Lesson 2.1 Skills Practice Name_________________________________________________________ Date__________________________
Patterns, Patterns, Patterns . . . Developing Sequences of Numbers from Diagrams and Contexts
Vocabulary Define each term in your own words. 1. sequence A sequence is a pattern involving an ordered arrangement of numbers, geometric figures, letters, or other objects.
2. term A term is an individual number, figure, or letter in a sequence. 3. ellipsis An ellipsis is three periods which mean “and so on.”
Problem Set Write or draw the term requested for each given sequence. 1. 3, 6, 9, 12, 15, …
2. Z, Y, X, W, V, U, …
What is the next term?
What is the tenth term? Q
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18 3. i, ii, iii, iiii, iiiii, …
4. What is the eighth term?
What is the twentieth term? iiiiiiiiiiiiiiiiiiii
,
,
,
,
,...
Chapter 2 Skills Practice • 355
Lesson 2.1 Skills Practice
5. I, II, III, IV, V, VI, …
page 2
6.
What is the eleventh term? XI
What is the sixth term?
Draw a picture and use a sequence to solve each problem. 7. Marta is decorating the rectangular top of a jewelry box with antique buttons that are all the same size. She has started by gluing 8 buttons across and 5 buttons down for a total of 13 buttons. Write a sequence of numbers to represent the number of buttons used for each group of buttons across and down that she uses to cover the box. How many total buttons will she need?
8. The cheerleaders wanted to create a pyramid for the halftime show. There are 6 members of the team who are strong enough to be at the bottom of the pyramid. Use a sequence to determine how many cheerleaders can participate in the pyramid.
6, 5, 4, 3, 2, 1. Twenty-one cheerleaders can participate in the pyramid.
356 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
13, 11, 9, 7, 5, 3. Marta will need 48 buttons.
Lesson 2.1 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 9. A banquet hall has hexagonal tables. One person can be seated at each side. The diagram shows how the tables are placed together for large parties. Write a sequence to determine the number of people that can be seated around one, two, three, four, five, six, seven, and eight tables. O
O
O
O O
O
6, 10, 14, 18, 22, 26, 30, 34
10. Kim has small wooden cube-shaped blocks. To make the next size cube using the blocks, she needs 8 blocks. Write a sequence to show the number of blocks needed for each increasingly larger cube that can be made. Include at least 6 terms in the sequence.
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1, 8, 27, 64, 125, 216 . . . 11. Clayton is making a trestle bridge for his miniature train display. The rods he is using are shaped to create a triangle when fitted together. He starts with 3 rods, making 1 triangle. To finish 1 side of the trestle, he needs 11 triangles. Write a sequence to determine the number of rods Clayton needs to make both sides of the trestle bridge.
3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 Clayton needs 46 rods to make both sides of the trestle bridge.
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Lesson 2.1 Skills Practice
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12. Keisha is slicing a large pizza into 32 equal slices. The pizza is already cut in half. She starts with 1 cut making 4 slices. She doubles the number of cuts she makes each time after that. Write a sequence showing the number of cuts she makes and another sequence showing the number of slices she creates. How many cuts should Keisha make to get 32 slices?
Cuts: 1, 2, 4, 8 Slices: 4, 8, 16, 32 Keisha should make a total of 15 cuts to get 32 slices.
Write a sequence to solve each problem. 13. Peter’s aquarium is too heavy to lift when it is filled with water. He needs to bail out at least half of the water and replace it with fresh water. The aquarium holds 10 gallons and the container he uses to bail water holds 3 pints. Write a sequence to show how the water decreases with each bailing and determine how many times he must bail with the pint container to remove at least half of the water in the aquarium. (Hint: There are 8 pints in 1 gallon.)
80, 77, 74, 71, 68, 65, 62, 59, 56, 53, 50, 47, 44, 41, 38 Peter must bail 14 times to remove at least half of the water.
358 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
10 gal 3 8 pt/gal 5 80 pt
Lesson 2.1 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ 14. A runner starts running a race as fast as he can, but he gradually runs out of energy and slows down along the way. He starts running at a pace of 6 minutes per mile. After every 2 miles, he slows down by 1 minute per mile. Write a sequence to show how many minutes it will take him to run 12 miles. 6, 12, 19, 26, 34, 42, 51, 60, 70, 80, 91, 102 It will take the runner 102 minutes (or 1 hour and 42 minutes) to run 12 miles.
15. Tanya dropped her lucky penny from a hot air balloon at about 700 feet. The penny fell 32 feet per second until it hit the ground. Write a sequence to show the height of the penny each second as it fell and determine about how many seconds it took for the penny to hit the ground. 700, 668, 636, 604, 572, 540, 508, 476, 444, 412, 380, 348, 316, 284, 252, 220, 188, 156, 124, 92, 60, 28, 24 It took the penny about 22 seconds to hit the ground.
16. Samuel earns $30 per week for mowing grass on Mondays. He also spends $8 per week on comic
© 2011 Carnegie Learning
books each Saturday. Samuel checks his account balance each Sunday and Wednesday. Starting at $0 on the first Sunday, write a sequence showing the amount of money Samuel has each time he checks his account balance. Assuming he does not spend his money on anything other than comic books, how long will it take Samuel to save enough money to buy a $200 bike? 0, 30, 22, 52, 44, 74, 66, 96, 88, 118, 110, 140, 132, 162, 154, 184, 176, 206 It will take Samuel just over 8 weeks to save $200.
Chapter 2 Skills Practice • 359
Lesson 2.1 Skills Practice
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17. The eighth grade is collecting books for a used-book sale. On the first day of collections, they received 20 books. Each day after that they received the amount they received the previous day plus 5 books. Write a sequence to show the number of books collected each day and the total number of books collected after 2 weeks (school days only). Collections each day: 20, 25, 30, 35, 40, 45, 50, 55, 60, 65 Total collections: 20, 45, 75, 110, 150, 195, 245, 300, 360, 425 They collected 425 books.
