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Course 1
Chapter 4Resource Masters
Course 3
Chapter 4Resource Masters
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce thematerial contained herein on the condition that such material be reproduced only forclassroom use; be provided to students, teacher, and families without charge; andbe used solely in conjunction with Glencoe Mathematics: Applications andConcepts, Course 3. Any other reproduction, for use or sale, is prohibited withoutprior written permission of the publisher.
Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240
Mathematics: Applications and Concepts, Course 3ISBN: 0-07-860147-9 Chapter 4 Resource Masters
1 2 3 4 5 6 7 8 9 10 024 12 11 10 09 08 07 06 05 04 03
Consumable Workbooks
Many of the worksheets contained in the Chapter Resource Mastersbooklets are available as consumable workbooks in both English andSpanish.
Study Guide and Intervention Workbook 0-07-860162-2
Study Guide and Intervention Workbook (Spanish) 0-07-860168-1
Practice: Skills Workbook 0-07-860163-0
Practice: Skills Workbook (Spanish) 0-07-860169-X
Practice: Word Problems Workbook 0-07-860164-9
Practice: Word Problems Workbook (Spanish) 0-07-860170-3
Reading to Learn Mathematics Workbook 0-07-861062-1
Answers for Workbooks The answers for Chapter 4 of theseworkbooks can be found in the back of this Chapter Resource Mastersbooklet.
Spanish Assessment Masters Spanish versions of forms 2A and 2C ofthe Chapter 4 Test are available in the Glencoe Mathematics: Applicationsand Concepts Spanish Assessment Masters, Course 3 (0-07-860172-X).
iii
Vocabulary Builder .............................vii
Family Letter............................................ix
Family Activity ........................................x
Lesson 4-1Study Guide and Intervention ........................185Practice: Skills ................................................186Practice: Word Problems................................187Reading to Learn Mathematics......................188Enrichment .....................................................189
Lesson 4-2Study Guide and Intervention ........................190Practice: Skills ................................................191Practice: Word Problems................................192Reading to Learn Mathematics......................193Enrichment .....................................................194
Lesson 4-3Study Guide and Intervention ........................195Practice: Skills ................................................196Practice: Word Problems................................197Reading to Learn Mathematics......................198Enrichment .....................................................199
Lesson 4-4Study Guide and Intervention ........................200Practice: Skills ................................................201Practice: Word Problems................................202Reading to Learn Mathematics......................203Enrichment .....................................................204
Lesson 4-5Study Guide and Intervention ........................205Practice: Skills ................................................206Practice: Word Problems................................207Reading to Learn Mathematics......................208Enrichment .....................................................209
Lesson 4-6Study Guide and Intervention ........................210Practice: Skills ................................................211Practice: Word Problems................................212Reading to Learn Mathematics......................213Enrichment .....................................................214
Lesson 4-7Study Guide and Intervention ........................215Practice: Skills ................................................216Practice: Word Problems................................217Reading to Learn Mathematics......................218Enrichment .....................................................219
Lesson 4-8Study Guide and Intervention ........................220Practice: Skills ................................................221Practice: Word Problems................................222Reading to Learn Mathematics......................223Enrichment .....................................................224
Chapter 4 AssessmentChapter 4 Test, Form 1 ..........................225–226Chapter 4 Test, Form 2A........................227–228Chapter 4 Test, Form 2B........................229–230Chapter 4 Test, Form 2C........................231–232Chapter 4 Test, Form 2D........................233–234Chapter 4 Test, Form 3 ..........................235–236Chapter 4 Extended Response Assessment .237Chapter 4 Vocabulary Test/Review.................238Chapter 4 Quizzes 1 & 2................................239Chapter 4 Quizzes 3 & 4................................240Chapter 4 Mid-Chapter Test ...........................241Chapter 4 Cumulative Review........................242Chapter 4 Standardized Test Practice....243–244
Standardized Test Practice Student Recording Sheet ..............................A1
Standardized Test Practice Rubric...................A2ANSWERS .............................................A3–A32
CONTENTS
iv
Teacher’s Guide to Using the Chapter 4 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resources youuse most often. The Chapter 4 Resource Masters includes the core materials needed forChapter 4. These materials include worksheets, extensions, and assessment options. Theanswers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in theGlencoe Mathematics: Applications and Concepts, Course 3, TeacherWorks CD-ROM.
Vocabulary Builder Pages vii-viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.
When to Use Give these pages to studentsbefore beginning Lesson 4-1. Encouragethem to add these pages to theirmathematics study notebook. Remind themto add definitions and examples as theycomplete each lesson.
Family Letter and Family ActivityPage ix is a letter to inform your students’families of the requirements of the chapter.The family activity on page x helps themunderstand how the mathematics studentsare learning is applicable to real life.
When to Use Give these pages to studentsto take home before beginning the chapter.
Study Guide and InterventionThere is one Study Guide and Interventionmaster for each lesson in Chapter 4.
When to Use Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.
Practice: Skills There is one master foreach lesson. These provide practice thatmore closely follows the structure of thePractice and Applications section of theStudent Edition exercises.
When to Use These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Practice: Word Problems There is onemaster for each lesson. These providepractice in solving word problems that applythe concepts of the lesson.
When to Use These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Reading to Learn Mathematics Onemaster is included for each lesson. The firstsection of each master asks questions aboutthe opening paragraph of the lesson in theStudent Edition. Additional questions askstudents to interpret the context of andrelationships among terms in the lesson.Finally, students are asked to summarizewhat they have learned using variousrepresentation techniques.
When to Use This master can be used as astudy tool when presenting the lesson or asan informal reading assessment afterpresenting the lesson. It is also a helpful toolfor ELL (English Language Learner)students.
v
Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.
When to Use These may be used as extracredit, short-term projects, or as activitiesfor days when class periods are shortened.
Assessment OptionsThe assessment masters in the Chapter 4Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter AssessmentChapter Tests
• Form 1 contains multiple-choice questionsand is intended for use with basic levelstudents.
• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.
• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.
All of the above tests include a free-responseBonus question.
• The Extended-Response Assessmentincludes performance assessment tasksthat are suitable for all students. Ascoring rubric is included for evaluationguidelines. Sample answers are providedfor assessment.
• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used inconjunction with one of the chapter testsor as a review worksheet.
Intermediate Assessment• Four free-response quizzes are included
to offer assessment at appropriateintervals in the chapter.
• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice and free-response questions.
Continuing Assessment• The Cumulative Review provides
students an opportunity to reinforce andretain skills as they proceed through theirstudy of Glencoe Mathematics:Applications and Concepts, Course 3. Itcan also be used as a test. This masterincludes free-response questions.
• The Standardized Test Practice offerscontinuing review of pre-algebra conceptsin various formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, short response, grid-in, andextended response questions. Bubble-inand grid-in answer sections are providedon the master.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questions thatappear in the Student Edition on pages 202–203. This improves students’familiarity with the answer formats theymay encounter in test taking.
• Detailed rubrics for assessing theextended response questions on page 203are provided on page A2.
• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.
• Full-size answer keys are provided for theassessment masters in this booklet.
This is an alphabetical list of new vocabulary terms you will learn inChapter 4. As you study the chapter, complete each term’s definitionor description. Remember to add the page number where you foundthe term. Add this page to your math study notebook to reviewvocabulary at the end of the chapter.
Vo
cab
ula
ry B
uild
er
© Glencoe/McGraw-Hill vii Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn MathematicsVocabulary Builder
Vocabulary TermFound
Definition/Description/Exampleon Page
congruent
corresponding parts
cross products
dilation[deye-LAY-shuhn]
indirect measurement
polygon
proportion
rate
rate of change
© Glencoe/McGraw-Hill viii Mathematics: Applications and Concepts, Course 3
Vocabulary TermFound
Definition/Description/Exampleon Page
ratio
rise
run
scale
scale drawing
scale factor
scale model
similar
slope
unit rate
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn MathematicsVocabulary Builder (continued)
© Glencoe/McGraw-Hill ix Mathematics: Applications and Concepts, Course 3
Family LetterNAME ________________________________________ DATE ______________ PERIOD _____
Dear Parent or Guardian:
“When am I ever going to use this stuff?” Students in math
classes often ask this question. Too often, math seems to be a
series of procedures that one learns and then uses to solve a
particular type of problem—without having any application to
the real world. In our math class, however, we try to take
mathematics beyond the classroom to a point where students
will realize and appreciate its importance in their daily lives.
In Chapter 4, Proportions, Algebra, and Geometry, your
child will learn about ratios, rates, and proportions. Your child
will also learn about slope as a rate of change and will find the
slope of a line. In addition, your child will learn to make scale
models and use indirect measurement. In the study of this
chapter, your child will complete a variety of daily classroom
assignments and activities and possibly produce a chapter
project.By signing this letter and returning it with your child, you agree
to encourage your child by getting involved. Enclosed is an
activity that you can do with your child that also relates the
math we will be learning in Chapter 4 to the real world. You
may also wish to log on to the Online Study Tools for self-
check quizzes, Parent and Student Study Guide pages, and
other study help at www.msmath3.net. If you have any
questions or comments, feel free to contact me at school.
Sincerely,
Fam
ily L
ette
r
Signature of Parent or Guardian ______________________________________ Date ________
© Glencoe/McGraw-Hill x Mathematics: Applications and Concepts, Course 3
Family ActivityNAME ________________________________________ DATE ______________ PERIOD _____
Scale Drawings and ModelsWork with a family member. Below is a scale drawing of a house plan. Thescale for the drawing is �
12� inch � 3 feet. Use the drawing to answer the
following questions. You will need a ruler to complete this activity.
1. What are the dimensions of the kitchen in the drawing?
2. What are the dimensions of the kitchen in real life?
3. What is the area of Bedroom 2 in the drawing?
4. What is the area of Bedroom 2 in real life?
5. How many square feet of carpet will be needed to carpet the living roomand the hallway?
1.2�14
�in.by 1�12
�in.2.13�12
�ft by 9 ft3.3 in24.108 ft25.310�12
�ft2
Bedroom 2
Bath Bedroom 1
Bedroom 3 Kitchen
Living Room
Less
on
4–1
© Glencoe/McGraw-Hill 185 Mathematics: Applications and Concepts, Course 3
Express 35 wins to 42 losses in simplest form.
�3452�
� �56� Divide the numerator and denominator by the greatest common factor, 7.
The ratio in simplest form is �56� or 5:6.
Express 1 foot to 3 inches in simplest form.
To simplify a ratio involving measurements, both quantities must have the same unitof measure.
�31in
fcohotes� � �
132
iinncchheess
� Convert 1 foot to 12 inches.
� �41ininchch
es� Divide the numerator and denominator by 3.
The ratio in simplest form is �41� or 4:1.
Express 309 miles in 6 hours as a unit rate.
�3609
homuirless
� � �51
1.5
hmou
irles
� Divide the numerator and denominator by 6 to get a denominator of 1.
The unit rate is 51.5 miles per hour.
Express each ratio in simplest form.
1. 3 out of 9 students 2. 8 passengers:2 cars
3. 5 out of 10 dentists 4. 35 boys:60 girls
5. 18 red apples to 42 green apples 6. 50 millimeters to 1 meter
Express each rate as a unit rate.
7. 12 waves in 2 hours 8. 200 miles in 4 hours
9. 21 gallons in 2.4 minutes 10. $12 for 4.8 pounds
11. $49,500 in 12 months 12. 112 feet in 5 seconds
A rate is a ratio that compares two quanitities with different types of units. A unit rate is a rate with adenominator of 1.
A ratio is a comparison of two numbers by division. Since a ratio can be written as a fraction, it can be simplified.
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionRatios and Rates
© Glencoe/McGraw-Hill 186 Mathematics: Applications and Concepts, Course 3
Express each ratio in simplest form.
1. 15 cats:50 dogs 2. 18 adults to 27 teens
3. 27 nurses to 9 doctors 4. 12 losses in 32 games
5. 50 centimeters:1 meter 6. 1 foot:1 yard
7. 22 players:2 teams 8. $28:8 pounds
9. 8 completions:12 passes 10. 21 hired out of 105 applicants
11. 18 hours out of 1 day 12. 64 boys to 66 girls
13. 66 miles on 4 gallons 14. 48 wins:18 losses
15. 112 peanuts:28 cashews 16. 273 miles in 6 hours
Express each rate as a unit rate.
17. 96 students in 3 buses 18. $9,650 for 100 shares of stock
19. $21.45 for 13 gallons of gasoline 20. 125 meters in 10 seconds
21. 30.4 pounds of tofu in 8 weeks 22. 6.5 inches of rainfall in 13 days
23. 103.68 miles in 7.2 hours 24. $94.99 for 7 pizzas
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: SkillsRatios and Rates
© Glencoe/McGraw-Hill 187 Mathematics: Applications and Concepts, Course 3
Practice: Word ProblemsRatios and Rates
NAME ________________________________________ DATE ______________ PERIOD _____
Less
on
4–1
1. COOKING In a bread dough recipe,there are 3 eggs for every 9 cups offlour. Express this ratio in simplestform.
2. WILDLIFE Dena counted 14 robins out of150 birds. Express this ratio insimplest form.
3. INVESTMENTS Josh earned dividends of$2.16 on 54 shares of stock. Find thedividends per share.
4. TRANSPORTATION When Denise boughtgasoline, she paid $18.48 for 11.2gallons. Find the price of gasoline pergallon.
5. WATER FLOW Jacob filled his 60-gallonbathtub in 5 minutes. How fast was thewater flowing?
6. TRAVEL On her vacation, Charmaine’sflight lasted 4.5 hours. She traveled954 miles. Find the average speed ofthe plane.
7. HOUSING Mr. And Mrs. Romero boughta 1,200 square-foot house for $111,600.How much did they pay per squarefoot?
8. SHOPPING A breakfast cereal comes intwo different sized packages. The8-ounce box costs $2.88, while the12-ounce box costs $3.60. Which box isthe better buy? Explain your reasoning.
© Glencoe/McGraw-Hill 188 Mathematics: Applications and Concepts, Course 3
Pre-Activity Read the introduction at the top of page 156 in your textbook.Write your answers below.
1. Which combination of ingredients would you use to make a smalleramount of the same recipe? Explain.
2. In order to make the same recipe of trail mix, how many scoops ofpeanuts should you use for every scoop of raisins?
Reading the Lesson3. What does it mean if the ratio of red marbles to blue marbles is 3 to 5?
4. What is another way to write the ratio 3 to 5?
5. What must you do before you can simplify the ratio 30 minutes to 8 hours? What is the simplified ratio?
Helping You Remember6. When you go to a bank to exchange money of one currency for another,
the bank uses a conversion rate to calculate the amount of money in thenew currency. Find out what the current conversion rate is to exchangeU.S. dollars to Canadian dollars at a local bank. Then write the rate as aratio of one currency compared to the other.
NAME ________________________________________ DATE ______________ PERIOD _____
Reading to Learn MathematicsRatios and Rates
© Glencoe/McGraw-Hill 189 Mathematics: Applications and Concepts, Course 3
Bargain HuntingRates are useful and meaningful when expressed as a unit rate.For example, which is the better buy—one orange for $0.29 or12 oranges for $3.00?
To find the unit rate for 12 oranges, divide $3.00 by 12. Theresult is $0.25 per orange. If a shopper needs to buy at least12 oranges, then 12 oranges for $3.00 is the better buy.
For each exercise below, rates are given in Column A and Column B. In the blank next to each exercise number, write the letter of the column that contains the better buy.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
OR
ANG
ES
EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____
Less
on
4–1
Column A Column B
1 apple for $0.19 3 apples for $0.59
20 pounds of pet food for $14.99 50 pounds of pet food for $37.99
A car that travels 308 miles on11 gallons of gasoline
A car that travels 406 miles on14 gallons of gasoline
10 floppy discs for $8.99 25 floppy discs for $19.75
1-gallon can of paint for $13.99 5-gallon bucket of paint for$67.45
84 ounces of liquid detergentfor $10.64
48 ounces of liquid detergentfor $6.19
5,000 square feet of lawn foodfor $11.99
12,500 square feet of lawn foodfor $29.99
2 compact discs for $26.50 3 compact discs for $40.00
8 pencils for $0.99 12 pencils for $1.49
1,000 sheets of computer paperfor $8.95
5,000 sheets of computer paperfor $41.99
© Glencoe/McGraw-Hill 190 Mathematics: Applications and Concepts, Course 3
INCOME The graph shows Mr. Jackson’s annual income between 1994 and 2002.Find the rate of change in Mr. Jackson’s income between 1994 and 1997.
Use the formula for the rate of change.Let (x1, y1) � (1994, 48,500) and (x2, y2) � (1997, 53,000).
�yx
2
2
––
yx
1
1� ��
531,090907
��
4189,95400
� Write the formula for rate of change.
� �4,5
300� Simplify.
� �1,5
100� Express this rate as a unit rate.
Between 1994 and 1997, Mr. Jackson’s income increased an average of $1,500 per year.
SURF For Exercises 1–3, use the graph that shows the average daily wave height as measured by an ocean buoy over a nine-day period.
1. Find the rate of change in the average daily wave height between day 1 and day 3.
2. Find the rate of change in the average daily wave height between day 3 and day 7.
3. Find the rate of change in the average daily wave height between day 7 and day 9.
y
x
Days
7
9
11
13
15
1 3 5 7 9
Day
Wave Height
(7, 14)
(9, 11)
(3, 12)
(1, 8)
0
'94 '96 '98 '00 '02
50,000
45,000
55,000
60,000
65,000
Annu
al In
com
e ($
)
Year
Mr. Jackson's Income
y
x
1994, 48,500
2002, 57,000
1997, 53,000
0
To find the rate of change between two data points, divide the difference of the y-coordinates by the
difference of the x-coordinates. The rate of change between (x1, y1) and (x2, y2) is �xy
2
2�
� yx
1
1�.
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionRate of Change
© Glencoe/McGraw-Hill 191 Mathematics: Applications and Concepts, Course 3
TEMPERATURE Use the table below that shows the high temperature ofa city for the first part of August.
1. Find the rate of change in the high temperature between August 1 andAugust 5.
2. Find the rate of change in the high temperature between August 5 andAugust 14.
3. During which of these two time periods did the high temperature risefaster?
4. Find the rate of change in the high temperature between August 14 andAugust 15. Then interpret its meaning.
COMPANY GROWTH Use the graph that shows the number of employees at a company between 1994 and 2002.
5. Find the rate of change in the number of employees between 1994 and 1996.
6. Find the rate of change in the number of employees between 1996 and 1999.
7. During which of these two time periods did the number of employees grow faster?
8. Find the rate of change in the number of employees between 1999 and 2002. Then interpret its meaning.
y
x
Num
ber o
f Em
ploy
ees
10
20
30
40
50
01994 1996 1998 2000 2002
Year
Company Growth
(1999, 41)
(2002, 38)(1996, 32)
(1994, 18)
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: SkillsRate of Change
Less
on
4–2
Date 1 5 14 15
High Temperature (ºF) 85 93 102 102
© Glencoe/McGraw-Hill 192 Mathematics: Applications and Concepts, Course 3
ELECTIONS For Exercises 1–3, use the table that shows the total numberof people who had voted in District 5 at various times on election day.
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word ProblemsRate of Change
1. Find the rate of change in the numberof voters between 8:00 A.M. and10:00 A.M. Then interpret its meaning.
2. Find the rate of change in the numberof voters between 10:00 A.M. and1:00 P.M. Then interpret its meaning.
3. During which of these two time periodsdid the number of people who hadvoted so far increase faster? Explainyour reasoning.
4. MUSIC At the end of 1999, Candace had47 CDs in her music collection. At theend of 2002, she had 134 CDs. Find therate of change in the number of CDs inCandace’s collection between 1999 and2002.
5. FITNESS In 1992, the price of an annualmembership at Mr. Jensen’s health clubwas $225. In 2002, the price of thesame membership was $319.50. Findthe rate of change in the price of theannual membership between 1992 and2002.
6. HIKING Last Saturday Fumio and Kishiwent hiking in the mountains. Whenthey started back at 2:00 P.M., theirelevation was 3,560 feet above sealevel. At 6:00 P.M., their elevation was2,390 feet. Find the rate of change oftheir elevation between 2:00 P.M. and6:00 P.M. Then interpret its meaning.
Time 8:00 A.M. 10:00 A.M. 1:00 P.M. 4:30 P.M. 7:00 P.M.
Number of Voters 141 351 798 1,008 1,753
Less
on
4–2
Pre-Activity Read the introduction at the top of page 160 in your textbook.Write your answers below.
1. By how many bears did Alicia’s collection increase between 1997 and1999? Between 1999 and 2002?
2. Between which years did Alicia’s collection increase the fastest?
Reading the Lesson3. What does a rate of change measure on a graph?
4. On a graph, what does it mean when a rate of change is negative?
5. Complete the sentence: When a quantity does not change over a period oftime, it is said to have a __________ rate of change.
Helping You Remember6. Write out in words the formula for finding a rate of change between two
data points (x1, y1) and (x2, y2).
Reading to Learn MathematicsRate of Change
© Glencoe/McGraw-Hill 193 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
© Glencoe/McGraw-Hill 194 Mathematics: Applications and Concepts, Course 3
Analyzing GraphsA graph can be used to represent many real-life situations. Graphs such asthese often have time as the dimension on the horizontal axis. By analyzingthe rate of change of different parts of a graph, you can draw conclusionsabout what was happening in the real-life situation at that time.
TRAVEL The graph at the right represents the speedof a car as it travels along the road. Describe whatis happening in the graph.
• At the origin, the car is stopped.
• Where the line shows a fast, positive rate ofchange, the car is speeding up.
• Then the car is going at a constant speed,shown by the horizontal part of the graph.
• The car is slowing down where the graphshows a negative rate of change.
• The car stops and stays still for a short time. Then it speeds up again.The starting and stopping process repeats continually.
Analyze each graph.
1. Ashley is riding her bicycle along a scenic trail.Describe what is happening in the graph.
2. The graph shows the depth of water in a pond as youtravel out from the shore. Describe what is happening in the graph.
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
car is acceleratingmaintaining speed
car is slowing downcar is stopped
Spee
d (
mp
h)
Time (min)0
Spee
d (
ft/s
)
Time (min)0
Dep
th (
ft)
Distance from Shore (ft)0
Less
on
4–3
Study Guide and InterventionSlope
© Glencoe/McGraw-Hill 195 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
Find the slope of the line in the graph.
Choose two points on the line. The vertical change from pointA to point B is 4 units while the horizontal change is 2 units.
slope � �rriusne
� Definition of slope
� �42� The rise is 4, and the run is 2.
� 2 Simplify.
The slope of the line is 2.
The points in the table lie on a line. Find the slope of the line.
slope � �rriusne
� �cchhaannggee
iinn
yx
�
� ��34� or ��
43�
The slope of the line is ��43�.
Find the slope of each line.
1. 2. 3.
The points given in each table lie on a line. Find the slope of the line.
4. 5.
y
xO
y
xO
y
xO
The slope of a line is the ratio of the rise, or vertical change, to the run, or horizontal change.
y
xO
rise: 4
run: 2
B
A
x �2 1 4 7
y 5 1 �3 �7
� � �
� � �� 3
x �5 0 5 10
y 4 3 2 1
x 3 5 7 9
y �1 2 5 8
� 3 � 3
� 4 � 4 � 4
←←
Practice: SkillsSlope
© Glencoe/McGraw-Hill 196 Mathematics: Applications and Concepts, Course 3
Find the slope of each line.
1. 2. 3.
4. 5. 6.
The points given in each table lie on a line. Find the slope of the line.Then graph the line.
7. 8. 9.
10. 11. 12.
y
xO
y
xO O
y
xO
y
xO
y
xO
y
xO
y
xO
y
xO
y
xO
y
xO
y
xO
y
xO
NAME ________________________________________ DATE ______________ PERIOD _____
x �4 �2 0 2
y 3 3 3 3
x �7 �5 �3 �1
y �6 �3 0 3
x �8 �4 0 4
y 8 5 2 �1
x �2 �1 0 1
y 2 1 0 �1
x 1 3 5 7
y 6 5 4 3
x 0 3 6 9
y 1 2 3 4
Less
on
4–3
Practice: Word ProblemsSlope
© Glencoe/McGraw-Hill 197 Mathematics: Applications and Concepts, Course 3
FLOWERS For Exercises 1 and 2, use LONG DISTANCE For Exercises 3–6, use the graph that shows the depth of the the graph that compares the costs of water in a vase of flowers over 8 days. long distance phone calls with three
different companies.
NAME ________________________________________ DATE ______________ PERIOD _____
y
x0
1
1 2 3 4 5 6 7 8 9 10
23456789
10
Depth of Water in Vase
Dept
h (in
.)
Day
1. Find the slope of the line. 2. Interpret the meaning this slope as a
rate of change.
y
x0 1 2 3 4 5 6 7 8 9
0.50
1.00
1.50
2.00
2.50
Long Distance Charges
Cost
($)
Length of Call (minutes)
Company A
Company B
Company C
3. Find the slope of the line for CompanyA. Then interpret this slope as a rate ofchange.
4. Find the slope of the line for Company B. Then interpret this slope as a rate of change.
5. Find the slope of the line for CompanyC. Then interpret this slope as a rate ofchange.
6. Which company charges the least foreach additional minute? Explain yourreasoning.
Pre-Activity Read the introduction at the top of page 166 in your textbook.Write your answers below.
1. Pick several pairs of points from those plotted and find the rate of changebetween them. Write each rate in simplest form.
2. What is true of these rates?
Reading the Lesson3. Slope can be positive, negative, or zero. For each one of these possibilities
draw an example of a line with that kind of slope.
Helping You Remember4. The slope of a line is defined by the rise compared to the run between any
two points on the line. Think about the words rise and run. How can youremember which word represents vertical change and which wordrepresents horizontal change?
y
xO
y
xO
y
xO
Reading to Learn MathematicsSlope
© Glencoe/McGraw-Hill 198 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
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© Glencoe/McGraw-Hill 199 Mathematics: Applications and Concepts, Course 3
Chien-Shiung WuAmerican physicist Chien-Shiung Wu (1912–1997) was born in Shanghai, China. In 1936, she came to the United States to further her studies in science. She received her doctorate in physics in 1940 from the University of California, and became known as one of the world’s leading physicists. In 1975, she was awarded the National Medal of Science.
