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Seventh Edition Intermediate Algebra An Applied Approach Student Support Edition Richard N. Aufmann Palomar College, California Vernon C. Barker Palomar College, California Joanne S. Lockwood New Hampshire Community Technical College Houghton Mifflin Company Boston New York Publisher: Richard Stratton Executive Editor: Mary Finch Senior Marketing Manager: Katherine Greig Associate Editor: Carl Chudyk Art and Design Manager: Jill Haber Cover Design Manager: Anne S. Katzeff Senior Photo Editor: Jennifer Meyer Dare Senior Composition Buyer: Chuck Dutton New Title Project Manager: James Lonergan Editorial Assistant: Nicole Catavolos Marketing Assistant: Erin Timm Cover photo © Getty Images, Inc./Comstock Images Photo Credits Chapter 1: p. 1, Stock Works / CORBIS; p. 44 Sky Bonillo / PhotoEdit, Inc.; p. 52 David Stoecklein / CORBIS; p. 54 Stephen Mark Needham / Foodpix / Getty Images. Chapter 2: p. 55, Michael Newman / PhotoEdit, Inc.; p. 72 Leonard de Selva / CORBIS; p. 82 Michael S. Yamashita / CORBIS; p. 93 Richard Cummins / CORBIS; p. 106 Stephen Chernin / Getty Images; p. 113 Alan Oddie / PhotoEdit, Inc. Chapter 3: p. 119 Jeff Greenberg / PhotoEdit, Inc.; p. 125 Craig Tuttle / CORBIS; p. 131 Ulrike Welsch / PhotoEdit, Inc.; p. 141 Robert W. Ginn / PhotoEdit, Inc.; p. 162 Eric Fowke / PhotoEdit, Inc.; p. 172 Royalty-Free / CORBIS; p. 173 David Keaton / CORBIS; p. 185 The Granger Collection; p. 188 Stan Honda / Getty Images. Chapter 4: p. 199 David Stoecklein / CORBIS; p. 232 Spencer Grant / PhotoEdit, Inc.; p. 237 Jose Carillo / PhotoEdit, Inc.; p. 238 Royalty-Free / CORBIS; p. 239 Michael Newman / PhotoEdit, Inc.; p. 245 AP / Wide World Photos; p. 247 Michael Newman / PhotoEdit, Inc.; p. 254 Susan Van Etten / PhotoEdit, Inc. Chapter 5: p. 257 AP / Wide World Photos; p. 269 Stocktrek / CORBIS; p. 270 NASA / JPL Handout / Reuters Newmedia Inc. / CORBIS; p. 270 John Neubauer / PhotoEdit, Inc.; p. 325 David Young-Wolff / PhotoEdit, Inc.; p. 327 Roger Ressmeyer / CORBIS; p. 334 Susan Van Etten / PhotoEdit, Inc. Chapter 6: p. 339 Rachel Epstein / PhotoEdit, Inc.; p. 365 Allan Morgan; p. 366 Michael Newman / PhotoEdit, Inc.; p. 369 James Marshall / CORBIS; p. 374 Joel W. Rogers / CORBIS; p. 374 HMS Group / CORBIS; p. 379 Tony Freeman / PhotoEdit, Inc.; p. 384 Jonathan Nourak / PhotoEdit, Inc.; p. 392 Royalty-Free / CORBIS. Chapter 7: p. 395 Benjamin Shearn / TAXI / Getty Images; p. 419 Bettmann / CORBIS; p. 421 Sandor Szabo / EPA / Landov; p. 433 Royalty-Free / CORBIS; p. 442 Sky Bonillo / PhotoEdit, Inc. Chapter 8: p. 443 David Young-Wolff / PhotoEdit, Inc.; p. 458 Photex / CORBIS; p. 477 Bill Aron / PhotoEdit, Inc.; p. 478 Reuters / CORBIS; p. 480 Dale C. Spartas / CORBIS. Chapter 9: p. 491 Tim Boyle / Getty Images; p. 492 Lon C. Diehl / PhotoEdit, Inc.; p. 500 Jim Craigmyle / CORBIS; p. 507 Rich Clarkson / Getty Images; p. 508 Vic Bider / PhotoEdit, Inc.; p. 511 Nick Wheeler / CORBIS; p. 517 Jose Fuste Raga / CORBIS; p. 521 Joel W. Rogers / CORBIS; p. 522 Robert Brenner / PhotoEdit, Inc.; p. 533 Michael Newman / PhotoEdit, Inc.; p. 542 Kim Sayer / CORBIS. Chapter 10: p. 543 Rudi Von Briel / PhotoEdit, Inc.; p. 556 The Granger Collection; p. 573 Express Newspapers / Getty Images; p. 574 Richard T. Nowitz / CORBIS; p. 574 Courtesy of the Edgar Fahs Smith Image Collection / University of Pennsylvania Library, Philadelphia, PA 19104-6206; p. 575 Bettmann / CORBIS; p. 577 Mark Harmel / STONE / Getty Images; p. 578 Myrleen Fergusun Cate / PhotoEdit, Inc.; p. 579 Michael Johnson – www.earthwindow.com; p. 580 Roger Ressmeyer / CORBIS; p. 583 David Young-Wolff / PhotoEdit, Inc.; p. 588 Macduff Everton / CORBIS; p. 592 Frank Siteman / PhotoEdit, Inc. Chapter 11: p. 593 Roger Ressmeyer / CORBIS; p. 594 Jeff Greenberg / PhotoEdit, Inc.; p. 595 Jennifer Waddell / Houghton Mifflin Company; p. 596 Galen Rowell / CORBIS; p. 597 Bettmann / CORBIS; p. 627 Photodisc Green / Getty Images; p. 628 Joseph Sohm; Visions of America / CORBIS; p. 638 Mark Cooper / CORBIS. Chapter 12: p. 639 Colin Young-Wolff / PhotoEdit, Inc.; p. 646 The Granger Collection; p. 652 Ariel Skelley / CORBIS; p. 662 William James Warren / CORBIS; p. 663 The Granger Collection; p. 664 The Granger Collection; p. 669 AP / Wide World Photos; p. 678 David Young-Wolff / PhotoEdit, Inc.; p. 680 Tony Freeman / PhotoEdit, Inc. Copyright © 2009 by Houghton Mifflin Company. All rights reserved. No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system