18. Scientists determined that the population of an endangered species was decreasing by one half each year. At the start of a 7-year study, the species had a population of 8000. Write a sequence that shows the population at the start of each year during the study.
© 2011 Carnegie Learning
8000, 4000, 2000, 1000, 500, 250, 125
360 • Chapter 2 Skills Practice
Lesson 2.2 Skills Practice Name_________________________________________________________ Date__________________________
Every Graph Tells a Story Describing Characteristics of Graphs
Vocabulary Explain the difference between the set of terms. 1. Explain the difference between a graph that is discrete and a graph that is continuous. A discrete graph is a graph that consists of isolated points. A continuous graph is a graph with no breaks in it.
2. Explain the difference between a graph that is linear and a graph that is nonlinear. A linear graph is a graph that is a line or a series of collinear points. A nonlinear graph is a graph that is not a line and not a series of collinear points.
Problem Set Tell whether each graph is discrete or continuous. Also, tell whether each graph is increasing, decreasing, both, or neither.
© 2011 Carnegie Learning
1.
2.
y
y
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 1
2
3
4
5
6
7
8
9
10
The graph is discrete and decreasing.
x
1
2
3
4
5
6
7
8
9
10
x
The graph is continuous and both increasing and decreasing.
Chapter 2 Skills Practice • 361
Lesson 2.2 Skills Practice
3.
page 2
4.
y
y
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 1
2
3
4
5
6
7
8
9
10
x
1
2
3
4
5
6
7
8
9
10
x
The graph is discrete and neither
The graph is continuous and decreasing.
increasing nor decreasing.
6.
y
y
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 1
2
3
4
5
6
7
8
9
The graph is continuous and both decreasing and increasing.
362 • Chapter 2 Skills Practice
10
x
1
2
3
4
5
6
7
8
9
10
x
The graph is continuous and increasing.
© 2011 Carnegie Learning
5.
Lesson 2.2 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ Tell whether each graph is linear or nonlinear. Also, tell whether each graph is increasing, decreasing, both, or neither. 7.
8.
y
y
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 1
2
3
4
5
6
7
8
9
10
x
1
2
3
4
5
6
7
8
9
10
x
The graph is linear and increasing.
The graph is linear and neither increasing nor decreasing.
© 2011 Carnegie Learning
9.
10.
y
y
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 1
2
3
4
5
6
7
8
9
10
x
1
2
3
4
5
6
7
8
9
The graph is nonlinear and both
The graph is nonlinear and neither
increasing and decreasing.
increasing nor decreasing.
10
x
Chapter 2 Skills Practice • 363
Lesson 2.2 Skills Practice
11.
page 4
y 10 9 8 7 6 5 4 3 2 1 1
2
3
4
5
6
7
8
9
10
x
The graph is linear and increasing. 12.
y 10 9 8 7 6 5 4 3 2 1 2
3
4
5
6
7
8
9
10
The graph is nonlinear and increasing.
364 • Chapter 2 Skills Practice
x
© 2011 Carnegie Learning
1
Lesson 2.2 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ Tell a story to describe each graph. 13.
The plant starts with many leaves and
y
loses a few and then loses a lot in a short amount of time. Then, the plant starts Number of leaves on plant
slowly gaining leaves. Perhaps the plant was not watered during the time when a large number of leaves were dropping off. Finally, the plant was watered and started to grow again.
x
© 2011 Carnegie Learning
Day
Chapter 2 Skills Practice • 365
Lesson 2.2 Skills Practice
14.
page 6
The rocket rose quickly to a peak height
y
and then slowly dropped back down to
Height of rocket
the ground.
x Second
15.
The amount of heating oil used increased
y
over a short time, slowly decreased, and then increased quickly again. Perhaps the weather turned cold quickly, slowly
x Day
366 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
Heating oil used
warmed, and then got cold again.
Lesson 2.2 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ 16.
Jason’s savings increased at a steady
y
rate, fell off quickly, and then increased steadily again. Perhaps Jason withdrew Jason’s savings account balance
a large amount of money from savings to make a purchase and then started building his savings again.
x Month
17.
Dan steadily increased the distance he
y
ran and then ran the same distance for a few days. He suddenly stopped running completely and then increased his
© 2011 Carnegie Learning
Distance Dan ran
distance slowly. Perhaps he was sick or had an injury that caused him to stop running and had to start back slowly.
x Day
Chapter 2 Skills Practice • 367
Lesson 2.2 Skills Practice
18.
page 8
The puppy grew steadily for months
y
until he reached his full-grown weight, which he maintained, though it
Weight of a puppy
fluctuated slightly.
x
© 2011 Carnegie Learning
Month
368 • Chapter 2 Skills Practice
Lesson 2.3 Skills Practice Name_________________________________________________________ Date__________________________
To Be or Not To Be a Function? Defining and Recognizing Functions
Vocabulary Write the term from the box that best completes each sentence. scatter plot output relation input vertical line test mapping set domain range function
1. A(n)
relation
is any set of ordered pairs or the mapping between a set of inputs and a
set of outputs. 2. The first coordinate of an ordered pair in a relation is the 3. The second coordinate of an ordered pair is the 4. A(n)
function
5. A(n)
scatter plot
6. The
vertical line test
input
output
.
.
maps each input to one and only one output. is a graph of a collection of ordered pairs. is a visual method of determining whether a relation represented as a
graph is a function by visualizing whether any vertical lines would intersect the graph of the relation at more than one point or not. 7. A(n)
mapping
shows objects in two sets connected together to represent a relationship
between the two sets.
© 2011 Carnegie Learning
8. A(n)
set
is a collection of numbers, geometric figures, letters, or other objects that
have some characteristic in common. 9. The
domain
10. The
range
of a function is the set of all inputs of the function. of a function is the set of all outputs of the function.
Chapter 2 Skills Practice • 369
Lesson 2.3 Skills Practice
page 2
Problem Set Write the corresponding ordered pairs and tell whether each relation is a function. 1.
1 2 3 4
4 6 8 10
(1, 4), (2, 6), (3, 3), (3, 5), (4, 4), (4, 6)
The relation is a function.