Wu is most famous for an experiment that she conducted in 1957. The outcome of the experiment was considered the most significant discovery in physics in more than seventy years. The exercise below will help you learn some facts about it.
The points given in each table lie on a line. Find the slope of the line.The word or phrase following the solution will complete thestatement correctly.
1. 2.
At the time of the experiment, Wu The site of the experiment was the was a professor at . in Washington, D.C.slope � 3: Columbia University slope � 0: National Bureau of Standardsslope � 1: Stanford University slope � 3: Smithsonian Institution
3. 4.
The experiment involved a substance In the experiment, the substance wascalled . cooled to .
slope � 2: carbon 14 slope � �43�: �273�C
slope � 1: cobalt 60 slope � �34�: �100°C
??
??
EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____
x �2 1 4 7
y �3 1 5 9
x 0 2 4 6
y 2 4 6 8
x �2 �1 0 1
y 3 3 3 3
x 0 1 2 3
y 1 4 7 10
Study Guide and InterventionSolving Proportions
© Glencoe/McGraw-Hill 200 Mathematics: Applications and Concepts, Course 3
Determine whether the pair of ratios �2204� and �
1128� forms a proportion.
Find the cross products.
Since the cross products are not equal, the ratios do not form a proportion.
Solve �1320� � �7
k0�.
�1320�
� �7k0�
Write the equation.
12 � 70 � 30 � k Find the cross products.
840 � 30k Multiply.
�83400
� � �3300k
� Divide each side by 30.
28 � k Simplify. The solution is 28.
Determine whether each pair of ratios forms a proportion.
1. �1170�
, �152� 2. �
69�, �
1128�
3. �182�
, �1105�
4. �175�
, �1332�
5. �79�, �
4693�
6. �284�
, �1228�
7. �47�, �
1721�
8. �2305�
, �3405�
9. �1284�
, �34�
Solve each proportion.
10. �5x
� � �1255�
11. �34� � �
1c2� 12. �
69� � �
1r0�
13. �1264�
� �1z5�
14. �58� � �1
s2�
15. �1t4� � �
1101�
16. �w6� � �
27.8� 17. �
5y� � �16
7.8� 18. �1
x8�
� �376�
2024
1218
�→ 24 · 12 � 288→ 20 · 18 � 360
NAME ________________________________________ DATE ______________ PERIOD _____
A proportion is an equation that states that two ratios are equivalent. To determine whether a pair ofratios forms a proportion, use cross products. You can also use cross products to solve proportions.
Practice: SkillsSolving Proportions
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© Glencoe/McGraw-Hill 201 Mathematics: Applications and Concepts, Course 3
Determine whether each pair of ratios forms a proportion.
1. �58�, �
23� 2. �
73�, �
164� 3. �
68�, �1
92�
4. �196�, �
161� 5. �
5150�
, �122� 6. �
68�, �
1250�
7. �59�, �
1257�
8. �138�
, �1616�
9. �171�
, �1253�
10. �193�
, �1137�
11. �432�
, �750�
12. �67�, �
3469�
Solve each proportion.
13. �142�
� �9y
� 14. �168�
� �4c� 15. �
7z� � �
8142�
16. �150�
� �w8
� 17. �9x
� � �145�
18. �260�
� �5y
�
19. �59� � �
6r� 20. �n
8� � �
170� 21. �
d5� � �
1820�
22. �5y
� � �1130�
23. �228�
� �3p5�
24. �1t1� � �
11010
�
25. �1m.2� � �
35� 26. �
01..95�
� �1a0�
27. �37� � �4
k.2�
28. �6x.3� � �
158� 29. �
39.6� � �0
b.5�
30. �11.45�
� �4y.2�
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word ProblemsSolving Proportions
© Glencoe/McGraw-Hill 202 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
1. USAGE A 12-ounce bottle of shampoolasts Enrique 16 weeks. How longwould you expect an 18-ounce bottleof the same brand to last him?
2. COMPUTERS About 13 out of 20 homeshave a personal computer. On a streetwith 60 homes, how many would youexpect to have a personal computer?
3. SNACKS A 6-ounce package of fruitsnacks contains 45 pieces. How manypieces would you expect in a 10-ouncepackage?
4. TYPING Ingrid types 3 pages in thesame amount of time that Tanya types4.5 pages. If Ingrid and Tanya starttyping at the same time, how manypages will Tanya have typed whenIngrid has typed 11 pages?
5. SCHOOL A grading machine can grade48 multiple-choice tests in 1 minute.How long will it take the machine tograde 300 tests?
6. AMUSEMENT PARKS The waiting time toride a roller coaster is 20 minutes when150 people are in line. How long is thewaiting time when 240 people are inline?
7. PRODUCTION A shop produces 39wetsuits every 2 weeks. How long willit take the shop to produce 429wetsuits?
8. FISH Of the 50 fish that Jim caughtfrom the lake, 14 were trout. Theestimated population of the lake is7,500 fish. About how many troutwould you expect to be in the lake?
Reading to Learn MathematicsSolving Proportions
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Pre-Activity Read the introduction at the top of page 170 in your textbook.Write your answers below.
1. Write a ratio that compares the number of Calories from fat to the totalnumber of Calories. Write the ratio as a fraction in simplest form.
2. Suppose you plan to eat two such granola bars. Write a ratio comparingthe number of Calories from fat to the total number of Calories.
3. Is the ratio of Calories the same for two granola bars as it is for onegranola bar? Why or why not?
Reading the Lesson4. Complete the sentence: If two ratios form a proportion, then the ratios
are said to be __________.
5. Do the ratios �ab� and �d
c� always form a proportion? Why or why not?
6. Explain how you can use cross products to solve proportions in which oneof the terms is not known.
Helping You Remember7. For the proportion �
ab� and �d
c�, why do you think the products ad and bc are
called cross products?
© Glencoe/McGraw-Hill 203 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
© Glencoe/McGraw-Hill 204 Mathematics: Applications and Concepts, Course 3
People of the United StatesA national census is taken every ten years. The 1990 census revealed thatthere were about 250,000,000 people in the United States, and that about 8 out of 100 of these people were 5–13 years old. To find the number ofpeople in the United States that were 5–13 years old, use the ratio ofpeople 5–13 years old and create a proportion.
�1800�
� �250,0n00,000�
To solve the proportion, find cross products.
8 � 250,000,000 � 2,000,000,000 and n � 100 � 100n
Then divide: 2,000,000,000 100 � 20,000,000.
In 1990, about 20,000,000 people in the United States were 5–13 years old.
Use the approximate ratios in each exercise to create a proportion,given that there were about 250,000,000 people in the United States.Then solve and choose the correct answer from the choices at the right.
1. The United States is a diverse collection of different ________ A. 200,000,000races and ethnic origins. Asians or Pacific Islandersaccounted for about �1
300�
of the population of theUnited States. About how many people of Asian orPacific-Island origin lived in the United States?
2. African-Americans accounted for about �235�
of the ________ B. 22,500,000population of the United States. About how manyAfrican-American people lived in the United States?
3. People of Hispanic origin accounted for about �1900�
________ C. 7,500,000of the population of the United States. About howmany people of Hispanic origin lived in theUnited States?
4. Caucasian people accounted for about �45� of the ________ D. 2,000,000
population of the United States. About how manypeople of white or Caucasian origin lived in theUnited States?
5. People of American-Indian, Eskimo, or Aluet origin ______ E. 30,000,000
accounted for about �1,0800� of the population of the
United States. About how many people of
American-Indian, Eskimo, or Aluet origin lived in
the United States?
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
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Study Guide and InterventionSimilar Polygons
© Glencoe/McGraw-Hill 205 Mathematics: Applications and Concepts, Course 3
Determine whether �ABC is similar to �DEF. Explain your reasoning.
�A � �D, �B � �E, �C � �F,
�DAB
E�� �
46� or �
23�, �
BE
CF�
� �69� or �
23�, �D
ACF�
� �182�
or �23�
The corresponding angles are congruent, and the corresponding sides are proportional.
Thus, �ABC is similar to �DEF.
Given that polygon KLMN � polygon PQRS, write a proportion tofind the measure of P�Q�. Then solve.
The ratio of corresponding sides from polygon KLMN topolygon PQRS is �
43�. Write a proportion with this scale
factor. Let x represent the measure of P�Q�.
�PK
QL� � �
43� K�L� corresponds to P�Q�. The scale factor is �
43
�.
�5x� � �
43� KL � 5 and PQ � x
5 � 3 � x � 4 Find the cross products.
�145� � �
44x� Multiply. Then divide each side by 4.
3.75 � x Simplify.
1. Determine whether the polygons 2. The triangles below are similar. Write abelow are similar. Explain your proportion to find each missing measure.reasoning. Then solve.
12
6 4
815x11
5
124
Kx
3
5
N
LP Q
S RM
4
B
8
E
CA D F
646
12
9
NAME ________________________________________ DATE ______________ PERIOD _____
Two polygons are similar if their corresponding angles are congruent and their corresponding sidesare proportional.
© Glencoe/McGraw-Hill 206 Mathematics: Applications and Concepts, Course 3
Determine whether each pair of polygons is similar. Explain yourreasoning.
1. 2.
3. 4.
5. 6.
7. 8.
x
6
9.6
14
22.4
9.6
6
10
6 6.5
1.5
3.63.9
x
x
1.8
2.6
6.5
8 8
2.6
44
x
6 7
7
3
3.53.520
8
14
10
74
151
101
150
100
15
8
10
12
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: SkillsSimilar Polygons
Practice: Word ProblemsSimilar Polygons
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© Glencoe/McGraw-Hill 207 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
1. JOURNALISM The editor of the schoolnewspaper must reduce the size of agraph to fit in one column. The originalgraph is 2 inches by 2 inches, and thescale factor from the original to thereduced graph is 8:3. Find thedimensions of the graph as it willappear in one column of the newspaper.
2. PHOTOCOPIES Lydia plans to use aphotocopy machine to increase the sizeof a small chart that she has made aspart of her science project. The originalchart is 4 inches by 5 inches. If sheuses a scale factor of 5:11, will thechart fit on a sheet of paper 8�
12� inches
by 11 inches? Explain.
No; it will be 8�45
� in. by 11 in.
3. MICROCHIPS The image of a microchipin a projection microscope measures 8inches by 10 inches. The width of theactual chip is 4 millimeters. How longis the chip?
4. PROJECTIONS A drawing on atransparency is 11.25 centimeters wideby 23.5 centimeters tall. The width ofthe image of drawing projected onto ascreen is 2.7 meters. How tall is thedrawing on the screen?
5. GEOMETRY Polygon ABCD is similar topolygon FGHI. Each side of polygonABCD is 3�
14� times longer than the
corresponding side of polygon FGHI.Find the perimeter of polygon FGHI.
6. KITES A toy company produces twokites whose shapes are geometricallysimilar. Find the length of the missingside of the smaller kite.
25 in.25 in.
30 in.22.5 in.
30 in.xB
A
D
I
H
F
G
C
3 in.
2 in.
5 in.
3 in.
Pre-Activity Complete the Mini Lab at the top of page 178 in your textbook.Write your answers below.
1. Compare the angles of the triangles by matching them up. Identify theangle pairs that have equal measure.
2. Express the ratios �DLK
F�, �
EJK
F�, and �
DL
EJ�
to the nearest tenth.
3. What do you notice about the ratios of the matching sides of matchingtriangles?
Reading the Lesson4. Complete the sentence: If two polygons are similar, then their
corresponding angles are __________, and their corresponding sides are__________.
5. If two polygons have corresponding angles that are congruent, does thatmean that the polygons are similar? Why or why not?
6. If the sides of one square are 3 centimeters and the sides of anothersquare are 9 centimeters, what is the ratio of corresponding sides from the first square to the second square?
Helping You Remember7. Look up the everyday definition of the word similar in a dictionary. How
does the definition relate to what you learned in this lesson?
Reading to Learn MathematicsSimilar Polygons
© Glencoe/McGraw-Hill 208 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
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4–5
© Glencoe/McGraw-Hill 209 Mathematics: Applications and Concepts, Course 3
Similar and Congruent FiguresIf a 4-inch by 5-inch photograph is enlarged to an 8-inch by 10-inchphotograph, the photographs are said to be similar. They have the sameshape, but they do not have the same size. If a 4-inch by 5-inch photographis duplicated and a new 4-inch by 5-inch photograph is made, thephotographs are said to be congruent. They have the same size and shape.
In each exercise, identify which of the triangles are congruent toeach other and identify which of the shapes are similar to each other.Use the symbol for � congruence and the symbol � for similarity.
1. 2.
3. 4.
5.
EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____
a
b
cd
f
a
bc
d
AB
C
DJ L
H NK M
A B C D
H K LM N
P
Q
R T
AB
T
C
D
Q
G
HJ
LKM
NP
Study Guide and InterventionScale Drawings and Models
© Glencoe/McGraw-Hill 210 Mathematics: Applications and Concepts, Course 3
INTERIOR DESIGN A designer has made ascale drawing of a living room for oneof her clients. The scale of the drawingis 1 inch � 1�
13� feet. On the drawing, the
sofa is 6 inches long. Find the actuallength of the sofa.
Let x represent the actual length of the sofa. Write and solve a proportion.
The actual length of the sofa is 8 feet.
Find the scale factor for the drawing in Example 1.
Write the ratio of 1 inch to 1�13� feet in simplest form.
� �116
iinn.�.�� Convert 1�
13
� feet to inches.
The scale factor is �116�
or 1:16. This means that each distance on the drawing is �116�
theactual distance.
LANDSCAPING Yutaka has made a scale drawingof his yard. The scale of the drawing is1 centimeter = 0.5 meter.
1. The length of the patio is 4.5 centimeters in thedrawing. Find the actual length.
2. The actual distance between the water faucet andthe pear tree is 11.2 meters. Find the correspondingdistance on the drawing.
3. Find the scale factor for the drawing.
1 in.�1�
13� ft
To find the scale factor for scale drawings and models, write the ratio given by the scale in simplestform.
1 in. 6 in.
1 ft13
x ft�
1 · x � 1 · 613
x � 8
drawing distance → actual distance →
← drawing length← actual length
Find the cross products.
Simplify.
↓ ↓Drawing Scale Actual Length
NAME ________________________________________ DATE ______________ PERIOD _____
1 in. = 1 ft
Sofa
13
1 cm = 0.5 m
Patio
PondPath
Water Faucet
PearTree
Garden
Distances on a scale drawing or model are proportional to real-life distances. The scale is determinedby the ratio of a given length on a drawing or model to its corresponding actual length.
Practice: SkillsScale Drawings and Models
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© Glencoe/McGraw-Hill 211 Mathematics: Applications and Concepts, Course 3
ARCHITECTURE The scale on a set of architectural drawings for a houseis 1.5 inches � 2 feet. Find the length of each part of the house.
7. What is the scale factor of these drawings?
TOWN PLANNING For Exercises 8–11, use the following information.
As part of a downtown renewal project, businesses have constructeda scale model of the town square to present to the city commissionfor its approval. The scale of the model is 1 inch � 7 feet.
8. The courthouse is the tallest building in the town square. If it is
5�12� inches tall in the model, how tall is the actual building?
9. The business owners would like to install new lampposts that areeach 12 feet tall. How tall are the lampposts in the model?
10. In the model, the lampposts are 3�37� inches apart. How far apart
will they be when they are installed?
11. What is the scale factor?
12. MAPS On a map, two cities are 6�12� inches apart. The actual distance
between the cities is 104 miles. What is the scale of the map?
NAME ________________________________________ DATE ______________ PERIOD _____
Room Drawing Length Actual Length
1. Living Room 15 inches
2. Dining Room 10.5 inches
3. Kitchen 12�34� inches
4. Laundry Room 8�14� inches
5. Hall 13�78� inches
6. Garage 16.5 inches
Practice: Word ProblemsScale Drawings and Models
© Glencoe/McGraw-Hill 212 Mathematics: Applications and Concepts, Course 3
CAMPUS PLANNING For Exercises 1–3, use thefollowing information.
The local school district has made a scale modelof the campus of Engels Middle School includinga proposed new building. The scale of the modelis 1 inch � 3 feet.
NAME ________________________________________ DATE ______________ PERIOD _____
1. An existing gymnasium is 8 inches tallin the model. How tall is the actualgymnasium?
2. The new building is 22.5 inches fromthe gymnasium in the model. Whatwill be the actual distance from thegymnasium to the new building if itis built?
3. What is the scale factor of the model? 4. MAPS On a map, two cities are 5�34�
inches apart. The scale of the map is�12� inch � 3 miles. What is the actualdistance between the towns?
34�12
� mi
5. TRUCKS The bed of Jerry’s pickup truckis 6 feet long. On a scale model of thetruck, the bed is 8 inches long. What isthe scale of the model?
6 ft
6. HOUSING Marta is making a scaledrawing of her apartment for a schoolproject. The apartment is 28 feet wide.On her drawing, the apartment is 7 inches wide. What is the scale ofMarta’s drawing?
28 ft
Gym
nasi
um
Park
ing
AcademicBuilding
View of Campus from Above
NewBuilding
Pre-Activity Read the introduction at the top of page 184 in your textbook.Write your answers below.
1. How many units wide is the room?
2. The actual width of the room is 18 feet. Write a ratio comparing thedrawing width to the actual width.
3. Simplify the ratio you found and compare it to the scale shown at thebottom of the drawing.
Reading the Lesson4. Give another example of a scale drawing or scale model that is different
from the examples of scale drawings and scale models given on pages184–185 in your textbook.
5. Complete the sentence: distances on a scale model are __________ todistances in real life.
6. What is the scale factor for a model if part of the model that is 4 inchescorresponds to a real-life object that is 16 inches?
Helping You Remember7. Make a scale drawing of a room, such as your classroom or your bedroom.
Select an appropriate scale so that your drawing is a reasonable size. Besure to indicate your scale on your drawing. Use another piece of paper ifnecessary.
Reading to Learn MathematicsScale Drawings and Models
Less
on
4–6
© Glencoe/McGraw-Hill 213 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
© Glencoe/McGraw-Hill 214 Mathematics: Applications and Concepts, Course 3
Scale DrawingsThe figure at the right has an area of 6 square units. If the figurerepresented a map, and was drawn to a scale of 1 unit � 3 feet, thelengths of the sides would be 6 ft and 9 ft. So, the figure wouldrepresent an area of 54 square feet.
The ratio of the actual area of the figure to the scale area of thefigure can be expressed as a ratio.
�ascctaulaelaarreeaa
� � �564�
� �19� or 1 to 9
Find the actual area and the scale area of these figures. Thendetermine the ratio of actual area to scale area.
1. Scale: 1 unit � 4 ft 2. Scale: 1 unit � 50 cm
actual area actual area
scale area scale area
ratio ratio
3. Scale: 1 unit � 8 mi 4. Scale: 1 unit � 12 m
actual area actual area
scale area scale area
ratio ratio
5. Scale: 1 unit � 18 in. 6. Scale: 1 unit � 6 km
actual area actual area
scale area scale area
ratio ratio
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
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© Glencoe/McGraw-Hill 215 Mathematics: Applications and Concepts, Course 3
LIGHTING George is standing next to alightpole in the middle of the day. George’s shadow is 1.5 feet long, and the lightpole’s shadow is 4.5 feet long. If George is 6 feet tall, how tall is the lightpole?
Write a proportion and solve.
George’s shadow → 1.5 6 George’s height
lightpole’s shadow → 4.5 h lightpole’s height
1.5 � h � 4.5 � 6 Find the cross products.
1.5h � 27 Multiply.
�11.5.5h
� � �12.75�
Divide each side by 1.5.
h � 18 Simplify.
The lightpole is 18 feet tall.
1. MONUMENTS A statue casts a shadow 30 feet long. At the same time, a person who is 5 feet tall casts a shadow that is 6 feet long. How tall is the statue?
2. BUILDINGS A building casts a shadow 72 meters long. At the same time, a perking meter that is 1.2 meters tall casts a shadow that is 0.8 meter long. How tall is the building?
3. SURVEYING The two triangles shown in the figure are similar. Find the distance d across Red River. 1 m
.9 m
1.8 m
Red River
d
h ft
72 m
1.2 m
0.8 m
h ft
30 ft
5 ft
6 ft
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionIndirect Measurement
Distances or lengths that are difficult to measure directly can sometimes be found using the propertiesof similar polygons and proportions. This kind of measurement is called indirect measurement.
h ft
6 ft
4 ft12 1 ft1
2
→→
�
Practice: SkillsIndirect Measurement
© Glencoe/McGraw-Hill 216 Mathematics: Applications and Concepts, Course 3
Write a proportion and solve the problem.
1. HEIGHT How tall is Becky? 2. FLAGS How tall is the flagpole?
3. BEACH How deep is the water 4. ACCESSIBILITY How high is the ramp50 feet from shore? when it is 2 feet from the building?
(Hint: �ABE � �ACD)
5. AMUSEMENT PARKS The triangles in 6. CLASS CHANGES The triangles in the figurethe figure are similar. How far is the are similar. How far is the entrance towater ride from the roller coaster? the gymnasium from the band room?Round to the nearest tenth.
45 m
Information Booth
Water Ride
Ferris Wheel
Roller Coaster
Park Entrance21 m10 m
d m
30 m
25 m
Tennis Court
Band Room
Gymnasium
Cafeteria
Fountain
32 m
d m
2 ft
h ftA
BC
DE20 ft
2.5 fth ft
50 ft8 ft
1 ft
9 ft
h ft
6 ft12
31 ft12
7 ft
3 fth ft
4 ft
NAME ________________________________________ DATE ______________ PERIOD _____
© Glencoe/McGraw-Hill 217 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
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Practice: Word ProblemsIndirect Measurement
Less
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4–7
1. HEIGHT Paco is 6 feet tall and casts a12-foot shadow. At the same time,Diane casts an 11-foot shadow. How tallis Diane?
2. LIGHTING If a 25-foot-tall house casts a75-foot shadow at the same time that astreetlight casts a 60-foot shadow, howtall is the streetlight?
3. FLAGPOLE Lena is 5�12� feet tall and casts
an 8-foot shadow. At the same time, aflagpole casts a 48-foot shadow. Howtall is the flagpole?
4. LANDMARKS A woman who is 5 feet5 inches tall is standing near the Space Needle in Seattle, Washington;she casts a 13-inch shadow at the sametime that the Space Needle casts a121-foot shadow. How tall is the SpaceNeedle?
5. NATIONAL MONUMENTS A 42-footflagpole near the WashingtonMonument casts a shadow that is14 feet long. At the same time, theWashington Monument casts a shadowthat is 185 feet long. How tall is theWashington Monument?
6. ACCESSIBILITY A ramp slopes upwardfrom the sidewalk to the entrance of abuilding at a constant incline. If theramp is 2 feet high when it is 5 feetfrom the sidewalk, how high is theramp when it is 7 feet from thesidewalk?
5 ft
2 ft
© Glencoe/McGraw-Hill 218 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
Pre-Activity Read the introduction at the top of page 188 in your textbook.Write your answers below.
1. How is the caveman measuring the distance to the Sun?
Reading the Lesson2. Complete the following sentence.
When you solve a problem using shadow reckoning, the objects beingcompared and their shadows form two sides of _______________.
3. Suppose that you are standing near a building and you see the shadowscast by you and the building. If you know the length of each of theseshadows and you know how tall you are, write a proportion in words thatyou can use to find the height of the building.
4. STATUE If a statue casts a 6-foot shadow and a 5-foot mailbox casts a4-foot shadow, how tall is the statue?
Helping You Remember5. Work with a partner. Have your partner draw two triangles that are
similar with the lengths of two corresponding sides labeled and thelength of one additional side labeled. Tell your partner how to write aproportion to solve for the length of the side corresponding to theadditional side labeled.
Reading to Learn MathematicsIndirect Measurement
© Glencoe/McGraw-Hill 219 Mathematics: Applications and Concepts, Course 3
Indirect MeasurementA proportion can be used to determine the heightof tall structures if three variables of the proportionare known. The three known variables are usuallythe height a of the observer, the length b of theobserver’s shadow, and the length d of thestructure’s shadow. However, a proportion can besolved given any three of the four variables.
This chart contains information about various observers and tallbuildings. Use proportions and your calculator to complete the chartof tall buildings of the world.
EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____
Less
on
X–1
Less
on
4–7
a
b
c
d
ab
cd
�
Height ofObserver
Length ofShadow
BuildingLocation
Height ofBuilding
Length ofShadow
1. 5 ft 8 in. Natwest,London 80 ft
2. 4 ft 9 in. Columbia SeafirstCenter, Seattle 954 ft 318 ft
3. 5 ft 10 in. 14 in. Wachovia Building,Winston-Salem 410 ft
4. 15 in. Waterfront Towers,Honolulu 400 ft 83 ft 4 in.
5. 6 ft CN Tower,Toronto 1,821 ft 303 ft 6 in.
6. 5 ft 9 in. 1 ft 11 in. Gateway Arch,St. Louis 630 ft
7. 5 ft 3 in. 1 ft 9 in. Eiffel Tower,Paris 328 ft
8. 8 in. Texas CommerceTower, Houston 1,002 ft 167 ft
9. 5 ft 6 in. 11 in. John HancockTower, Boston 131 ft 8 in.
10. 5 ft 4 in. 8 in. Sears Tower,Chicago 181 ft 9 in.
11. 5 ft 6 in. Barnett Tower,Jacksonville 631 ft 105 ft 2 in.
© Glencoe/McGraw-Hill 220 Mathematics: Applications and Concepts, Course 3
Graph �ABC with vertices A(�2, �1),B(2, 3), and C(2, �1). Then graph its image �A�B�C�after a dilation with ascale factor of �
32�.
A(�2, �1) → ��2 � �32�, �1 � �
32�� → A��3, ��
32��
B(2, 3) → �2 � �32�, 3 � �
32�� → B�3, 4�
12��
C(2, �1) → �2 � �32�, �1 � �
32�� → C�3, ��
32��
Segment M�N� is a dilation of segment MN. Find the scale factor ofthe dilation and classify it as an enlargement or a reduction.
