13; $3267 [D] y = 80x + 13; $3293 115. Find an equation for the line with undefined slope and passing through the point (–9, –5). 116. Find the y-intercept of a line that passes through – ,2 3b g and has a slope of 4.

117. A line passes through point (–2, –2) and has a slope of 2. Sketch the line and write its equation in slope-intercept form.

118. Write the equation of the horizontal line that passes through the point (7, –3). 119. Erik pays $315 in advance on his account at the athletic club. Each time he uses the club, $5 is deducted from the account. Write an equation that represents the value remaining in his account after x visits to the club. Find the value remaining in the account after 15 visits. [A] V = 5 – 315x; $240 [B] V = 315 – 5x; $1590

18

[C] V = 315 – 5x; $240 [D] V = 315 – 5x; $1604 120. Write an equation of the line shown on the graph.

–3

(–3, 0)

(0, –4)

–4 –2 –1 1

–4

–2

–1

1

x

y

121. Write the equation of the line in slope-intercept form that passes through the points (7, –1) and (2, 9). 122. In 1980 the average price of a home in Brainerd County was $100,000. By 1986 the average price of a home was $118,000. Write a linear model for the price of a home, P, in Brainerd County in terms of the year, t. Let t = 0 correspond to 1980. 123. Which equation matches the scatter plot?

x

y

0 1 2 3 4 5

5

10

15

20

25

30

[A] y x = 2 5 [B] y x = 5 5 [C] y x= 5 2 [D] y x= 5 2

124. In the table, x represents the number of weeks you worked at a summer job and y represents the balance in your savings account. Construct a scatter plot for this data and find an equation you think best represents the data.

x

y

1 2 3 4 5 6 7 8

14 22 26 29 35 39 46 49

19

125. What type of relationship is shown by the scatter plot?

x

y

–10 10

–10

10

[A] weak negative correlation [B] strong negative correlation [C] strong positive correlation [D] weak positive correlation 126. Write an equation for the line, in point-slope form, that passes through the points (–4, –2) and (3, –5). Use (–4, –2) as the point x y1 1, .b g 127. Write an equation in point-slope form of the line that passes through the point (–3, 4) and

has the slope 1

2. Then rewrite the equation in slope-intercept form.

128. A man decides to take out $170 per month from his savings account. After 7 months, he has $2793 in his account. Write a linear equation in point-slope form which models the amount in the savings account in terms of the number of months.

129. Write y = 8

7x +

3

7 in standard form.

20

[A] y = 8 4x [B] 8 7x y = –3 [C] x = 7

8y –

3

8 [D] 7y = 8 3x

130. Write the standard form of the equation of the line with slope –4 passing through the point (–1, 6). 131. Which of the following lines are parallel to each other? 2 6 3 6 2 3 2 6 3x y x y x y ; ;

132. The warehouse store has cashews that sell for $4.25 a pound and pecans that sell for $2.50 a pound. Write a linear equation that represents how much of each type of nut can be bought with $19. 133. A radio disc jockey kept track of the number of requests for songs by a certain artist, and the time of day the request calls were made. The data is displayed below:

#

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

of requests

time of day p m p m p m p m p m p m p m

2 7 1 9 5 2 8

2 3 4 5 6 7 8

Display the data on a scatter plot, and determine whether the data can be represented by a linear model. 134. A large factory knows that if it sells its new gadgets for $7 each, it can sell 950 per month, and if it sells the same gadgets for $9, it will sell 800 per month. Assuming the relationship between price and sales is linear, predict the monthly sales of gadgets to the nearest whole number if the price is $10. [A] 755 [B] 710 [C] 775 [D] 725 135. A real estate sales agent receives a salary of $250 per week plus a commission of 2% of sales. Write a linear model for the weekly income y in terms of sales x. 136. Sketch a graph of the inequality 4 x .

137. Write the inequality illustrated by the graph below.

–4 –3 –2 –1 0 1 2 x

138. Solve the inequality. –3x > 9

21

139. Solve x 3 9.

140. Solve and graph the inequality: 5 2 3 3x x < ( )

[A]

–10 –5 0 5 10

[B]

–10 –5 0 5 10

[C]

–10 –5 0 5 10

[D]

–10 –5 0 5 10

141. Solve the inequality 4 3 3 x x .

142. Solve the inequality 11

33 x .

143. In order to collect a salary bonus, Tony Jones must get at least 240 hits this season. In the second to last week of the season, Tony started with 217 hits and got 18 more. Write an inequality that describes how many hits Tony must get in the season’s last week. 144. Solve the inequality 2 1 2x . 145. Solve the inequality 2 1 2 2x . 146. Graph: –5 < x 7 147. Graph the solution to the inequality “x is greater than 3 or less than or equal to 0.”

