Elementary algebra

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Rectangle Triangle w a c h l A=lw A P l w P = l + 2w area perimeter length width Parallelogram b A = bh A area P perimeter b base h altitude a, c sides P=a+b+c Right Triangle h c b A = bh A area b base h altitude ( height) Trapezoid b a Pythagorean theorem: a2 + b2 = c2 a, b legs c hypotenuse Circle b1 h r b2 A = h (b1 + b2 ) A area b1, b2 bases h altitude A = πr2 C = πr A area C circumference r radius Cube Rectangular Prism b s s s V = s3 c S = 6s2 V S s a volume total surface area length of a side Sphere V = abc S = ac + ab + 2bc V S a b c volume total surface area width length height Right Circular Cylinder r r V = πr 3 V S r S = 4πr h V = πr 2h S = πr + 2π rh V S r h volume total surface area radius altitude (height) volume total surface area radius Pyramid Right Circular Cone h r base V B h V = Bh volume area of base altitude ( height) s h V = πr h V S r h s S = πr + πr s volume total surface area radius altitude (height) slant height ELEMENTARY ALGEBRA NINTH EDITION This page intentionally left blank NINTH EDITION ELEMENTARY ALGEBRA Jerome E Kaufmann Karen L Schwitters Seminole State College of Florida Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Elementary Algebra, Ninth Edition Jerome E Kaufmann and Karen L Schwitters Mathematics Editor: Marc Bove Developmental Editor: Meaghan Banks Assistant Editor: Stefanie Beeck Editorial Assistant: Kyle O’Loughlin © 2011, 2007 Brooks/Cole, Cengage Learning ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher Media Editor: Maureen Ross Marketing Manager: Joe Rogove For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 Marketing Assistant: Angela Kim Marketing Communications Manager: Katy Malatesta Content Project Manager: Tanya Nigh Creative Director: Rob Hugel For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions Further permissions questions can be e-mailed to permissionrequest@cengage.com Senior Art Director: Vernon Boes Print Buyer: Karen Hunt Rights Acquisitions Account Manager, Text: Timothy Sisler Rights Acquisitions Account Manager, Image: Dan Schlotman Production Service: Susan Graham Text Designer: Diane Beasley Copy Editor: Susan Graham Illustrator: Network Graphics Cover Designer: Irene Morris Cover Image: Fotolia Library of Congress Control Number: 2009926193 Student Edition: ISBN-13: 978-1-4390-4917-4 ISBN-10: 1-4390-4917-3 Brooks/Cole 20 Davis Drive Belmont, CA 94002-3098 USA Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil, and Japan Locate your local office at www.cengage.com/global Compositor: MacMillan Publishing Services Cengage Learning products are represented in Canada by Nelson Education, Ltd To learn more about Brooks/Cole, visit www.cengage.com/brooks/cole Purchase any of our products at your local college store or at our preferred online store www.ichapters.com Printed in the United