Write the ratio of the x- or y-coordinate of one vertex of thedilated figure to the x- or y-coordinate of the correspondingvertex of the original figure. Use the x-coordinates of N(1, �2)and N(2, �4).
� �21� or 2
The scale factor is 2. Since the image is larger than the originalfigure, the dilation is an enlargement.
1. Polygon ABCD has vertices A(2, 4), B(�1, 5), C(�3, �5), and
D(3, �4). Find the coordinates of its image after a dilation
with a scale factor of �12�. Then graph polygon ABCD and its
dilation.
2. Segment PQ is a dilation of segment PQ. Find the scale
factor of the dilation and classify it as an enlargement or a
reduction.
x-coordinate of point N���x-coordinate of point N
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionDilations
The image produced by enlarging or reducing a figure is called a dilation.
y
xO
y
xO
MM
N
N
y
xO
y
xO
PP
Q Q
© Glencoe/McGraw-Hill 221 Mathematics: Applications and Concepts, Course 3
Find the coordinates of the vertices of triangle A�B�C� after triangleABC is dilated using the given scale factor. Then graph triangle ABCand its dilation.
1. A(1, 1), B(1, 3), C(3, 1); scale factor 3 2. A(�2, �2), B(�1, 2), C(2, 1); scale factor 2
3. A(�4, 6), B(2, 6), C(0, 8); scale factor �12� 4. A(�3, �2), B(1, 2), C(2, �3); scale factor 1.5
Segment P�Q� is a dilation of segment PQ. Find the scale factor of the dilationand classify it as an enlargement or a reduction.
5. 6.
2;
7. 8.
NAME ________________________________________ DATE ______________ PERIOD _____
Less
on
X–2
Practice: SkillsDilations
Less
on
4–8
y
xO
y
xO
y
xO
y
xO
y
xO
P
Q
P
Q
y
xOP
Q
P
Q
y
xO
P
P
y
xO
PP
Q
Q
© Glencoe/McGraw-Hill 222 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Word ProblemsDilations
1. EYES Dave’s optometrist used medicineto dilate his eyes. Before dilation, hispupils had a diameter of 4.1millimeters. After dilation, his pupilshad a diameter of 8.2 millimeters.What was the scale factor of thedilation?
2. BIOLOGY A microscope increases thesize of objects by a factor of 8. Howlarge will a 0.006 millimeterparamecium appear?
3. PHOTOGRAPHY A photograph wasenlarged to a width of 15 inches. If thescale factor was �
32�, what was the width
of the original photograph?
4. MOVIES Film with a width of 35millimeters is projected onto a screenwhere the width is 5 meters. What isthe scale factor of this enlargement?
�1,0
700�
5. PHOTOCOPYING A 10-inch long copy ofa 2.5-inch long figure needs to be madewith a copying machine. What is theappropriate scale factor?
6. MODELS A scale model of a boat isgoing to be made using a scale of �5
10�
.If the original length of the boat is 20 meters, what is the length of themodel?
7. MODELS An architectural model is 30 inches tall. If the scale used to buildthe model is �1
120�
, what is the height ofthe actual building?
8. ADVERTISING An advertiser needs a4-inch picture of a 14-foot automobile.What is the scale factor of thereduction?
�412�
© Glencoe/McGraw-Hill 223 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
Less
on
X–2
Pre-Activity Complete the Mini Lab at the top of page 194 in your textbook.Write your answers below.
1. Multiply each coordinate by 2 to find the coordinates of points A, B,and C.
2. On the same coordinate plane, graph points A, B, and C. Then draw �ABC.
3. Determine whether �ABC � �ABC. Explain your reasoning.
Reading the Lesson4. If you are given the coordinates of a figure and the scale factor of a
dilation of that figure, how can you find the coordinates of the newfigure?
5. When you graph a figure and its image after a dilation, how can youcheck your work?
Helping You Remember6. Complete the table below to help you remember the effects of different
scale factors.
Reading to Learn MathematicsDilations
Less
on
4–8
If the scale factor is Then the dilation is
between 0 and 1
greater than 1
equal to 1
y
xO
© Glencoe/McGraw-Hill 224 Mathematics: Applications and Concepts, Course 3
Dilation and AreaA dilation of a shape creates a new shape that is similar to theoriginal. The ratio of the new image to the original is called thescale factor.
Plot and draw each shape. Then perform the dilation ofeach shape using a scale factor of two. After the new imagehas been drawn, determine the area of both the originalshape and its dilation.
1. A(2, 1), B(7, 1), C(4, 4)
Area of original ________
Area of dilation ________
2. circle with radius (1, 2) to (4, 2)
Area of original ________
Area of dilation ________
3. R(�3, 2), E(�3, �2), C(4, �2), I(4, 2) 4. S(�3, 3), Q(�3, �3), A(3, �3), R(3, 3)
Area of original ________ Area of original ________
Area of dilation ________ Area of dilation ________
5. What general statement can be made about the area of a figure whencompared to its area after being dilated by scale factor 2?
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
y
xO
Write the letter for the correct answer in the blank at the right of each question.
1. Express 4 inches:32 inches in simplest form.A. 8:1 B. 1:8 C. 2:16 D. 16:1 1.
2. Express 18 blue-eyed students to 20 brown-eyed students in simplest form.F. 3 to 4 G. 9 to 10 H. 4 to 5 I. 90 to 100 2.
3. Express 150 tickets for 30 students as a unit rate.
A. 5 tickets per student B. �15� ticket per student
C. 150 tickets per student D. �310�
ticket per student 3.
4. Express 12 miles in 5 hours as a unit rate.
F. �152�
mi/h G. 12 mi/h H. 2.4 mi/h I. 2 mi/h 4.
DANCE For Questions 5 and 6, use the table at the right that shows the number of boys at the school dance at different times.
5. Find the rate of change in the number of boys between 6:00 and 6:15.A. 50 boys/min B. 65 boys/min C. 15 boys/min D. 1 boy/min 5.
6. Find the rate of change in the number of boys between 6:15 and 6:18.F. 1 boy/min G. 2 boys/min H. 3 boys/min I. 6 boys/min 6.
7. Find the slope of the line of the graph at the right.
A. 2 B. �12�
C. �2 D. ��12� 7.
For Questions 8 and 9, the points given in each table lie on a line. Find the slope of the line.
8. F. 1 G. 4
H. �14� I. �4 8.
9. A. �23� B. ��
23�
C. �2 D. 3 9.
10. Which pair of ratios form a proportion?
F. �2115�
, �75� G. �1
90�
, �1101�
H. �56�, �
23� I. �1
47�
, �1270�
10.
11. Solve �29� � �3
b6�
.
A. 8 B. 4 C. 2 D. 7 11.
12. Solve �56� � �
1d1�.
F. 8�13� G. 12 H. 13.2 I. �6
56�
12.
y
xO
© Glencoe/McGraw-Hill 225 Mathematics: Applications and Concepts, Course 3
Chapter 4 Test, Form 1
Ass
essm
ent
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
x 0 3 6 9
y 5 3 1 �1
x �3 1 5 9
y �2 �1 0 1
Time 6:00 6:15 6:18 6:30 6:50
Number of Boys 50 65 71 90 87
13. Which pair of polygons is similar?A. B.
C. D. 13.
14. The triangles shown are similar.Find the missing measure.F. 18.75 G. 7.5H. 48 I. 12 14.
15. MAPS The scale on a map is 1 centimeter � 50 kilometers. Findthe actual distance for a map distance of 3 centimeters.A. 150 km B. 3 km C. 150 cm D. 3 cm 15.
16. MOVIES In a science fiction movie, the model of one of the aliens was12 inches tall. In the movie, the alien was seen as 6 feet tall. Whatwas the scale used?F. 2 in. � 1 ft G. 1 in. � 2 ft H. 1 in. � 6 ft I. 6 in. � 1 ft 16.
17. FLAGS A flagpole casts a 12-foot shadow. A bush next to it is 4 feet talland casts a 2-foot shadow. How tall is the flagpole?A. 24 ft B. 6 ft C. 12 ft D. 36 ft 17.
18. FORESTRY How tall is the tree?F. 15 ft G. 2.4 ftH. 60 ft I. 4.2 ft 18.
19. Triangle ABC has vertices A(�1, 0), B(�3, 4), and C(2, 3). Find the coordinates of vertex A after the triangle is dilated using a scale factor of 2.A. (�1, 2) B. (�2, 0) C. (0, �1) D. (1, 0) 19.
20. PROJECTIONS An image that is 10 inches wide on a transparency is30 inches wide when projected onto a screen. What is the scale factor?
F. 30 G. �110�
H. �13� I. 3 20.
Bonus Write a proportion to find the B:missing measure. Then solve.
x3 m
9 m
6 m
21 m
x ft 6 ft
25 ft 10 ft
15
30
2415
x
4
6
9 8
12
185 3
10
6
5
4
2 5 5
33
322
168
9 5
© Glencoe/McGraw-Hill 226 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 4 Test, Form 1 (continued)
Write the letter for the correct answer in the blank at the right of each question.
1. Express 9 inches:3 yards in simplest form.A. 3:1 B. 1:4 C. 12:1 D. 1:12 1.
2. Express 112 passengers to 8 minivans in simplest form.F. 14 to 1 G. 896 to 1 H. 28 to 1 I. 1 to 14 2.
3. Express $10.78 for 11 dozen eggs as a unit rate.A. $0.22/dozen B. $0.89/dozen C. $1.20/dozen D. $0.98/dozen 3.
4. Express 1,211 gallons of water in 28 hours as a unit rate.
F. 85 gal/h G. �1473�
gal/h H. 43�14� gal/h I. 173 gal/h 4.
FOOTBALL For Questions 5 and 6, use the information and graph given. The graph shows the attendance at school football games for each of the past six weeks.
5. Find the rate of change in attendance between week 3 and week 4.A. �25 fans/week B. 25 fans/weekC. 50 fans/week D. 100 fans/week 5.
6. Find the rate of change in attendance between week 1 and week 6.F. �25 fans/week G. 20 fans/week H. 50 fans/week I. 10 fans/week 6.
7. Find the slope of the line.
A. �23� B. ��
23�
C. �32� D. ��
32� 7.
For Questions 8 and 9, the points given in each table lie on a line. Find the slope of the line.
8. F. 5 G. �5H. 0 I. 4 8.
9. A. ��43� B. ��
34�
C. �34� D. �
43� 9.
10. Solve �3a6�
� �38�.
F. �23� G. 12 H. 13.5 I. 96 10.
y
xO
y
x0
300
1 2 3 4 5 6
350
400
450
Attendance atFootball Games
Num
ber o
f Fan
s
Week
© Glencoe/McGraw-Hill 227 Mathematics: Applications and Concepts, Course 3
Ass
essm
ent
Chapter 4 Test, Form 2A
Ass
essm
ent
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
x 1 5 9 13
y �6 �3 0 3
x �5 0 5 10
y 4 4 4 4
11. FUEL ECONOMY A car uses 40 gallons of gasoline to travel 980 miles.How many miles will the car travel on 5 gallons of gasoline?A. 4.9 mi B. 250 mi C. 175.5 mi D. 122.5 mi 11.
12. The pair of polygons is similar. Use a proportion to find the missing measure.
F. 12.5 G. 15 H. 20 I. 14.5 12.
13. MAPS The distance between two cities on a map is 4�18� inches. Find
the actual distance if the scale on the map is 2 inches � 40 miles.
A. 165 mi B. 82�12� mi C. 41�
14� mi D. 100 mi 13.
14. PROJECTIONS An image that is 28 mm wide on a transparency is 154 mmwide when projected onto a screen. What is the scale factor?
F. �121� G. 5 H. 6 I. �
125� 14.
15. LIGHTING How tall is the streetlight at the right?A. 18 ft B. 5 ftC. 25 ft D. 13 ft 15.
16. ARCHITECTURE A fence post 8.4 feet tall casts a shadow 12.6 feet long. A nearby building casts a shadow 96 feet long. How tall is the building?F. 81 ft G. 72 ft H. 144 ft I. 64 ft 16.
17. Triangle ABC has vertices A(�4, 4), B(1, 0), and C(�1, �2). Findthe coordinates vertex A after the triangle is dilated using a scalefactor of 3.5.A. (�14, 14) B. (14, �14) C. (14, 14) D. (�14, �14) 17.
18. Segment D�E� with endpoints D�(�4, 8) and E�(2, �2) is a dilationof segment DE with endpoints D(�9, 12) and E(3, �3). Find thescale factor of the dilation.
F. �32� G. �
23� H. �
31� I. �
13� 18.
Bonus The ratio of red marbles in a bag to green marbles is 2:3. B:If two red marbles are taken away, the ratio becomes 1:2.How many red marbles are in the bag?
x ft
10 ft
5 ft
2 ft
x6
10
12
12.5
7.5
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 4 Test, Form 2A (continued)
© Glencoe/McGraw-Hill 228 Mathematics: Applications and Concepts, Course 3
Write the letter for the correct answer in the blank at the right of each question.
1. Express 10 inches:5 feet in simplest form.A. 1:6 B. 2:1 C. 1:2 D. 1:5 1.
2. Express 35 wins to 25 losses in simplest form.F. 5 to 7 G. 13 to 10 H. 6 to 5 I. 7 to 5 2.
Express each rate as a unit rate.
3. $11.70 for 13 pounds of grapesA. $0.90/lb B. $9.90/lb C. $0.09/lb D. $9.00/lb 3.
4. 1,350 miles in 24 hours
F. 65 mi/h G. 225 mi/h H. 56�14� mi/h I. �2
425�
mi/h 4.
ENROLLMENT For Questions 5 and 6, use theinformation and graph given. The graphshows the number of girls enrolled at HillElementary for each of the past six years.
5. Find the rate of change in enrollmentbetween year 2 and year 3.A. �10 girls/year B. 30 girls/yearC. 10 girls/year D. 60 girls/year 5.
6. Find the rate of change in enrollmentbetween year 1 and year 6.F. �10 girls/year G. 12 girls/year H. 10 girls/year I. 60 girls/year 6.
7. Find the slope of the line.
A. �12� B. ��
12�
C. 2 D. �2 7.
For Questions 8 and 9, the points given in each table lie on a line. Find the slope of the line.
8. F. �32� G. �
23�
H. ��23� I. ��
32� 8.
9. A. 2 B. �2C. �3 D. 0 9.
10. Solve �58� � �3
c6�
.
F. �425�
G. 22.5 H. 57.6 I. 1�19� 10.
y
xO
y
x0
200
1 2 3 4 5 6
220
240
260
280
Enrollment atHill Elementary
Num
ber o
f Girl
s
Year
© Glencoe/McGraw-Hill 229 Mathematics: Applications and Concepts, Course 3
Ass
essm
ent
Ass
essm
ent
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 4 Test, Form 2B
x 5 7 9 11
y �3 �3 �3 �3
x �3 �1 1 3
y 7 4 1 �2
11. FUEL ECONOMY A car uses 35 gallons of gasoline to travel 840 miles.How many gallons are used to go 156 miles?A. 19.5 gal B. 7.2 gal C. 188 gal D. 6.5 gal 11.
12. The pair of polygons is similar. Use a proportion to find the missing measure.
F. 6 G. 12 H. 6.75 I. 8.4 12.
13. MAPS The distance between two cities on a map is 2.75 centimeters.Find the actual distance if the scale on the map is1 centimeter � 60 kilometers.A. 165 km B. 21 km C. 180 km D. 150 km 13.
14. PROJECTIONS An image that is 12�12� inches wide on the transparency
is 35 inches wide on a screen. What is the scale factor?
F. �3152�
G. �154� H. 3 I. �
3153�
14.
15.FLAGS How tall is the flagpole?A. 18 ft B. 63 ftC. 21 ft D. 36 ft 15.
16. ARCHITECTURE A 16-foot tree casts a shadow 18 feetlong at the same time that a building casts a 72-footshadow. How tall is the building?F. 81 ft G. 72 ft H. 64 ft I. 96 ft 16.
17. Triangle ABC has vertices A(�2, �4), B(�3, 1), and C(2, 2).Find the coordinates of vertex A after the triangle is dilatedusing a scale factor of 0.5.A. A�(�4, �8) B. A�(�1.5, �3.5) C. A�(�1, �2) D. A�(�4, �2) 17.
18. Segment R�S� with endpoints R�(13.5, 0) and S�(0, 4.5) is adilation of segment RS with endpoints R(�9, 0) and S(0, 3).Find the scale factor of the dilation.
F. �32� G. �
23� H. �
91� I. �
16� 18.
Bonus The ratio of red beans in a bag to green beans is 1:2. B:If two red beans are eaten, the ratio becomes 1:3. Howmany green beans are in the bag?
16 ft
9 ft
4 ft
12
915 x
9
11.25
© Glencoe/McGraw-Hill 230 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 4 Test, Form 2B (continued)
1. Find the slope of the line. 1.
For Questions 2 and 3, express each ratio in simplest form.
2. 95 girls to 105 boys 2.
3. 84 out of 144 students 3.
4. Express the rate 296 miles in 5 hours as a unit rate. 4.
5. Which is the better buy, 12 reams of paper for $24.50 or5 reams of paper for $15.25? Explain your reasoning. 5.
RAINFALL For Questions 6 and 7, use the information in the table. The table shows the amount of rain in Shawn’s rain gauge at selected times during a recent storm.
6. Find the rate of change in rainfall between 2:10 and 2:15. 6.
7. Find the rate of change in rainfall between 2:30 and 3:00. 7.
8. The points in the table lie on 8.a line. Find the slope of the line. Then graph the line.
9. Find the slope of the line and interpret its meaning as a rate of change. 9.
For Questions 10 and 11, solve each proportion.
10. �4b8�
� �196�
10.
11. �1f2� � �
4505�
11.
y
xO
© Glencoe/McGraw-Hill 231 Mathematics: Applications and Concepts, Course 3
Chapter 4 Test, Form 2C
Ass
essm
ent
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
y
xO
y
x0
4
1 2 3 4 5 6 7 8 9
812162024283236
Baby-sitting Money
Amou
nt E
arne
d
Number of Hours
Time 2:10 2:15 2:30 3:00
Inches of Rain 0.5 1 1.5 2.1
x �2 0 2 4
y 4 3 2 1
12. SWIMMING Aretha swims 3 laps every 50 seconds. How 12.many laps will she swim in 120 seconds?
13. Determine whether the pair of polygons is similar. 13.Explain your reasoning.
14. The pair of polygons is 14.similar. Write a proportion to find the missing measure.Then solve.
For Questions 15 and 16, the scale on a map is 1 inch � 575 miles. Find the actual distance for each map distance. 15.
15. 3�14� inches 16. 7�
12� inches 16.
17. PLAYGROUND The triangles formed 17.by the slide and the person are similar. How tall is the slide?
18. ROAD SIGNS A road sign casts 18.a shadow that is 4 feet long.At the same time, a 6-foot man standing next to the sign casts a shadow that is 2.4 feet long. How tall is the sign?
19. Polygon ABCD has vertices A��4�12�, 3�, B(2, 5), C��
12�, �1� 19.
and D(�3, �8). Find the coordinates of its image after a
dilation using a scale factor of �12�.
20. In the figure below �X�Y�Z� is a 20.dilation of �XYZ. Find the scale factor of the dilation, and classify it as an enlargement or a reduction.
Bonus A recipe calls for 2 pounds, 8 ounces of apples B:for 8 servings. How many apples, in poundsand ounces, are needed for 12 servings?
y
xO
X� Y�
YX
Z�
Z
© Glencoe/McGraw-Hill 232 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 4 Test, Form 2C (continued)
8
611
4
3 5.5
6
55
82 2
3.2x
42 in.
26 in.15 in.
1. Find the slope of the line. 1.
For Questions 2 and 3, expresseach ratio in simplest form.
2. 77 out of 121 dentists 2.
3. 85 men to 110 women 3.
4. Express the rate 315 miles in 6 hours as a unit rate. 4.
5. Which is the better buy, $14.60 for 36 juice boxes or $9.50 5.for 24 juice boxes? Explain.
FOOTBALL For Questions 6 and 7, use the information below and in the table. The table shows the total number of tickets sold at the gate by each time shown.
6. Find the rate of change in ticket sales between 5:15 6.and 5:20.
7. Find the rate of change in ticket sales between 5:35 7.and 6:00.
8. The points in the table lie on 8.a line. Find the slope of the line. Then graph the line.
9. Find the slope of the line and interpret its meaning as a rate of change. 9.
For Questions 10 and 11, solve each proportion.
10. �58� � �3
d6�
10.
11. �1356�
� �5r� 11.
12. HEART RATE If a person’s heart beats 96 times in 12.60 seconds, how many times does it beat in 45 seconds?
y
xO
© Glencoe/McGraw-Hill 233 Mathematics: Applications and Concepts, Course 3
Chapter 4 Test, Form 2D
Ass
essm
ent
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
y
xO
y
x0
1
10 20 30 40 50 60 70 80 90100
23456789
10
Gallo
ns U
sed
Miles Driven
Gasoline Usage
Time 5:15 5:20 5:35 6:00
Total Tickets Sold 27 47 197 1,072
x �4 �1 2 5
y �1 1 3 5
13. Determine whether the 13.pair of polygons is similar.Explain your reasoning.
14. The pair of polygons is 14.similar. Write a proportionto find the missing measure.Then solve.
For Questions 15 and 16, the scale on a map is 1 inch � 240 miles. Find the actual distance for each map distance.
15. �18� inch 15.
16. 2�34� inches 16.
17. FORESTRY How tall is the tree? 17.
18. MONUMENTS A statue casts 18.a shadow 25 feet long. A boystanding next to the statue is4.5 feet tall and casts ashadow that is 3.6 feet long. How tall is the statue? 19.
19. Polygon MNOP has vertices M(�2, �2), N(�3, 3), O(1, 3),and P(3, �1). Find the coordinates of its image after a dilation using a scale factor of �
13�.
20. The figure �D�E�F� is a dilation 20.of �DEF. Find the scale factor of the dilation and classify it as an enlargement or reduction.
Bonus �GHI has vertices at G(–4, 1), H(3, 2) and I(5, –6). B:�GHI is dilated using a scale factor of �
21�, and the
new triangle is then dilated using a scale factor of �23�.
Find the coordinate of the vertices of the new triangle after the second dilation.
© Glencoe/McGraw-Hill 234 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 4 Test, Form 2D (continued)
4
21
2
38.25
9
8.25
12
11
11
4
5 x
14 ft2.5 ft
4 ft
y
xO 2 4 6 8 10
2
4
6
8
E�
D�
F�E
DF
1. Express 45 inches:3 feet in simplest form. 1.
2. Which is the better buy, 120 peak-time minutes for $24.95 2.or 180 peak-time minutes for $35.95? Explain your reasoning.
For Questions 3 and 4, use the graph and information below. The graph shows a dolphin’s depth below the ocean’s surface as it swims.
3. Find the rate of change in 3.the dolphin’s depth between 1 and 2 minutes.
4. During which time period was 4.the rate of change in depth 0 feet per minute? How can you tell this from the graph?
5. Five days ago there were 6 cells growing in a sample. 5.Today there are 192 cells. Find the rate of change in the number of cells.
Find the slope of each line.
6. 7. 6.
7.
8. The points given in the table lie 8.on a line. Find the slope of the line. Then graph the line.
For Questions 9 and 10, the scale on a map is 1 inch � 330 miles. Find the actual distance.
9. 1�12� inches 9.
10. 4.75 inches 10.
11. Solve �p4� � �
01..66�
. 11.
© Glencoe/McGraw-Hill 235 Mathematics: Applications and Concepts, Course 3
Ass
essm
ent
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 4 Test, Form 3
y
x0
5
1 2 3 4 5 6
101520
Dolphins
Feet
Bel
owW
ater
's Su
rfac
e
Minutes
y
xO
y
xO
x �3 �2 �1 0
y 5 1 �3 �7y
xO
12. TICKET SALES Eight student tickets cost $160.50. How 12.much will 20 student tickets cost?
For Questions 13 and 14, each pair of polygons is similar.Write a proportion to find each missing measure. Then solve. 13.
13. 14.
14.
15. �EFG ~ �HIJ. Each side 15.of �HIJ is 2�
14� times longer
than the corresponding sides of �EFG. Find the perimeter of �EFG.
16. MONUMENTS The St. Louis arch is 630 feet tall. A model 16.of the arch is 9 feet. What is the scale of the model?
17. GEOGRAPHY How wide is 17.Citrus Lake?
18. ARCHITECTURE The Sears Tower in Chicago, Illinois, is 18.443 meters tall. A smaller building nearby casts a shadow 6.8 meters long. At the same time the Sears Tower casts a shadow 8.6 meters long. How tall is the smaller building to the nearest meter?
19. Polygon ABCD has vertices A��4, �13��, B��2�
12�, 8�, 19.
C�2, 3�14��, and D(0, �1). Find the vertices for a dilation
using a scale factor of 2.
20. In the figure �L�M�N� is a dilation 20.of �LMN. Find the scale factor,and classify the dilation as an enlargement or as a reduction.
Bonus After burning for 5 minutes, a 600-gram candle weighs B:540 grams. Assuming the candle burns at the same rate, how many grams will burn away in 32 minutes?
60 yd
30 yd
75 ydx
16
1618
5
5.6255
20 x
© Glencoe/McGraw-Hill 236 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 4 Test, Form 3 (continued)
12 m
20 m
14 m
H J
I
E G
F
130 m 110 m
55 m
y
xO 2 4 6 8 10
2
4
6
8
L�M�
N�N
ML
Demonstrate your knowledge by giving a clear, concise solution toeach problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solution in more than one way orinvestigate beyond the requirements of the problem. If necessary,record your answer on another piece of paper.
1. Ratios are used to make concrete. A recommended concrete mix is 1 partcement, 2 parts sand, 4 parts gravel, and water to moisten.
a. Explain what is meant by ratio.
b. Write three ratios that describe the concrete mix. Write each ratio in adifferent form.
c. Explain what is meant by a proportion.
d. Suppose 400 pounds of sand were loaded into a mixer. Tell how muchcement and gravel should be added. Show your work.