148. Junior tickets to an event are available to teenagers below age eighteen at reduced rates. Write an inequality describing the age requirement for a person of age A who can buy a junior

22

ticket. Solve: 149. x 4 2 =

150. 5 = 6 2x

151. Solve the equation algebraically. 15 7 x

152. Solve the inequality 2 2 x .

153. Sketch the graph of the inequality 2 1 3x .

154. Sketch the graph of the inequality x 2 2 .

155. Graph: y x 5

[A]

x

y

[B]

x

y

[C]

x

y

[D]

x

y

156. Sketch a graph of the inequality 3 2 6x y .

23

157. Graph: x 3

[A]

x

y

[B]

x

y

[C]

x

y

[D]

x

y

158. You have $4500 to buy stock and have decided on American Enterprises (AE) and Allied Junk Yards (AJY). AE sells for $27.50 per share and AJY sells for $45.25 per share. Write an inequality which restricts the purchase of x shares of AE and y shares of AJY. 159. Construct a stem-and-leaf plot for the data. 41, 30, 23, 58, 34, 52, 46, 59, 35, 37, 57, 51, 36, 44, 49 160. Name the mode or modes in the following sample. 11, 23, 29, 3, 30, 22, 23, 7, 10, 16, 10 [A] 10, 23 [B] 3, 30 [C] 16.7 [D] 19 161. Find the median of the collection of numbers. 40, 54, 9, 48, 37, 81, 16, 38, 29, 30

24

162. Find the means of the pounds of weight loss for dieters on Plan A and Plan B. Which plan resulted in a greater average weight loss? Weight Losses of 5 patients lbs.

Plan A

Plan B

b g2 13 2 10 6

6 7 15 14 6

163. Find the first, second, and third quartiles of the data. Then draw a box-and-whisker plot of the data. 29, 24, 32, 29, 28, 29, 32, 23, 25, 24, 33, 32, 35, 33, 28 164. Which data are represented by the box-and-whisker plot?

6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

[A] 31, 23, 8, 24, 35, 30, 15 [B] 31, 25, 8, 24, 37, 30, 15 [C] 31, 25, 8, 14, 35, 30, 15 [D] 31, 25, 8, 24, 35, 30, 15 165. Solve the system by graphing: x y = – 2 y x= 2 5

[A]

x

y

3 1, b g

25

[B]

x

y

1 3, – b g

[C]

x

y

FHG

IKJ

2

3

4

3,

[D]

x

y

5

3

5

3, FHGIKJ

166. Graph: x y

x y

– –

1

2 10

26

[A]

x

y

[B]

x

y

[C]

x

y

[D]

x

y

Use a straightedge to draw straight lines. 167. Solve the linear system by graphing. x y 1 3 5x y

Use a straightedge to draw straight lines. 168. Solve the linear system by graphing.

y x

y x

2

32

3

27

169. The Rogers family is going to the county fair. They have two ticket options as shown in the chart below.

Ticket

Option

Admission

Price

Price Per

RideA $4 30¢

B $2 70¢

A. Write an equation that shows the cost per person for each option. B. Use graphing to solve the system of equations. [A] A. C r = + 4 0 3. C r = + 2 70 B. (5, 5.5) [B] A. C r = + 2 0 7. C r = + 4 30 B. (0.05, 0.055) [C] A. C r = + 4 30 C r = + 2 70 B. (0.05, 0.055) [D] A. C r = + 4 0 3. C r = + 2 0 7. B. (5, 5.5) 170. Solve the system by substitution: y x

y x

3 2

4

171. Solve by substitution: x y 2 9 = y x = 3 6

28

172. Use substitution to solve the linear system. 3

2 2

x y

x y

= 15

+ =

173. Use substitution to solve the linear system. 6

x y

x y

4

2 4

174. The length of a rectangle is 6 cm more than two times the width. If the perimeter of the rectangle is 36 cm, what are its dimensions? 175. Solve by linear combinations: 2 6

6

x y

x y

–

–

176. Use linear combinations to solve the linear system. 3 4 21x y 4 2 6x y

177. Use linear combinations to solve the linear system. 4 3 2

3 2 3

x y

x y

178. Find the solution of the system, if it exists. 2 5 7x y 4 10 2x y

179. Marc sold 563 tickets for the school play. Student tickets cost $4 and adult tickets cost $6. Marc’s sales totaled $2840. How many adult tickets and how many student tickets did Marc sell? [A] 289 adult, 274 student [B] 294 adult, 269 student [C] 274 adult, 289 student [D] 269 adult, 294 student 180. Solve the linear system by any method. 3 2 3x y 6 2 3x y

181. Solve the linear system by any method. 5 2 3

6 2

x y

x y

182. Solve the linear system by any method.

29

6 4 1

2 5 1

x y

x y

=

=

183. A group of 52 people attend a ball game. There were three times as many children as adults in the group. Write a system of equations that you could use to set up this problem, where a is the number of adults and c is the number of children in the group. Solve the system of equations for c, the number of children in the group. 184. A total of $10,000 is invested in two funds paying 5% and 7% annual interest. The combined annual interest is $644. How much of the $10,000 is invested in each fund? 185. Which system of equations has no solution? [A] x y

x y

8 1

8 6–

[B] x y

x y

8 1

5 10 6–

[C] x y

x y

8 1

4 32 4

[D] x y

x y

8 1

8 1

186. Determine if the system has no solutions, one solution, or many solutions. 3x y = –5

6 2x y = 10

187. Express each equation in slope-intercept form. Then determine, without solving the system, whether the system of equations has exactly one solution, no solution, or an infinite number of solutions.