The relation is not a function.
4. 5
3 4 5 6
(1, 4), (2, 6), (3, 8), (4, 10)
3.
1 2 3 4
6
10
7
20
8
30
10
(5, 20), (6, 10), (7, 10), (8, 30), (10, 30) The relation is a function.
Input
Output
4
8
8
12
12
16
16
20
20
24
(4, 8), (8, 12), (12, 16), (16, 20), (20, 24) . The relation is a function
370 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
2.
Lesson 2.3 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 5.
6.
Input
Output
x
y
15
0
0
15
10
5
5
10
5
10
10
5
10
15
15
10
15
20
20
15
(15, 0), (10, 5), (5, 10), (10, 15), (15, 20)
(0, 15), (5, 10), (10, 5), (15, 10), (20, 15)
The relation is not a function.
The relation is a function.
Determine whether each graph represents a function. Use the vertical line test, if necessary.
© 2011 Carnegie Learning
7.
8.
y
y
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 1
2
3
4
5
6
7
8
9
10
x
1
2
3
4
5
6
7
8
9
10
x
The scatter plot is not a function.
The scatter plot is a function. No vertical
A vertical line can be drawn through
lines cross more than one point.
(4, 1) and (4, 5).
Chapter 2 Skills Practice • 371
Lesson 2.3 Skills Practice
9.
page 4
10.
y
y
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 1
2
3
4
5
6
7
8
9
10
x
1
2
3
4
5
6
7
8
9
10
x
The scatter plot is not a function.
The graph is not a function. A vertical line
A vertical line can be drawn through
will cross two y-values for most x-values.
(3, 2) and (3, 6).
12.
y
y
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1 1
2
3
4
5
6
7
8
9
10
x
1
2
3
4
5
6
7
8
9
10
x
The graph is a function. No vertical line
The graph is not a function. A vertical line
will cross two y-values for any x-value.
will cross two y-values for most x-values.
372 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
11.
Lesson 2.3 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ Determine whether each equation is a function. If it is not a function, explain why not. 13. y 5 3x 1 1
14. y 5 x2 The equation is a function.
The equation is a function.
______
16. y 5 √ x 1 5
15. y2 5 x The equation is not a function. For example, 3 5 9 and (23) 5 9. Each x-value except 0
The equation is not a function. For example, ______ ______ and 23 5 √ 4 1 5 . Each x-value 3 5 √4 1 5
can be mapped to two y-values.
except 25 can be mapped to two y-values.
2
2
17. y 5 2|x|
__
18. √y 5 x 2 8 The equation is a function.
The equation is a function.
1 x 19. y 5 __ 2
20. | y| 5 6 1 4x
The equation is a function.
The equation is not a function. For example, |10 | 5 6 1 4(1) and |210 | 5 6 1 4(1). Each x-value greater than 21.5 can be
© 2011 Carnegie Learning
mapped to two y-values. Determine whether each given situation represents a function. Explain your answer. 21. Input: Lila mails 6 different valentines to her friends.
Output: Each of Lila’s 6 friends receives a valentine from her. Yes. Each friend receives just 1 valentine from Lila.
Chapter 2 Skills Practice • 373
Lesson 2.3 Skills Practice
page 6
22. Input: There is 1 copy of a popular book in the library.
Output: The book has been checked out by 45 different people. No. One book is mapped to 45 people.
23. Input: The principal of a school sends the same memo to all of the teachers.
Output: There are 28 teachers in the school. No. One memo is mapped to 28 teachers.
24. Input: There are 13 cats for adoption at the animal shelter.
Output: Each cat is adopted by a different family. Yes. Each family adopts just 1 cat.
25. Input: There are 3 showings of a play.
Output: Over 200 people attend each showing. No. Each showing is mapped to over 200 people.
26. Input: Garrett bakes 2 dozen cookies for the bake sale.
Output: Twenty-four people buy a cookie.
27. Input: The new issue of Sports Today is published.
Output: Issues are sent to millions of readers. No. The new issue is mailed to millions of readers.
28. Input: Yi Ling has French on Mondays, Wednesdays, and Fridays, and German on Tuesdays and Thursdays.
Output: Yi Ling’s language classes per day. Yes. Each school day Yi Ling has only 1 language class.
374 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
Yes. Each cookie is bought by just 1 person.
Lesson 2.4 Skills Practice Name_________________________________________________________ Date__________________________
Scaling a Cliff Linear Functions
Vocabulary Define the term in your own words. 1. linear function A function whose graph is a straight line is a linear function.
Problem Set Identify the dependent quantity and the independent quantity in each problem situation. 1. Terrence is purchasing canned vegetables at his local grocery store to donate to the local food pantry. Each can costs $0.39. The total amount of money spent on the canned vegetables is the dependent quantity. The number of cans he purchases is the independent quantity.
2. Rosita’s pet rabbits eat 12 ounces of rabbit food every day. The number of ounces of rabbit food eaten is the dependent quantity. The number of days is
© 2011 Carnegie Learning
the independent quantity.
3. The amount of electricity used by a light changes as the knob on the dimmer switch is turned. The amount of electricity used by the light is the dependent quantity. The position of the dimmer switch is the independent quantity.
Chapter 2 Skills Practice • 375
Lesson 2.4 Skills Practice
page 2
4. Stephanie is selling Girl Scout cookies to raise money for her local troop. For each box of cookies she sells, the troop receives $2.00. The total amount of money she raises for the troop is the dependent quantity. The number of boxes she sells is the independent quantity.
5. The height reached by a water-propelled rocket is directly related to the amount of water pressure within the rocket. The height reached by the rocket is the dependent quantity. The amount of water pressure in the rocket is the independent quantity.
6. As an engineer opens the release gate on a dam’s spillway, the amount of water released from the lake increases. The amount of water released from the lake is the dependent quantity. The amount the release
© 2011 Carnegie Learning
gate is opened is the independent quantity.