2. a. Polygons ABCD and EFGH are similar.Explain what this means.
b. In the above polygons, identify the corresponding sides. How can you use this information to find thelengths of the sides B�C�, E�F�, and G�H�?
c. You can also use indirect measurement to find a missing measurement. Draw a diagram illustratingthe following situation. Then solve the problem.Show your work.An 8-foot barber pole casts a shadow 2 feet long. The barber standing
next to the pole is 5�35� feet tall. How long is his shadow?
d. Explain how using a scale drawing to find a measurement is relatedto using similar polygons and indirect measurement.
e. If a dilated image is smaller than the original, is the scale factorlarger or smaller than 1? Explain.
© Glencoe/McGraw-Hill 237 Mathematics: Applications and Concepts, Course 3
Chapter 4 Extended Response Assessment
Ass
essm
ent
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
A
B
CDH G
E
F
4
9
9
6
12
Write whether each sentence is true or false. If false, replace the underlined wordto make a true sentence.
1. If the slope of a line is �23�, the ratio corresponding to a rise 1.
of 2 is 3.
2. In a proportion, the two cross products are opposites. 2.
3. A simple closed figure in a plane formed by at least three 3.line segments is called a polygon.
4. A proportion is a special kind of ratio in which two 4.quantities with different types of units are compared.
5. The average amount of snow that fell each hour over a 5.period of several hours is an example of a rate of change.
6. If two polygons are scale factors, their corresponding angles 6.are congruent and their corresponding sides are proportional.
7. Distances on a scale drawing are proportional to distances in 7.real life.
8. A comparison of two numbers by division is called a ratio. 8.
9. In a scale drawing, the indirect measurement is determined 9.by the ratio of a given length on the drawing to its corresponding actual length.
10. Slope is the dilation of the vertical change between two 10.points to the horizontal change between the points.
In your own words, define each term.
11. unit rate
12. corresponding parts
congruent (p. 179)
corresponding parts (p. 178)
cross products (p. 170)
dilation (p. 194)
indirect measurement (p. 188)
polygon (p. 178)
proportion (p. 170)
rate (p. 157)
rate of change (p. 160)
ratio (p. 156)
rise (p. 166)
run (p. 166)
scale (p. 184)
scale drawing (p. 184)
scale factor (p. 179)
scale model (p. 184)
similar (p. 178)
slope (p. 166)
unit rate (p. 157)
© Glencoe/McGraw-Hill 238 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 4 Vocabulary Test/Review
© Glencoe/McGraw-Hill 239 Mathematics: Applications and Concepts, Course 3
Ass
essm
ent
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Express each ratio in simplest form.
1. 12 goals in 15 attempts 1.
2. 27 winners chosen out of 90 contestants 2.
3. 44 out of 100 dentists 4. 6 cups for each quart 3.
Express each rate as a unit rate. 4.
5. 253 students for 11 teachers 5.
6. $555 for 6 chairs 6.
7. 165 students for 60 computers 7.
SCIENCE Use the information belowand in the table.
Sara decided to study the growth of a plant for her science project. She recorded the height of her plant in the table.
8. Find the rate of change in the height 8.of the plant from week 1 to week 3.
9. Find the rate of change in the height 9.of the plant from week 9 to week 15.
10. During which of these two time periods did the plant grow 10.faster?
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Find the slope of each line.
1. 2. 1.
Solve each proportion. 2.
3. �85� = �1
a5�
3.
4. �13000�
� �6c� 4.
5. �7t� � �
1238�
5.
Chapter 4 Quiz(Lessons 4-1 and 4-2)
Chapter 4 Quiz(Lessons 4-3 and 4-4)
Week Height
6 2
3 2 cm
6 2�12� cm
9 4 cm
15 8 cm
y
xO
x �2 0 2 4y 1 4 7 10
© Glencoe/McGraw-Hill 240 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Ass
essm
ent
1. FLAGS A flagpole casts a shadow 9 feet long at the same 1.time that a 6-foot man casts a shadow of 2.5 feet. How tall is the flagpole?
2. FORESTRY A tree casts a shadow 75 feet long at the 2.same time that an 8-foot sign casts a shadow 10 feet long. How tall is the tree?
For Questions 3 and 4, find the coordinates of the vertices of �X�Y�Z� after �XYZ is dilated using the given scale factor.
3. X(�1, �2), Y(2, 1), Z(4, �1); scale factor 3 3.
4. X(3, �2), Y(0, 0), Z(4, 4); scale factor �12� 4.
5. Segment A�B� with endpoints A���12�, 2� and B��1�
12�, 3� is a 5.
dilation of segment AB. If segment AB has endpoints A(2, 8) and B(6, 12), find the scale factor of the dilation. Then classify the dilation as an enlargement or as a reduction.
Chapter 4 Quiz(Lessons 4-5 and 4-6)
Chapter 4 Quiz(Lessons 4-7 and 4-8)
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Each pair of polygons is similar. Write a proportion to find each missing measure. Then solve.
1. 2. 1.
2.
For Questions 3 and 4, the scale on a map is 1 inch � 3.40 miles. Find the actual distance for each map distance.
3. �78� inch 4. 5�
12� inches 4.
5. MULTIPLE-CHOICE TEST ITEM Polygon ABCD is similar to polygon PQRS. Each side of polygon ABCD is 1�
12� times
longer than the corresponding side of polygon PQRS.If the perimeter of polygon ABCD is 15 inches, what is the perimeter of polygon PQRS? A. 22�
12� inches B. 10 inches 5.
C. 37 inches D. 16�12� inches
x
912
16
x
20 12
8
Write the letter for the correct answer in the blank at the right of each question.
1. Express $42 for 4 days in simplest form.A. 1:4 B. 42:1 C. 2:21 D. 21:2 1.
2. Express 154 miles on 7 gallons as a unit rate.F. 22 mi/gal G. 0.05 mi/galH. 147 mi/gal I. 7 mi/gal 2.
3. Express $2.76 for 12 sandwich rolls as a unit rate.A. $4.35/roll B. $2.76/roll C. $0.23/roll D. $12/roll 3.
4. The points given in the table lie on a line. Find the slope of the line.
F. –1 G. 3 H. ��13� I. �3 4.
5. Solve �1c5�
� �1200�
.A. 30 B. 15 C. 13 D. 7.5 5.
SCHOOL For Exercises 6 and 7, use the following table.
6. Find the rate of change in the number of copies between 6.month 1 and month 3.
7. Find the rate of change in the number of copies between 7.month 6 and month 9 to the nearest whole number.
8. GARDENING If it takes Sheila 1.5 hours to plant 8.28 tomato plants, how long will it take her to plant 98 plants?
9. RACECAR A car on a racetrack drove 96 miles in 9.60 minutes. How many miles did it drive in 10 minutes?
10. Find the slope of the line and 10.interpret its meaning as a rate of change.
© Glencoe/McGraw-Hill 241 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 4 Mid-Chapter Test(Lessons 4-1 through 4-4)
y
nO
10
10 20 30 40 50 60 70 80 90100
2030405060
Gallo
ns o
f Jui
ce
Number of Students
x 0 3 6 9
y �4 �5 �6 �7
Month 1 3 6 9
Number of Copies Made 420 619 800 1,215
1. Evaluate �x�
�32
y� if x � 5 and y � �3. (Lesson 1-6) 1.
2. Solve �17 � q � 9. (Lesson 1-8) 2.
3. Find �1396�
� �45�. Write in simplest form. (Lesson 2-3) 3.
4. Find 3�23� � 5�
16�. Write in simplest form. (Lesson 2-6) 4.
5. Evaluate 43 � 22. (Lesson 2-8) 5.
6. Find �729�. (Lesson 3-1) 6.
7. Estimate the solution of x2 � 80 to the nearest integer. 7.(Lesson 3-2)
8. Name all sets of numbers to which �49� belongs. 8.(Lesson 3-3)
9. Find the distance between the points (4, 9) and (�3, �5). 9.Round to the nearest tenth. (Lesson 3-6)
10. Express 220 miles on 11 gallons in simplest form. 10.(Lesson 4-1)
11. Express $15.50 for 5 pounds of cashews as a unit rate. 11.(Lesson 4-1)
12. Find the slope of the line.(Lesson 4-3) 12.
13. Solve �45� � �
1y0�. (Lesson 4-4) 13.
14. The scale on a map is 1 inch � 14.40 miles. Find the actual distance if two towns are 2�
14� inches apart on the map.
(Lesson 4-6)
15. A flagpole casts a shadow 10 feet long at the same time 15.that an 6-foot man casts a shadow that is 4 feet long.How tall is the flagpole? (Lesson 4-7)
16. Segment B�C� is a dilation of segment BC. The endpoints 16.are B(�6, 4), C(2, �8), B�(�9, 6) and C�(3, �12). Find the scale factor of the dilation and classify it as an enlargementor as a reduction. (Lesson 4-8)
© Glencoe/McGraw-Hill 242 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 4 Cumulative Review(Chapters 1–4)
y
xO
1. Jill purchased a pair of shoes that cost $59.00. After tax, thetotal cost was $63.43. Which equation could be used to findthe amount of the tax? (Lesson 1-8)A. x � 63.43 � 59 B. 59 � x � 63.43C. x � 59 � 63.43 D. x � 63.43 � 59 1.
2. A board that is 49�12� inches long is cut into pieces that are
4�18� inches long. How many pieces are there? (Lesson 2-4)
F. 9 G. 10 H. 11 I. 12 2.
3. The distance between Lakeland and Iceville is 129 kilometers.If there are 1,000 meters in a kilometer, use scientific notationto write the distance from Lakeland to Iceville in meters.(Lesson 2-9)A. 1.29 � 105 B. 1.29 � 102 3.C. 1.29 � 103 D. 1.29 � 10�3
4. The area of a square is 144 square meters. What is theperimeter? (Lesson 3-1)F. 12 meters G. 24 meters H. 48 meters I. 288 meters 4.
5. Randall walked 80 yards east and then walked 50 yards north.How far is Randall from his starting point to the nearest tenth?(Lesson 3-4)A. 62.5 yd B. 94.3 yd C. 130.0 yd D. 8,900.0 yd 5.
6. Find the distance between (�3, 4) and (7, �7). Round to thenearest tenth. (Lesson 3-6)F. 4.6 units G. 10 units H. 14.9 units I. 11 units 6.
7. Which of the following cannot be written as a ratio? (Lesson 4-1)A. $6 out of $10 earned B. $20 for every $100 donated 7.C. $15 less than the average D. $48 for three baseball caps
price
8. A recipe calls for 12�12� pounds of carrots for 60 servings. How
many pounds of carrots are needed for 1,000 servings? (Lesson 4-4)
F. 2,083�13� G. 208�
13� H. 500�
13� I. 4,800 8.
9. Polygons ABC and XYZ are similar.Find the length of Y�Z�. (Lesson 4-5)A. 3 cm B. 1 cm 9.C. 8 cm D. 2 cm
DCBA
IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
© Glencoe/McGraw-Hill 243 Mathematics: Applications and Concepts, Course 3
Ass
essm
ent
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Standardized Test Practice (Chapter 4)
Part 1: Multiple Choice
Instructions: Fill in the appropriate oval for the best answer.
A B
CX Y
Z
9 cm
3 cm8 cm
6 cm
4 cm
10. Evaluate the expression m(n � p) if 10. 11.m � 1�
35�, n � �
29�, and p � �
13�. (Lesson 2-6)
11. Estimate �77� to the nearest tenth.(Lesson 3-3)
12. Find the slope of the line.(Lesson 4-3) 12.
13. A 6-foot man casts a shadow that 13.is 7.5 feet long. A flagpole near the man casts a shadow that is 45 feet long. How tall is the flagpole?(Lesson 4-7)
14. ELECTIONS The table shows the number of people who had voted by each time in Precinct 109.
a. Find the rate of change in the number of voters between 10 A.M. and 12 P.M. Interpret its meaning.
b. During which time period was the rate of change 0? Explain.
c. During which time period was the rate of change the greatest?
Part 3: Extended Response
Instructions: Write your answers below or to the right of the problems.
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
Part 2: Short Response/Grid In
Instructions: Enter your grid in answers by writing each digit of the answer in acolumn box and then shading in the appropriate circle that corresponds to that entry.Write answers to short answer questions in the space provided.
© Glencoe/McGraw-Hill 244 Mathematics: Applications and Concepts, Course 3
NAME ________________________________________ DATE ______________ PERIOD _____
Standardized Test Practice (continued)
y
xO
Time 8 A.M. 10 A.M. 12 P.M. 2 P.M. 3 P.M.
Number of Voters 25 67 149 275 275
© Glencoe/McGraw-Hill A1 Mathematics: Applications and Concepts, Course 3
An
swer
s
Standardized Test PracticeStudent Recording Sheet (Use with pages 202–203 of the Student Edition.)
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Part 1:
Solve the problem and write your answer in the blank.
For grid in questions, also enter your answer by writing each number or symbolin a box. Then fill in the corresponding circle for that number of symbol.
7. 8. 9. 10.
8. (grid in)
9. (grid in)
10. (grid in)
11. (grid in) 11. 12. 13.
12. (grid in)
13. (grid in)
14.
15.
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
Select the best answer from the choices given and fill in the corresponding oval.
Multiple Choice
1.
2.
3.
4.
5.
6. IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
Part 2: Short Response/Grid in
Record your answers for Questions 16 and 17 on the back of this paper.
Part 3: Extended Response
General Scoring Guidelines• If a student gives only a correct numerical answer to a problem but does not show how he or she
arrived at the answer, the student will be awarded only 1 credit. All extended response questionsrequire the student to show work.
• A fully correct answer for a multiple-part question requires correct responses for all parts of thequestion. For example, if a question has three parts, the correct response to one or two parts of thequestion that required work to be shown is not considered a fully correct response.
• Students who use trial and error to solve a problem must show their method. Merely showing thatthe answer checks or is correct is not considered a complete response for full credit.
Exercise 16 Rubric
Standardized Test PracticeRubrics (Use to score the Extended Response questions on page 203 of the Student Edition.)
Score Specific Criteria4 The 4 points are correctly graphed and a line is drawn through the points. The slope
of the line is correctly determined to be �92�. The value of the slope is translated to
mean that Susan’s rate of pay is $4.50 per hour. The amount of money Susan willmake for 10 hours of work is correctly determined to be $45.
3 The 4 points are correctly graphed and the line is correctly drawn, but acomputational error in finding one of the values is made.
2 The 4 points are correctly graphed and the line is correctly drawn, but two of theother values are incorrect. ORThe 4 points are not correctly graphed and a different line is drawn, but thenumerical answers are all correct for the graph drawn.
1 The 4 points are correctly graphed and the line is correctly drawn, but none of thevalues are correct. ORThe 4 points are not correctly graphed and a different line is drawn, but one or twoof the numerical answers are correct for the graph drawn.
0 Response is completely incorrect.
Score Specific Criteria4 The coordinates of the vertices of the triangle after the dilation using a scale factor
of �23� are found to be A�(�4, 2), B�(2, 4), and C�(4, �6). The graphs of �ABC and this
dilation are correct. A scale factor greater than 1 is given for an enlargement the�ABC. This scale factor is correctly used to find the coordinates of the vertices of thedilation.
3 The work is mostly correct, but a computational error is made in finding thecoordinates of one of the vertices of a dilated figure. ORThe work is mostly correct, but one of the vertices is incorrectly graphed.
2 The graphs of �ABC and its dilation using a scale factor of �23� are correct, but scale
factor for an enlargement is incorrect or not given. ORThe coordinates of the dilations are correctly given, but the graphs are incorrect ornot shown.
1 The coordinates of one of the dilations are correctly given, but the coordinates of theother dilation are incorrect or not given. The graph is incorrect or not shown. ORThe coordinates of the dilation are incorrect or not given and the graph is incorrector not shown, but a correct scale factor of an enlargement is given.
0 Response is completely incorrect.
Exercise 17 Rubric
© Glencoe/McGraw-Hill A2 Mathematics: Applications and Concepts, Course 3
© Glencoe/McGraw-Hill A3 Mathematics: Applications and Concepts, Course 3
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Con
cept
s, C
ours
e 3
Exp
ress
35
win
s to
42
loss
esin
sim
ple
st f
orm
.
�3 45 2��
�5 6�D
ivid
e th
e nu
mer
ator
and
den
omin
ator
by
the
grea
test
com
mon
fact
or,
7.
Th
e ra
tio
in s
impl
est
form
is
�5 6�or
5:6
.
Exp
ress
1 f
oot
to 3
in
ches
in s
imp
lest
for
m.
To
sim
plif
y a
rati
o in
volv
ing
mea
sure
men
ts,b
oth
qu
anti
ties
mu
st h
ave
the
sam
e u
nit
of m
easu
re.
� 31 inf co hot es�
��1 32 ii nn cc hh ee ss
�C
onve
rt 1
foot
to
12 in
ches
.
��4 1in inch ches
�D
ivid
e th
e nu
mer
ator
and
den
omin
ator
by
3.
Th
e ra
tio
in s
impl
est
form
is
�4 1�or
4:1
.
Exp
ress
309
mil
es i
n 6
hou
rsas
a u
nit
rat
e.
�3 609h
om ui rle ss�
��51
1.5 hm oui rle
s�
Div
ide
the
num
erat
or a
nd d
enom
inat
or b
y 6
to g
et a
den
omin
ator
of
1.
Th
e u
nit
rat
e is
51.
5 m
iles
per
hou
r.
Exp
ress
eac
h r
atio
in
sim
ple
st f
orm
.
1.3
out
of 9
stu
den
ts�1 3�
2.8
pass
enge
rs:2
car
s�4 1�
3.5
out
of 1
0 de
nti
sts
�1 2�4.
35 b
oys:
60 g
irls
� 17 2�
5.18
red
app
les
to 4
2 gr
een
app
les
�3 7�6.
50 m
illi
met
ers
to 1
met
er� 21 0�
Exp
ress
eac
h r
ate
as a
un
it r
ate.
7.12
wav
es i
n 2
hou
rs8.
200
mil
es i
n 4
hou
rs6
wav
es/h
50m
i/h
9.21
gal
lon
s in
2.4
min
ute
s10
.$1
2 fo
r 4.
8 po
un
ds8.
75g
al/m
in$2
.50/
lb
11.
$49,
500
in 1
2 m
onth
s12
.11
2 fe
et i
n 5
sec
onds
$4,1
25/m
on
th22
.4ft
/s
A r
ate
is a
rat
io t
hat
com
pare
s tw
o qu
aniti
ties
with
diff
eren
t ty
pes
of u
nits
.A u
nit
rate
is a
rat
e w
ith a
deno
min
ator
of
1.
A r
atio
is a
com
paris
on o
f tw
o nu
mbe
rs b
y di
visi
on.S
ince
a r
atio
can
be
writ
ten
as a
fra
ctio
n, it
ca
n be
sim
plifi
ed.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Rat
ios
and
Rat
es
Answers (Lesson 4-1)
An
swer
s
© Glencoe/McGraw-Hill A4 Mathematics: Applications and Concepts, Course 3
©G
lenc
oe/M
cGra
w-H
ill18
8M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Pre-
Act
ivit
yR
ead
th
e in
tro
du
ctio
n a
t th
e to
p o
f p
age
156
in y
ou
r te
xtb
oo
k.W
rite
yo
ur
answ
ers
bel
ow
.
1.W
hic
h c
ombi
nat
ion
of
ingr
edie
nts
wou
ld y
ou u
se t
o m
ake
a sm
alle
ram
oun
t of
th
e sa
me
reci
pe?
Exp
lain
.co
mb
inat
ion
#2;
Sam
ple
an
swer
:In
th
e o
rig
inal
bat
ch,t
her
e ar
e tw
ice
asm
any
sco
op
s o
f p
ean
uts
as
rais
ins.
2.In
ord
er t
o m
ake
the
sam
e re
cipe
of
trai
l m
ix,h
ow m
any
scoo
ps o
fpe
anu
ts s
hou
ld y
ou u
se f
or e
very
sco
op o
f ra
isin
s?2
Rea
din
g t
he
Less
on
3.W
hat
doe
s it
mea
n i
f th
e ra
tio
of r
ed m
arbl
es t
o bl
ue
mar
bles
is
3 to
5?
Fo
r ev
ery
3 re
d m
arb
les,
ther
e ar
e 5
blu
e m
arb
les.
4.W
hat
is
anot
her
way
to
wri
te t
he
rati
o 3
to 5
?S
amp
le a
nsw
er:
3:5
or
�3 5�
5.W
hat
mu
st y
ou d
o be
fore
you
can
sim
plif
y th
e ra
tio
30 m
inu
tes
to
8 h
ours
? W
hat
is
the
sim
plif
ied
rati
o?C
onv
ert
min
ute
s to
ho
urs
or
ho
urs
to
min
ute
s;1:
16.
Hel
pin
g Y
ou
Rem
emb
er6.
Wh
en y
ou g
o to
a b
ank
to e
xch
ange
mon
ey o
f on
e cu
rren
cy f
or a
not
her
,th
e ba
nk
use
s a
con
vers
ion
rat
e to
cal
cula
te t
he
amou
nt
of m
oney
in
th
en
ew c
urr
ency
.Fin
d ou
t w
hat
th
e cu
rren
t co
nve
rsio
n r
ate
is t
o ex
chan
geU
.S.d
olla
rs t
o C
anad
ian
dol
lars
at
a lo
cal
ban
k.T
hen
wri
te t
he
rate
as
ara
tio
of o
ne
curr
ency
com
pare
d to
th
e ot
her
.S
amp
le a
nsw
er:
1 U
.S.d
olla
r to
1.5
6 C
anad
ian
do
llars
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Read
ing
to L
earn
Mat
hem
atic
sR
atio
s an
d R
ates
©G
lenc
oe/M
cGra
w-H
ill18
7M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Prac
tice:
Wor
d Pr
oble
ms
Rat
ios
and
Rat
es
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Lesson 4–1
1.C
OO
KIN
GIn
a b
read
dou
gh r
ecip
e,th
ere
are
3 eg
gs f
or e
very
9 c
ups
of
flou
r.E
xpre
ss t
his
rat
io i
n s
impl
est
form
.1:
3
2.W
ILD
LIFE
Den
a co
un
ted
14 r
obin
s ou
t of
150
bird
s.E
xpre
ss t
his
rat
io i
nsi
mpl
est
form
.7:
75
3.IN
VES
TMEN
TSJo
sh e
arn
ed d
ivid
ends
of
$2.1
6 on
54
shar
es o
f st
ock.
Fin
d th
edi
vide
nds
per
sh
are.
$0.0
4/sh
are
4.TR
AN
SPO
RTA
TIO
NW
hen
Den
ise
bou
ght
gaso
lin
e,sh
e pa
id $
18.4
8 fo
r 11
.2ga
llon
s.F
ind
the
pric
e of
gas
olin
e pe
rga
llon
.$1
.65/
gal
5.W
ATE
R F
LOW
Jaco
b fi
lled
his
60-
gall
onba
thtu
b in
5 m
inu
tes.
How
fas
t w
as t
he
wat
er f
low
ing?
12 g
al/m
in
6.TR
AV
ELO
n h
er v
acat
ion
,Ch
arm
ain
e’s
flig
ht
last
ed 4
.5 h
ours
.Sh
e tr
avel
ed95
4 m
iles
.Fin
d th
e av
erag
e sp
eed
ofth
e pl
ane.
212
mi/h
7.H
OU
SIN
GM
r.A
nd
Mrs
.Rom
ero
bou
ght
a 1,
200
squ
are-
foot
hou
se f
or $
111,
600.
How
mu
ch d
id t
hey
pay
per
squ
are
foot
?$9
3/ft
2
8.SH
OPP
ING
A b
reak
fast
cer
eal
com
es i
ntw
o di
ffer
ent
size
d pa
ckag
es.T
he
8-ou
nce
box
cos
ts $
2.88
,wh
ile
the
12-o
un
ce b
ox c
osts
$3.
60.W
hic
h b
ox i
sth
e be
tter
bu
y? E
xpla
in y
our
reas
onin
g.T
he
12-o
z b
ox a
t $0
.30/
oz;
the
8-o
z b
ox c
ost
s $0
.36
per
oz,
but
the
12-o
z b
ox c
ost
s $0
.30
per
oz.
Answers (Lesson 4-1)
© Glencoe/McGraw-Hill A5 Mathematics: Applications and Concepts, Course 3
©G
lenc
oe/M
cGra
w-H
ill19
0M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
INC
OM
ET
he
grap
h s
how
s M
r.J
ack
son
’s
ann
ual
in
com
e b
etw
een
199
4 an
d 2
002.
Fin
d t
he
rate
of
chan
ge i
n M
r.J
ack
son
’s
inco
me
bet
wee
n 1
994
and
199
7.
Use
th
e fo
rmu
la f
or t
he
rate
of
chan
ge.
Let
(x 1
,y1)
�(1
994,
48,5
00)
and
(x2,
y 2)�
(199
7,53
,000
).
�y x2 2
– –y x1 1
���5
3 1,0 90 90 7� �
4 18 9, 95 400�
Writ
e th
e fo
rmul
a fo
r ra
te o
f ch
ange
.
��4,
5 300 �S
impl
ify.
��1,
5 100 �E
xpre
ss t
his
rate
as
a un
it ra
te.
Bet
wee
n 1
994
and
1997
,Mr.
Jack
son
’s i
nco
me
incr
ease
d an
av
erag
e of
$1,
500
per
year
.
SUR
FF
or E
xerc
ises
1–3
,use
th
e gr
aph
th
at
show
s th
e av
erag
e d
aily
wav
e h
eigh
t as
m
easu
red
by
an o
cean
bu
oy o
ver
a n
ine-
day
p
erio
d.
1.F
ind
the
rate
of
chan
ge i
n t
he
aver
age
dail
y w
ave
hei
ght
betw
een
day
1 a
nd
day
3.2
ft/d
ay
2.F
ind
the
rate
of
chan
ge i
n t
he
aver
age
dail
y w
ave
hei
ght
betw
een
day
3 a
nd
day
7.0.