without the prior written permission of Houghton Mifflin Company unless such copying is expressly permitted by federal copyright law. Address inquiries to College Permissions, Houghton Mifflin Company, 222 Berkeley Street, Boston, MA 02116-3764. Printed in the U.S.A. Library of Congress Control Number: 2007938114 Instructor’s Annotated Edition ISBN-10: 0-547-05651-6 ISBN-13: 978-0-547-05651-7 For orders, use student text ISBNs ISBN-10: 0-547-01642-5 ISBN-13: 978-0-547-01642-9 123456789-WEB-12 11 10 09 08 Copyright © Houghton Mifflin Company. All rights reserved. Preface xi AIM for Success AIM1 Review of Real Numbers 1 Prep Test 2 Section 1.1 Introduction to Real Numbers 3 Objective A To use inequality and absolute value symbols with real numbers 3 Objective B To write sets using the roster method and set-builder notation 6 Objective C To perform operations on sets and write sets in interval notation 8 Section 1.2 Operations on Rational Numbers 17 Objective A To add, subtract, multiply, and divide integers 17 Objective B To add, subtract, multiply, and divide rational numbers 19 Objective C To evaluate exponential expressions 21 Objective D To use the Order of Operations Agreement 22 Section 1.3 Variable Expressions 29 Objective A To use and identify the properties of the real numbers 29 Objective B To evaluate a variable expression 31 Objective C To simplify a variable expression 32 Section 1.4 Verbal Expressions and Variable Expressions 37 Objective A To translate a verbal expression into a variable expression 37 Objective B To solve application problems 40 Focus on Problem Solving: Polya’s Four-Step Process 43 • Projects and Group Activities: Water Displacement 45 • Chapter 1 Summary 46 • Chapter 1 Review Exercises 50 • Chapter 1 Test 53 First-Degree Equations and Inequalities 55 Prep Test 56 Section 2.1 Solving First-Degree Equations 57 Objective A To solve an equation using the Addition or the Multiplication Property of Equations 57 Objective B To solve an equation using both the Addition and the Multiplication Properties of Equations 60 Objective C To solve an equation containing parentheses 61 Objective D To solve a literal equation for one of the variables 62 Section 2.2 Applications: Puzzle Problems 67 Objective A To solve integer problems 67 Objective B To solve coin and stamp problems 69 Section 2.3 Applications: Mixture and Uniform Motion Problems 73 Objective A To solve value mixture problems 73 Contents 1 2 iii iv Contents Copyright © Houghton Mifflin Company. All rights reserved. Objective B To solve percent mixture problems 75 Objective C To solve uniform motion problems 77 Section 2.4 First-Degree Inequalities 83 Objective A To solve an inequality in one variable 83 Objective B To solve a compound inequality 86 Objective C To solve application problems 88 Section 2.5 Absolute Value Equations and Inequalities 95 Objective A To solve an absolute value equation 95 Objective B To solve an absolute value inequality 97 Objective C To solve application problems 99 Focus on Problem Solving: Understand the Problem 105 • Projects and Group Activities: Electricity 106 • Chapter 2 Summary 109 • Chapter 2 Review Exercises 112 • Chapter 2 Test 115 • Cumulative Review Exercises 117 Linear Functions and Inequalities in Two Variables 119 Prep Test 120 Section 3.1 The Rectangular Coordinate System 121 Objective A To graph points in a rectangular coordinate system 121 Objective B To find the length and midpoint of a line segment 123 Objective C To graph a scatter diagram 125 Section 3.2 Introduction to Functions 131 Objective A To evaluate a function 131 Section 3.3 Linear Functions 143 Objective A To graph a linear function 143 Objective B To graph an equation of the form 145 Objective C To find the x- and the y-intercepts of a straight line 148 Objective D To solve application problems 150 Section 3.4 Slope of a Straight Line 155 Objective A To find the slope of a line given two points 155 Objective B To graph a line given a point and the slope 159 Section 3.5 Finding Equations of Lines 166 Objective A To find the equation of a line given a point and the slope 166 Objective B To find the equation of a line given two points 167 Objective C To solve application problems 169 Section 3.6 Parallel and Perpendicular Lines 175 Objective A To find parallel and perpendicular lines 175 Section 3.7 Inequalities in Two Variables 181 Objective A To graph the solution set of an inequality in two variables 181 Focus on Problem