4 2 12

6 3 23

x y

x y

–

–

188. Find the solution of the system, if it exists. 7 8

7 4

x y

x y

189. The Modern Grocery has cashews that sell for $3.75 a pound and peanuts that sell for $2.75 a pound. How much of each must Albert, the grocer, mix to get 40 pounds of mixture that he can sell for $3.00 per pound? Express the problem as a system of linear equations and solve using the method of your choice. 190. Graph the system of linear inequalities. y x 1

y 4

191. Write a system of linear inequalities that defines the shaded region.

30

x

y

–10 10

–10

10

192. You can work a total of no more than 40 hours per week at your two jobs. Housecleaning pays $7 per hour, and your sales job pays $11 per hour. You need to earn at least $344 per week to cover your expenses. Write a system of inequalities that shows the various numbers of hours you can work at each job. 193. Fuel x costs $2 per gallon and Fuel y costs $3 per gallon. You have at most $18 to spend on fuel. Write a system of linear inequalities to represent this situation. Sketch a graph of the system.

194. William baby-sits for $4 per hour. He also works as a tutor for $7 per hour. Because of school, his parents only allow him to work 14 hours per week. How many hours can William tutor and baby-sit and still make at least $65 per week? Write a system of inequalities for this situation, then graph the solution set. 195. Simplify. Leave your answer in exponential form. 71 75 [A] 74 [B] 75 [C] 76 [D] 496 196. Simplify: ( )59 4

[A] 513 [B] 536 [C] 454 [D] 572

31

197. Simplify ( ) ( ) .8 23 2 2 3x x

198. Simplify ( ) ( ) ( ). x x x2 2 2 3

199. Evaluate ( )a b3 2 3 when a = –1 and b = –2.

200. Sara bought 4 fish. Every month the number of fish she has doubles. After m months she will have F fish, where F m 4 2 . How many fish will Sara have after 3 months if she keeps all

of them and the fish stay healthy? 201. Simplify: a a–5 –3

[A] a15 [B] a8 [C] 1

8a [D]

115a

202. Multiply: 23 5 80 [A] 0 [B] 40 [C] 240 [D] 320 203. Rewrite the expression using positive exponents. ( ) ( ) 3 20 1 1 2x y

204. Rewrite the expression using positive exponents.

3

4

0

3x

205. Evaluate [ ( ) ] 3 2 1x when x = 2.

206. Graph the function: y x = 3

207. Simplify: 35

7

6 4

5

x y

xy

[A] 5 5x

y [B] –

3 7

9

x

y [C] –

5 5x

y [D]

3 7

9

x

y


8

2

4

3

3

xy

x y

xy

y

.

209. Evaluate the expression 5 5

5

4 5

6

.

32

210. Without looking, Jin pulls a pencil out of her pencil box and then puts it back. She does this a number of times. There are 5 pencils in her pencil box. The probability of Jin pulling the same

pencil out of her pencil box 3 times in a row is 1

5

3FHGIKJ , or 0.008. Find the probability of Jin

pulling the same pencil out of her pencil box 7 times in a row, and use the power of a quotient property to evaluate. Find the decimal equivalent to the nearest hundred-thousandth. 211. Write 31,600 in scientific notation. 212. Write 0.0000691 in scientific notation. [A] 0.691 10 4 [B] 691 10 7 [C] 691 10 6 [D] 6.91 10 5

213. Rewrite 394 109. in decimal form. 214. Rewrite 315 10 8. in decimal form. 215. Evaluate ( ) ( )7 10 4 103 5 without a calculator. Write the result in decimal form.

216. Last year a large trucking company delivered about 1 million loads of goods at an average value of $25,000 per load. What was the total value of goods delivered? Express your answer in scientific notation. 217. Write an exponential function to model the situation. Tell what each variable represents. A price of $110 increases 9% each month. 218. Writing: Explain the difference between a linear function and an exponential function. Give an example of each function type. 219. Which function increases faster, y x 2 or y = 2x? Use a graph or a table to confirm your

answer. 220. The amount, A, of 85 grams of a certain radioactive material remaining after t years can be found by the equation A t = 85 085( . ) . How much radioactive material is left after 9 years?

Round your answer to two decimal places. 221. The enrollment at Alpha-Beta School District has been declining 3% each year from 1994 to 2000. If the enrollment in 1994 was 2583, find the 2000 enrollment.

33

’95

500

1000

1500

2000

2500

x

y E

nrol

lmen

t

Year

’94 ’96 ’97 ’00 ’99 ’98 ’01

222. Graph the function and label as exponential growth or decay. y x = 3 05 .

223. Graph the function and label as exponential growth or decay. y x = 3 6

224. Choose the equation that represents exponential decay. a. y t ( . )089 b. y t ( . )216

Simplify: 225. 144

226. 81

49

227. Evaluate the expression. Give the exact value, if possible; otherwise, approximate to two decimal places. 39 228. Solve: x2 121

229. Solve the equation 1

3482x .

230. Solve the equation. Round your results to two decimal places. 5 752x Simplify: 231. 27 232. 60 6

34

233. Find the quotient and completely simplify the radical: 120

2

234. An object is dropped from an initial height of s feet. The object’s height at any time t, in seconds, is given by h t s 16 2 . How long does it take for an object dropped from 200 feet to hit the ground? Round your result to two decimal places. 235. Graph: y x x = 3 4 42