376 • Chapter 2 Skills Practice
Lesson 2.4 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ Complete the table and create a graph for each given problem situation. In the “Expression” row of the table, write a variable to represent the independent quantity in the first column and write an expression to represent the dependent quantity in terms of the independent quantity in the second column. 7. The Rivue Restaurant on the 25th floor of the Galt House in Louisville, Kentucky rotates 2.5 times every hour. Independent Quantity
Dependent Quantity
Quantity Name
Time
Number of Rotations
Unit of Measure
Hours
Rotations
1
2.5
2
5
4
10
6
15
10
25
t
2.5t
Expression 30
24 21 Number of Rotations
© 2011 Carnegie Learning
27
18 15 12 9 6 3 0 0
1
2
3
4
5
6
7
8
9
10
Time (hours)
Chapter 2 Skills Practice • 377
Lesson 2.4 Skills Practice
page 4
8. Horace begins measuring the diameter of a pumpkin in his pumpkin patch when it has a diameter of 6 inches. After he measures the pumpkin, its diameter begins to increase at a rate of 2 inches per week.
Independent Quantity
Dependent Quantity
Quantity Name
Time
Diameter
Unit of Measure
Weeks
Inches
0
6
1
8
3
12
5
16
10
26
t
2t 1 6
Expression
30 27
21 18 © 2011 Carnegie Learning
Pumpkin Diameter (inches)
24
15 12 9 6 3 0 0
1
2
3
4
5
6
Time (weeks)
378 • Chapter 2 Skills Practice
7
8
9
10
Lesson 2.4 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ 9. Gretchen is filling a water trough for her cows. The water trough has 10 centimeters of water in it when she begins filling it and the water level increases by 5 centimeters every minute. Independent Quantity
Dependent Quantity
Quantity Name
Time
Water Level
Unit of Measure
Minutes
Centimeters
1
15
4
30
8
50
12
70
15
85
t
5t 1 10
Expression
100 90
Water Level (centimeters)
© 2011 Carnegie Learning
80 70 60 50 40 30 20 10 0 0
2
4
6
8
10
12
14
16
18
20
Time (minutes)
Chapter 2 Skills Practice • 379
Lesson 2.4 Skills Practice
page 6
10. Carl initially had $200 in his savings account. Each week he withdraws $15. Independent Quantity
Dependent Quantity
Quantity Name
Time
Account Balance
Unit of Measure
Weeks
Dollars
1
185
3
155
5
125
8
80
10
50
w
200 2 15w
Expression
200 180
140 120 100 80 60 40 20 0 0
2
4
6
8
10
12
Time (weeks)
380 • Chapter 2 Skills Practice
14
16
18
20
© 2011 Carnegie Learning
Account Balance (dollars)
160
Lesson 2.4 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ 11. A washing machine rotates at a rate of 6 rotations per second during the spin cycle. Independent Quantity
Dependent Quantity
Quantity Name
Time
Number of Rotations
Unit of Measure
Seconds
Rotations
1
6
5
30
12
72
30
180
50
300
t
6t
Expression
300 270 240
Number of Rotations
© 2011 Carnegie Learning
210 180 150 120 90 60 30 0 0
5
10
15
20
25
30
35
40
45
50
Time (seconds)
Chapter 2 Skills Practice • 381
Lesson 2.4 Skills Practice
page 8
12. A corn mill produces 1 ounce of cornmeal with every 4 rotations of the stone-grinding wheel. Independent Quantity
Dependent Quantity
Quantity Name
Rotations
Cornmeal Produced
Unit of Measure
Rotations
Ounces
4
1
12
3
20
5
36
9
40
10
r
1 r __ 4
Expression
10 9
7 6 5 4 3 2 1 0 0
4
8
12
16
20
24
Number of Rotations
382 • Chapter 2 Skills Practice
28
32
36
40
© 2011 Carnegie Learning
Cornmeal Produced (ounces)
8
Lesson 2.4 Skills Practice
page 9
Name_________________________________________________________ Date__________________________ 13. A concrete truck has an initial load of 70 cubic yards of concrete. The truck pours concrete at a rate of 0.2 cubic yard per second. Independent Quantity
Dependent Quantity
Quantity Name
Time
Concrete Remaining in Truck
Unit of Measure
Seconds
Cubic Yards
10
68
20
66
50
60
100
50
200
30
t
70 2 0.2t
Expression
100 90
Concrete Remaining in Truck (cubic yards)
© 2011 Carnegie Learning
80 70 60 50 40 30 20 10 0 0
20
40
60
80
100 120 140 160 180 200
Time (seconds)
Chapter 2 Skills Practice • 383
Lesson 2.4 Skills Practice
page 10
14. A steamroller travels at a constant rate of 3.5 feet per second. Independent Quantity
Dependent Quantity
Quantity Name
Time
Distance Travelled
Unit of Measure
Seconds
Feet
5
17.50
10
35
25
87.50
50
175
100
350
t
3.5t
Expression
350 315
245 210 175 140 105 70 35 0 0
10
20
30
40
50
60
Time (seconds)
384 • Chapter 2 Skills Practice
70
80
90
100
© 2011 Carnegie Learning
Distance Travelled (feet)
280
Lesson 2.5 Skills Practice Name_________________________________________________________ Date__________________________
U.S. Shirts Using Tables, Graphs, and Equations, Part 1
Problem Set Complete the table of values to model each problem situation. 1. You pay $5 to enter a raffle, plus $1 for each raffle ticket. Number of Raffle Tickets Purchased
Total Cost (in dollars)
10
5 1 1(10) 5 15
11
5 1 1(11) 5 16
12
5 1 1(12) 5 17
13
5 1 1(13) 5 18
14
5 1 1(14) 5 19
15
5 1 1(15) 5 20
© 2011 Carnegie Learning
2. A company pays $500 for each computer, plus an $80 shipping charge. Number of Computers in Each Order
Total Cost (in dollars)
5
80 1 5(500) 5 2580
6
80 1 6(500) 5 3080
7
80 1 7(500) 5 3580
8
80 1 8(500) 5 4080
9
80 1 9(500) 5 4580
10
80 1 10(500) 5 5080
Chapter 2 Skills Practice • 385
Lesson 2.5 Skills Practice
page 2
3. Lauren has already read 55 pages of a novel. Each day, she reads another 30 pages. Number of Days
Number of Pages Read
2
55 1 30(2) 5 115
4
55 1 30(4) 5 175
6
55 1 30(6) 5 235
8
55 1 30(8) 5 295
10
55 1 30(10) 5 355
12
55 1 30(12) 5 415
4. Mr. Cloud is writing an autobiography. He has already written 32 pages. Each day, he writes
Number of Days
Number of Pages Written
10
32 1 5(10) 5 82
15
32 1 5(15) 5 107
20
32 1 5(20) 5 132
25
32 1 5(25) 5 157
30
32 1 5(30) 5 182
35
32 1 5(35) 5 207
386 • Chapter 2 Skills Practice
© 2011 Carnegie Learning
another 5 pages.