Solving: Find a Pattern 185 • Projects and Group Activities: Evaluating a Function with a Graphing Calculator 186 • Introduction to Graphing Calculators 186 • Wind-Chill Index 187 • Chapter 3 Summary 188 • Chapter 3 Review Exercises 192 • Chapter 3 Test 195 • Cumulative Review Exercises 197 Ax � By � C 3 Contents v Copyright © Houghton Mifflin Company. All rights reserved. Systems of Linear Equations and Inequalities 199 Prep Test 200 Section 4.1 Solving Systems of Linear Equations by Graphing and by the Substitution Method 201 Objective A To solve a system of linear equations by graphing 201 Objective B To solve a system of linear equations by the substitution method 204 Objective C To solve investment problems 207 Section 4.2 Solving Systems of Linear Equations by the Addition Method 213 Objective A To solve a system of two linear equations in two variables by the addition method 213 Objective B To solve a system of three linear equations in three variables by the addition method 216 Section 4.3 Solving Systems of Equations by Using Determinants 225 Objective A To evaluate a determinant 225 Objective B To solve a system of equations by using Cramer’s Rule 228 Section 4.4 Application Problems 233 Objective A To solve rate-of-wind or rate-of-current problems 233 Objective B To solve application problems 234 Section 4.5 Solving Systems of Linear Inequalities 241 Objective A To graph the solution set of a system of linear inequalities 241 Focus on Problem Solving: Solve an Easier Problem 245 • Projects and Group Activities: Using a Graphing Calculator to Solve a System of Equations 246 • Chapter 4 Summary 248 • Chapter 4 Review Exercises 251 • Chapter 4 Test 253 • Cumulative Review Exercises 255 Polynomials 257 Prep Test 258 Section 5.1 Exponential Expressions 259 Objective A To multiply monomials 259 Objective B To divide monomials and simplify expressions with negative exponents 261 Objective C To write a number using scientific notation 265 Objective D To solve application problems 266 Section 5.2 Introduction to Polynomial Functions 271 Objective A To evaluate polynomial functions 271 Objective B To add or subtract polynomials 274 Section 5.3 Multiplication of Polynomials 279 Objective A To multiply a polynomial by a monomial 279 Objective B To multiply two polynomials 280 Objective C To multiply polynomials that have special products 282 Objective D To solve application problems 283 Section 5.4 Division of Polynomials 289 Objective A To divide a polynomial by a monomial 289 Objective B To divide polynomials 290 4 5 vi Contents Copyright © Houghton Mifflin Company. All rights reserved. Objective C To divide polynomials by using synthetic division 292 Objective D To evaluate a polynomial function using synthetic division 294 Section 5.5 Factoring Polynomials 300 Objective A To factor a monomial from a polynomial 300 Objective B To factor by grouping 301 Objective C To factor a trinomial of the form 302 Objective D To factor 304 Section 5.6 Special Factoring 312 Objective A To factor the difference of two perfect squares or a perfect-square trinomial 312 Objective B To factor the sum or the difference of two perfect cubes 314 Objective C To factor a trinomial that is quadratic in form 315 Objective D To factor completely 316 Section 5.7 Solving Equations by Factoring 322 Objective A To solve an equation by factoring 322 Objective B To solve application problems 323 Focus on Problem Solving: Find a Counterexample 326 • Projects and Group Activities: Astronomical Distances and Scientific Notation 327 • Chapter 5 Summary 328 • Chapter 5 Review Exercises 332 • Chapter 5 Test 335 • Cumulative Review Exercises 337 Rational Expressions 339 Prep Test 340 Section 6.1 Multiplication and Division of Rational Expressions 341 Objective A To find the domain of a rational function 341 Objective B To simplify a rational function 342 Objective C To multiply rational expressions 344 Objective D To divide rational expressions 345 Section 6.2 Addition and Subtraction of Rational Expressions 351 Objective A To rewrite rational expressions in terms of a common denominator 351 Objective B To add or subtract rational expressions 353 Section 6.3 Complex Fractions 359 Objective A To simplify a complex fraction 359 Section 6.4 Ratio and Proportion 363 Objective A To solve a proportion 363 Objective B To solve application problems 364 Section 6.5 Rational Equations 367 Objective A To solve a fractional equation 367 Objective B To solve work problems 369 Objective