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Intermediate Algebra PDF

1027 Pages·2010·25.12 MB·English
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Get the most out of each worked example by using all of its features. EXAMPLE 1 Here, we state the given problem. Strategy Then, we explain what will be done to solve the problem. WHY Next, we explain why it will be done this way. T he steps that follow show how the problem is solved by using Solution the given strategy. 1ST STEP The given problem = The result of 1ST STEP This author note explains the 1ST Step 2ND STEP = The result of 2ND STEP This author note explains the 2ND Step 3RD STEP = The result of 3RD STEP This author note explains (the answer) the 3RD Step Self Check 1 A Similar Problem After reading the example, Now Try Problem 45 try the Self Check problem to test your understanding. The answer is given at the end of the section, right After you work the Self Check, before the Study Set. you are ready to try a similar problem in the Guided Practice section of the Study Set. EDITION 4 INTERMEDIATE ALGEBRA ALAN S.TUSSY CITRUS COLLEGE R.DAVID GUSTAFSON ROCK VALLEY COLLEGE DIANE R.KOENIG ROCK VALLEY COLLEGE Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Intermediate Algebra,Fourth Edition © 2011, 2006Brooks/Cole, Cengage Learning Alan S. Tussy, R. David Gustafson, Diane R. Koenig ALL RIGHTS RESERVED. No part of this work covered by the copyright Publisher: Charlie Van Wagner herein may be reproduced, transmitted, stored, or used in any form or by any means, graphic, electronic, or mechanical, including but not limited to Senior Developmental Editor: Danielle Derbenti photocopying, recording, scanning, digitizing, taping, Web distribution, Senior Development Editor for Market Strategies: information networks, or information storage and retrieval systems, except RitaLombard as permitted under Section 107or 108of the 1976United States Copyright Assistant Editor: Stefanie Beeck Act, without the prior written permission of the publisher. Editorial Assistant: Jennifer Cordoba Media Editor: Heleny Wong For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 Marketing Manager: Gordon Lee For permission to use material from this text or product, Marketing Assistant: Angela Kim submit all requests online at www.cengage.com/permissions Marketing Communications Manager: Katy Further permissions questions can be e-mailed to Malatesta [email protected] Content Project Manager: Jennifer Risden Creative Director: Rob Hugel Library of Congress Control Number: 20099339319 Art Director: Vernon Boes ISBN-13: 978-1-4390-4436-0 Print Buyer: Linda Hsu ISBN-10: 1-4390-4436-8 Rights Acquisitions Account Manager, Text: Mardell Glinksi-Schultz Brooks/Cole Rights Acquisitions Account Manager, Image: Don 20Davis Drive Schlotman Belmont, CA 94002-3098 Production Service: Graphic World Inc. USA Text Designer: Diane Beasley Photo Researcher: Bill Smith Group Cengage Learning is a leading provider of customized learning solutions Illustrators: Lori Heckelman; Graphic World Inc. with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan. Locate your local office at Cover Designer: Terri Wright www.cengage.com/global Cover Image: Background: © Pal Teravagimov Photography/Getty Images RF, Y Button: © Art Parts/Fotosearch RF Cengage Learning products are represented in Canada by Compositor: Graphic World Inc. Nelson Education, Ltd. To learn more about Brooks/Cole, visit www.cengage.com/brookscole Purchase any of our products at your local college store or at our preferred online store www.CengageBrain.com Printed in the United States of America 1 2 3 4 5 6 7 14 13 12 11 10 To the mathematics instructors of Edgewood High School,the University of Redlands,and California State University at Los Angeles, whose love of their discipline and dedication to their students continue to be an inspiration to me ALAN S.TUSSY To my wife,Carol,whose support has been invaluable R.DAVID GUSTAFSON To my husband,Brian,with love;and my daughters, Ashley,Brianna,and Carly,whom I love very much and who bring me great joy DIANE R.KOENIG This page intentionally left blank C O N T E N T S Study Skills Workshop S-1 CHAPTER 1 A Review of Basic Algebra 1 1.1 The Language of Algebra 2 1.2 The Real Numbers 10 1.3 Operations with Real Numbers 