Lesson 2.5 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ Create a graph of the data in each given table. 5. A video game store sells each game for $30. The store’s total fixed expenses are $500 each month. They record the number of games sold, g, and their total profit, p, in the table below. p
Number of Games Sold
Total Profit (in dollars)
20
100
30
400
1800
Total Profit (in dollars)
1600
40
700
50
1000
60
1300
70
2000
(70, 1600)
1400 (60, 1300)
1200 1000
(50, 1000)
800 (40, 700)
600 400
(30, 400)
200 (20, 100) 10
1600
20
30
40
50
60
80
70
90 100
g
Number of Games Sold
6. A paper store sells each ream of paper for $40. They will deliver it for a one-time fee of $25. An office records their total paper costs, c, in dollars, and the total number of reams delivered, r.
Number of Reams Delivered
Total Paper Costs (in dollars)
6
265
8
345
10
425
12
505
900 Total Paper Costs (in dollars)
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c 1000
800 700
(16, 655)
600
(14, 585)
500
(12, 505) (10, 425)
400
(8, 345)
300
(6, 265)
200
14
585
16
665
100 2
4
6
8
10
12
14 16
18
20
r
Number of Reams Delivered
Chapter 2 Skills Practice • 387
Lesson 2.5 Skills Practice
page 4
7. An architect is designing a new hotel. He is planning to have 10 windows in the lobby, and each hotel room will have 2 windows. The hotel will not have any other windows. He records the total number of windows, w, for different numbers of hotel rooms, r. w
Total Number of Windows
50
110
75
160
100
210
125
260
150
310
175
360
500 450 400 Total Number of Windows
Number of Hotel Rooms
(175, 360)
350
(150, 310)
300
(125, 260)
250
(100, 210)
200
(75, 160)
150
(50, 110)
100 50 20
40
60
80 100 120 140 160 180 200
r
Number of Hotel Rooms
8. A bookstore spends $300 on a new shipment of 200 books. They sell each book for $12. They record their total profit, p, in dollars, after selling b books. p
40
180
60
420
80
660
100
900
120
1140
140
1380
388 • Chapter 2 Skills Practice
1800 1600 1400
(140, 1380)
1200
(120, 1140)
1000 (100, 900)
800
(80, 660)
600
(60, 420)
400 200
(40, 180) 20
40
60
80 100 120 140 160 180 200
Number of Books Sold
b
© 2011 Carnegie Learning
Total Profit (in dollars) Total Profit (in dollars)
Number of Books Sold
2000
Lesson 2.5 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ Use the given information to answer each question. 9. As part of her workout, Dana stretches for 15 minutes before running. She then runs 1 mile in 10 minutes. What is the total time of her workout, including stretching, if Dana runs 5 miles? 15 1 5(10) 5 15 1 50 5 65 Dana’s total workout time is 65 minutes if she runs 5 miles.
10. Evan borrows $200 from his parents. He agrees to pay his parents back an extra dollar for each day that he owes them money. If he waits 90 days to pay back his parents, what is the total amount Evan owes them? 200 1 1(90) 5 200 1 90 5 290 If Evan waits 90 days to pay back his parents, he will owe them a total of $290.
11. A wholesale food store charges a yearly membership of $50. A café owner uses his membership to purchase cases of bottled water. Each case of bottled water costs $5. In 1 year, the café owner buys 200 cases of bottled water. Including the yearly membership, what is the café owner’s total yearly cost, in dollars, for the 200 cases of water?
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50 1 5(200) 5 50 1 1000 5 1050 The café owner’s total yearly cost is $1050 for 200 cases of water.
12. A magazine publisher charges a supermarket $2 for each magazine that the market orders, plus a monthly rental fee of $30 for a magazine rack. If the supermarket orders 350 magazines per month, what is their total cost, in dollars, for the 350 magazines? 30 1 2(350) 5 30 1 700 5 730 The total cost will be $730 if 350 magazines are ordered per month.
Chapter 2 Skills Practice • 389
Lesson 2.5 Skills Practice
page 6
Use the given information to answer each question. 13. Leah is ordering new beach towels. She will pay a $5 fixed shipping charge and $10 for each beach towel. If Leah has $55 dollars to spend on her beach towel order, how many beach towels can she buy?
50 5 5 _______ ___ 5 55 2 5 10
10
With $55, Leah can order 5 new beach towels.
14. Twelve people have a cold. Each day, 8 more people get sick. After how many days will 101 total people be sick?
_________ ___
12 89 5 11.125 101 2 5 8 8 Because the answer is a decimal, I estimated that after about 11 days, 101 people will be sick.
15. Jackson is ordering pizza for a party. He wants to order 4 pieces for himself, and 3 pieces for every person attending the party. If he orders a total of 34 slices of pizza, how many people are attending the party?
_______ ___
4 30 5 10 34 2 5 3 3
16. Sean is adding to his art collection. He already owns 7 paintings. Each time he visits an art gallery, he buys 2 more paintings. How many galleries will he need to visit if he wants to own at least 20 paintings?
_______ ___
7 13 5 6.5 20 2 5 2 2 Because Sean cannot visit half of a art gallery, he will need to visit 7 galleries to own at least 20 paintings.