C To solve uniform motion problems 371 Section 6.6 Variation 377 Objective A To solve variation problems 377 Focus on Problem Solving: Implication 383 • Projects and Group Activities: Graphing Variation Equations 384 • Transformers 384 • Chapter 6 Summary 385 • Chapter 6 Review Exercises 388 • Chapter 6 Test 391 • Cumulative Review Exercises 393 ax 2 � bx � c x 2 � bx � c 6 Contents vii Copyright © Houghton Mifflin Company. All rights reserved. Exponents and Radicals 395 Prep Test 396 Section 7.1 Rational Exponents and Radical Expressions 397 Objective A To simplify expressions with rational exponents 397 Objective B To write exponential expressions as radical expressions and to write radical expressions as exponential expressions 399 Objective C To simplify radical expressions that are roots of perfect powers 401 Section 7.2 Operations on Radical Expressions 407 Objective A To simplify radical expressions 407 Objective B To add or subtract radical expressions 408 Objective C To multiply radical expressions 409 Objective D To divide radical expressions 411 Section 7.3 Solving Equations Containing Radical Expressions 417 Objective A To solve a radical equation 417 Objective B To solve application problems 419 Section 7.4 Complex Numbers 423 Objective A To simplify a complex number 423 Objective B To add or subtract complex numbers 424 Objective C To multiply complex numbers 425 Objective D To divide complex numbers 428 Focus on Problem Solving: Another Look at Polya’s Four-Step Process 431 • Projects and Group Activities: Solving Radical Equations with a Graphing Calculator 432 • The Golden Rectangle 433 • Chapter 7 Summary 434 • Chapter 7 Review Exercises 436 • Chapter 7 Test 439 • Cumulative Review Exercises 441 Quadratic Equations 443 Prep Test 444 Section 8.1 Solving Quadratic Equations by Factoring or by Taking Square Roots 445 Objective A To solve a quadratic equation by factoring 445 Objective B To write a quadratic equation given its solutions 446 Objective C To solve a quadratic equation by taking square roots 447 Section 8.2 Solving Quadratic Equations by Completing the Square 453 Objective A To solve a quadratic equation by completing the square 453 Section 8.3 Solving Quadratic Equations by Using the Quadratic Formula 459 Objective A To solve a quadratic equation by using the quadratic formula 459 Section 8.4 Solving Equations That Are Reducible to Quadratic Equations 465 Objective A To solve an equation that is quadratic in form 465 Objective B To solve a radical equation that is reducible to a quadratic equation 466 Objective C To solve a fractional equation that is reducible to a quadratic equation 468 Section 8.5 Quadratic Inequalities and Rational Inequalities 471 Objective A To solve a nonlinear inequality 471 7 8 viii Contents Copyright © Houghton Mifflin Company. All rights reserved. Section 8.6 Applications of Quadratic Equations 475 Objective A To solve application problems 475 Focus on Problem Solving: Inductive and Deductive Reasoning 479 • Projects and Group Activities: Using a Graphing Calculator to Solve a Quadratic Equation 480 • Chapter 8 Summary 481 • Chapter 8 Review Exercises 484 • Chapter 8 Test 487 • Cumulative Review Exercises 489 Functions and Relations 491 Prep Test 492 Section 9.1 Properties of Quadratic Functions 493 Objective A To graph a quadratic function 493 Objective B To find the x-intercepts of a parabola 496 Objective C To find the minimum or maximum of a quadratic function 499 Objective D To solve application problems 500 Section 9.2 Graphs of Functions 509 Objective A To graph functions 509 Section 9.3 Algebra of Functions 515 Objective A To perform operations on functions 515 Objective B To find the composition of two functions 517 Section 9.4 One-to-One and Inverse Functions 523 Objective A To determine whether a function is one-to-one 523 Objective B To find the inverse of a function 524 Focus on Problem Solving: Proof in Mathematics 531 • Projects and Group Activities: Finding the Maximum or Minimum of a Function Using a Graphing Calculator 532 • Business Applications of Maximum and Minimum Values of Quadratic Functions 532 • Chapter 9 Summary 534 • Chapter 9 Review Exercises 537 • Chapter 9 Test 539 • Cumulative Review Exercises 541 Exponential and Logarithmic Functions 543 Prep Test 544 Section 10.1 Exponential Functions 545 Objective A To evaluate an exponential function 545 Objective B To graph an exponential function 547 Section 10.2 Introduction to Logarithms 552 Objective