[A]

x

y

[B]

x

y

[C]

x

y

[D]

x

y

236. Find the coordinates of the vertex and determine whether the graph opens up or down. y x 2 5

237. Graph the parabola: y x x = 2 2 2

238. Graph the parabola: y x x = 2 4 3

[A]

x

y

[B]

x

y

35

[C]

x

y

[D]

x

y

239. Solve x x2 9 20 by graphing.

x

y

–10 10

–10

10

240. Solve: x x2 4 1 = 0 [A] – 4 + 2 , – 4 – 25 5 [B] 4 + 2 , 4 – 25 5 [C] – 2 + , – 2 – 5 5 [D] 2 + , 2 – 5 5 Use the quadratic formula to solve the equation to the exact value or round to two decimal places. 241. x x2 5 0 242. 2 12x x 243. The height of an object thrown upward with velocity v feet per second is given by h t vt 16 2 , where t is time measured in seconds. If an object is thrown upward with a velocity of 80 ft/sec from ground level, (h = 0), how long will it take to return to ground level? 244. Find the discriminant: 2 5 42x x = 0 245. Decide how many solutions the equation has. x x2 4 4 0 246. Decide how many solutions the equation has. x x2 1 0

36

247. The formula for the path of a projectile is h t vt s 4 9 2. , where h is the height in meters, t is the time in seconds, v is the initial vertical velocity in meters per second, and s is the initial height in meters. A rocket is fired from a height of 0.5 meters at an initial vertical velocity of 45 meters per second. Will the rocket ever reach a height of 200 meters? 248. Graph y x x 2 5 .

[A]

x

y

[B]

x

y

[C]

x

y

[D]

x

y

249. Sketch the graph of the inequality. y x 2 4

250. Decide whether the point is a solution for the inequality. y x x 3 2 30 3 42 , ( , )

251. Name the type of model suggested by the graph.

37

x

y

–10 10

–10

10

252. The table gives the number of inner tubes, I, sold in a bike shop between 1985 and 1990.

Year,

Inner tubes,

t

I

1985 1986 1987 1988 1989 1990

30 42 55 66 82 95

Determine which model best fits the data. [A] exponential [B] absolute value [C] linear [D] quadratic 253. Identify the numerical coefficients: 5 143 6 4r r r 254. Write the polynomial in standard form: x x x3 42 5 5 255. Find the degree of the polynomial: x x x2 3 2 256. Classify 2 3e and state its degree. [A] monomial, 5 [B] binomial, 1 [C] trinomial, 2 [D] binomial, 3 257. Add the polynomials 5 7 22x x and 2 3 4 2 x x . 258. Add: ( ) + ( )7 3 5 7 5 36 6x x x x

259. Simplify: 2 6 3 3 4 44 3 4 3r r r r c h c h c h 260. Subtract: ( 2 9 94 3 2t t t t ) ( 2 4 83 2t t t ) 261. During the years 1992 through 1996, the average number of green grapes, G, sold by a large farmer’s market can be modeled by G = –0.11 t 2 + 1.98t + 44.65. The average number of red grapes, R, sold by the farmer’s market can be modeled by R t t= + 0 005 0 711 75992. . . . Determine the model representing the number of grapes, N, sold from 1992 through 1996.

38

262. Multiply: x x 7 6b gb g 263. Use the FOIL pattern to multiply ( )( ).2 5 3 4x x

264. Multiply ( )( ).7 4 7 4x x

265. Multiply using the vertical format: 6 2 5

7

2y y

y

[A] 6 40 9 353 2y y y [B] 36 12 5 353 2y y y

[C] 6 22y y [D] 6 44 19 353 2y y y

266. Multiply 3 2 5 32 2x x x( ).

267. Multiply: x x x 2 2 42b gc h 268. The sides of a rectangle have length x 1 and width x 3. Which equation below describes the area, A, of the rectangle in terms of x? [A] A x x = 2 2 3 [B] A x x= 2 4 3 [C] A x = 4 4 [D] A x= 2 2 Multiply: 269. ( )( )d d 7 7

270. 2 32 2x c h

[A] 4 94x [B] 4 12 94 2x x + [C] 4 4 92x x + [D] 4 12 94 2x x 271. ( )n 8 2

272. ( )2 3 2x y

273. Solve the equation ( )( ) .x x 4 2 0

39

274. Solve: ( )2 4x ( )2 5x = 0

275. State the x-intercepts of the graph of the equation. Then find the coordinates of the vertex. y x x ( )( )12 5

276. The vertex of a parabola is (2, –5). One x-intercept is –3. What is the other x-intercept? Factor: 277. x x2 13 42 278. x x2 6 8 279. m m2 6 8 280. 3 20 72x x Solve: 281. x x2 2 = 0 282. x x2 20 = 0 Solve: 283. x x2 4 12 0

284. Factor: 6 12x x 285. Solve the equation 4 7 2 02x x . 286. Find the missing term in the perfect square trinomial. ( )x 9 2 x x2 18

[A] 81 [B] 36 [C] 18 [D] 9 287. Solve: 3 54 2432x x = 0 288. Factor: 5 20 2 86 4 3x x x x 289. Factor out the greatest common monomial factor. 24 403 2u u 290. Solve: x x x3 22 8 = 0

291. Solve and then check by substituting the solution into the original proportion: t

3 =

6

54

40

Use your calculator as needed.

292. Solve the proportion 3

4

5

x x .

293. Solve the proportion x x

x

1

3

5.

294. A van travels 125 miles on 5 gallons of gas. How many gallons will it need to travel 625 miles? Give answers to one decimal place where needed. 295. What is 38% of 1250 yards? 296. 90 is 36% of what number? 297. 10 is what percent of 40? 298. A survey was taken to determine the favorite subjects of 6th graders. The results are represented by the graph below. About what percentage of students chose Social Studies as their favorite subject?