States of America 13 12 11 10 09 CONTENTS Some Basic Concepts of Arithmetic and Algebra 1.1 Numerical and Algebraic Expressions 1.2 Prime and Composite Numbers 1.3 Integers: Addition and Subtraction 1.4 Integers: Multiplication and Division 1.5 Use of Properties Chapter Summary 14 21 26 35 Chapter Review Problem Set Chapter Test 37 39 Real Numbers 41 2.1 Rational Numbers: Multiplication and Division 42 2.2 Addition and Subtraction of Rational Numbers 50 2.3 Real Numbers and Algebraic Expressions 2.4 Exponents 2.5 Translating from English to Algebra 69 Chapter Summary 75 82 Chapter Review Problem Set Chapter Test 85 87 Chapters – Cumulative Review Problem Set 59 88 Equations, Inequalities, and Problem Solving 91 3.1 Solving First-Degree Equations 92 3.2 Equations and Problem Solving 97 3.3 More on Solving Equations and Problem Solving 3.4 Equations Involving Parentheses and Fractional Forms 3.5 Inequalities 3.6 Inequalities, Compound Inequalities, and Problem Solving 111 120 Chapter Summary 127 135 Chapter Review Problem Set Chapter Test 103 139 141 v vi Contents Formulas and Problem Solving 143 4.1 Ratio, Proportion, and Percent 4.2 More on Percents and Problem Solving 4.3 Formulas 4.4 Problem Solving 4.5 More about Problem Solving 152 158 Chapter Summary 167 172 178 Chapter Review Problem Set Chapter Test 144 181 182 Chapters – Cumulative Review Problem Set 183 Exponents and Polynomials 185 5.1 Addition and Subtraction of Polynomials 5.2 Multiplying Monomials 5.3 Multiplying Polynomials 5.4 Dividing by Monomials 5.5 Dividing by Binomials 5.6 Integral Exponents and Scientific Notation Chapter Summary 192 197 204 208 212 220 Chapter Review Problem Set Chapter Test 186 223 225 Chapters – Cumulative Review Problem Set Factoring, Solving Equations, and Problem Solving 229 6.1 Factoring by Using the Distributive Property 6.2 Factoring the Difference of Two Squares 6.3 Factoring Trinomials of the Form x ϩ bx ϩ c 6.4 Factoring Trinomials of the Form ax ϩ bx ϩ c 6.5 Factoring, Solving Equations, and Problem Solving 242 249 255 264 Chapter Review Problem Set Chapter Test 230 236 Chapter Summary 226 266 268 Algebraic Fractions 269 7.1 Simplifying Algebraic Fractions 7.2 Multiplying and Dividing Algebraic Fractions 7.3 Adding and Subtracting Algebraic Fractions 7.4 Addition and Subtraction of Algebraic Fractions and Simplifying Complex Fractions 270 274 278 284 Contents 7.5 Fractional Equations and Problem Solving 7.6 More Fractional Equations and Problem Solving Chapter Summary 310 312 Chapters – Cumulative Review Problem Set 8.1 Cartesian Coordinate System 8.2 Graphing Linear Equations and Inequalities 8.3 Slope of a Line 8.4 Writing Equations of Lines 8.5 Systems of Two Linear Equations 8.6 Elimination-by-Addition Method Chapter Test 316 324 332 340 350 360 370 Chapter Review Problem Set 375 377 Roots and Radicals 379 9.1 Roots and Radicals 9.2 Simplifying