A To find the logarithm of a number 552 Objective B To use the Properties of Logarithms to simplify expressions containing logarithms 555 Objective C To use the Change-of-Base Formula 558 Section 10.3 Graphs of Logarithmic Functions 563 Objective A To graph a logarithmic function 563 Section 10.4 Solving Exponential and Logarithmic Equations 567 Objective A To solve an exponential equation 567 Objective B To solve a logarithmic equation 569 10 9 Contents ix Copyright © Houghton Mifflin Company. All rights reserved. Section 10.5 Applications of Exponential and Logarithmic Functions 573 Objective A To solve application problems 573 Focus on Problem Solving: Proof by Contradiction 581 • Projects and Group Activities: Solving Exponential and Logarithmic Equations Using a Graphing Calculator 582 • Credit Reports and FICO® Scores 583 • Chapter 10 Summary 584 • Chapter 10 Review Exercises 586 • Chapter 10 Test 589 • Cumulative Review Exercises 591 Conic Sections 593 Prep Test 594 Section 11.1 The Parabola 595 Objective A To graph a parabola 595 Section 11.2 The Circle 601 Objective A To find the equation of a circle and then graph the circle 601 Objective B To write the equation of a circle in standard form 603 Section 11.3 The Ellipse and the Hyperbola 607 Objective A To graph an ellipse with center at the origin 607 Objective B To graph a hyperbola with center at the origin 609 Section 11.4 Solving Nonlinear Systems of Equations 613 Objective A To solve a nonlinear system of equations 613 Section 11.5 Quadratic Inequalities and Systems of Inequalities 619 Objective A To graph the solution set of a quadratic inequality in two variables 619 Objective B To graph the solution set of a nonlinear system of inequalities 621 Focus on Problem Solving: Using a Variety of Problem-Solving Techniques 627 • Projects and Group Activities: The Eccentricity and Foci of an Ellipse 627 • Graphing Conic Sections Using a Graphing Calculator 629 • Chapter 11 Summary 630 • Chapter 11 Review Exercises 632 • Chapter 11 Test 635 • Cumulative Review Exercises 637 Sequences and Series 639 Prep Test 640 Section 12.1 Introduction to Sequences and Series 641 Objective A To write the terms of a sequence 641 Objective B To find the sum of a series 642 Section 12.2 Arithmetic Sequences and Series 647 Objective A To find the nth term of an arithmetic sequence 647 Objective B To find the sum of an arithmetic series 649 Objective C To solve application problems 650 Section 12.3 Geometric Sequences and Series 653 Objective A To find the nth term of a geometric sequence 653 Objective B To find the sum of a finite geometric series 655 Objective C To find the sum of an infinite geometric series 657 Objective D To solve application problems 660 Section 12.4 Binomial Expansions 663 Objective A To expand 663 �a � b�n 11 12 x Contents Copyright © Houghton Mifflin Company. All rights reserved. Focus on Problem Solving: Forming Negations 669 • Projects and Group Activities: ISBN and UPC Numbers 670 • Chapter 12 Summary 671 • Chapter 12 Review Exercises 674 • Chapter 12 Test 677 • Cumulative Review Exercises 679 Final Exam 681 Appendix A Keystroke Guide for the TI-83 and TI-83 Plus 687 Appendix B Proofs of Logarithmic Properties 697 Proof of the Formula for the Sum of n Terms of a Geometric Series 697 Proof of the Formula for the Sum of n Terms of an Arithmetic Series 698 Table of Symbols 698 Table of Properties 699 Table of Algebraic and Geometric Formulas 700 Solutions to You Try Its S1 Answers to Selected Exercises A1 Glossary G1 Index G8 Index of Applications G17 Copyright © Houghton Mifflin Company. All rights reserved. The seventh edition of Intermediate Algebra: An Applied Approach provides com- prehensive, mathematically sound coverage of the topics considered essential in an intermediate algebra course. The text has been designed not only to meet the needs of the traditional college student, but also to serve the needs of returning students whose mathematical proficiency may have declined during years away from formal education. In this new edition of Intermediate Algebra: An Applied Approach, we have con- tinued to integrate some of the approaches suggested by AMATYC. Each chapter opens with an illustration and a reference to a mathematical application within the chapter. At the end of each section there are Applying the Concepts exercises, which include writing, synthesis, critical thinking, and challenge problems. At the end of each chapter there is a “Focus on Problem