Math

Students Per Subject

43

Art 13

P.E.34Social

Studies93

English

61

[A] 49% [B] 38% [C] 62% [D] 93% 299. Michael put $3000 in a savings account. At the end of a year the account had earned $255 in interest. What was the yearly interest rate on the account? [A] 17.5% [B] 9.5% [C] 8.5% [D] 16.5% 300. The weight, W, of a beam varies directly with its length, l. A 10 foot beam weighs 530 pounds. Write an equation relating W to l. 301. R and S vary inversely. If R is 1800 when S is 0.15, find an equation relating R and S. 302. The price per person of renting a bus varies inversely with the number of people renting the bus. It costs $15 per person if 64 people rent the bus. How much will it cost per person if 37

41

people rent the bus?

303. Simplify: 6

2

x

x x

304. Simplify the expression x

x

2

4

2

2

b g.

305. Determine the value or values of the variable where the expression is defined.

x

x x

–1b gb gb g 5 3

306. Write and simplify the rational expression that represents the probability of randomly hitting the unshaded region of the rectangle.

5 2x x 6

x 4 x 6

Multiply:

307. 5

9

2y 36

12

x

y

308. x 2 x

x

6

42

[A] x

x

6

2 [B]

x

x

6

2 [C]

x

x

6

2 [D]

x

x x

6

2 42( )( )

309. Divide: x

x

2

2

x

x

2 4

2

[A] 1

2x [B]

1

2 x [C]

x

x

2

2 [D]

1

x


8

10

4

3

5

4x

x

x

x .

42

311. Divide: x

x

2 25

3

( x 5)

312. A square bird sanctuary has sides that are 10

2s meters long. Find its perimeter and then its

area.

313. Add: x

x x x x( )( ) +

( )( ) 2 2

2

2 2

314. Subtract: d

e

+ 9

d

e

7

315. Add: 6

5

1

5x x

[A] 7 25

7

x

[B]

7

5x [C]

7 25

252

x

x

[D] 7

252x

316. Subtract: x

x

5

5

3

Divide:

317. 2 4 3

2

2x x

x

318. ( x3 8 ) ( x 2 ) 319. Divide x x3 9 by x 2 . 320. Divide 8 3 1 32 3x x x by 3 1x .

[A] x x2 3 2 + 1

3 1x [B] x x2 3 2 +

1

3 1x

[C] x x2 3 3 + 2

3 1x [D] x x2 3 3 +

2

3 1x

Solve:

321. x x

2 53 =

43

322. d

d

d

d

1 91

323. 11

x x2

4

42

–

Solve:

324. x

x x x2 36

6

6

1

6

[A] 7 [B] 6 [C] –7 [D] no solution 325. After taking 4 quizzes, your average is 76 out of 100. What must your average score be on the next five quizzes to increase your average to 81?

326. Graph y = 3

5x.

44

Reference: [13.1.1] [1] 47.6

Reference: [13.1.2] [2] [D]

Reference: [13.1.3] [3] 234

Reference: [13.1.4] [4] [B]

Reference: [13.1.5] [5] [C]

Reference: [13.1.6] [6] 26

Reference: [13.1.7] [7] 44

Reference: [13.1.8] [8] [D]

Reference: [13.1.9]

[9]

Power Base Exponent Standard Form

25 2 5 32

3 3 4 81

5 5 3 125

8

4

3

8 8r r r

Reference: [13.1.10]

[10] 7

5x

45

Reference: [13.1.11] [11] x3

Reference: [13.1.12] [12] 1331 pumpkins

Reference: [13.1.13] [13] Yes

Reference: [13.1.14] [14] [D]

Reference: [13.1.15] [15] [B]

Reference: [13.1.16] [16] No

Reference: [13.1.17] [17] no

Reference: [13.1.18] [18] [B]

Reference: [13.1.19] [19] 10 plus the quotient of a number x and 4. (There are other correct phrases.)

Reference: [13.1.20] [20] d x 4

Reference: [13.1.21] [21] 7 = 4B

46

Reference: [13.1.22] [22] 7 < 4B

Reference: [13.1.23] [23] [D]

Reference: [13.1.24] [24] 559 calories

Reference: [13.1.25] [25] 4 A.M.

Reference: [13.1.26] [26] Yes, the table does represent a function. The collection of the input values is the domain: 2, 3, 4, and 5; and the collection of output values is the range: 13, 15, 17, and 19.


[27] Input

Output

1 2 3 4 5

11 16 21 26 31

Reference: [13.1.28] [28] C = 15n + 150


[29]

–10 –5 0 5 10

–3, –1, 1, 4


[30] –10, 5

4, 0,

2

3, 1,

3

2

47

Reference: [13.2.31] [31] –15

Reference: [13.2.32] [32] [C]

Reference: [13.2.33] [33] 13.61

Reference: [13.2.34] [34] 0

Reference: [13.2.35] [35] 7

Reference: [13.2.36] [36] [B]

Reference: [13.2.37] [37] –7

Reference: [13.2.38] [38] [A]

Reference: [13.2.39] [39] 10

Reference: [13.2.40] [40] 11


48

[41]

L

NMMM

O

QPPP

2 3

1 9

9 2


[42] 7 10

12 4

LNM

OQP

Reference: [13.2.43] [43] [C]

Reference: [13.2.44] [44] 32

Reference: [13.2.45] [45] [A]

Reference: [13.2.46] [46] [A]

Reference: [13.2.47] [47] [B]


[48] 40

3

Reference: [13.2.49] [49] 450 km

Reference: [13.2.50] [50] [B]