5 ft
/day
3.F
ind
the
rate
of
chan
ge i
n t
he
aver
age
dail
y w
ave
hei
ght
betw
een
day
7 a
nd
day
9.�
1.5
ft/d
ay
y
x
Days
79111315
13
57
9
Day
Wav
e H
eigh
t ( 7, 1
4) ( 9, 1
1)
( 3, 1
2)
( 1, 8
)
0
'94
'96
'98
'00
'02
50,0
00
45,0
00
55,0
00
60,0
00
65,0
00
Annual Income ($)
Year
Mr.
Jack
son'
s In
com
e
y
x
1994
, 48,
500
2002
, 57,
000
1997
, 53,
000
0
To f
ind
the
rate
of
chan
ge b
etw
een
two
data
poi
nts,
div
ide
the
diffe
renc
e of
the
y-c
oord
inat
es b
y th
e
diffe
renc
e of
the
x-c
oord
inat
es.T
he r
ate
of c
hang
e be
twee
n (x
1, y
1) a
nd (
x 2,
y 2)
is � xy 22
��y x1 1
�.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Rat
e o
f C
han
ge
©G
lenc
oe/M
cGra
w-H
ill18
9M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Bar
gai
n H
un
tin
gR
ates
are
use
ful
and
mea
nin
gfu
l w
hen
exp
ress
ed a
s a
un
it r
ate.
For
exa
mpl
e,w
hic
h i
s th
e be
tter
bu
y—on
e or
ange
for
$0.
29 o
r12
ora
nge
s fo
r $3
.00?
To
fin
d th
e u
nit
rat
e fo
r 12
ora
nge
s,di
vide
$3.
00 b
y 12
.Th
ere
sult
is
$0.2
5 pe
r or
ange
.If
a sh
oppe
r n
eeds
to
buy
at l
east
12 o
ran
ges,
then
12
oran
ges
for
$3.0
0 is
th
e be
tter
bu
y.
For
eac
h e
xerc
ise
bel
ow,r
ates
are
giv
en i
n C
olu
mn
A a
nd
C
olu
mn
B.I
n t
he
bla
nk
nex
t to
eac
h e
xerc
ise
nu
mb
er,w
rite
th
e le
tter
of
the
colu
mn
th
at c
onta
ins
the
bet
ter
bu
y.
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
BAAAABBBAA
OR
ANG
ES
Enric
hmen
tN
AM
E__
____
____
____
____
____
____
____
____
____
__D
ATE
___
____
____
___
PE
RIO
D
____
_
Lesson 4–1
Col
um
n A
Col
um
n B
1 ap
ple
for
$0.1
93
appl
es f
or $
0.59
20 p
oun
ds o
f pe
t fo
od f
or $
14.9
950
pou
nds
of
pet
food
for
$37
.99
A c
ar t
hat
tra
vels
308
mil
es o
n11
gal
lon
s of
gas
olin
eA
car
th
at t
rave
ls 4
06 m
iles
on
14 g
allo
ns
of g
asol
ine
10 f
lopp
y di
scs
for
$8.9
925
flo
ppy
disc
s fo
r $1
9.75
1-ga
llon
can
of
pain
t fo
r $1
3.99
5-ga
llon
bu
cket
of
pain
t fo
r$6
7.45
84 o
un
ces
of l
iqu
id d
eter
gen
tfo
r $1
0.64
48 o
un
ces
of l
iqu
id d
eter
gen
tfo
r $6
.19
5,00
0 sq
uar
e fe
et o
f la
wn
foo
dfo
r $1
1.99
12,5
00 s
quar
e fe
et o
f la
wn
foo
dfo
r $2
9.99
2 co
mpa
ct d
iscs
for
$26
.50
3 co
mpa
ct d
iscs
for
$40
.00
8 pe
nci
ls f
or $
0.99
12 p
enci
ls f
or $
1.49
1,00
0 sh
eets
of
com
pute
rpa
per
for
$8.9
55,
000
shee
ts o
f co
mpu
ter
pape
rfo
r $4
1.99
Answers (Lessons 4-1 and 4-2)
An
swer
s
© Glencoe/McGraw-Hill A6 Mathematics: Applications and Concepts, Course 3
©G
lenc
oe/M
cGra
w-H
ill19
2M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
ELEC
TIO
NS
For
Exe
rcis
es 1
–3,u
se t
he
tab
le t
hat
sh
ows
the
tota
l n
um
ber
of p
eop
le w
ho
had
vot
ed i
n D
istr
ict
5 at
var
iou
s ti
mes
on
ele
ctio
n d
ay.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Wor
d Pr
oble
ms
Rat
e o
f C
han
ge
1.F
ind
the
rate
of
chan
ge i
n t
he
nu
mbe
rof
vot
ers
betw
een
8:0
0 A.M
.an
d10
:00
A.M
.Th
en i
nte
rpre
t it
s m
ean
ing.
105
vote
rs/h
r;B
etw
een
8:0
0 A.M
.an
d 1
0:00
A.M
.,an
ave
rag
e o
f 10
5 p
eop
le v
ote
d e
ach
ho
ur.
2.F
ind
the
rate
of
chan
ge i
n t
he
nu
mbe
rof
vot
ers
betw
een
10:
00 A
.M.a
nd
1:00
P.M
.Th
en i
nte
rpre
t it
s m
ean
ing.
149
vote
rs/h
r;B
etw
een
10:
00A.M
.an
d 1
:00
P.M
.,an
ave
rag
e o
f14
9 p
eop
le v
ote
d e
ach
ho
ur.
3.D
uri
ng
wh
ich
of
thes
e tw
o ti
me
peri
ods
did
the
nu
mbe
r of
peo
ple
wh
o h
advo
ted
so f
ar i
ncr
ease
fas
ter?
Exp
lain
you
r re
ason
ing.
Bet
wee
n
10:0
0 A.M
.an
d 1
:00
P.M
.;th
e ra
teo
f ch
ang
e is
gre
ater
fo
r th
is t
ime
per
iod
.
4.M
USI
CA
t th
e en
d of
199
9,C
anda
ce h
ad47
CD
s in
her
mu
sic
coll
ecti
on.A
t th
een
d of
200
2,sh
e h
ad 1
34 C
Ds.
Fin
d th
era
te o
f ch
ange
in
th
e n
um
ber
of C
Ds
inC
anda
ce’s
col
lect
ion
bet
wee
n 1
999
and
2002
.29
CD
s/yr
5.FI
TNES
SIn
199
2,th
e pr
ice
of a
n a
nn
ual
mem
bers
hip
at
Mr.
Jen
sen
’s h
ealt
h c
lub
was
$22
5.In
200
2,th
e pr
ice
of t
he
sam
e m
embe
rsh
ip w
as $
319.
50.F
ind
the
rate
of
chan
ge i
n t
he
pric
e of
th
ean
nu
al m
embe
rsh
ip b
etw
een
199
2 an
d20
02.
$9.4
5/yr
6.H
IKIN
GL
ast
Sat
urd
ay F
um
io a
nd
Kis
hi
wen
t h
ikin
g in
th
e m
oun
tain
s.W
hen
they
sta
rted
bac
k at
2:0
0 P.
M.,
thei
rel
evat
ion
was
3,5
60 f
eet
abov
e se
ale
vel.
At
6:00
P.M
.,th
eir
elev
atio
n w
as2,
390
feet
.Fin
d th
e ra
te o
f ch
ange
of
thei
r el
evat
ion
bet
wee
n 2
:00
P.M
.an
d6:
00 P
.M.
Th
en i
nte
rpre
t it
s m
ean
ing.
�29
2.5
ft/h
;Th
ey d
esce
nd
ed a
tan
ave
rag
e ra
te o
f 29
2.5
ft/h
.
Tim
e8:
00 A
.M.
10:0
0 A.M
.1:
00 P
.M.
4:30
P.M
.7:
00 P
.M.
Nu
mb
er o
f V
oter
s14
135
179
81,
008
1,75
3
©G
lenc
oe/M
cGra
w-H
ill19
1M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
TEM
PER
ATU
RE
Use
th
e ta
ble
bel
ow t
hat
sh
ows
the
hig
h t
emp
erat
ure
of
a ci
ty f
or t
he
firs
t p
art
of A
ugu
st.
1.F
ind
the
rate
of
chan
ge i
n t
he
hig
h t
empe
ratu
re b
etw
een
Au
gust
1 a
nd
Au
gust
5.
2°/d
ay
2.F
ind
the
rate
of
chan
ge i
n t
he
hig
h t
empe
ratu
re b
etw
een
Au
gust
5 a
nd
Au
gust
14.
1°/d
ay
3.D
uri
ng
wh
ich
of
thes
e tw
o ti
me
peri
ods
did
the
hig
h t
empe
ratu
re r
ise
fast
er?
bet
wee
n A
ug
ust
1 a
nd
Au
gu
st 5
4.F
ind
the
rate
of
chan
ge i
n t
he
hig
h t
empe
ratu
re b
etw
een
Au
gust
14
and
Au
gust
15.
Th
en i
nte
rpre
t it
s m
ean
ing.
0°/d
ay;
Bet
wee
n A
ug
ust
14
and
Au
gu
st 1
5,th
e h
igh
tem
per
atu
re d
id n
ot
chan
ge.
CO
MPA
NY
GR
OW
THU
se t
he
grap
h t
hat
sh
ows
the
nu
mb
er o
f em
plo
yees
at
a c
omp
any
bet
wee
n 1
994
and
200
2.
5.F
ind
the
rate
of
chan
ge i
n t
he
nu
mbe
r of
em
ploy
ees
betw
een
199
4 an
d 19
96.
7 em
plo
yees
/yr
6.F
ind
the
rate
of
chan
ge i
n t
he
nu
mbe
r of
em
ploy
ees
betw
een
199
6 an
d 19
99.
3 em
plo
yees
/yr
7.D
uri
ng
wh
ich
of
thes
e tw
o ti
me
peri
ods
did
the
nu
mbe
r of
em
ploy
ees
grow
fas
ter?
bet
wee
n 1
994
and
199
6
8.F
ind
the
rate
of
chan
ge i
n t
he
nu
mbe
r of
em
ploy
ees
betw
een
199
9 an
d 20
02.T
hen
in
terp
ret
its
mea
nin
g.�
1 em
plo
yee/
yr;
Bet
wee
n 1
999
and
200
2,th
e n
um
ber
of
emp
loye
esd
ecre
ased
an
ave
rag
e o
f 1
emp
loye
e/yr
.
y
x
Number of Employees 1020304050 019
9419
9619
9820
0020
02
Year
Com
pany
Gro
wth
( 199
9, 4
1)
( 200
2, 3
8)( 1
996,
32)
( 199
4, 1
8)
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Ski
llsR
ate
of
Ch
ang
e
Lesson 4–2
Dat
e1
514
15
Hig
h T
emp
erat
ure
(ºF
)85
9310
210
2
Answers (Lesson 4-2)
© Glencoe/McGraw-Hill A7 Mathematics: Applications and Concepts, Course 3
©G
lenc
oe/M
cGra
w-H
ill19
4M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
An
alyz
ing
Gra
ph
sA
gra
ph c
an b
e u
sed
to r
epre
sen
t m
any
real
-lif
e si
tuat
ion
s.G
raph
s su
ch a
sth
ese
ofte
n h
ave
tim
e as
th
e di
men
sion
on
th
e h
oriz
onta
l ax
is.B
y an
alyz
ing
the
rate
of
chan
ge o
f di
ffer
ent
part
s of
a g
raph
,you
can
dra
w c
oncl
usi
ons
abou
t w
hat
was
hap
pen
ing
in t
he
real
-lif
e si
tuat
ion
at
that
tim
e.
TRA
VEL
Th
e gr
aph
at
the
righ
t re
pre
sen
ts t
he
spee
dof
a c
ar a
s it
tra
vels
alo
ng
the
road
.Des
crib
e w
hat
is h
app
enin
g in
th
e gr
aph
.
•A
t th
e or
igin
,th
e ca
r is
sto
pped
.
•W
her
e th
e li
ne
show
s a
fast
,pos
itiv
e ra
te o
fch
ange
,th
e ca
r is
spe
edin
g u
p.
•T
hen
th
e ca
r is
goi
ng
at a
con
stan
t sp
eed,
show
n b
y th
e h
oriz
onta
l pa
rt o
f th
e gr
aph
.
•T
he
car
is s
low
ing
dow
n w
her
e th
e gr
aph
show
s a
neg
ativ
e ra
te o
f ch
ange
.
•T
he
car
stop
s an
d st
ays
stil
l fo
r a
shor
t ti
me.
Th
en i
t sp
eeds
up
agai
n.
Th
e st
arti
ng
and
stop
pin
g pr
oces
s re
peat
s co
nti
nu
ally
.
An
alyz
e ea
ch g
rap
h.
1.A
shle
y is
rid
ing
her
bic
ycle
alo
ng
a sc
enic
tra
il.
Des
crib
e w
hat
is
hap
pen
ing
in t
he
grap
h.
Sam
ple
an
swer
:A
t th
e b
egin
nin
g,A
shle
y is
sit
tin
g
still
.Sh
e sp
eed
s u
p q
uic
kly,
then
slo
ws
do
wn
a li
ttle
.Th
en s
he
trav
els
at t
he
sam
e sp
eed
fo
r a
sho
rt t
ime.
Ash
ley
spee
ds
up
q
uic
kly
and
tra
vels
at
the
sam
e sp
eed
fo
r a
lon
g t
ime.
Fin
ally
,sh
e sl
ow
s d
ow
n s
low
ly
and
sto
ps.
2.T
he
grap
h s
how
s th
e de
pth
of
wat
er i
n a
pon
d as
you
trav
el o
ut
from
th
e sh
ore.
Des
crib
e w
hat
is
hap
pen
ing
in t
he
grap
h.
Sam
ple
an
swer
:A
t th
e b
egin
nin
g,t
he
wat
er g
ets
dee
per
slo
wly
.T
hen
th
ere
is a
fas
t in
crea
se in
dep
th.T
he
dep
th is
th
e sa
me
for
a sh
ort
dis
tan
ce,t
hen
in
crea
ses
slo
wly
fo
r a
lon
g d
ista
nce
.Th
en
the
dep
th d
ecre
ases
fo
r a
sho
rt d
ista
nce
b
efo
re b
egin
nin
g t
o in
crea
se a
gai
n.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enric
hmen
t
car i
s ac
cele
ratin
gm
aint
aini
ng s
peed
car i
s sl
owin
g do
wn
car i
s st
oppe
d
Speed (mph)
Tim
e (m
in)
0 Speed (ft/s)
Tim
e (m
in)
0 Depth (ft)
Dis
tan
ce f
rom
Sh
ore
(ft
)0
Lesson 4–2
Pre-
Act
ivit
yR
ead
th
e in
tro
du
ctio
n a
t th
e to
p o
f p
age
160
in y
ou
r te
xtb
oo
k.W
rite
yo
ur
answ
ers
bel
ow
.
1.B
y h
ow m
any
bear
s di
d A
lici
a’s
coll
ecti
on i
ncr
ease
bet
wee
n 1
997
and
1999
? B
etw
een
199
9 an
d 20
02?
14;1
5
2.B
etw
een
wh
ich
yea
rs d
id A
lici
a’s
coll
ecti
on i
ncr
ease
th
e fa
stes
t?b
etw
een
199
7 an
d 1
999;
Sam
ple
an
swer
:Wh
ile t
he
incr
ease
bet
wee
n e
ach
tim
e p
erio
d is
nea
rly
the
sam
e,th
e fi
rst
incr
ease
occ
urs
ove
r a
sho
rter
am
ou
nt
of
tim
e.
Rea
din
g t
he
Less
on
3.W
hat
doe
s a
rate
of
chan
ge m
easu
re o
n a
gra
ph?
Sam
ple
an
swer
:h
ow
fas
t a
seg
men
t g
oes
up
or
do
wn
wh
en t
he
gra
ph
is r
ead
fro
m le
ft t
o r
igh
t
4.O
n a
gra
ph,w
hat
doe
s it
mea
n w
hen
a r
ate
of c
han
ge i
s n
egat
ive?
Sam
ple
an
swer
:Th
ere
is a
dec
reas
e in
y-v
alu
es.
5.C
ompl
ete
the
sen
ten
ce:W
hen
a q
uan
tity
doe
s n
ot c
han
ge o
ver
a pe
riod
of
tim
e,it
is
said
to
hav
e a
____
____
__ r
ate
of c
han
ge.
zero
Hel
pin
g Y
ou
Rem
emb
er6.
Wri
te o
ut
in w
ords
th
e fo
rmu
la f
or f
indi
ng
a ra
te o
f ch
ange
bet
wee
n t
wo
data
poi
nts
(x 1
,y1)
an
d (x
2,y 2
).S
amp
le a
nsw
er:T
o f
ind
th
e ra
teo
f ch
ang
e b
etw
een
tw
o d
ata
po
ints
,div
ide
the
dif
fere
nce
inth
e y-
coo
rdin
ates
by
the
dif
fere
nce
in t
he
x-co
ord
inat
es.
Read
ing
to L
earn
Mat
hem
atic
sR
ate
of
Ch
ang
e
©G
lenc
oe/M
cGra
w-H
ill19
3M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Answers (Lesson 4-2)
An
swer
s
© Glencoe/McGraw-Hill A8 Mathematics: Applications and Concepts, Course 3
Prac
tice:
Ski
llsS
lop
e
©G
lenc
oe/M
cGra
w-H
ill19
6M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Fin
d t
he
slop
e of
eac
h l
ine.
1.�1 3�
2.�3 2�
3.�
�3 2�
4.�
�1 5�5.
06.
�2
Th
e p
oin
ts g
iven
in
eac
h t
able
lie
on
a l
ine.
Fin
d t
he
slop
e of
th
e li
ne.
Th
en g
rap
h t
he
lin
e.
7.8.
9.
�1 3��
�1 2��
1
10.
11.
12.
0�3 2�
��3 4�
y
xO
y
xO
O
y
xO
y
xO
y
xO
y
xO
y
xO
y
xO
y
xO
y
xO
y
xO
y
xON
AM
E__
____
____
____
____
____
____
____
____
____
__D
ATE
___
____
____
___
PE
RIO
D
____
_
x�
4�
20
2
y3
33
3
x�
7�
5�
3�
1
y�
6�
30
3
x�
8�
40
4
y8
52
�1
x�
2�
10
1
y2
10
�1
x1
35
7
y6
54
3
x0
36
9
y1
23
4
Lesson 4–3
Stud
y Gu
ide
and
Inte
rven
tion
Slo
pe
©G
lenc
oe/M
cGra
w-H
ill19
5M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Fin
d t
he
slop
e of
th
e li
ne
in t
he
grap
h.
Ch
oose
tw
o po
ints
on
th
e li
ne.
Th
e ve
rtic
al c
han
ge f
rom
poi
nt
Ato
poi
nt
Bis
4 u
nit
s w
hil
e th
e h
oriz
onta
l ch
ange
is
2 u
nit
s.
slop
e �
�r ri us ne �D
efin
ition
of
slop
e
��4 2�
The
ris
e is
4,
and
the
run
is 2
.
�2
Sim
plify
.
Th
e sl
ope
of t
he
lin
e is
2.
Th
e p
oin
ts i
n t
he
tab
le l
ie o
n a
lin
e.F
ind
th
e sl
ope
of t
he
lin
e.
slop
e �
�r ri us ne ��c ch ha an ng ge e
i in ny x
�
��� 34 �
or �
�4 3�
Th
e sl
ope
of t
he
lin
e is
��4 3�.
Fin
d t
he
slop
e of
eac
h l
ine.
1.�3 2�
2.�3 5�
3.�
�1 4�
Th
e p
oin
ts g
iven
in
eac
h t
able
lie
on
a l
ine.
Fin
d t
he
slop
e of
th
e li
ne.
4.�3 2�
5.�
�1 5�
y
xO
y
xO
y
xO
The
slo
pe
of a
line
is t
he r
atio
of
the
rise,
or
vert
ical
cha
nge,
to
the
run,
or
horiz
onta
l cha
nge.
y
xOris
e: 4
run:
2
B
A
x�
21
47
y5
1�
3�
7
��
�
�
�
�
� 3
x�
50
510
y4
32
1
x3
57
9
y�
12
58
� 3
� 3
� 4
� 4
� 4
← ←
Answers (Lesson 4-3)
© Glencoe/McGraw-Hill A9 Mathematics: Applications and Concepts, Course 3
Pre-
Act
ivit
yR
ead
th
e in
tro
du
ctio
n a
t th
e to
p o
f p
age
166
in y
ou
r te
xtb
oo
k.W
rite
yo
ur
answ
ers
bel
ow
.
1.P
ick
seve
ral
pair
s of
poi
nts
fro
m t
hos
e pl
otte
d an
d fi
nd
the
rate
of
chan
gebe
twee
n t
hem
.Wri
te e
ach
rat
e in
sim
ples
t fo
rm.
All
rate
s o
f ch
ang
e eq
ual
8 f
t/s.
2.W
hat
is
tru
e of
th
ese
rate
s?T
hey
are
all
the
sam
e.
Rea
din
g t
he
Less
on
3.S
lope
can
be
posi
tive
,neg
ativ
e,or
zer
o.F
or e
ach
on
e of
th
ese
poss
ibil
itie
sdr
aw a
n e
xam
ple
of a
lin
e w
ith
th
at k
ind
of s
lope
.
Sam
ple
an
swer
:S
amp
le a
nsw
er:
Sam
ple
an
swer
:p
osi
tive
slo
pe
neg
ativ
e sl
op
eze
ro s
lop
e
Hel
pin
g Y
ou
Rem
emb
er4.
Th
e sl
ope
of a
lin
e is
def
ined
by
the
rise
com
pare
d to
th
e ru
n b
etw
een
an
ytw
o po
ints
on
th
e li
ne.
Th
ink
abou
t th
e w
ords
ris
ean
d ru
n.H
ow c
an y
oure
mem
ber
wh
ich
wor
d re
pres
ents
ver
tica
l ch
ange
an
d w
hic
h w
ord
repr
esen
ts h
oriz
onta
l ch
ange
?S
amp
le a
nsw
er:
Ris
eis
a v
erti
cal
acti
on
,as
in r
isin
gfr
om
yo
ur
seat
at
the
tab
le;
run
is a
ho
rizo
nta
l act
ion
,as
in r
un
nin
gar
ou
nd
a t
rack
.
y
xO
y
xO
y
xORe
adin
g to
Lea
rn M
athe
mat
ics
Slo
pe
©G
lenc
oe/M
cGra
w-H
ill19
8M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Lesson 4–3
Prac
tice:
Wor
d Pr
oble
ms
Slo
pe
©G
lenc
oe/M
cGra
w-H
ill19
7M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
FLO
WER
SF
or E
xerc
ises
1 a
nd
2,u
se
LON
G D
ISTA
NC
EF
or E
xerc
ises
3–6
,use
th
e gr
aph
th
at s
how
s th
e d
epth
of
the
the
grap
h t
hat
com
par
es t
he
cost
s of
w
ater
in
a v
ase
of f
low
ers
over
8 d
ays.
lon
g d
ista
nce
ph
one
call
s w
ith
th
ree
dif
fere
nt
com
pan
ies.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
y
x01
12
34
56
78
910
2345678910
Dep
th o
f Wat
er in
Vas
e
Depth (in.)
Day
1.F
ind
the
slop
e of
th
e li
ne.
��3 4�
2.In
terp
ret
the
mea
nin
g th
is s
lope
as
a
rate
of
chan
ge.
Th
e d
epth
of
the
wat
er is
dec
reas
ing
by
�3 4�in
chea
ch d
ay.
y
x0
12
34
56
78
9
0.50
1.00
1.50
2.00
2.50
Long
Dis
tanc
e Ch
arge
s
Cost ($)
Leng
th o
f Cal
l (m
inut
es)
Com
pany
A
Com
pany
B
Com
pany
C
3.F
ind
the
slop
e of
th
e li
ne
for
Com
pan
yA
.Th
en i
nte
rpre
t th
is s
lope
as
a ra
te o
fch
ange
.0.
25;T
he
cost
of
a ca
llw
ith
Co
mp
any
A in
crea
ses
$0.2
5ea
ch m
in.
4.F
ind
the
slop
e of
th
e li
ne
for
Com
pan
y B
.Th
en i
nte
rpre
t th
is s
lope
as
a r
ate
of c
han
ge.
0.12
5;T
he
cost
of
a ca
ll w
ith
Co
mp
any
Bin
crea
ses
$0.1
25 e
ach
min
.
5.F
ind
the
slop
e of
th
e li
ne
for
Com
pan
yC
.Th
en i
nte
rpre
t th
is s
lope
as
a ra
te o
fch
ange
.0.
05;T
he
cost
of
a ca
llw
ith
Co
mp
any
C in
crea
ses
$0.0
5ea
ch m
in.
6.W
hic
h c
ompa
ny
char
ges
the
leas
t fo
rea
ch a
ddit
ion
al m
inu
te?
Exp
lain
you
rre
ason
ing.
Co
mp
any
C;
Co
mp
any
C c
har
ges
$0.
05 f
or
each
ad
dit
ion
al m
in,w
hile
Co
mp
anie
s A
an
d B
ch
arg
e $0
.25
and
$0.
125,
resp
ecti
vely
.
Answers (Lesson 4-3)
An
swer
s
© Glencoe/McGraw-Hill A10 Mathematics: Applications and Concepts, Course 3
Stud
y Gu
ide
and
Inte
rven
tion
So
lvin
g P
rop
ort
ion
s
©G
lenc
oe/M
cGra
w-H
ill20
0M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Det
erm
ine
wh
eth
er t
he
pai
r of
rat
ios
�2 20 4�an
d �1 12 8�
form
s a
pro
por
tion
.
Fin
d th
e cr
oss
prod
uct
s.
Sin
ce t
he
cros
s pr
odu
cts
are
not
equ
al,t
he
rati
os d
o n
ot f
orm
a p
ropo
rtio
n.
Sol
ve �1 32 0�
�� 7k 0�
.
�1 32 0��
� 7k 0�W
rite
the
equa
tion.
12 �
70�
30 �
kF
ind
the
cros
s pr
oduc
ts.