Solving,” which introduces students to various problem-solving strategies. This is followed by “Projects and Group Activities,” which can be used for cooperative-learning activities. NEW! Changes to the Seventh Edition In response to user requests, in this edition of the text students are asked to write solution sets of inequalities in both set-builder notation and in interval notation, as well as to graph solution sets of inequalities in one variable on the number line. See, for example, pages 89 and 90 in Section 2.4. Section 3 of Chapter 6 now presents two methods of simplifying a complex frac- tion: (1) multiplying the numerator and denominator of the complex fraction by the least common multiple of the denominators and (2) multiplying the numera- tor by the reciprocal of the denominator of the complex fraction. We have found that students who are taught division of a polynomial by a mono- mial as a separate topic are subsequently more successful in factoring a mono- mial from a polynomial. Therefore, we have added a new objective, “To divide a polynomial by a monomial,” to Section 4 of Chapter 5. The concept of function is given greater emphasis in this edition of the text. For example, Chapter 6 begins with a new objective titled “To find the domain of a rational function.” The next objective is on simplifying rational functions. In Section 9.3, the material on composition of functions has been expanded, and students are given more opportunities to apply the concept to applications. In the previous edition, complex numbers were presented in Section 7.3. In this edition, complex numbers have been moved to the last section of the chap- ter. This provides for a better flow of the material in Chapter 7 and places com- plex numbers immediately before Chapter 8, Quadratic Equations, where it is used extensively. In Section 2 of Chapter 10, the introduction to logarithms has been rewritten. Motivation for the need for logarithms is developed within the context of an application. The slower pace of the presentation of this topic will help students to better understand and apply the concept of logarithm. The in-text examples are now highlighted by a prominent HOW TO bar. Students looking for a worked-out example can easily locate one of these problems. As another aid for students, more annotations have been added to the Ex- amples provided in the paired Example/You Try It boxes. This will assist Preface xi xii Preface Copyright © Houghton Mifflin Company. All rights reserved. students in understanding what is happening in key steps of the solution to an exercise. Throughout the text, data problems have been updated to reflect current data and trends. Also, titles have been added to the application exercises in the exer- cise sets. These changes emphasize the relevance of mathematics and the variety of problems in real life that require mathematical analysis. The Chapter Summaries have been remodeled and expanded. Students are pro- vided with definitions, rules, and procedures, along with examples of each. An objective reference and a page reference accompany each entry. We are confident that these will be valuable aids as students review material and study for exams. In many chapters, the number of exercises in the Chapter Review Exercises has been increased. This will provide students with more practice on the concepts presented in the chapter. The calculator appendix has been expanded to include instruction on more func- tions of the graphing calculator. Notes entitled Integrating Technology appear throughout the book and many refer the student to this appendix. Annotated illustrations of both a scientific calculator and a graphing calculator appear on the inside back cover of this text. NEW! Changes to the Student Support Edition With the student in mind, we have expanded the AIM for Success. Getting Started introduces students to the skills they need to develop to be successful and to the dedicated organization and study resources available for each chap- ter. Students can use the Chapter Checklist to track their assignments, solve the Math Word Scramble to cement their understanding of vocabulary, and complete the Concept Review in preparation for a chapter test. Online homework powered by WebAssign® is now available through Houghton Mifflin’s course management system in HM MathSPACE®. Developed by teachers for teachers, WebAssign allows instructors to focus on what really matters— teaching rather than grading. Instructors can