Reference: [13.2.51] [51] 60x – 40 2x

49

Reference: [13.2.52] [52] –x

Reference: [13.2.53] [53] [B]

Reference: [13.2.54] [54] [D]

Reference: [13.2.55] [55] – 4

Reference: [13.2.56] [56] 100r

Reference: [13.2.57] [57] 8 3d

Reference: [13.2.58] [58] –4

Reference: [13.2.59] [59] 7 + 3x

Reference: [13.2.60] [60] $13,282.9


[61] 10

17

50

Reference: [13.2.62] [62] [C]

Reference: [13.2.63] [63] [A]

Reference: [13.2.64] [64] 1 to 3

Reference: [13.3.65] [65] 15

Reference: [13.3.66] [66] 63°

Reference: [13.3.67] [67] 5

Reference: [13.3.68] [68] 245

Reference: [13.3.69] [69] [D]

Reference: [13.3.70] [70] n = –4

Reference: [13.3.71] [71] –5


[72] 26

3

51

Reference: [13.3.73] [73] 37.0 C

Reference: [13.3.74] [74] 3

Reference: [13.3.75] [75] –2

Reference: [13.3.76] [76] –0.71

Reference: [13.3.77] [77] [D]

Reference: [13.3.78] [78] 1.43 years

Reference: [13.3.79] [79] original temperature: – 25 x 14 –11

Reference: [13.3.80] [80] [C]

Reference: [13.3.81] [81] 439.2 miles

Reference: [13.3.82] [82] 5.9 m

Reference: [13.3.83] [83] 34

52

Reference: [13.3.84] [84] 9 pictures can fit

1 4 16

1 4 16

1 4 16

1 4 16

1 4 16

1 4 16

1 4 16

1 4 16

1

121

2

1 2

1


[85]

10

50

Seconds

Distance

30 meters

Reference: [13.3.86] [86] $61.95


[87] yx

= 3 6

2

53

Reference: [13.4.88] [88] A(–8, 5), B(1, 5), C(4, –5), D(–2, –7)


[89] (3, 1)

1

1 2 3

–2

–3

–4

–1–2

(–2, 2)

(2, –3)

x

y

2

(4, 0)

4


[90]

400

800

8 10642

1200

x

y

Wei

ght (

in p

ound

s)

Age (in months)12

Weight tends to increase with age and the pattern of the points is approximately linear.


[91] 5

23, FHGIKJ


[92] x

y x

3 1 0 2 41

24

11

2

9

24 3 2

54

x

y

–10 10

–10

10

Reference: [13.4.93] [93] (–3, 4)

5

–5 –4 –2 1 –1

1

2

3

x

y

(–3, 4)

Reference: [13.4.94] [94] [D]

Reference: [13.4.95] [95] [B]


[96]

2 4 6 8 10

100

300

400

500

t

y

55


[97] Slope: 5

8

(–4, 2)

–4 –2 2 4

–4

–2

2

4

x

y

(4, –3)

Reference: [13.4.98] [98] 0

Reference: [13.4.99] [99] 975 feet per minute

Reference: [13.4.100] [100] x ky ; 99

Reference: [13.4.101] [101] The data show direct variation; 1.25; g d = 125.


[102] V

T 0.11

Reference: [13.4.103] [103] m y = , = 2 12

Reference: [13.4.104] [104] y x 3 2

56

–3 –2 1 2 3

–2

–1

1

2

x

y

Reference: [13.4.105] [105] m y –8 –9, - int. , not parallel


[106]

Totalcost

Number ofCDs bought

10

1020304050607080

x

y

0

Reference: [13.4.107] [107] [A]


[108] 7

4

Reference: [13.4.109] [109] It does. Domain: {0, 1, 2, 3, 4}

Reference: [13.4.110] [110] V(x) = 392 – 6x; $284

57


[111]

input ( ) output (0.1 + 250)

$3,700 $620.00

$2,460 $496.00

$5,670 $817.00

s s


[112] y x 3

25


[113] y = 4

52x

Reference: [13.5.114] [114] [A]

Reference: [13.5.115] [115] x = – 9

Reference: [13.5.116] [116] 11

Reference: [13.5.117] [117] y x 2 2

(–2, –2) –4 –3 1 2 3 4

–4 –3 –2

2 3 4

x

y

58

Reference: [13.5.118] [118] y = –3

Reference: [13.5.119] [119] [C]


[120] y x 4

34

Reference: [13.5.121] [121] y x 2 13

Reference: [13.5.122] [122] P t = + 100,0003000

Reference: [13.5.123] [123] [D]

Reference: [13.5.124] [124] y x 5 10

1 2 3 4 5 6 7 8

10 20

30

40

50

60 70

80

y

Reference: [13.5.125] [125] [B]


59

[126] y x 23

74 = ( )


[127] y x y x 41

23

1

2

11

2 = ( ); = +

Reference: [13.5.128] [128] y 2793 = 170 7( ) x

Reference: [13.5.129] [129] [B]

Reference: [13.5.130] [130] 4x y = 2

Reference: [13.5.131] [131] 2 6 3 2 6 3x y x y ,

Reference: [13.5.132] [132] 4 25 2 50 19. . x y +


[133]

5

5

10

time

requests

The data can’t be represented by a linear model.

60

Reference: [13.5.134] [134] [D]

Reference: [13.5.135] [135] y x 250 0 02.