840
�30
kM
ultip
ly.
�8 34 00 ��
�3 30 0k �D
ivid
e ea
ch s
ide
by 3
0.
28�
kS
impl
ify.
Th
e so
luti
on i
s 28
.
Det
erm
ine
wh
eth
er e
ach
pai
r of
rat
ios
form
s a
pro
por
tion
.
1.�1 17 0�
, �1 52 �
no
2.�6 9�,
�1 12 8�ye
s3.
� 18 2�, �
1 10 5�ye
s
4.� 17 5�
, �1 33 2�
no
5.�7 9�,
�4 69 3�ye
s6.
� 28 4�, �
1 22 8�n
o
7.�4 7�,
�1 72 1�n
o8.
�2 30 5�, �
3 40 5�n
o9.
�1 28 4�, �
3 4�ye
s
Sol
ve e
ach
pro
por
tion
.
10.
� 5x ��
�1 25 5�3
11.
�3 4��
�1 c2 �16
12.
�6 9��
�1 r0 �15
13.
�1 26 4��
� 1z 5�10
14.
�5 8��
� 1s 2�7.
515
.�1 t4 �
��1 10 1�
15.4
16.
�w 6��
�2 7.8 �2.
417
.�5 y�
�� 16
7 .8�12
18.
� 1x 8��
� 37 6�3.
5
20 2412 18
�→
24
· 12
� 2
88→
20
· 18
� 3
60
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
A p
rop
ort
ion
is a
n eq
uatio
n th
at s
tate
s th
at t
wo
ratio
s ar
e eq
uiva
lent
.To
dete
rmin
e w
heth
er a
pai
r of
ratio
s fo
rms
a pr
opor
tion,
use
cro
ss p
rodu
cts.
You
can
also
use
cro
ss p
rodu
cts
to s
olve
pro
port
ions
.
Lesson 4–3
©G
lenc
oe/M
cGra
w-H
ill19
9M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Ch
ien
-Sh
iun
g W
uA
mer
ican
ph
ysic
ist
Ch
ien
-Sh
iun
g W
u (
1912
–199
7) w
as
born
in
Sh
angh
ai,C
hin
a.In
193
6,sh
e ca
me
to t
he
Un
ited
S
tate
s to
fu
rth
er h
er s
tudi
es i
n s
cien
ce.S
he
rece
ived
her
do
ctor
ate
in p
hys
ics
in 1
940
from
th
e U
niv
ersi
ty o
f C
alif
orn
ia,a
nd
beca
me
know
n a
s on
e of
th
e w
orld
’s l
eadi
ng
phys
icis
ts.I
n 1
975,
she
was
aw
arde
d th
e N
atio
nal
Med
al
of S
cien
ce.
Wu
is
mos
t fa
mou
s fo
r an
exp
erim
ent
that
sh
e co
ndu
cted
in
195
7.T
he
outc
ome
of t
he
expe
rim
ent
was
con
side
red
the
mos
t si
gnif
ican
t di
scov
ery
in p
hys
ics
in m
ore
than
se
ven
ty y
ears
.Th
e ex
erci
se b
elow
wil
l h
elp
you
lea
rn s
ome
fact
s ab
out
it.
Th
e p
oin
ts g
iven
in
eac
h t
able
lie
on
a l
ine.
Fin
d t
he
slop
e of
th
e li
ne.
Th
e w
ord
or
ph
rase
fol
low
ing
the
solu
tion
wil
l co
mp
lete
th
est
atem
ent
corr
ectl
y.
1.2.
At
the
tim
e of
th
e ex
peri
men
t,W
uT
he
site
of
the
expe
rim
ent
was
th
e w
as a
pro
fess
or a
t .
in W
ash
ingt
on,D
.C.
slop
e �
3:C
olu
mbi
a U
niv
ersi
tysl
ope
�0:
Nat
ion
al B
ure
au o
f S
tan
dard
ssl
ope
�1:
Sta
nfo
rd U
niv
ersi
tysl
ope
�3:
Sm
ith
son
ian
In
stit
uti
onC
olu
mb
ia U
niv
ersi
tyN
atio
nal
Bu
reau
of
Sta
nd
ard
s
3.4.
Th
e ex
peri
men
t in
volv
ed a
su
bsta
nce
In t
he
expe
rim
ent,
the
subs
tan
ce w
asca
lled
.
cool
ed t
o .
slop
e �
2:ca
rbon
14
slop
e �
�4 3�:�
273�
C
slop
e �
1:co
balt
60
slop
e �
�3 4�:�
100°
C
cob
alt
60�
273�
C
??
??
Enric
hmen
tN
AM
E__
____
____
____
____
____
____
____
____
____
__D
ATE
___
____
____
___
PE
RIO
D
____
_
x�
21
47
y�
31
59
x0
24
6
y2
46
8
x�
2�
10
1
y3
33
3
x0
12
3
y1
47
10
Answers (Lessons 4-3 and 4-4)
© Glencoe/McGraw-Hill A11 Mathematics: Applications and Concepts, Course 3
Prac
tice:
Wor
d Pr
oble
ms
So
lvin
g P
rop
ort
ion
s
©G
lenc
oe/M
cGra
w-H
ill20
2M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
1.U
SAG
EA
12-
oun
ce b
ottl
e of
sh
ampo
ola
sts
En
riqu
e 16
wee
ks.H
ow l
ong
wou
ld y
ou e
xpec
t an
18-
oun
ce b
ottl
eof
th
e sa
me
bran
d to
las
t h
im?
24 w
k
2.C
OM
PUTE
RS
Abo
ut
13 o
ut
of 2
0 h
omes
hav
e a
pers
onal
com
pute
r.O
n a
str
eet
wit
h 6
0 h
omes
,how
man
y w
ould
you
expe
ct t
o h
ave
a pe
rson
al c
ompu
ter?
39 h
om
es
3.SN
AC
KS
A 6
-ou
nce
pac
kage
of
fru
itsn
acks
con
tain
s 45
pie
ces.
How
man
ypi
eces
wou
ld y
ou e
xpec
t in
a 1
0-ou
nce
pack
age?
75 p
iece
s
4.TY
PIN
GIn
grid
typ
es 3
pag
es i
n t
he
sam
e am
oun
t of
tim
e th
at T
anya
typ
es4.
5 pa
ges.
If I
ngr
id a
nd
Tan
ya s
tart
typi
ng
at t
he
sam
e ti
me,
how
man
ypa
ges
wil
l Tan
ya h
ave
type
d w
hen
Ingr
id h
as t
yped
11
page
s?16
.5 p
ages
5.SC
HO
OL
A g
radi
ng
mac
hin
e ca
n g
rade
48 m
ult
iple
-ch
oice
tes
ts i
n 1
min
ute
.H
ow l
ong
wil
l it
tak
e th
e m
ach
ine
togr
ade
300
test
s?6.
25 m
in
6.A
MU
SEM
ENT
PAR
KS
Th
e w
aiti
ng
tim
e to
ride
a r
olle
r co
aste
r is
20
min
ute
s w
hen
150
peop
le a
re i
n l
ine.
How
lon
g is
th
ew
aiti
ng
tim
e w
hen
240
peo
ple
are
inli
ne?
32 m
in
7.PR
OD
UC
TIO
NA
sh
op p
rodu
ces
39w
etsu
its
ever
y 2
wee
ks.
How
lon
g w
ill
it t
ake
the
shop
to
prod
uce
429
wet
suit
s?22
wk
8.FI
SHO
f th
e 50
fis
h t
hat
Jim
cau
ght
from
th
e la
ke,1
4 w
ere
trou
t.T
he
esti
mat
ed p
opu
lati
on o
f th
e la
ke i
s7,
500
fish
.Abo
ut
how
man
y tr
out
wou
ld y
ou e
xpec
t to
be
in t
he
lake
?2,
100
tro
ut
Prac
tice:
Ski
llsS
olv
ing
Pro
po
rtio
ns
Lesson 4–4
©G
lenc
oe/M
cGra
w-H
ill20
1M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Det
erm
ine
wh
eth
er e
ach
pai
r of
rat
ios
form
s a
pro
por
tion
.
1.�5 8�,
�2 3�n
o2.
�7 3�,�1 64 �
yes
3.�6 8�,
� 19 2�ye
s
4.�1 96 �
, �1 61 �
no
5.�5 15 0�
, �1 22 �
no
6.�6 8�,
�1 25 0�ye
s
7.�5 9�,
�1 25 7�ye
s8.
� 13 8�, �
1 61 6�ye
s9.
� 17 1�, �
1 25 3�n
o
10.
� 19 3�, �
1 13 7�n
o11
.� 43 2�
, �75 0�
yes
12.
�6 7�,�3 46 9�
no
Sol
ve e
ach
pro
por
tion
.
13.
� 14 2��
� 9y �3
14.
� 16 8��
�4 c�12
15.
�7 z��
�8 14 2�1
16.
� 15 0��
� w8 �16
17.
� 9x ��
� 14 5�2.
418
.� 26 0�
�� 5y �
1.5
19.
�5 9��
�6 r�10
.820
.� n8 �
��1 70 �
5.6
21.
�d 5��
�1 82 0�0.
75
22.
� 5y ��
�1 13 0�6.
523
.� 22 8�
�� 3p 5�
2.5
24.
�1 t1 ��
�1 10 10 �1.
21
25.
�1 m.2 ��
�3 5�2
26.
�0 1. .9 5��
� 1a 0�6
27.
�3 7��
� 4k .2�1.
8
28.
�6 x.3 ��
�1 58 �1.
7529
.�3 9.6 �
�� 0b .5�
0.2
30.
� 11 .4 5��
�4 y.2 �0.
45
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Answers (Lesson 4-4)
An
swer
s
© Glencoe/McGraw-Hill A12 Mathematics: Applications and Concepts, Course 3
©G
lenc
oe/M
cGra
w-H
ill20
4M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Peo
ple
of
the
Un
ited
Sta
tes
A n
atio
nal
cen
sus
is t
aken
eve
ry t
en y
ears
.Th
e 19
90 c
ensu
s re
veal
ed t
hat
ther
e w
ere
abou
t 25
0,00
0,00
0 pe
ople
in
th
e U
nit
ed S
tate
s,an
d th
at a
bou
t 8
out
of 1
00 o
f th
ese
peop
le w
ere
5–13
yea
rs o
ld.T
o fi
nd
the
nu
mbe
r of
peop
le i
n t
he
Un
ited
Sta
tes
that
wer
e 5–
13 y
ears
old
,use
th
e ra
tio
ofpe
ople
5–1
3 ye
ars
old
and
crea
te a
pro
port
ion
.
� 18 00��� 25
0,0n 00
,000
�
To
solv
e th
e pr
opor
tion
,fin
d cr
oss
prod
uct
s.
8
250,
000,
000
�2,
000,
000,
000
and
n
100
�10
0n
Th
en d
ivid
e:2,
000,
000,
000
10
0�
20,0
00,0
00.
In 1
990,
abou
t 20
,000
,000
peo
ple
in t
he
Un
ited
Sta
tes
wer
e 5–
13 y
ears
old
.
Use
th
e ap
pro
xim
ate
rati
os i
n e
ach
exe
rcis
e to
cre
ate
a p
rop
orti
on,
give
n t
hat
th
ere
wer
e ab
out
250,
000,
000
peo
ple
in
th
e U
nit
ed S
tate
s.T
hen
sol
ve a
nd
ch
oose
th
e co
rrec
t an
swer
fro
m t
he
choi
ces
at t
he
righ
t.
1.T
he
Un
ited
Sta
tes
is a
div
erse
col
lect
ion
of
diff
eren
t__
____
__A
.20
0,00
0,00
0ra
ces
and
eth
nic
ori
gin
s.A
sian
s or
Pac
ific
Isl
ande
rsac
cou
nte
d fo
r ab
out
� 13 00�of
th
e po
pula
tion
of
the
Un
ited
Sta
tes.
Abo
ut
how
man
y pe
ople
of A
sian
or
Pac
ific
-Isl
and
orig
in l
ived
in
th
e U
nit
ed S
tate
s?
2.A
fric
an-A
mer
ican
s ac
cou
nte
d fo
r ab
out
� 23 5�of
th
e__
____
__B
.22
,500
,000
popu
lati
on o
f th
e U
nit
ed S
tate
s.A
bou
t h
ow m
any
Afr
ican
-Am
eric
an p
eopl
e li
ved
in t
he
Un
ited
Sta
tes?
3.P
eopl
e of
His
pan
ic o
rigi
n a
ccou
nte
d fo
r ab
out
� 19 00�__
____
__C
.7,
500,
000
of t
he
popu
lati
on o
f th
e U
nit
ed S
tate
s.A
bou
t h
owm
any
peop
le o
f H
ispa
nic
ori
gin
liv
ed i
n t
he
Un
ited
Sta
tes?
4.C
auca
sian
peo
ple
acco
un
ted
for
abou
t �4 5�
of t
he
____
____
D.
2,00
0,00
0po
pula
tion
of
the
Un
ited
Sta
tes.
Abo
ut
how
man
ype
ople
of
wh
ite
or C
auca
sian
ori
gin
liv
ed i
n t
he
Un
ited
Sta
tes?
5.P
eopl
e of
Am
eric
an-I
ndi
an,E
skim
o,or
Alu
et o
rigi
n__
____
E.
30,0
00,0
00
acco
un
ted
for
abou
t � 1,
08 00�of
th
e po
pula
tion
of
the
Un
ited
Sta
tes.
Abo
ut
how
man
y pe
ople
of
Am
eric
an-I
ndi
an,E
skim
o,or
Alu
et o
rigi
n l
ived
in
the
Un
ited
Sta
tes?
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enric
hmen
t
C E B A D
Read
ing
to L
earn
Mat
hem
atic
sS
olv
ing
Pro
po
rtio
ns
Lesson 4–4
Pre-
Act
ivit
yR
ead
th
e in
tro
du
ctio
n a
t th
e to
p o
f p
age
170
in y
ou
r te
xtb
oo
k.W
rite
yo
ur
answ
ers
bel
ow
.
1.W
rite
a r
atio
th
at c
ompa
res
the
nu
mbe
r of
Cal
orie
s fr
om f
at t
o th
e to
tal
nu
mbe
r of
Cal
orie
s.W
rite
th
e ra
tio
as a
fra
ctio
n i
n s
impl
est
form
.
� 12 1�
2.S
upp
ose
you
pla
n t
o ea
t tw
o su
ch g
ran
ola
bars
.Wri
te a
rat
io c
ompa
rin
gth
e n
um
ber
of C
alor
ies
from
fat
to
the
tota
l n
um
ber
of C
alor
ies.
� 12 1�
3.Is
th
e ra
tio
of C
alor
ies
the
sam
e fo
r tw
o gr
anol
a ba
rs a
s it
is
for
one
gran
ola
bar?
Wh
y or
wh
y n
ot?
Th
e ra
tio
s ar
e eq
ual
bec
ause
mu
ltip
lyin
g t
he
nu
mer
ato
r an
d d
eno
min
ato
r o
f a
frac
tio
n b
yth
e sa
me
amo
un
t cr
eate
s an
eq
uiv
alen
t fr
acti
on
.
Rea
din
g t
he
Less
on
4.C
ompl
ete
the
sen
ten
ce:I
f tw
o ra
tios
for
m a
pro
port
ion
,th
en t
he
rati
osar
e sa
id t
o be
___
____
___.
pro
po
rtio
nal
5.D
o th
e ra
tios
�a b�an
d � dc �
alw
ays
form
a p
ropo
rtio
n?
Wh
y or
wh
y n
ot?
No
;S
amp
le a
nsw
er:T
he
rati
os
on
ly f
orm
a p
rop
ort
ion
if t
he
cro
ss p
rod
uct
s ad
and
bc
are
equ
al.
6.E
xpla
in h
ow y
ou c
an u
se c
ross
pro
duct
s to
sol
ve p
ropo
rtio
ns
in w
hic
h o
ne
of t
he
term
s is
not
kn
own
.S
amp
le a
nsw
er:
Fin
d t
he
cro
ssp
rod
uct
s,th
en d
ivid
e b
oth
sid
es o
f th
e eq
uat
ion
by
the
con
stan
t th
at is
mu
ltip
lied
by
the
un
kno
wn
var
iab
le.
Hel
pin
g Y
ou
Rem
emb
er7.
For
th
e pr
opor
tion
�a b�an
d � dc �,
wh
y do
you
th
ink
the
prod
uct
s ad
and
bcar
eca
lled
cro
ss p
rod
uct
s?S
amp
le a
nsw
er:
If y
ou
dra
w li
nes
fro
m a
to d
and
fro
m b
to c
in t
he
pro
po
rtio
n,t
he
lines
fo
rm a
cro
ss.
©G
lenc
oe/M
cGra
w-H
ill20
3M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Answers (Lesson 4-4)
© Glencoe/McGraw-Hill A13 Mathematics: Applications and Concepts, Course 3
©G
lenc
oe/M
cGra
w-H
ill20
6M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Det
erm
ine
wh
eth
er e
ach
pai
r of
pol
ygon
s is
sim
ilar
.Exp
lain
you
rre
ason
ing.
1.2.
Yes;
corr
esp
on
din
gN
o;
corr
esp
on
din
gan
gle
s ar
e co
ng
ruen
t an
dan
gle
s ar
e co
ng
ruen
t,bu
t
�1 10 5��
� 18 2��
�1 10 5��
� 18 2�.
�1 10 50 0��
�1 10 51 1�.
3.4.
Yes;
corr
esp
on
din
gYe
s;co
rres
po
nd
ing
ang
les
are
con
gru
ent
and
ang
les
are
con
gru
ent
and
�1 74 ��
�2 10 0��
�8 4�.�6 3�
�� 37 .5�
�� 37 .5�
.
5.6.
� 2x .6��
�8 4�;5.
2�6 x.5 �
��2 1. .6 8�
;4.
5
7.8.
� 1x .5��
� 36 .6�;
2.5
�1 x0 ��
� 96 .6�;
16
x
6
9.6
14
22.4
9.6
6
10
66.
5
1.5
3.6
3.9
x
x
1.8
2.6
6.5
88
2.6
44
x
67
7
3
3.5
3.5
208
1410
74
151
101
150
100
15
8
10
12
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Ski
llsS
imila
r P
oly
go
ns
Lesson 4–5
Stud
y Gu
ide
and
Inte
rven
tion
Sim
ilar
Po
lyg
on
s
©G
lenc
oe/M
cGra
w-H
ill20
5M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Det
erm
ine
wh
eth
er �
AB
Cis
sim
ilar
to
�D
EF
.Exp
lain
you
r re
ason
ing.
�A
��
D,�
B �
�E
,�C
��
F,
� DAB E�
��4 6�
or �2 3�,
�B EC F�
��6 9�
or �2 3�,
� DAC F�
�� 18 2�
or �2 3�
Th
e co
rres
pon
din
g an
gles
are
con
gru
ent,
and
the
corr
espo
ndi
ng
side
s ar
e pr
opor
tion
al.
Th
us,
�A
BC
is s
imil
ar t
o �
DE
F.
Giv
en t
hat
pol
ygon
KL
MN
�p
olyg
on P
QR
S,w
rite
a p
rop
orti
on t
ofi
nd
th
e m
easu
re o
f P�
Q�.T
hen
sol
ve.
Th
e ra
tio
of c
orre
spon
din
g si
des
from
pol
ygon
KL
MN
topo
lygo
n P
QR
Sis
�4 3�.W
rite
a p
ropo
rtio
n w
ith
th
is s
cale
fact
or.L
et x
repr
esen
t th
e m
easu
re o
f P�
Q�.
� PKQL �
��4 3�
K�L�
corr
espo
nds
to P�
Q�.T
he s
cale
fact
or is
�4 3�.
�5 x��
�4 3�K
L�
5 an
d P
Q�
x
5�
3�
x �
4F
ind
the
cros
s pr
oduc
ts.
�1 45 ��
�4 4x �M
ultip
ly.T
hen
divi
de e
ach
side
by
4.
3.75
�x
Sim
plify
.
1.D
eter
min
e w
het
her
th
e po
lygo
ns
2.T
he
tria
ngl
es b
elow
are
sim
ilar
.Wri
te a
belo
w a
re s
imil
ar.E
xpla
in y
our
prop
orti
on t
o fi
nd
each
mis
sin
g m
easu
re.
reas
onin
g.T
hen
sol
ve.
No
;co
rres
po
nd
ing
an
gle
s�1 x5 �
��6 4�;
x�
10ar
e co
ng
ruen
t,bu
t
�1 12 1��
�5 4�.
1264 8
15x
11
5
124
Kx
3
5
N
LP
Q
SR
M
4
B
8
E
CA
DF
64
6
12
9
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Two
poly
gons
are
sim
ilar
if th
eir
corr
espo
ndin
g an
gles
are
con
grue
nt a
nd t
heir
corr
espo
ndin
g si
des
are
prop
ortio
nal.
Answers (Lesson 4-5)
An
swer
s
© Glencoe/McGraw-Hill A14 Mathematics: Applications and Concepts, Course 3
Pre-
Act
ivit
yC
om
ple
te t
he
Min
i Lab
at
the
top
of
pag
e 17
8 in
yo
ur
text
bo
ok.
Wri
te y
ou
r an
swer
s b
elo
w.
1.C
ompa
re t
he
angl
es o
f th
e tr
ian
gles
by
mat
chin
g th
em u
p.Id
enti
fy t
he
angl
e pa
irs
that
hav
e eq
ual
mea
sure
.m
�D
�m
�L
,m�
E�
m�
J,m
�F
�m
�K
2.E
xpre
ss t
he
rati
os �D L
KF �, �
E JKF �
,an
d �D L
E J�to
th
e n
eare
st t
enth
.0.
7;0.
7;0.
7
3.W
hat
do
you
not
ice
abou
t th
e ra
tios
of
the
mat
chin
g si
des
of m
atch
ing
tria
ngl
es?
Th
ey a
re a
pp
roxi
mat
ely
equ
al.
Rea
din
g t
he
Less
on
4.C
ompl
ete
the
sen
ten
ce:I
f tw
o po
lygo
ns
are
sim
ilar
,th
en t
hei
rco
rres
pon
din
g an
gles
are
___
____
___,
and
thei
r co
rres
pon
din
g si
des
are
____
____
__.
con
gru
ent;
pro
po
rtio
nal
5.If
tw
o po
lygo
ns
hav
e co
rres
pon
din
g an
gles
th
at a
re c
ongr
uen
t,do
es t
hat
mea
n t
hat
th
e po
lygo
ns
are
sim
ilar
? W
hy
or w
hy
not
?S
amp
lean
swer
:N
o;
the
po
lyg
on
s ar
e si
mila
r o
nly
if t
hei
rco
rres
po
nd
ing
sid
es a
re p
rop
ort
ion
al.
6.If
th
e si
des
of o
ne
squ
are
are
3 ce
nti
met
ers
and
the
side
s of
an
oth
ersq
uar
e ar
e 9
cen
tim
eter
s,w
hat
is
the
rati
o of
cor
resp
ondi
ng
side
s fr
om
the
firs
t sq
uar
e to
th
e se
con
d sq
uar
e?�1 3�
Hel
pin
g Y
ou
Rem
emb
er7.
Loo
k u
p th
e ev
eryd
ay d
efin
itio
n o
f th
e w
ord
sim
ilar
in a
dic
tion
ary.
How
does
th
e de
fin
itio
n r
elat
e to
wh
at y
ou l
earn
ed i
n t
his
les
son
?S
amp
lean
swer
:Th
e w
ord
sim
ilar
mea
ns
hav
ing
ch
arac
teri
stic
s in
com
mo
n;
sim
ilar
po
lyg
on
s h
ave
con
gru
ent
ang
les
inco
mm
on
an
d p
rop
ort
ion
al s
ides
in c
om
mo
n.
Read
ing
to L
earn
Mat
hem
atic
sS
imila
r P
oly
go
ns
©G
lenc
oe/M
cGra
w-H
ill20
8M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Wor
d Pr
oble
ms
Sim
ilar
Po
lyg
on
s
Lesson 4–5
©G
lenc
oe/M
cGra
w-H
ill20
7M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
1.JO
UR
NA
LISM
Th
e ed
itor
of
the
sch
ool
new
spap
er m
ust
red
uce
th
e si
ze o
f a
grap
h t
o fi
t in
on
e co
lum
n.T
he
orig
inal
grap
h i
s 2
inch
es b
y 2
inch
es,a
nd
the
scal
e fa
ctor
fro
m t
he
orig
inal
to
the
redu
ced
grap
h i
s 8:
3.F
ind
the
dim
ensi
ons
of t
he
grap
h a
s it
wil
lap
pear
in
on
e co
lum
n o
f th
e n
ewsp
aper
.
�3 4�in
.by
�3 4�in
.
2.PH
OTO
CO
PIES
Lyd
ia p
lan
s to
use
aph
otoc
opy
mac
hin
e to
in
crea
se t
he
size
of a
sm
all
char
t th
at s
he
has
mad
e as
part
of
her
sci
ence
pro
ject
.Th
e or
igin
alch
art
is 4
in
ches
by
5 in
ches
.If
she
use
s a
scal
e fa
ctor
of
5:11
,wil
l th
ech
art
fit
on a
sh
eet
of p
aper
8�1 2�
inch
esby
11
inch
es?
Exp
lain
.
No
;it
will
be
8 �4 5�
in.b
y 11
in.
3.M
ICR
OC
HIP
ST
he
imag
e of
a m
icro
chip
in a
pro
ject
ion
mic
rosc
ope
mea
sure
s 8
inch
es b
y 10
in
ches
.Th
e w
idth
of
the
actu
al c
hip
is
4 m
illi
met
ers.
How
lon
gis
th
e ch
ip?
5 m
m
4.PR
OJE
CTI
ON
SA
dra
win
g on
atr
ansp
aren
cy i
s 11
.25
cen
tim
eter
s w
ide
by 2
3.5
cen
tim
eter
s ta
ll.T
he
wid
th o
fth
e im
age
of d
raw
ing
proj
ecte
d on
to a
scre
en i
s 2.
7 m
eter
s.H
ow t
all
is t
he
draw
ing
on t
he
scre
en?