create assignments from a ready- to-use database of algorithmic questions based on end-of-section exercises, or write and customize their own exercises. With WebAssign, instructors can cre- ate, post, and review assignments; deliver, collect, grade, and record assignments instantly; offer practice exercises, quizzes, and homework; and assess student performance to keep abreast of individual progress. An Online Multimedia eBook is now available in HM MathSPACE, integrating numerous assets such as video explanations and tutorials to expand upon and reinforce concepts appearing in the text. Visit college.hmco.com/pic/aufmanninterappliedSSE7e to enter HM MathSPACE. NEW! Changes to the Instructor’s Annotated Edition The Instructor’s Annotated Edition now contains full-sized pages. Most Instruc- tor Notes, In-Class Exercises, Suggested Assignments, and Quick Quizzes remain at point-of-use for teaching convenience. Additional instructor features are avail- able in HM MathSPACE®. Preface xiii Copyright © Houghton Mifflin Company. All rights reserved. ACKNOWLEDGMENTS The authors would like to thank the people who have reviewed this manuscript and provided many valu- able suggestions. Dorothy A. Brown, Camden County College, NJ Kim Doyle, Monroe Community College, NY Said Fariabi, San Antonio College, TX Kimberly A. Gregor, Delaware Technical and Community College, DE Allen Grommet, East Arkansas Community College, AR Anne Haney Rose M. Kaniper, Burlington County College, NJ Mary Ann Klicka, Bucks County Community College, PA Helen Medley, Kent State University, OH Steve Meidinger, Merced College, CA Dr. James R. Perry, Owens Community College, OH Gowribalan Vamadeva, University of Cincinnati, OH Susan Wessner, Tallahassee Community College, FL The authors also would like to thank the following students for their recommendations and criticisms regarding the material offered in the opening pages of the Student Support Edition. Matthew Berg, Vanderbilt University, TN Gregory Fulchino, Middlebury College, VT Emma Goehring, Trinity College, CT Gili Malinsky, Boston University, MA Julia Ong, Boston University, MA Anjali Parasnis-Samar, Mount Holyoke College, MA Teresa Reilly, University of Massachusetts–Amherst, MA xiv Copyright © Houghton Mifflin Company. All rights reserved. Page 236 Student Success Aufmann Interactive Method Intermediate Algebra: An Applied Approach uses an interactive style that engages students in try- ing new skills and reinforcing learning through structured exercises. UPDATED! AIM for Success— Getting Started Getting Started helps students develop the study skills necessary to achieve success in college mathematics. It also provides students with an explanation of how to effectively use the features of the text. AIM for Success—Getting Started can be used as a lesson on the first day of class or as a student project. Interactive Approach Each section is divided into objectives, and every objective contains one or more HOW TO examples. Annotations explain what is happening in key steps of each complete worked-out solution. Each objective continues with one or more matched-pair examples. The first example in each set is worked out, much like the HOW TO examples. The second example, called “You Try It,” is for the student. Complete worked-out solutions to these examples appear in the appendix for students to check their work. Study Tips These margin notes provide reminders of study skills and habits presented in the AIM for Success. Manage Your Time We know how busy you are outside of school. Do you have a full-time or a part-time job? Do you have children? Visit your family often? Play basketball or write for the school newspaper? It can be stressful to balance all of the impor- tant activities and responsibilities in your life. Making a time management plan will help you create a schedule that gives you enough time for everything you need to do. Let’s get started! Use the grids on pages AIM6 and AIM7 to fill in your weekly schedule. First, fill in all of your responsibilities that take up certain set hours during the week. Be sure to include: each class you are taking time you spend at work any other commitments (child care, tutoring, volunteering, etc.) When planning your schedule, give some thought to how much time you realistically have available each week. For example, if you work 40 hours a week, take 15 units, spend the rec- ommended study time given at the right, and sleep 8 hours a day, you will use over 80% of