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Ten people are attending the party if he orders 34 slices of pizza.
Lesson 2.5 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ Write an equation in two variables to model each given situation. 17. A person’s nails grow at an average rate of 1 millimeter per week. You measure one of your nails to be 10 millimeters long. Write an equation that relates ℓ, the total length of your nail, to t, the time in weeks. ℓ 5 t 1 10
18. Devin earns $500 each week, plus $15 for each hour of overtime. Write an equation to represent Devin’s total weekly salary, s, if he works t hours of overtime. s 5 500 1 15t
19. A manager is hired at a starting salary of $60,000 per year. Each year, her salary increases by $5000. Write an equation to represent her yearly salary, s, at any given time t, in years. s 5 60,000 1 5000t
20. A hair stylist earns $70 per day, plus $20 for each haircut. Write an equation that relates his total daily income d, in dollars, for any number of haircuts, h.
© 2011 Carnegie Learning
d 5 70 1 20h
21. A clothing company charges $5 for each belt that it sells. It also charges a fixed delivery fee of $8 per order. Write an equation that relates the total charge c, in dollars, for an order of b belts. c 5 5b 1 8
22. A dry cleaner charges $2 to dry clean a shirt, and $10 to dry clean a jacket. Write an equation that relates the total dry cleaning bill b, in dollars, for s shirts and one jacket. b 5 2s 1 10
Chapter 2 Skills Practice • 391
© 2011 Carnegie Learning
392 • Chapter 2 Skills Practice
Lesson 2.6 Skills Practice Name_________________________________________________________ Date__________________________
Hot Shirts Using Tables, Graphs, and Equations, Part 2
Vocabulary Define each term in your own words. 1. point of intersection The point of intersection is the point at which two lines on a graph intersect. This indicates where two data points are equivalent to each other.
2. estimation Estimation is the process of determining the approximate value of an expression, often done through rounding.
Problem Set Estimate each value of each expression. Then, calculate the exact value. 1. 750.25 1 225.50 975; 975.75
© 2011 Carnegie Learning
3. 25 3 101 2500; 2525
2. 1.98 1 1.73 4; 3.71
4. 236 3 4 960; 944
5. 146.9 2 92.5
6. 4261 2 2637
60; 54.4
1700; 1624
Chapter 2 Skills Practice • 393
Lesson 2.6 Skills Practice
page 2
Use the given information to complete each table and answer the question. 7. Job A will pay a $30,000 salary per year for the first year, with a $1200 raise each year. Job B will pay a $30,000 salary per year for the first year, with a 3% raise each year. Complete the table to show the annual salaries for the first 4 years, rounding each salary to the nearest dollar. In the fourth year, which job will pay the greater salary?
Year
Job A
Job B
1
$30,000
$30,000
2
$30,000 1 $1200 5 $31,200
$30,000 3 1.03 5 $30,900
3
$31,200 1 $1200 5 $32,400
$30,900 3 1.03 5 $31,827
4
$32,400 1 $1200 5 $33,600
$31,827 3 1.03 5 $32,782
Job A will pay a greater salary. 8. Job C is offering you a $40,000 salary for the first year, plus a one-time $3000 signing bonus. Each year, you get a $1500 raise. Job D is offering you $40,000 for the first year, and each year you get a 5% raise. Complete the table to show the annual salaries for the first 4 years. Which job will pay
Year
Job C
Job D
1
$40,000 1 $3000 5 $43,000
$40,000
2
$40,000 1 $1500 5 $41,500
$40,000 3 1.05 5 $42,000
3
$41,500 1 $1500 5 $43,000
$42,000 3 1.05 5 $44,100
4
$43,000 1 $1500 5 $44,500
$44,100 3 1.05 5 $46,305
After 4 years, Job C has paid: $43,000 1 $41,500 1 $43,000 1 $44,500 5 $172,000 Job D has paid: $40,000 1 $42,000 1 $44,100 1 $46,305 5 $172,405 Job D will pay me more for 4 years of work.
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you more in total for all 4 years?
Lesson 2.6 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 9. You have a choice between two different investment options. You will invest $6000. Investment Plan A estimates that you will earn 6% of your account balance each year. Investment Plan B estimates that you will earn $370 each year. Complete the table to show the account balance for the first 4 years. After 4 years, which investment plan would have a greater account balance?
Year
Plan A
Plan B
1
$6000
$6000
2
$6000 3 1.06 5 $6360
$6000 1 $370 5 $6370
3
$6360 3 1.06 5 $6741.60
$6370 1 $370 5 $6740
4
$6741.60 3 1.06 5 $7146.10
$6740 1 $370 5 $7110
After 4 years, Plan A would have a greater account balance than Plan B. 10. You invest $5000 into each of two different accounts. In Account A, you will earn $50 each month. In Account B, you will earn 1% of your account balance at the end of each month. Complete the table to show the account balance for the first 4 months. After 4 months, which investment plan
© 2011 Carnegie Learning
would have a greater account balance?
Month
Account A
Account B
1
$5000
$5000
2
$5000 1 $50 5 $5050
$5000 3 1.01 5 $5050
3
$5050 1 $50 5 $5100
$5050 3 1.01 5 $5100.50
4
$5100 1 $50 5 $5150
$5100.50 3 1.01 5 $5151.51
After 4 months, Account B would have a greater account balance.
Chapter 2 Skills Practice • 395
Lesson 2.6 Skills Practice
page 4
11. On Big Country Dairy Farms, the average Holstein cow produces 40 pounds of milk daily in its first year of production and an additional 3 pounds of milk daily in each year after the first. The average Jersey cow produces 35 pounds of milk daily in its first year of production and an additional 4.5 pounds of milk daily in each year after the first. Complete the table to show each type of cows’ daily milk production for the first 5 years. After 5 years, which type of cow produces the most milk daily?