[136] 543 x 0 1 2 6

Reference: [13.6.137] [137] x 2

Reference: [13.6.138] [138] x < – 3

Reference: [13.6.139] [139] {..., 3, 4, 5}

Reference: [13.6.140] [140] [B]


[141] x 1

4

Reference: [13.6.142] [142] x < –6

Reference: [13.6.143] [143] x + 217 + 18 240 x 5 hits


61

[144] 3 1x


[145] 1

2

3

2x


[146]

–10 –5 0 5 10


[147] –1 0 1 2 3 4 5 x

Reference: [13.6.148] [148] 13 18 A

Reference: [13.6.149] [149] {–6, –2}


[150] 11

2,

1

2

Reference: [13.6.151] [151] 8, –8

Reference: [13.6.152] [152] 0 4 x

62


[153] –3 –2 –1 0 1 2 3 x


[154] –6 –4 –2 0 2 4 6 x

Reference: [13.6.155] [155] [D]


[156]

–1 1 2 3

–3

–2

–1

1

x

y

Reference: [13.6.157] [157] [A]

Reference: [13.6.158] [158] 27 50 4525 4500. .x y


[159]

2 3

3 0 4 5 6 7

4 1 4 6 9

5 1 2 7 8 9

63

Reference: [13.6.160] [160] [A]

Reference: [13.6.161] [161] 37.5

Reference: [13.6.162] [162] Plan A: 6.6 Plan B: 9.6 Plan B has the greater average weight loss


[163]

22 24 26 28 30 32 34 36

first quartile: 25, second quartile: 29, third quartile: 32

Reference: [13.6.164] [164] [D]

Reference: [13.7.165] [165] [B]

Reference: [13.7.166] [166] [C]

Reference: [13.7.167] [167] (–1, 2)

64

–3 –1 1 –1

1

2

x

y

(–1, 2)

Reference: [13.7.168] [168] (–3, 0)

–5

–3

–1

1

x

y

(–3, 0)

Reference: [13.7.169] [169] [D]

Reference: [13.7.170] [170] (2, 8)

Reference: [13.7.171] [171] (3, 3)

Reference: [13.7.172] [172] (4, –3)


[173] FHGIKJ

10

9

16

9,

65

Reference: [13.7.174] [174] width 4 cm, length 14 cm

Reference: [13.7.175] [175] (–4, –2)

Reference: [13.7.176] [176] (3, –3)

Reference: [13.7.177] [177] (–5, 6)

Reference: [13.7.178] [178] No solution

Reference: [13.7.179] [179] [B]


[180] 2

3

1

2, FHGIKJ


[181] 1

2

1

4, FHGIKJ


[182] FHGIKJ

1

38

4

19,

Reference: [13.7.183] [183] Sample Acceptable Response: a c = 52

66

c a = 3 by substitution: a a 3 52 = 4

4

52

4

a =

a = 13 c = 3(13) = 39 children

Reference: [13.7.184] [184] $2800 at 5%; $7200 at 7%

Reference: [13.7.185] [185] [A]

Reference: [13.7.186] [186] many solutions

Reference: [13.7.187] [187] y x = + 2 6

y x = 223

3

no solution

Reference: [13.7.188] [188] No solution


[189] x y

x y

. .

40

375 2 75 120 +

x = 10 pounds of cashews y = 30 pounds of peanuts


67

[190]

x

y

–10 10

–10

10

Reference: [13.7.191] [191] y x 7 y x 7

Reference: [13.7.192] [192] h s 40 7 11 344h s


[193] 2 3 18

0 0

x y

x y

,

(9, 0) (0, 0)

(0, 6)

2 4 6 8

2

4

6

8

x

y

Reference: [13.7.194] [194] x 0 y 0 4 7 65x y + x y + 14

68

x

y

04 8 12 16 20 24 28

4

8

12

16

20

24

28

Reference: [13.8.195] [195] [C]

Reference: [13.8.196] [196] [B]

Reference: [13.8.197] [197] 512 12x

Reference: [13.8.198] [198] x9

Reference: [13.8.199] [199] –64

Reference: [13.8.200] [200] 32

Reference: [13.8.201] [201] [C]

Reference: [13.8.202] [202] [B]

69


[203] 42 2x y


[204] –x3

4


[205] 1

12


[206]

–10 10

–10

10

x

y

Reference: [13.8.207] [207] [A]


[208] 2 2y

x


[209] 1

125

70


[210] 1

5

7FHGIKJ or 0.00001

Reference: [13.8.211] [211] 316 104.

Reference: [13.8.212] [212] [D]

Reference: [13.8.213] [213] 3,940,000,000

Reference: [13.8.214] [214] 0.0000000315

Reference: [13.8.215] [215] 2800

Reference: [13.8.216] [216] $ 2 5 1010.

Reference: [13.8.217] [217] p x 110 109( . ) ; p is the total price, and x is the number of months

Reference: [13.8.218] [218] Sample answer: A linear function in one in which the growth is constant. Its graph is a straight line; example: y = 2x + 3. An exponential function in one in which the rate of growth is not constant. Its graph is a curve; example: y x ( . )15 .