5.64
m
5.G
EOM
ETRY
Pol
ygon
AB
CD
is s
imil
ar t
opo
lygo
n F
GH
I.E
ach
sid
e of
pol
ygon
AB
CD
is 3
�1 4�ti
mes
lon
ger
than
th
eco
rres
pon
din
g si
de o
f po
lygo
n F
GH
I.F
ind
the
peri
met
er o
f po
lygo
n F
GH
I.
42�1 4�
in.
6.K
ITES
A t
oy c
ompa
ny
prod
uce
s tw
oki
tes
wh
ose
shap
es a
re g
eom
etri
call
ysi
mil
ar.F
ind
the
len
gth
of
the
mis
sin
gsi
de o
f th
e sm
alle
r ki
te.
18.7
5 in
.25
in.
25 in
.
30 in
.22
.5 in
.
30 in
.x
B
A
D
I
H
F
G
C
3 in
.
2 in
. 5 in
.
3 in
.
Answers (Lesson 4-5)
© Glencoe/McGraw-Hill A15 Mathematics: Applications and Concepts, Course 3
Stud
y Gu
ide
and
Inte
rven
tion
Sca
le D
raw
ing
s an
d M
od
els
©G
lenc
oe/M
cGra
w-H
ill21
0M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
INTE
RIO
R D
ESIG
NA
des
ign
er h
as m
ade
asc
ale
dra
win
g of
a l
ivin
g ro
om f
or o
ne
of h
er c
lien
ts.T
he
scal
e of
th
e d
raw
ing
is 1
in
ch �
1 �1 3�
feet
.On
th
e d
raw
ing,
the
sofa
is
6 in
ches
lon
g.F
ind
th
e ac
tual
len
gth
of
the
sofa
.
Let
xre
pres
ent
the
actu
al l
engt
h o
f th
e so
fa.W
rite
an
d so
lve
a pr
opor
tion
.
Th
e ac
tual
len
gth
of
the
sofa
is
8 fe
et.
Fin
d t
he
scal
e fa
ctor
for
th
e d
raw
ing
in E
xam
ple
1.
Wri
te t
he
rati
o of
1 i
nch
to
1 �1 3�
feet
in
sim
ples
t fo
rm.
�� 11 6i in n.
�.
��C
onve
rt 1
�1 3�fe
et t
o in
ches
.
Th
e sc
ale
fact
or i
s � 11 6�
or 1
:16.
Th
is m
ean
s th
at e
ach
dis
tan
ce o
n t
he
draw
ing
is � 11 6�
the
actu
al d
ista
nce
.
LAN
DSC
API
NG
Yu
tak
a h
as m
ade
a sc
ale
dra
win
gof
his
yar
d.T
he
scal
e of
th
e d
raw
ing
is1
cen
tim
eter
= 0
.5 m
eter
.
1.T
he
len
gth
of
the
pati
o is
4.5
cen
tim
eter
s in
th
edr
awin
g.F
ind
the
actu
al l
engt
h.
2.25
m2.
Th
e ac
tual
dis
tan
ce b
etw
een
th
e w
ater
fau
cet
and
the
pear
tre
e is
11.
2 m
eter
s.F
ind
the
corr
espo
ndi
ng
dist
ance
on
th
e dr
awin
g.22
.4 c
m3.
Fin
d th
e sc
ale
fact
or f
or t
he
draw
ing.
� 51 0�
1 in
.� 1 �
1 3�ft
To f
ind
the
scal
e fa
ctor
for
scal
e dr
awin
gs a
nd m
odel
s, w
rite
the
ratio
giv
en b
y th
e sc
ale
in s
impl
est
form
.
1 in
.6
in.
1 f
t1 3
x ft
�
1 · x
� 1
· 6
1 3x
� 8
draw
ing
dist
ance
→
actu
al d
ista
nce
→
← d
raw
ing
leng
th←
act
ual l
engt
h
Fin
d th
e cr
oss
prod
ucts
.
Sim
plify
.
↓↓
Dra
win
g S
cale
Act
ual L
engt
h
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
1 in
. = 1
ft
Sofa
1 3
1 cm
= 0
.5 m
Patio
Pond
Path
Wat
er F
auce
t
Pear
Tree
Gard
en
Dis
tanc
es o
n a
scal
e dr
awin
g or
mod
el a
re p
ropo
rtio
nal t
o re
al-li
fe d
ista
nces
.The
sca
leis
det
erm
ined
by t
he r
atio
of
a gi
ven
leng
th o
n a
draw
ing
or m
odel
to
its c
orre
spon
ding
act
ual l
engt
h.
Lesson 4–5
©G
lenc
oe/M
cGra
w-H
ill20
9M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Sim
ilar
and
Co
ng
ruen
t Fi
gu
res
If a
4-i
nch
by
5-in
ch p
hot
ogra
ph i
s en
larg
ed t
o an
8-i
nch
by
10-i
nch
phot
ogra
ph,t
he
phot
ogra
phs
are
said
to
be s
imil
ar.T
hey
hav
e th
e sa
me
shap
e,bu
t th
ey d
o n
ot h
ave
the
sam
e si
ze.I
f a
4-in
ch b
y 5-
inch
ph
otog
raph
is d
upl
icat
ed a
nd
a n
ew 4
-in
ch b
y 5-
inch
ph
otog
raph
is
mad
e,th
eph
otog
raph
s ar
e sa
id t
o be
con
gru
ent.
Th
ey h
ave
the
sam
e si
ze a
nd
shap
e.
In e
ach
exe
rcis
e,id
enti
fy w
hic
h o
f th
e tr
ian
gles
are
con
gru
ent
toea
ch o
ther
an
d i
den
tify
wh
ich
of
the
shap
es a
re s
imil
ar t
o ea
ch o
ther
.U
se t
he
sym
bol
for
�co
ngr
uen
ce a
nd
th
esy
mb
ol�
for
sim
ilar
ity.
1.2.
a�
b;
a �
b;
c�
db
�c;
a �
c
3.4.
AB
H �
LK
C;
CD
P �
MN
P;
QR
T �
MN
P;
QR
T �
CD
PB
CG
�JK
M;
AQ
H �
LH
Q;
BT
D �
BC
G;
AB
D �
CB
D;
HK
J �
NM
L;
JKM
�JN
P;
HK
J �
AB
D;
HK
J �
CB
D;
BT
D �
JNP
;L
MN
�D
BC
;L
MN
�D
BA
BC
G �
JNP
;B
TD
�JK
M
5.
AD
C �
HK
J;A
DC
�A
BD
;A
DC
�C
BD
;A
DC
�L
MN
;A
DC
�D
BC
;A
DC
�D
BA
Enric
hmen
tN
AM
E__
____
____
____
____
____
____
____
____
____
__D
ATE
___
____
____
___
PE
RIO
D
____
_
a
b
cd
f
a
bc
d
AB
C
DJ
L
HN
KM
AB
CD
HK
LM
N
P
Q RT
AB
T C
D
Q
G
H J
LK
M
NP
Answers (Lessons 4-5 and 4-6)
An
swer
s
© Glencoe/McGraw-Hill A16 Mathematics: Applications and Concepts, Course 3
Prac
tice:
Wor
d Pr
oble
ms
Sca
le D
raw
ing
s an
d M
od
els
©G
lenc
oe/M
cGra
w-H
ill21
2M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
CA
MPU
S PL
AN
NIN
GF
or E
xerc
ises
1–3
,use
th
efo
llow
ing
info
rmat
ion
.
Th
e lo
cal
sch
ool
dist
rict
has
mad
e a
scal
e m
odel
of t
he
cam
pus
of E
nge
ls M
iddl
e S
choo
l in
clu
din
ga
prop
osed
new
bu
ildi
ng.
Th
e sc
ale
of t
he
mod
elis
1 i
nch
�3
feet
.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
1.A
n e
xist
ing
gym
nas
ium
is
8 in
ches
tal
lin
th
e m
odel
.How
tal
l is
th
e ac
tual
gym
nas
ium
?24
ft
2.T
he
new
bu
ildi
ng
is 2
2.5
inch
es f
rom
the
gym
nas
ium
in
th
e m
odel
.Wh
atw
ill
be t
he
actu
al d
ista
nce
fro
m t
he
gym
nas
ium
to
the
new
bu
ildi
ng
if i
tis
bu
ilt?
67.5
ft
3.W
hat
is
the
scal
e fa
ctor
of
the
mod
el?
� 31 6�
4.M
APS
On
a m
ap,t
wo
citi
es a
re 5
�3 4�
inch
es a
part
.Th
e sc
ale
of t
he
map
is
�1 2�in
ch �
3 m
iles
.Wh
at i
s th
e ac
tual
dist
ance
bet
wee
n t
he
tow
ns?
34�1 2�
mi
5.TR
UC
KS
Th
e be
d of
Jer
ry’s
pic
kup
tru
ckis
6 f
eet
lon
g.O
n a
sca
le m
odel
of
the
tru
ck,t
he
bed
is 8
in
ches
lon
g.W
hat
is
the
scal
e of
th
e m
odel
?
1 in
.��3 4�
ft
6 ft
6.H
OU
SIN
GM
arta
is
mak
ing
a sc
ale
draw
ing
of h
er a
part
men
t fo
r a
sch
ool
proj
ect.
Th
e ap
artm
ent
is 2
8 fe
et w
ide.
On
her
dra
win
g,th
e ap
artm
ent
is
7 in
ches
wid
e.W
hat
is
the
scal
e of
Mar
ta’s
dra
win
g?1
in.�
4 ft
28 ft
Gymnasium
Parking
Acad
emic
Build
ing
View
of C
ampu
s fro
m A
bove
New
Build
ing
Prac
tice:
Ski
llsS
cale
Dra
win
gs
and
Mo
del
s
Lesson 4–6
©G
lenc
oe/M
cGra
w-H
ill21
1M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
AR
CH
ITEC
TUR
ET
he
scal
e on
a s
et o
f ar
chit
ectu
ral
dra
win
gs f
or a
hou
seis
1.5
in
ches
�2
feet
.Fin
d t
he
len
gth
of
each
par
t of
th
e h
ouse
.
7.W
hat
is
the
scal
e fa
ctor
of
thes
e dr
awin
gs?
� 11 6�
TOW
N P
LAN
NIN
GF
or E
xerc
ises
8–1
1,u
se t
he
foll
owin
g in
form
atio
n.
As
par
t of
a d
own
tow
n r
enew
al p
roje
ct,b
usi
nes
ses
hav
e co
nst
ruct
eda
scal
e m
odel
of
the
tow
n s
qu
are
to p
rese
nt
to t
he
city
com
mis
sion
for
its
app
rova
l.T
he
scal
e of
th
e m
odel
is
1 in
ch �
7 fe
et.
8.T
he
cou
rth
ouse
is
the
tall
est
buil
din
g in
th
e to
wn
squ
are.
If i
t is
5 �1 2�
inch
es t
all
in t
he
mod
el,h
ow t
all
is t
he
actu
al b
uil
din
g?
38�1 2�
ft
9.T
he
busi
nes
s ow
ner
s w
ould
lik
e to
in
stal
l n
ew l
ampp
osts
th
at a
reea
ch 1
2 fe
et t
all.
How
tal
l ar
e th
e la
mpp
osts
in
th
e m
odel
?
1 �5 7�
in.
10.
In t
he
mod
el,t
he
lam
ppos
ts a
re 3
�3 7�in
ches
apa
rt.H
ow f
ar a
part
wil
l th
ey b
e w
hen
th
ey a
re i
nst
alle
d?24
ft
11.
Wh
at i
s th
e sc
ale
fact
or?
� 81 4�
12.
MA
PSO
n a
map
,tw
o ci
ties
are
6�1 2�
inch
es a
part
.Th
e ac
tual
dis
tan
cebe
twee
n t
he
citi
es i
s 10
4 m
iles
.Wh
at i
s th
e sc
ale
of t
he
map
?1
in.�
16 m
i
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Roo
mD
raw
ing
Len
gth
Act
ual
Len
gth
1.L
ivin
g R
oom
15 i
nch
es20
ft
2.D
inin
g R
oom
10.5
in
ches
14 f
t
3.K
itch
en12
�3 4�in
ches
17 f
t
4.L
aun
dry
Roo
m8 �
1 4�in
ches
11 f
t
5.H
all
13�7 8�
inch
es18
.5 f
t
6.G
arag
e16
.5 i
nch
es22
ft
Answers (Lesson 4-6)
© Glencoe/McGraw-Hill A17 Mathematics: Applications and Concepts, Course 3
©G
lenc
oe/M
cGra
w-H
ill21
4M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Scal
e D
raw
ing
sT
he
figu
re a
t th
e ri
ght
has
an
are
a of
6 s
quar
e u
nit
s.If
th
e fi
gure
repr
esen
ted
a m
ap,a
nd
was
dra
wn
to
a sc
ale
of 1
un
it �
3 fe
et,t
he
len
gth
s of
th
e si
des
wou
ld b
e 6
ft a
nd
9 ft
.So,
the
figu
re w
ould
repr
esen
t an
are
a of
54
squ
are
feet
.
Th
e ra
tio
of t
he
actu
al a
rea
of t
he
figu
re t
o th
e sc
ale
area
of
the
figu
re c
an b
e ex
pres
sed
as a
rat
io.
�a sc ct au la el aa rr ee aa�
�� 56 4�
��1 9�
or 1
to
9
Fin
d t
he
actu
al a
rea
and
th
e sc
ale
area
of
thes
e fi
gure
s.T
hen
det
erm
ine
the
rati
o of
act
ual
are
a to
sca
le a
rea.
1.S
cale
:1 u
nit
�4
ft2.
Sca
le:1
un
it �
50 c
m
actu
al a
rea
15ac
tual
are
a 16
scal
e ar
ea
240
scal
e ar
ea
40,0
00
rati
o 1
to 1
6ra
tio
1 to
2,5
00
3.S
cale
:1 u
nit
�8
mi
4.S
cale
:1 u
nit
�12
m
actu
al a
rea
12ac
tual
are
a 30
scal
e ar
ea
768
scal
e ar
ea
4,32
0
rati
o 1
to 6
4ra
tio
1 to
144
5.S
cale
:1 u
nit
�18
in
.6.
Sca
le:1
un
it �
6 km
actu
al a
rea
10ac
tual
are
a 24
scal
e ar
ea3,
240
scal
e ar
ea
864
rati
o 1
to 3
24ra
tio
1 to
36
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enric
hmen
t
Pre-
Act
ivit
yR
ead
th
e in
tro
du
ctio
n a
t th
e to
p o
f p
age
184
in y
ou
r te
xtb
oo
k.W
rite
yo
ur
answ
ers
bel
ow
.
1.H
ow m
any
un
its
wid
e is
th
e ro
om?
9
2.T
he
actu
al w
idth
of
the
room
is
18 f
eet.
Wri
te a
rat
io c
ompa
rin
g th
edr
awin
g w
idth
to
the
actu
al w
idth
.9
un
its:
18 f
eet
3.S
impl
ify
the
rati
o yo
u f
oun
d an
d co
mpa
re i
t to
th
e sc
ale
show
n a
t th
ebo
ttom
of
the
draw
ing.
2,3.
Bo
th t
he
rati
o a
nd
th
e sc
ale
ind
icat
e th
at 1
un
it o
n t
he
dra
win
g is
eq
ual
to
2 f
eet
inre
alit
y.
Rea
din
g t
he
Less
on
4.G
ive
anot
her
exa
mpl
e of
a s
cale
dra
win
g or
sca
le m
odel
th
at i
s di
ffer
ent
from
th
e ex
ampl
es o
f sc
ale
draw
ings
an
d sc
ale
mod
els
give
n o
n p
ages
184–
185
in y
our
text
book
.S
amp
le a
nsw
er:
scal
e m
od
els
of
build
ing
s
5.C
ompl
ete
the
sen
ten
ce:d
ista
nce
s on
a s
cale
mod
el a
re _
____
____
_ to
dist
ance
s in
rea
l li
fe.
pro
po
rtio
nal
6.W
hat
is
the
scal
e fa
ctor
for
a m
odel
if
part
of
the
mod
el t
hat
is
4 in
ches
corr
espo
nds
to
a re
al-l
ife
obje
ct t
hat
is
16 i
nch
es?
�1 4�
Hel
pin
g Y
ou
Rem
emb
er7.
Mak
e a
scal
e dr
awin
g of
a r
oom
,su
ch a
s yo
ur
clas
sroo
m o
r yo
ur
bedr
oom
.S
elec
t an
app
ropr
iate
sca
le s
o th
at y
our
draw
ing
is a
rea
son
able
siz
e.B
esu
re t
o in
dica
te y
our
scal
e on
you
r dr
awin
g.U
se a
not
her
pie
ce o
f pa
per
ifn
eces
sary
.S
ee s
tud
ents
’wo
rk.
Read
ing
to L
earn
Mat
hem
atic
sS
cale
Dra
win
gs
and
Mo
del
s
Lesson 4–6
©G
lenc
oe/M
cGra
w-H
ill21
3M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Answers (Lesson 4-6)
An
swer
s
© Glencoe/McGraw-Hill A18 Mathematics: Applications and Concepts, Course 3
Prac
tice:
Ski
llsIn
dir
ect
Mea
sure
men
t
©G
lenc
oe/M
cGra
w-H
ill21
6M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Wri
te a
pro
por
tion
an
d s
olve
th
e p
rob
lem
.
1.H
EIG
HT
How
tal
l is
Bec
ky?
2.FL
AG
SH
ow t
all
is t
he
flag
pole
?
�h 3��
�7 4�;5 �
1 4�ft
�;
22�3 4�
ft
3.B
EAC
HH
ow d
eep
is t
he
wat
er
4.A
CC
ESSI
BIL
ITY
How
hig
h i
s th
e ra
mp
50 f
eet
from
sh
ore?
wh
en i
t is
2 f
eet
from
th
e bu
ildi
ng?
(Hin
t:�
AB
E�
�A
CD
)
�h 1��
�5 80 �;
6.25
ft
� 2h .5��
�1 28 0�;
2.25
ft
5.A
MU
SEM
ENT
PAR
KS
Th
e tr
ian
gles
in
6.C
LASS
CH
AN
GES
Th
e tr
ian
gles
in
th
e fi
gure
the
figu
re a
re s
imil
ar.H
ow f
ar i
s th
ear
e si
mil
ar.H
ow f
ar i
s th
e en
tran
ce t
ow
ater
rid
e fr
om t
he
roll
er c
oast
er?
the
gym
nas
ium
fro
m t
he
ban
d ro
om?
Rou
nd
to t
he
nea
rest
ten
th.
� 1d 0��
�4 25 1�;
�21
.4 m
� 3d 2��
�3 20 5�;
38.4
m
45 m
Info
rmat
ion
Boot
h
Wat
er R
ide
Ferr
is W
heel
Rolle
r Coa
ster
Park
Ent
ranc
e21
m10
md
m
30 m
25 m
Tenn
is C
ourt
Band
Roo
m
Gym
nasi
um Cafe
teria
Foun
tain
32 m
d m
2 ft
h ft
A
BC
DE
20 ft
2.5
fth
ft
50 ft
8 ft
1 ft
31�1 2�
�9
h � 6 �1 2�
9 ft
h ft
6ft
1 2
31ft
1 2
7 ft
3 ft
h ft
4 ft
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Lesson 4–7
©G
lenc
oe/M
cGra
w-H
ill21
5M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
LIG
HTI
NG
Geo
rge
is s
tan
din
g n
ext
to a
ligh
tpol
e in
th
e m
idd
le o
f th
e d
ay.G
eorg
e’s
shad
ow i
s 1.
5 fe
et l
ong,
and
th
e li
ghtp
ole’
s sh
adow
is
4.5
feet
lon
g.If
Geo
rge
is 6
fee
t ta
ll,h
ow t
all
is t
he
ligh
tpol
e?
Wri
te a
pro
port
ion
an
d so
lve.
Geo
rge’
s sh
adow
→1.
56
Geo
rge’
s he
ight
light
pole
’s s
hado
w→
4.5
hlig
htpo
le’s
hei
ght
1.5
�h
�4.
5 �
6F
ind
the
cros
s pr
oduc
ts.
1.5h
�27
Mul
tiply
.
�1 1.5 .5h ��
� 12 .7 5�D
ivid
e ea
ch s
ide
by 1
.5.
h�
18S
impl
ify.
Th
e li
ghtp
ole
is 1
8 fe
et t
all.
1.M
ON
UM
ENTS
A s
tatu
e ca
sts
a sh
adow
30
feet
lo
ng.
At
the
sam
e ti
me,
a pe
rson
wh
o is
5 f
eet
tall
cas
ts a
sh
adow
th
at i
s 6
feet
lon
g.H
ow
tall
is
the
stat
ue?
25 f
t
2.B
UIL
DIN
GS
A b
uil
din
g ca
sts
a sh
adow
72
met
ers
lon
g.A
t th
e sa
me
tim
e,a
perk
ing
met
er t
hat
is
1.2
met
ers
tall
cas
ts a
sh
adow
th
at i
s 0.
8 m
eter
lo
ng.
How
tal
l is
th
e bu
ildi
ng?
108
m
3.SU
RV
EYIN
GT
he
two
tria
ngl
es s
how
n i
n t
he
figu
re a
re s
imil
ar.F
ind
the
dist
ance
dac
ross
R
ed R
iver
.2m
1 m
.9 m
1.8
m
Red
Rive
rd
h ft
72 m
1.2
m
0.8
m
h ft
30 ft
5 ft
6 ft
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Ind
irec
t M
easu
rem
ent
Dis
tanc
es o
r le
ngth
s th
at a
re d
iffic
ult
to m
easu
re d
irect
ly c
an s
omet
imes
be
foun
d us
ing
the
prop
ertie
sof
sim
ilar
poly
gons
and
pro
port
ions
.Thi
s ki
nd o
f m
easu
rem
ent
is c
alle
d in
dir
ect
mea
sure
men
t.
h ft
6 ft
4ft
1 21
ft1 2
→→
�
Answers (Lesson 4-7)
© Glencoe/McGraw-Hill A19 Mathematics: Applications and Concepts, Course 3
©G
lenc
oe/M
cGra
w-H
ill21
8M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Pre-
Act
ivit
yR
ead
th
e in
tro
du
ctio
n a
t th
e to
p o
f p
age
188
in y
ou
r te
xtb
oo
k.W
rite
yo
ur
answ
ers
bel
ow
.
1.H
ow i
s th
e ca
vem
an m
easu
rin
g th
e di
stan
ce t
o th
e S
un
?H
e is
mea
suri
ng
th
e d
ista
nce
as
if it
wer
e a
flat
su
rfac
e d
irec
tly
infr
on
t o
f h
im.
Rea
din
g t
he
Less
on
2.C
ompl
ete
the
foll
owin
g se
nte
nce
.W
hen
you
sol
ve a
pro
blem
usi
ng
shad
ow r
ecko
nin
g,th
e ob
ject
s be
ing
com
pare
d an
d th
eir
shad
ows
form
tw
o si
des
of _
____
____
____
__.
sim
ilar
tria
ng
les
3.S
upp
ose
that
you
are
sta
ndi
ng
nea
r a
buil
din
g an
d yo
u s
ee t
he
shad
ows
cast
by
you
an
d th
e bu
ildi
ng.
If y
ou k
now
th
e le
ngt
h o
f ea
ch o
f th
ese
shad
ows
and
you
kn
ow h
ow t
all
you
are
,wri
te a
pro
port
ion
in
wor
ds t
hat
you
can
use
to
fin
d th
e h
eigh
t of
th
e bu
ildi
ng.
Sam
ple
an
swer
:
�
4.ST
ATU
EIf
a s
tatu
e ca
sts
a 6-
foot
sh
adow
an
d a
5-fo
ot m
ailb
ox c
asts
a4-
foot
sh
adow
,how
tal
l is
th
e st
atu
e?7.
5 ft
Hel
pin
g Y
ou
Rem
emb
er5.
Wor
k w
ith
a p
artn
er.H
ave
you
r pa
rtn
er d
raw
tw
o tr
ian
gles
th
at a
resi
mil
ar w
ith
th
e le
ngt
hs
of t
wo
corr
espo
ndi
ng
side
s la
bele
d an
d th
ele
ngt
h o
f on
e ad
diti
onal
sid
e la
bele
d.T
ell
you
r pa
rtn
er h
ow t
o w
rite
apr
opor
tion
to
solv
e fo
r th
e le
ngt
h o
f th
e si
de c
orre
spon
din
g to
th
ead
diti
onal
sid
e la
bele
d.S
ee s
tud
ents
’wo
rk.
hei
gh
t o
f th
e bu
ildin
g�
��
my
hei
gh
tsh
ado
w o
f th
e bu
ildin
g�
��
my
shad
ow
Read
ing
to L
earn
Mat
hem
atic
sIn
dir
ect
Mea
sure
men
t
©G
lenc
oe/M
cGra
w-H
ill21
7M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Lesson X–1
Prac
tice:
Wor
d Pr
oble
ms
Ind
irec
t M
easu
rem
ent
Lesson 4–7
1.H
EIG
HT
Pac
o is
6 f
eet
tall
an
d ca
sts
a12
-foo
t sh
adow
.At
the
sam
e ti
me,
Dia
ne
cast
s an
11-
foot
sh
adow
.How
tal
lis
Dia
ne?
5 �1 2�
ft
2.LI
GH
TIN
GIf
a 2
5-fo
ot-t
all
hou
se c
asts
a75
-foo
t sh
adow
at
the
sam
e ti
me
that
ast
reet
ligh
t ca
sts
a 60
-foo
t sh
adow
,how
tall
is
the
stre
etli
ght?
20 f
t
3.FL
AG
POLE
Len
a is
5�1 2�
feet
tal
l an
d ca
sts
an 8
-foo
t sh
adow
.At
the
sam
e ti
me,
afl
agpo
le c
asts
a 4
8-fo
ot s
had
ow.H
owta
ll i
s th
e fl
agpo
le?