Year
Holstein’s Daily Milk Production (pounds)
Jersey’s Daily Milk Production (pounds)
1
40
35
2
40 1 3 5 43
35 1 4.5 5 39.50
3
43 1 3 5 46
39.50 1 4.5 5 44
4
461 3 5 49
44 1 4.5 5 48.50
5
49 1 3 5 52
48.50 1 4.5 5 53
After 5 years, the average Jersey cow produces the most milk daily. 12. Jerry puts a different type of fertilizer on each of his two pumpkin patches. A pumpkin from Patch A measures 13 ounces in week 1 and grows at a rate of 3.2 ounces per week. A pumpkin from Patch B measures 9 ounces in week 1 and grows at a rate of 3.6 ounces per week. Complete the table to
Week
Weight of the Patch A Pumpkin (ounces)
Weight of the Patch B Pumpkin (ounces)
1
13
9
2
13 1 3.2 5 16.20
9 1 3.6 5 12.60
3
16.20 1 3.2 5 19.40
12.60 1 3.6 5 16.20
4
19.40 1 3.2 5 22.60
16.20 1 3.6 5 19.80
5
22.60 1 3.2 5 25.80
19.80 1 3.6 5 23.40
After 5 weeks, the pumpkin from Patch A is the largest.
396 • Chapter 2 Skills Practice
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show the growth for each pumpkin for 5 weeks. After 5 weeks, which pumpkin is the largest?
Lesson 2.6 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ Use the given equations to answer each question. 13. Two catering companies host children’s sports banquets. Company A charges a fixed fee of $100 plus $3 per person. Company B charges a fixed fee of $75 plus $4 per person. The total charge for each company for any number of persons, p, can be calculated using the equations shown.
Company A: c 5 3p 1 100
Company B: c 5 4p 1 75
Which company would charge less to cater for 200 people? Company A: c 5 3(200) 1 100 5 700 Company B: c 5 4(200) 1 100 5 900 Company A would charge $200 less to cater for 200 people.
14. Lana is joining a gym. Get Fit charges $20 per month, plus a $99 initial set-up fee. Work It Out charges $30 per month, plus a $50 initial set-up fee. The equations show the total cost after any number of months, m.
Get Fit: c 5 20m 1 99
Work It Out: c 5 30m 1 50
Which gym would cost less if you planned on being a member for 4 months?
© 2011 Carnegie Learning
Get Fit: c 5 20(4) 1 99 5 179 Work It Out: c 5 30(4) 1 50 5 170 Work It Out would cost $9 less to be a member for 4 months.
Chapter 2 Skills Practice • 397
Lesson 2.6 Skills Practice
page 6
15. Theodore and Jeffrey are comparing their text messaging plans. Theodore’s cell phone company charges according to the equation c 5 5 1 0.10m. Jeffrey’s cell phone company charges according to the equation c 5 3 1 0.15m. Let c represent the total cost in dollars for m text messages sent and received. Which plan charges more to send or receive a total of 100 text messages? Theodore’s plan: c 5 5 1 0.10(100) 5 5 1 10 5 15 Jeffrey’s plan: c 5 3 1 0.15(100) 5 3 1 15 5 18 Jeffrey’s plan charges $3 more to send or receive a total of 100 text messages.
16. Anthony and Lisa are both joining DVD rental programs. The cost of Anthony’s program per month can be represented by the equation c 5 10 1 1m. The cost of Lisa’s program per month can be represented by the equation c 5 5 1 2m. Let c represent the monthly cost if m DVDs are rented. Who would pay more if they each rented 7 movies in 1 month? Anthony would pay: c 5 10 1 1(7) 5 10 1 7 5 17 Lisa would pay: c 5 5 1 2(7) 5 5 1 14 5 19 Lisa would pay $2 more if they each rented 7 movies.
17. A coffee shop is ordering new coffee mugs. The total charges for The Mug Company are by c 5 25 1 0.50m. Let c represents the total cost of m mugs. If the coffee shop needs to order 100 mugs, which company should they order from? The Mug Company: c 5 15 1 1.5(100) 5 15 1 150 5 $165 A Perfect Mug: c 5 25 1 0.50(100) 5 25 1 50 5 $75 The coffee shop should order from A Perfect Mug because they will charge $90 less for an order of 100 mugs.
398 • Chapter 2 Skills Practice
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represented by the equation c 5 15 1 1.5m. The total charges for A Perfect Mug are represented
Lesson 2.6 Skills Practice
page 7
Name_________________________________________________________ Date__________________________ 18. You are flying to visit some relatives in Boston. Budget Airline charges $150 for a round-trip ticket, plus an additional $0.20 per pound of luggage, which is represented by the equation c 5 150 1 0.20p. Let c represent the cost, and let p represent the pounds of luggage. Cheap Air charges $75 for a round-trip ticket, plus an additional $0.80 per pound of luggage, which is represented by the equation c 5 75 1 0.80p. If you are bringing 30 pounds of luggage, on which airline should you fly? Budget Airline: c 5 150 1 0.20(30) 5 150 1 6 5 $156 Cheap Air: c 5 75 1 0.80(30) 5 75 1 24 5 $99 You should fly on Cheap Air because it will cost $57 less than flying on Budget Airline.
Use the given graph to answer each question. 19. You need to choose a shipping company. Ship Fast charges $2.00 per package plus $1.00 per pound. Speedy Delivery charges $3.00 per package plus $0.50 per pound. The graph of the equations that represent this situation is shown. For what package weight do both companies charge the same price? y 10 9
Shipping Cost (in dollars)
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8 Ship Fast
7 6
Speedy Delivery
5 4 3 2 1 1
2
3
4
5
6
7
8
9
10
x
Weight (in pounds)
A package weighing 2 pounds will cost the same to ship using either company.