Reference: [13.8.219] [219] When 1 < x < 2, y = 2x is greater. When x > 2, [] is greater. When x = 1 and x = 2, the

71

functions are equal.

y

x O

2

2

y = 2x

y = 2 x

Reference: [13.8.220] [220] 19.69 yr

Reference: [13.8.221] [221] 2152


[222]

x

y

–5 5

–5

5

exponential decay


72

[223]

x

y

–5 5

–5

5

exponential growth

Reference: [13.8.224] [224] a. y t ( . )089

Reference: [13.9.225] [225] 12


[226] 9

7

Reference: [13.9.227] [227] 6.24

Reference: [13.9.228] [228] 11, –11

Reference: [13.9.229] [229] 12, –12

Reference: [13.9.230] [230] 3.87, –3.87

73

Reference: [13.9.231] [231] 3 3

Reference: [13.9.232] [232] 6 10

Reference: [13.9.233] [233] 2 15

Reference: [13.9.234] [234] 3.54 seconds

Reference: [13.9.235] [235] [A]

Reference: [13.9.236] [236] (0, –5), opens up


[237]

x

y

–10 10

–10

10

Reference: [13.9.238] [238] [D]

74


[239]

x

y

–10 10

–10

10 x –5 and x –4

Reference: [13.9.240] [240] [D]

Reference: [13.9.241] [241] 2.79, –1.79


[242] 1, 1

2

Reference: [13.9.243] [243] 5 seconds

Reference: [13.9.244] [244] –7

Reference: [13.9.245] [245] 1

Reference: [13.9.246] [246] None

75

Reference: [13.9.247] [247] No

Reference: [13.9.248] [248] [D]


[249]

–3 1 3 –1

1

2

3

5

x

y

Reference: [13.9.250] [250] Yes

Reference: [13.9.251] [251] absolute value

Reference: [13.9.252] [252] [C]

Reference: [13.10.253] [253] 5, 1, –1, –14

Reference: [13.10.254] [254] 5 2 54 3x x x

Reference: [13.10.255] [255] 3


76

[256] [B]

Reference: [13.10.257] [257] x x2 4

Reference: [13.10.258] [258] 4 10 106x x

Reference: [13.10.259] [259] 6 7 34 3r r

Reference: [13.10.260] [260] 2 11 5 74 3 2t t t t

Reference: [13.10.261] [261] N = – . . .0105 1269 120 642t t + +

Reference: [13.10.262] [262] x x2 42

Reference: [13.10.263] [263] 6 7 202x x

Reference: [13.10.264] [264] 49 162x

Reference: [13.10.265] [265] [D]

Reference: [13.10.266] [266] 6 15 94 3 2x x x

77

Reference: [13.10.267] [267] x x3 8 8

Reference: [13.10.268] [268] [A]

Reference: [13.10.269] [269] d 2 49

Reference: [13.10.270] [270] [B]

Reference: [13.10.271] [271] n n2 16 64

Reference: [13.10.272] [272] 4 12 92 2x xy y

Reference: [13.10.273] [273] –4, –2


[274] x x = , = 2 21

2

Reference: [13.10.275] [275] x-intercepts: 12, –5

coordinates of vertex: 7

2

289

4, FHG

IKJ

Reference: [13.10.276] [276] 7

78

Reference: [13.10.277] [277] ( )( )x x 7 6

Reference: [13.10.278] [278] ( )( )x x 4 2

Reference: [13.10.279] [279] ( )( )m m 4 2

Reference: [13.10.280] [280] ( 3 1x )( x 7 )

Reference: [13.10.281] [281] 0, –2

Reference: [13.10.282] [282] x x = or = 4 5–

Reference: [13.10.283] [283] –2, 6

Reference: [13.10.284] [284] 3 1 2 1x x b gb g


[285] –2, 1

4

Reference: [13.10.286] [286] [A]


79

[287] x 9

Reference: [13.10.288] [288] x (5 23x )( x 2 ) ( )x 2

Reference: [13.10.289] [289] 8 3 52u u( )

Reference: [13.10.290] [290] 2 , 0, 4


[291] 1

3

Reference: [13.11.292] [292] 10

Reference: [13.11.293] [293] 5, –3

Reference: [13.11.294] [294] 25 gallons

Reference: [13.11.295] [295] 475 yards

Reference: [13.11.296] [296] 250


80

[297] 25%

Reference: [13.11.298] [298] [B]

Reference: [13.11.299] [299] [C]

Reference: [13.11.300] [300] W = 53l

Reference: [13.11.301] [301] RS = 270

Reference: [13.11.302] [302] $25.95


[303] 6

1x


[304] x

x

2

2

Reference: [13.11.305] [305] x x – ,3 5


[306] 4 2

5 2

x

x


81

[307] 5

3

xy

Reference: [13.11.308] [308] [A]

Reference: [13.11.309] [309] [B]


[310] 3

4 5x


[311] x

x

5

3


[312] Perimeter: 40

2( )s meters

Area: 100

22

s b g


[313] 1

2x


[314] 16

e

Reference: [13.11.315] [315] [C]

82


[316]

2 25

3 15

x

x


[317] xx

+ 23

2

Reference: [13.11.318] [318] x x2 2 4


[319]

x xx

2 2 51

2

Reference: [13.11.320] [320] [B]

Reference: [13.11.321] [321] 10

Reference: [13.11.322] [322] 3 3,

Reference: [13.11.323] [323] 1

Reference: [13.11.324] [324] [C]

Reference: [13.11.325] [325] 85

83


[326]

x

y

–10 10

–10

10

Documents

McDougal Littell · 2012-05-30 · 36. A hot air balloon rises 486 feet. It then descends 133 feet. Find the elevation of the hot air balloon, assuming its journey started at sea