23 1.4 Simplifying Algebraic Expressions Using Properties mages of Real Numbers 37 Getty I 1.5 Solving Linear Equations Using Properties of Equality 49 midt/ 11..67 SUosilnvign gEq Fuoarmtiounlas st;oG Seoolmvee Ptrryoblem61s 72 © Baerbel Sch 1.8 More about Problem Solving 83 THINK IT THROUGH Fastest Growing Occupations 86 Chapter Summary and Review 98 Chapter Test 112 CHAPTER 2 Graphs,Equations of Lines,and Functions 115 2.1 The Rectangular Coordinate System 116 2.2 Graphing Linear Equations 128 2.3 Rate of Change and the Slope of a Line 143 THINK IT THROUGH Community Colleges 148 2.4 Writing Equations of Lines 156 m/iofoto 2TH.I5NK ITA TnH RInOtUroGdHuctiCoons tt oo fF Huinricntgions 177170 © iStockphotos.co 2.6 Graphs of Functions 186 Chapter Summary and Review 201 Chapter Test 211 Cumulative Review 213 v vi Contents CHAPTER 3 Systems of Equations 215 3.1 Solving Systems of Equations by Graphing 216 THINK IT THROUGH Bachelor’s Degrees 220 3.2 Solving Systems of Equations Algebraically 228 3.3 Problem Solving Using Systems of Two Equations 237 my 3.4 Solving Systems of Equations in Three Variables 254 Ala mages/ 3.5 Problem Solving Using Systems of Three Equations 262 © Radius I 3.6 Solving Systems of Equations Using Matrices 270 3.7 Solving Systems of Equations Using Determinants 280 Chapter Summary and Review 291 Chapter Test 301 Cumulative Review 303 CHAPTER 4 Inequalities 305 4.1 Solving Linear Inequalities in One Variable 306 THINK IT THROUGH Changing Values 307 4.2 Solving Compound Inequalities 319 THINK IT THROUGH Study Abroad 326 w Brookes/Corbis 44..34 SLionlevianrg In Aebqsuoalulittiee sV ainlu Tew Eoq Vuaartiiaobnlse sand I3n4e2qualities 331 Andre 4.5 Systems of Linear Inequalities 351 © Chapter Summary and Review 361 Chapter Test 369 Cumulative Review 371 Contents vii CHAPTER 5 Exponents,Polynomials,and Polynomial Functions 375 5.1 Exponents 376 5.2 Scientific Notation 388 THINK IT THROUGH The American Educational System 390 5.3 Polynomials and Polynomial Functions 396 5.4 Multiplying Polynomials 410 Alamy 55..56 TThhee DGrifefaetreesntc Ceo omf Tmwoon S Fqaucatorers a;nthde F Saucmto rainngd bDyif Gferroeunpcein g 421 Adrian Sherratt/ of Two Cubes 429 © 5.7 Factoring Trinomials 437 5.8 Summary of Factoring Techniques 448 5.9 Solving Equations by Factoring 451 Chapter Summary and Review 462 Chapter Test 473 Cumulative Review 475 CHAPTER 6 Rational Expressions and Equations 477 6.1 Rational Functions and Simplifying Rational Expressions 478 THINK IT THROUGH Learning and Remembering 481 6.2 Multiplying and Dividing Rational Expressions 491 6.3 Adding and Subtracting Rational Expressions 501 mages 6.4 Simplifying Complex Fractions 512 Getty I 666...567 DSyivnitdhientgic P Doilvynisoiomnials 532522 Reggie Casagrande/ Solving Rational Equations 540 6.8 Problem Solving Using Rational Equations 551 6.9 Proportion and Variation 560 Chapter Summary and Review 576 Chapter Test 589 Cumulative Review 591 viii Contents CHAPTER 7 Radical Expressions,Equations, and Functions 595 7.1 Radical Expressions and Radical Functions 596 7.2 Simplifying and Combining Radical Expressions 611 7.3 Multiplying and Dividing Radical Expressions 621 7.4 m/Sean Locke 7.5 SRoatlvioinnga lR Eaxdpicoanle Enqtusatio6n4s2 632 © istockphoto.co 7TH.I6NK ITG TeHoRmOUetGriHc ApPpytlihcaagtioornesa no fT Rriapdleiscals 656654 7.7 Complex Numbers 665 Chapter Summary and Review 679 Chapter Test 689 Cumulative Review 691 CHAPTER 8 Quadratic Equations,Functions, and Inequalities 693 8.1 The Square Root Property and Completing the Square 694 8.2 The Quadratic Formula 706 8.3 Quadratic Functions and Their Graphs 717 Getty Images T8H.I4NK IT THROUGH Automobile Accidents 726 mage Source Black/ 8.5 TFQohuream dDriasctirc7im a3n3inda Ontt haenrd N Eoqnulaintieoanrs I nTehqatu Calaitnie Bse Wr7it4t2en in Quadratic © I Chapter Summary and Review 756 Chapter Test 764 Cumulative Review 766

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Offering a uniquely modern, balanced approach, Tussy/Gustafson/Koenig's INTERMEDIATE ALGEBRA, Fourth Edition, integrates the best of traditional drill and practice with the best elements of the reform movement. To many developmental math students, algebra is like a foreign language. They have diffic
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