the available hours in a week. That leaves less than 20% of the hours in a week for family, friends, eating, recreation, and other activities. Visit h // ll h / T A K E N O T E We realize that your weekly schedule may change. Visit college.hmco.com/pic/ aufmanninterapplied SSE7e to print out addi- tional blank schedule forms, if you need them. T A K E N O T E To solve an equation using the Addition or the Multiplication Property of Equations An equation expresses the equality of two mathematical expressions. The ex- pressions can be either numerical or variable expressions. The equation at the right is a condi- tional equation. The equation is true if the variable is replaced by 3. The equa- tion is false if the variable is replaced by 4. A conditional equation is true for at least one value of the variable. The replacement value(s) of the variable that will make an equation true is (are) called the root(s) of the equation or the solution(s) of the equation. The solu- tion of the equation is 3 because is a true equation. The equation at the right is an identity. Any replacement for x will result in a true equation. The equation at the right has no solution because there is no number that equals itself plus one. Any replacement value for x will result in a false equation. This equation is a con- tradiction. Each of the equations at the right is a first-degree equa- tion in one variable. All variables have an exponent of 1. 3 � 2 � 5 x � 2 � 5 Equations x2 � 2y � 7 x � 8 � 11 2 � 8 � 10 A conditional equation A true equation A false equation 4 � 2 � 5 3 � 2 � 5 x � 2 � 5 x � 2 � x � 2 x � x � 1 3�a � 2� � 14a 3y � 2 � 5y x � 2 � 12 2.1 Solving Fi s g q Objective A Before you begin a new chap- ter, you should take some time to review previously learned skills. One way to do this is to complete the Prep Test. See page 56. This test focuses on the particular skills that will be required for the new chapter. S t u d y T i p Before you begin a new chap- ter, you should take some time to review previously learned skills. One way to do this is to complete the Prep Test. See page 56. This test focuses on the particular skills that will be required for the new chapter. S t u d y T i p Page 57 Page 57 Page AIM4 Page S13 Example 2 An investor has a total of $20,000 deposited in three different accounts, which earn annual interest rates of 9%, 7%, and 5%. The amount deposited in the 9% account is twice the amount in the 7% account. If the total annual interest earned for the three accounts is $1300, how much is invested in each account? Strategy • Amount invested at 9%: x Amount invested at 7%: y Amount invested at 5%: z • The amount invested at 9% (x) is twice the amount invested at 7% (y): The sum of the interest earned for all three accounts is $1300: The total amount invested is $20,000: Solution (1) (2) (3) Solve the system of equations. Substitute 2y for x in Equation (2) and Equation (3). (4) (5) Solve the system of equations in two variables by multiplying Equation (5) by and adding to Equation (4). Substituting the value of y into Equation (1), . Substituting the values of x and y into Equation (3), . The investor placed $6000 in the 9% account, $3000 in the 7% account, and $11,000 in the 5% account. z � 11,000 x � 6000 y � 3000 0.10y � 300 �0.15y � 0.05z � �1000 0.25y � 0.05z � 1300 �0.05 3y � z � 20,000 0.25y � 0.05z � 1300 2y � y � z � 20,000 0.09�2y� � 0.07y � 0.05z � 1300 x � y � z � 20,000 0.09x � 0.07y � 0.05z � 1300 x � 2y x � y � z � 20,000 0.09x � 0.07y � 0.05z � 1300 x � 2y You Try It 2 A coin bank contains only nickels, dimes, and quarters. The value of the 19 coins in the bank is $2. If there are twice as many nickels as dimes, find the number of each type of coin in the bank. Your strategy Your solution Principal Rate Interest Amount at 9% x 0.09 0.09x Amount at 7% y 0.07 0.07y Amount at 5% z 0.05 0.05z Solution on p. S13 • 0.09(2y) � 0.07y � 0.25y • 2y � y � 3y You Try It 2 Strategy • Number of dimes: d Number of nickels: n Number of quarters: q • There are 19 coins in a bank that contains only nickels, dimes, and quarters. The value of the coins is $2. There are twice as many nickels as dimes. Solution (1) (2) (3) Solve the system of equations. Substitute 2d for n in Equation (1) and Equation (3). (4) (5) l h f 20d � 25q � 200 3d � q � 19 5�2d� � 10d � 25q � 200 2d � d � q � 19 5n � 10d � 25q � 200 n � 2d n � d � q � 19 �n � 2d� �5n � 10d � 25q � 200� �n � d � q � 19�

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