33 f
t
4.LA
ND
MA
RK
SA
wom
an w
ho
is 5
fee
t5
inch
es t
all
is s
tan
din
g n
ear
the
Spa
ce N
eedl
e in
Sea
ttle
,Was
hin
gton
;sh
e ca
sts
a 13
-in
ch s
had
ow a
t th
e sa
me
tim
e th
at t
he
Spa
ce N
eedl
e ca
sts
a12
1-fo
ot s
had
ow.H
ow t
all
is t
he
Spa
ceN
eedl
e?61
4 ft
5.N
ATI
ON
AL
MO
NU
MEN
TSA
42-
foot
flag
pole
nea
r th
e W
ash
ingt
onM
onu
men
t ca
sts
a sh
adow
th
at i
s14
fee
t lo
ng.
At
the
sam
e ti
me,
the
Was
hin
gton
Mon
um
ent
cast
s a
shad
owth
at i
s 18
5 fe
et l
ong.
How
tal
l is
th
eW
ash
ingt
on M
onu
men
t?55
5 ft
6.A
CC
ESSI
BIL
ITY
A r
amp
slop
es u
pwar
dfr
om t
he
side
wal
k to
th
e en
tran
ce o
f a
buil
din
g at
a c
onst
ant
incl
ine.
If t
he
ram
p is
2 f
eet
hig
h w
hen
it
is 5
fee
tfr
om t
he
side
wal
k,h
ow h
igh
is
the
ram
p w
hen
it
is 7
fee
t fr
om t
he
side
wal
k?2.
8 ft
5 ft
2 ft
Answers (Lesson 4-7)
An
swer
s
© Glencoe/McGraw-Hill A20 Mathematics: Applications and Concepts, Course 3
©G
lenc
oe/M
cGra
w-H
ill22
0M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Gra
ph
�A
BC
wit
h v
erti
ces
A(�
2,�
1),
B(2
,3),
and
C(2
,�1)
.Th
en g
rap
h i
ts
imag
e �
A�B
�C�a
fter
a d
ilat
ion
wit
h a
scal
e fa
ctor
of
�3 2�.
A(�
2,�
1)→
��2
��3 2�,
�1
��3 2� �
→A
� ��3,
��3 2� �
B(2
,3)
→�2
��3 2�,
3 �
�3 2� �→
B� �3
,4�1 2� �
C(2
,�1)
→�2
��3 2�,
�1
��3 2� �
→C
� �3,�
�3 2� �S
egm
ent
M�N
�is
a d
ilat
ion
of
segm
ent
MN
.Fin
d t
he
scal
e fa
ctor
of
the
dil
atio
n a
nd
cla
ssif
y it
as
an e
nla
rgem
ent
or a
red
uct
ion
.
Wri
te t
he
rati
o of
th
e x-
or
y-co
ordi
nat
e of
on
e ve
rtex
of
the
dila
ted
figu
re t
o th
e x-
or
y-co
ordi
nat
e of
th
e co
rres
pon
din
gve
rtex
of
the
orig
inal
fig
ure
.Use
th
e x-
coor
din
ates
of
N(1
,�2)
and
N�(
2,�
4).
��2 1�
or 2
Th
e sc
ale
fact
or i
s 2.
Sin
ce t
he
imag
e is
lar
ger
than
th
e or
igin
alfi
gure
,th
e di
lati
on i
s an
en
larg
emen
t.
1.P
olyg
on A
BC
Dh
as v
erti
ces
A(2
,4),
B(�
1,5)
,C(�
3,�
5),a
nd
D(3
,�4)
.Fin
d th
e co
ordi
nat
es o
f it
s im
age
afte
r a
dila
tion
wit
h a
sca
le f
acto
r of
�1 2�.T
hen
gra
ph p
olyg
on A
BC
Dan
d it
s
dila
tion
.
A�(
1,2)
,B� ��
�1 2�,2 �
1 2� �,C
� ���3 2�,
�2 �
1 2� �,D
� �1�1 2�,
�2 �
2.S
egm
ent
P�Q
�is
a d
ilat
ion
of
segm
ent
PQ
.Fin
d th
e sc
ale
fact
or o
f th
e di
lati
on a
nd
clas
sify
it
as a
n e
nla
rgem
ent
or a
redu
ctio
n.
�2 3�;re
du
ctio
n
x-co
ordi
nat
e of
poi
nt
N�
��
�x-
coor
din
ate
of p
oin
t N
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Dila
tio
ns
The
imag
e pr
oduc
ed b
y en
larg
ing
or r
educ
ing
a fig
ure
is c
alle
d a
dila
tio
n.
y
xO
A�
C
B
B�
C�
A
y
xO
M�
M
N
N�
y
xOB�
AB
CC
�
A�
D�
D
y
xO
PP
�
Q�
Q
©G
lenc
oe/M
cGra
w-H
ill21
9M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Ind
irec
t M
easu
rem
ent
A p
ropo
rtio
n c
an b
e u
sed
to d
eter
min
e th
e h
eigh
tof
tal
l st
ruct
ure
s if
th
ree
vari
able
s of
th
e pr
opor
tion
are
know
n.T
he
thre
e kn
own
var
iabl
es a
re u
sual
lyth
e h
eigh
t a
of t
he
obse
rver
,th
e le
ngt
h b
of t
he
obse
rver
’s s
had
ow,a
nd
the
len
gth
dof
th
est
ruct
ure
’s s
had
ow.H
owev
er,a
pro
port
ion
can
be
solv
ed g
iven
an
y th
ree
of t
he
fou
r va
riab
les.
Th
is c
har
t co
nta
ins
info
rmat
ion
ab
out
vari
ous
obse
rver
s an
d t
all
bu
ild
ings
.Use
pro
por
tion
s an
d y
our
calc
ula
tor
to c
omp
lete
th
e ch
art
of t
all
bu
ild
ings
of
the
wor
ld.
Enric
hmen
tN
AM
E__
____
____
____
____
____
____
____
____
____
__D
ATE
___
____
____
___
PE
RIO
D
____
_
Lesson X–1 Lesson 4–7
a
b
c
d
a bc d
�
Hei
ght
ofO
bse
rver
Len
gth
of
Sh
adow
Bu
ild
ing
Loc
atio
nH
eigh
t of
Bu
ild
ing
Len
gth
of
Sh
adow
1.5
ft8
in.
Nat
wes
t,L
ondo
n60
0 ft
80 f
t
2.4
ft 9
in
.19
in.
Col
um
bia
Sea
firs
tC
ente
r,S
eatt
le95
4 ft
318
ft
3.5
ft 1
0 in
.14
in
.W
ach
ovia
Bu
ildi
ng,
Win
ston
-Sal
em41
0 ft
82 f
t
4.6
ft15
in
.W
ater
fron
t T
ower
s,H
onol
ulu
400
ft83
ft
4 in
.
5.6
ft1
ftC
N T
ower
,T
oron
to1,
821
ft30
3 ft
6 i
n.
6.5
ft 9
in
.1
ft 1
1 in
.G
atew
ay A
rch
,S
t.L
ouis
630
ft21
0 ft
7.5
ft 3
in
.1
ft 9
in
.E
iffe
l Tow
er,
Par
is98
4 ft
328
ft
8.4
ft8
in.
Tex
as C
omm
erce
Tow
er,H
oust
on1,
002
ft16
7 ft
9.5
ft 6
in
.11
in
.Jo
hn
Han
cock
Tow
er,B
osto
n79
0 ft
131
ft 8
in
.
10.
5 ft
4 i
n.
8 in
.S
ears
Tow
er,
Ch
icag
o1,
454
ft18
1 ft
9 i
n.
11.
5 ft
6 i
n.
11 in
.B
arn
ett
Tow
er,
Jack
son
vill
e63
1 ft
105
ft 2
in
.
Answers (Lessons 4-7 and 4-8)
© Glencoe/McGraw-Hill A21 Mathematics: Applications and Concepts, Course 3
©G
lenc
oe/M
cGra
w-H
ill22
2M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice:
Wor
d Pr
oble
ms
Dila
tio
ns
1.EY
ESD
ave’
s op
tom
etri
st u
sed
med
icin
eto
dil
ate
his
eye
s.B
efor
e di
lati
on,h
ispu
pils
had
a d
iam
eter
of
4.1
mil
lim
eter
s.A
fter
dil
atio
n,h
is p
upi
lsh
ad a
dia
met
er o
f 8.
2 m
illi
met
ers.
Wh
at w
as t
he
scal
e fa
ctor
of
the
dila
tion
?2
2.B
IOLO
GY
A m
icro
scop
e in
crea
ses
the
size
of
obje
cts
by a
fac
tor
of 8
.How
larg
e w
ill
a 0.
006
mil
lim
eter
para
mec
ium
app
ear?
0.04
8 m
m
3.PH
OTO
GR
APH
YA
ph
otog
raph
was
enla
rged
to
a w
idth
of
15 i
nch
es.I
f th
esc
ale
fact
or w
as �3 2�,
wh
at w
as t
he
wid
thof
th
e or
igin
al p
hot
ogra
ph?
10 in
.
4.M
OV
IES
Fil
m w
ith
a w
idth
of
35m
illi
met
ers
is p
roje
cted
on
to a
scr
een
wh
ere
the
wid
th i
s 5
met
ers.
Wh
at i
sth
e sc
ale
fact
or o
f th
is e
nla
rgem
ent?
�1,0 700 �
5.PH
OTO
CO
PYIN
GA
10-
inch
lon
g co
py o
fa
2.5-
inch
lon
g fi
gure
nee
ds t
o be
mad
ew
ith
a c
opyi
ng
mac
hin
e.W
hat
is
the
appr
opri
ate
scal
e fa
ctor
?4
6.M
OD
ELS
A s
cale
mod
el o
f a
boat
is
goin
g to
be
mad
e u
sin
g a
scal
e of
� 51 0�.
If t
he
orig
inal
len
gth
of
the
boat
is
20 m
eter
s,w
hat
is
the
len
gth
of
the
mod
el?
0.4
m o
r 40
cm
7.M
OD
ELS
An
arc
hit
ectu
ral
mod
el i
s 30
in
ches
tal
l.If
th
e sc
ale
use
d to
bu
ild
the
mod
el i
s � 11 20�
,wh
at i
s th
e h
eigh
t of
the
actu
al b
uil
din
g?3,
600
in.o
r30
0 ft
8.A
DV
ERTI
SIN
GA
n a
dver
tise
r n
eeds
a4-
inch
pic
ture
of
a 14
-foo
t au
tom
obil
e.W
hat
is
the
scal
e fa
ctor
of
the
redu
ctio
n?
� 41 2�
©G
lenc
oe/M
cGra
w-H
ill22
1M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Fin
d t
he
coor
din
ates
of
the
vert
ices
of
tria
ngl
e A
�B�C
�af
ter
tria
ngl
eA
BC
is d
ilat
ed u
sin
g th
e gi
ven
sca
le f
acto
r.T
hen
gra
ph
tri
angl
e A
BC
and
its
dil
atio
n.
1.A
(1,1
),B
(1,3
),C
(3,1
);sc
ale
fact
or 3
2.A
(�2,
�2)
,B(�
1,2)
,C(2
,1);
scal
e fa
ctor
2
A�(
3,3)
,B�(
3,9)
,C�(
9,3)
A�(
�4,
�4)
,B�(
�2,
4),C
�(4,
2)
3.A
(�4,
6),B
(2,6
),C
(0,8
);sc
ale
fact
or �1 2�
4.A
(�3,
�2)
,B(1
,2),
C(2
,�3)
;sca
le f
acto
r 1.
5
A�(
�2,
3),B
�(1,
3),C
�(0,
4)A
�(�
4.5,
�3)
,B�(
1.5,
3),C
�(3,
�4.
5)
Seg
men
t P
�Q�
is a
dil
atio
n o
f se
gmen
t P
Q.F
ind
th
e sc
ale
fact
or o
f th
e d
ilat
ion
and
cla
ssif
y it
as
an e
nla
rgem
ent
or a
red
uct
ion
.
5.6.
�1 2�;re
du
ctio
n2;
2;en
larg
emen
t
7.8.
�2 3�;re
du
ctio
n�3 2�;
enla
rgem
ent
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Lesson X–2
Prac
tice:
Ski
llsD
ilati
on
s
Lesson 4–8
y
xO
A�
C�
B�
B AC
y
xO
A
CB
A�
B�
C�
y
xO
A�
B�
C�
AB
Cy
xO
AC
B
C�
A�
B�
y
xO
P�
Q�
P
Q
y
xO
P�
Q�
P
Q
y
xO
P�
P
�
y
xO
P�
P
Q
Q�
Answers (Lesson 4-8)
An
swer
s
© Glencoe/McGraw-Hill A22 Mathematics: Applications and Concepts, Course 3
©G
lenc
oe/M
cGra
w-H
ill22
4M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
Dila
tio
n a
nd
Are
aA
dil
atio
n o
f a
shap
e cr
eate
s a
new
sh
ape
that
is
sim
ilar
to
the
orig
inal
.Th
e ra
tio
of t
he
new
im
age
to t
he
orig
inal
is
call
ed t
he
scal
e fa
ctor
.
Plo
t an
d d
raw
eac
h s
hap
e.T
hen
per
form
th
e d
ilat
ion
of
each
sh
ape
usi
ng
a sc
ale
fact
or o
f tw
o.A
fter
th
e n
ew i
mag
eh
as b
een
dra
wn
,det
erm
ine
the
area
of
bot
h t
he
orig
inal
shap
e an
d i
ts d
ilat
ion
.S
ee s
tud
ents
’wo
rk.
1.A
(2,1
),B
(7,1
),C
(4,4
)
Are
a of
ori
gin
al _
____
___
7.5
sq.u
nit
s
Are
a of
dil
atio
n _
____
___
30 s
q.u
nit
s
2.ci
rcle
wit
h r
adiu
s (1
,2)
to (
4,2)
Are
a of
ori
gin
al _
____
___
28.2
6 sq
.un
its
Are
a of
dil
atio
n _
____
___
113.
04 s
q.u
nit
s
3.R
(�3,
2),E
(�3,
�2)
,C(4
,�2)
,I(4
,2)
4.S
(�3,
3),Q
(�3,
�3)
,A(3
,�3)
,R(3
,3)
Are
a of
ori
gin
al _
____
___
Are
a of
ori
gin
al _
____
___
28 s
q.u
nit
s36
sq
.un
its
Are
a of
dil
atio
n _
____
___
Are
a of
dil
atio
n _
____
___
112
sq.u
nit
s14
4 sq
.un
its
5.W
hat
gen
eral
sta
tem
ent
can
be
mad
e ab
out
the
area
of
a fi
gure
wh
enco
mpa
red
to i
ts a
rea
afte
r be
ing
dila
ted
by s
cale
fac
tor
2?
Acc
ept
log
ical
res
po
nse
s;th
e ar
ea o
f a
fig
ure
is 4
tim
es g
reat
erw
hen
dila
ted
by
scal
e fa
cto
r 2.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enric
hmen
t
y
xO
©G
lenc
oe/M
cGra
w-H
ill22
3M
athe
mat
ics:
App
licat
ions
and
Con
cept
s, C
ours
e 3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Lesson X–2
Pre-
Act
ivit
yC
om
ple
te t
he
Min
i Lab
at
the
top
of
pag
e 19
4 in
yo
ur
text
bo
ok.
Wri
te y
ou
r an
swer
s b
elo
w.
1.M
ult
iply
eac
h c
oord
inat
e by
2 t
o fi
nd
the
coor
din
ates
of
poin
ts A
�,B
�,an
d C
�.A
�(0,
0),B
�(2,
8),C
�(8,
6)
2.O
n t
he
sam
e co
ordi
nat
e pl
ane,
grap
h p
oin
ts
A�,
B�,
and
C�.
Th
en d
raw
�A
�B�C
�.
3.D
eter
min
e w
het
her
�A
BC
��
A�B
�C�.
Exp
lain
you
r re
ason
ing.
Yes;
corr
esp
on
din
g s
ides
of
the
two
tri
ang
les
are
pro
po
rtio
nal
.
Rea
din
g t
he
Less
on
4.If
you
are
giv
en t
he
coor
din
ates
of
a fi
gure
an
d th
e sc
ale
fact
or o
f a
dila
tion
of
that
fig
ure
,how
can
you
fin
d th
e co
ordi
nat
es o
f th
e n
ewfi
gure
?S
amp
le a
nsw
er:
Mu
ltip
ly e
ach
co
ord
inat
e by
th
esc
ale
fact
or.
5.W
hen
you
gra
ph a
fig
ure
an
d it
s im
age
afte
r a
dila
tion
,how
can
you
chec
k yo
ur
wor
k?S
amp
le a
nsw
er:
Dra
w li
nes
th
rou
gh
th
eo
rig
in a
nd
eac
h o
f th
e ve
rtic
es o
f th
e o
rig
inal
fig
ure
.Th
eve
rtic
es o
f th
e d
ilate
d im
age
sho
uld
lie
on
th
ose
sam
e lin
es.
Hel
pin
g Y
ou
Rem
emb
er6.
Com
plet
e th
e ta
ble
belo
w t
o h
elp
you
rem
embe
r th
e ef
fect
s of
dif
fere
nt
scal
e fa
ctor
s.Read
ing
to L
earn
Mat
hem
atic
sD
ilati
on
s
Lesson 4–8
If t
he
scal
e fa
ctor
is
Th
en t
he
dil
atio
n i
s
betw
een
0 a
nd
1a
red
uct
ion
grea
ter
than
1an
en
larg
emen
t
equ
al t
o 1
the
sam
e si
ze a
s th
e o
rig
inal
fig
ure
y
xO
� A
�
C�
B�
B
A
C
Answers (Lesson 4-8)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. H
C
H
A
I
C
H
D
F
D
7 m
I
B
F
A
F
A
I
D
H
A
F
B
H
A
G
D
H
A
G
B
Chapter 4 Assessment Answer KeyForm 1 Form 2APage 225 Page 226 Page 227
(continued on the next page)
© Glencoe/McGraw-Hill A23 Mathematics: Applications and Concepts, Course 3
An
swer
s
11.
12.
13.
14.
15.
16.
17.
18.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
B: 12 green beans
F
C
H
D
G
A
H
D
G
D
I
B
H
B
H
A
I
A
8 red marbles
G
A
I
C
F
B
G
D
Chapter 4 Assessment Answer KeyForm 2A (continued) Form 2BPage 228 Page 229 Page 230
© Glencoe/McGraw-Hill A24 Mathematics: Applications and Concepts, Course 3
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 3 lb, 12 oz
2; enlargement
A���2�14
�, 1�12
��B��1, 2�
12
�� C���14
�, ��12
��D���1�
12
�, �4�
10 ft
72.8 in.
4,312.5 mi
1,868.75 mi
Sample answer:
�52
� � �6x
�; 2.4
Yes; correspondingangles are
congruent and
�63
� � �84
� � �51.15�.
7.2 laps
16.5
27
8; $8 for each hour
y
xO
��12
�;0.02 in./min
0.1 in./min
12 reams for $24.50;12 reams for $24.50 isabout $2.04/ream and5 reams for $15.25 is
$3.05/ream.
59.2 mi/h
�172�
19:21
0
Chapter 4 Assessment Answer KeyForm 2CPage 231 Page 232
© Glencoe/McGraw-Hill A25 Mathematics: Applications and Concepts, Course 3
An
swer
s
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
G���5�13
�, 1�13
��H��4, 2�
23
��I��6�
23
�, �8�
�12
�; reduction
M����23
�, ��23
��N�(�1, 1), O���
13
�, 1�P��1, �
13
��
31.25 ft
22.4 ft
660 mi
30 mi
Sample answer:
�192� � �
5x
�; 3.75
Yes; correspondingangles are congruent
and �24
� = �12
�.
72 times
12
22.5
�110�; �
110� gal/mi
y
xO
�23
�
35 tickets/min
4 tickets/min
$9.50 for 24 juice boxes; $14.60 for 36 boxes is about
$0.41/box, and $9.50for 24 boxes is about
$0.40/box.
52.5 mi/h
17:22
�171�
�3
Chapter 4 Assessment Answer KeyForm 2DPage 233 Page 234
© Glencoe/McGraw-Hill A26 Mathematics: Applications and Concepts, Course 3
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 384 g
�12
�; reduction
A���8, �23
��, B�(�5, 16),
C��4, 6�12
��, D�(0, �2)
350 m
120 m
�710�
20�49
� m
Sample answer:
�9600� � �
7x5�; 50 yd
Sample answer:
�156� � �
2x0�; 6.25
$401.25
1.5
1,567.5 mi
495 mi
�4;
�12
�
�1
37.2 cells/day
Between 5 and 6 min;the line segment
between these twotimes is horizontal.
10 ft/min
180 min for $35.95;120 min for $24.95 isabout $0.21/min and180 min for $35.95 is
about $0.20/min.
5:4
Chapter 4 Assessment Answer KeyForm 3Page 235 Page 236
© Glencoe/McGraw-Hill A27 Mathematics: Applications and Concepts, Course 3
An
swer
s
y
xO
Chapter 4 Assessment Answer Key Page 237, Extended Response Assessment
Scoring Rubric
© Glencoe/McGraw-Hill A28 Mathematics: Applications and Concepts, Course 3
Level Specific Criteria
4 The student demonstrates a thorough understanding of the mathematicsconcepts and/or procedures embodied in the task. The student hasresponded correctly to the task, used mathematically sound procedures,and provided clear and complete explanations and interpretations. Theresponse may contain minor flaws that do not detract from thedemonstration of a thorough understanding.
3 The student demonstrates an understanding of the mathematics conceptsand/or procedures embodied in the task. The student’s response to thetask is essentially correct with the mathematical procedures used and theexplanations and interpretations provided demonstrating an essential butless than thorough understanding. The response may contain minor errorsthat reflect inattentive execution of the mathematical procedures orindications of some misunderstanding of the underlying mathematicsconcepts and/or procedures.
2 The student has demonstrated only a partial understanding of themathematics concepts and/or procedures embodied in the task. Althoughthe student may have used the correct approach to obtaining a solution ormay have provided a correct solution, the student’s work lacks an essentialunderstanding of the underlying mathematical concepts. The responsecontains errors related to misunderstanding important aspects of the task,misuse of mathematical procedures, or faulty interpretations of results.
1 The student has demonstrated a very limited understanding of themathematics concepts and/or procedures embodied in the task. Thestudent’s response to the task is incomplete and exhibits many flaws.Although the student has addressed some of the conditions of the task, thestudent reached an inadequate conclusion and/or provided reasoning thatwas faulty or incomplete. The response exhibits many errors or may beincomplete.
0 The student has provided a completely incorrect solution oruninterpretable response, or no response at all.
© Glencoe/McGraw-Hill A29 Mathematics: Applications and Concepts, Course 3
Chapter 4 Assessment Answer Key Page 237, Extended Response Assessment
Sample Answers
1. a. A ratio is a comparison of twonumbers by division.
b. 1 to 2; 1:4; �24�
c. A proportion is an equation thatshows that two ratios are equivalent.
d. �12� � �40
x0� �
42� � �40
x0�
2x � 400 2x � 1,600
x � 200 lbs cement x � 800 lbs gravel
2. a. Two polygons are similar if theircorresponding angles are congruentand their corresponding sides are inproportion.
b. A�B� and E�F�; B�C� and F�G�; C�D� and G�H�;and D�A� and H�E�; You can find theratio of the lengths of one pair ofcorresponding sides where bothlengths are known. Because theratios of the lengths of all thecorresponding sides are equal, youcan use the ratio you found to formproportions to find the lengths of thesides whose lengths are not given—B�C�, E�F�, and G�H�.
c.
5�35� is the same as 5.6.
�58.6� � �2
x�
2(5.6) � 8x
11.2 � 8x
x � 1.4
The man’s shadow is 1.4 feet long.
d. All three involve using proportionsand ratios to find a missingmeasurement.
e. The scale factor would be smallerthan 1 because it is the ratio of thedilated image to the original.
x
8 ft
2 ft
5 ft35
In addition to the scoring rubric found on A28, the following sample answers maybe used as guidance in evaluating extended response assessment items.
An
swer
s
1. false; run
2. false; equal
3. true
4. false; rate
5. true
6. false; similar
7. true
8. true
9. false; scale
10. false; ratio
11. a rate that issimplified so it hasa denominator of 1
12. the parts of similarfigures that “match”
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Quiz (Lessons 4-3 and 4-4)
Page 239
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
Quiz (Lessons 4-7 and 4-8)
Page 240
1.
2.
3.
4.
5.�14
�; reduction
X��1�12
�, �1�, Y�(0, 0),
Z�(2, 2)
X�(�3, �6), Y�(6, 3),Z�(12, �3)
60 ft
21.6 ft
B
220 mi
35 mi
Sample answer:�8x
� � �2102�; x � 4.8
Sample answer:�1x6� � �
192�; x � 12
3.25
20
24
��12
�
�32
�
week 9 to week 15
�23
� cm/week
�12
� cm/week
2.75 students/computer
$92.50/chair
23 students/teacher
�32
�
�1215�
�130�
�45
�
Chapter 4 Assessment Answer KeyVocabulary Test/Review Quiz (Lessons 4-1 and 4-2) Quiz (Lessons 4-5 and 4-6)
Page 238 Page 239 Page 240
© Glencoe/McGraw-Hill A30 Mathematics: Applications and Concepts, Course 3
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.�32
�; enlargement
15 ft
90 mi
12.5
��12
�
$ 3.10/lb
�210�
15.7 units
whole, integer,rational
9 or �9
27
256
8�56
�
�1495�
�8
�4
�12
�; �12
� gal of
juice/student
16/mi
5.25 h
� 138 copies/mo
99.5 copies/mo
D
H
C
F
D
Chapter 4 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 241 Page 242
© Glencoe/McGraw-Hill A31 Mathematics: Applications and Concepts, Course 3
An
swer
s
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. 11.
12.
13.
14. a. 41 voters/h; Between 10 A.M.and 12 P.M. an average of 41people voted each hour.
b. Between 2 P.M. and 3 P.M.; therewas no change in the numberof voters during this timeperiod.
c. between 12 P.M. and 2 P.M.
36 ft
�32
�
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
8.8
0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9
9/8
DCBA
IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
IHGF
DCBA
Chapter 4 Assessment Answer KeyStandardized Test PracticePage 243 Page 244
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