Chapter 2 Skills Practice • 399
Lesson 2.6 Skills Practice
page 8
20. Tate is ordering flour for her bakery. Baker’s Supplies charges $0.30 per pound, plus a $10 delivery fee. Best Flour charges $0.80 per pound, but delivery is free. The graph of the equations that represent this situation is shown. For what weight of flour is the cost equal for both companies? y 30 27
Charge (in dollars)
24 21 18 15
Baker’s Supplies
12 9 6
Best Flour
3 3
6
12
9
15
18
21
24
27
30
x
Weight (in pounds)
For 20 pounds of flour, the two companies charge the same total price. 21. Franklin is buying fabric. For the same material, Sew Right charges $4.00 per yard and an initial $5.00 convenience fee. Stitch Plus charges $6.00 per yard and a $2.00 convenience fee. The graph of the equations that represent this situation is shown. Which store should he buy the fabric from if he is buying 5 yards of material? y 30 27
Charge (in dollars)
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Stitch Plus
24
Sew Right
21 18 15 12 9 6 3 1
2
3
4
5
6
7
8
9
10
x
Length (in yards)
Franklin should buy from Sew Right because it charges less for 5 yards of fabric.
400 • Chapter 2 Skills Practice
Lesson 2.6 Skills Practice
page 9
Name_________________________________________________________ Date__________________________ 22. An ice cream shop is choosing a milk delivery service. The Spotted Cow charges $2.80 per gallon plus a $2 delivery fee. Dairy Farms charges $2.10 per gallon plus a $10 delivery fee. The graph of the equations that represent this situation is shown. Who charges more to deliver 15 gallons of milk? y 50 45
Charge (in dollars)
40 35 30
Dairy Farms
25 20 15 Spotted Cow
10 5 3
6
9
12
15
18
21
24
27
30
x
Gallons of Milk
© 2011 Carnegie Learning
The Spotted Cow charges more to deliver 15 gallons of milk.
Chapter 2 Skills Practice • 401
Lesson 2.6 Skills Practice
page 10
23. Aiko is trying to select a prepaid cell phone. The Texnel phone costs $15 per month plus $0.15 per minute. The Konia phone costs $25 per month plus $0.05 per minute. The graph of the equations that represent this situation is shown. If Aiko plans to talk an average of 150 minutes per month, which plan should she choose? 50
y
45 40
Cost of Plan ($)
35 30
Konia
25 Texnel
20 15 10 5 0
x 0
20
40
60
80 100 120 140 160 180 200 Minutes Used
Aiko should choose the Konia phone if she talks 150 minutes per month. 24. A middle school principal is trying to select a publisher for the student handbook. Page One Publishing charges a start-up fee of $50 plus $0.75 per handbook printed. Page Two Publishing charges a start-up fee of $200 plus $0.25 per handbook printed. The graph of the equations that represent this situation is shown. Which publishing company should the principal choose if the school plans to print 200 handbooks? 500
y
450
© 2011 Carnegie Learning
400
Printing Cost ($)
350 300 Page Two
250 200
Page One
150 100 50
x
0 0
50 100 150 200 250 300 350 400 450 500 Number of Handbooks Printed
The principal should choose Page One Publishing to print 200 handbooks.
402 • Chapter 2 Skills Practice
Lesson 2.7 Skills Practice Name_________________________________________________________ Date__________________________
What, Not Lines? Introduction to Non-Linear Functions
Vocabulary Sketch a graph of each given function. 1. absolute value function
2. square or quadratic function
y
3. cube or cubic function
y
y
x
x
x
Problem Set Complete the table for each given function and use the values to graph the function. 1. y 5 |x| 1 3
© 2011 Carnegie Learning
y
x
y 5 |x| 1 3
26
9
23
6
21
4
0
3
1
4
8 6 4 2 x
0 -8
-6
-4
0
-2
2
4
6
8
-2 -4 -6
3
6
6
9
-8
Chapter 2 Skills Practice • 403
Lesson 2.7 Skills Practice
page 2
2. y 5 __ 1 x2 2
y
x
1 2 y 5 __ x 2
8
24
8
6
22
2
21
0.50
4 2
0
0
1
0.50
x
0 -8
-6
-4
0
-2
2
4
6
8
2
4
6
8
-2 -4 -6
3
4.50
4
8
-8
3. y 5 x3 2 2 y
x
y 5 x3 2 2
22
210
21.5
¯ 25.38
21
23
8
6 4 2
22
1
21
1.2
¯ 20.27
1.7
¯ 2.91
2
6
-6
-4
0
-2 -2 -4
404 • Chapter 2 Skills Practice
-6 -8
© 2011 Carnegie Learning
0
x
0 -8
Lesson 2.7 Skills Practice
page 3
Name_________________________________________________________ Date__________________________ 4. y 5 __ 1 |x| 2
y
x
1 y 5 __ |x| 2
8
28
4
6
24
2
22
1
0
0
2
1
4 2 x
0 -8
-6
-4
0
-2
2
4
6
8
-2 -4 -6
4
2
8
4
-8
5. y 5 x2 24
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y
x
y 5 x2 24
23
5
22
0
21
23
8 6 4 2 -8
0
24
1
23
2
0
3
5
x
0 -6
-4
0
-2
2
4
6
8
-2 -4 -6 -8
Chapter 2 Skills Practice • 405
Lesson 2.7 Skills Practice
page 4
6. y 5 __ 1 x3 2
x
1 3 y 5 __ x 2
22.5
¯ 27.81
22
24
21
20.50
y 8 6 4 2
0
0
1
0.5
2
4
2.5
¯ 7.81
x
0 -8
-6
-4
0
-2
2
4
6
8
-2 -4 -6 -8
7. y 5 2|x|
y
x
y 5 2|x|
25
10
23
6
21
2
0
0
1
2
8 6 4 2 -8
-6
-4
0
-2 -2 -4 -6
2
4
4
8
406 • Chapter 2 Skills Practice
x
0
-8
2
4
6
8 © 2011 Carnegie Learning
Lesson 2.7 Skills Practice
page 5
Name_________________________________________________________ Date__________________________ 8. y 5 __ 1 x2 4
y
x
1 y 5 __ x2 4
8
26
9
6
24
4
22
1
4 2
0
0
2
1
x
0 -8
-6
-4
0
-2
2
4
6
8
-2 -4 -6
4
6
9
-8
© 2011 Carnegie Learning
4
Chapter 2 Skills Practice • 407
© 2011 Carnegie Learning
408 • Chapter 2 Skills Practice