Radicals 9.3 More on Simplifying Radicals 9.4 Products and Quotients Involving Radicals 9.5 Solving Radical Equations Chapter Summary 380 385 Chapter Test 391 397 402 409 Chapter Review Problem Set 412 413 Chapters – Cumulative Review Problem Set 10 313 Coordinate Geometry and Linear Systems 315 Chapter Summary 298 307 Chapter Review Problem Set Chapter Test 292 414 Quadratic Equations 417 10.1 Quadratic Equations 10.2 Completing the Square 10.3 Quadratic Formula 10.4 Solving Quadratic Equations—Which Method? 10.5 Solving Problems Using Quadratic Equations Chapter 10 Summary 418 426 431 447 Chapter 10 Review Problem Set Chapter 10 Test 450 449 436 440 vii 532 Answers to Odd-Numbered Problems 19 24 25 21 26 ϩ 210 23 23 Ϫ 526 25 ϩ 220 27 22 Ϫ 26 29 426 Ϫ 8215 31 56 ϩ 1522 33 Ϫ9 Ϫ 26 50 35 22 ϩ 26 ϩ 23 ϩ 37 15 43 x2y 45 5x 47 12a2b 57 26 ϩ 59 25 Ϫ 23 61 42x ϩ xϪ4 65 39 15 Ϫ3 22 ϩ 12 14 Ϫ20 Ϫ 30 23 23 x Ϫ 32x xϪ9 5186 15 e f 13 л 21 23 e f 33 41 43 51 л e f 17 5366 25 5Ϫ3, Ϫ26 e f 19 566 27 566 11 5146 21 526 29 526 31 5126 5 Ϫ 22 10 22 10 25 11 Ϫ10 13 627 14 Ϫ26 19 526 18 23 17.3 214 15 57 566 61 536 67 47 Ϫ 23 22 20 16 210 21 5.2 225 12 17 22 1.2 35 32xy 4y2 39 Ϫ40 36 Ϫ2 2x 16 210 58 546 55 59 50, 96 62 516 63 46 22 ϩ 26 52 25 Ϫ1726 56 60 5Ϫ5, Ϫ46 64 66 65 72 66 26 68 74 0.05 2x 33 x 37 22 12 Ϫ5xy 22x 19 x 22x 34 38 18 22 3 40 10 28 41 6ϩ2 42 210 Ϫ 12215 43 ϩ 221 ϩ 215 ϩ 235 44 Ϫ24 Ϫ 726 45 ϩ 242 46 Ϫ18 Ϫ 25 Ϫ5.6 2.8 22 522 215xy 5y 13 2.1 10 26 325 20 426 210 11 14 3xy 23x 15 26 18 Ϫ 5215 17 1222 Ϫ 12 23 22 Ϫ 23 24 536 21 22 25 5Ϫ2, 16 22 556 23 л Chapters 1–9 Cumulative Review Problem Set (page 414) 13 Ϫ64 64 144 Ϫ8 Ϫ9 9 Ϫ29 Ϫx ϩ 17 15 12 4x (x Ϫ 2) (x ϩ 3) Ϫ8x Ϫ 41 15 16 60x4y4 1x ϩ 621x Ϫ 32 11 Ϫ 10 49 13 5y 14 xϪ4 17 Ϫ8 x2 18 Ϫ3a3 b 19 21 Ϫ5x2 Ϫ 12x Ϫ 3n4 20 27x2 ϩ 30x Ϫ 22 6x3 Ϫ x2 Ϫ 13x Ϫ 23 3x3y6 Ϫ 4y3 24 2x2 Ϫ 2x Ϫ 25 y Ϫ x 26 4.67 gallons 27 25% 29 130 feet (c) 11.042110Ϫ6 3x 23 27 4xy 23x 28 a b 29 4y 23x 30 22xy 32 2y 54 49 52 Ϫ7 22x 51 1822 30 314 square inches 24 Ϫ6.9 25 2ab 23b 26 5y2 22x 210xy 31 5y 8 Ϫ49 Chapter Review Problem Set (page 412) Ϫ7 40 53 Ϫ22 16 24210 5256 35 536 37 eϪ f 39 526 56 feet; 106 feet; 148 feet 3.2 feet; 5.1 feet; 7.3 feet 47 5186 49 54, 126 5576 53 51106 55 52526 242 Ϫ 215 23 Ϫ1222 Problem Set 9.5 (page 407) 5496 48 322 ϩ 223 Chapter Test (page 413) ϩ 22 ϩ 23 ϩ 26 69 a ϩ 72a ϩ 10 67 a Ϫ 25 51 27 ϩ 252 41 51 49 x 26 Ϫ 23xy 51 x ϩ 22x Ϫ 15 53 x Ϫ 49 55 63 47 37 17x Ϫ 2213x ϩ 42 31 (a) 18.521104 (d) 15.321107 33 312x ϩ 3212x Ϫ 32 35 15 Ϫ x216 ϩ 5x2 28 108 (b) 192110Ϫ4 32 2x12x ϩ 5213x Ϫ 42 34 1y ϩ 321x Ϫ 22 36 41x ϩ 121x Ϫ 121x2 ϩ 12 38 827 39 Ϫ325 40 26 22ab 42 6y 22xy 43 Ϫ 44 48 18 45 216 Ϫ 36 26 46 11 47 423 Ϫ 422 41 48 Ϫ 213 25 ϩ 262 13 49 22 50 3725 12 625 Answers to Odd-Numbered Problems 51 y 52 59 Ϫ2 (3, 5) (0, 4) 66 1Ϫ2, 426 70 eϪ y y 54 78 5Ϫ2, 26 (0, 3) (1, 2) x 23 f 74 55006 (5, 1) 61 2x Ϫ 3y ϭ 62 4x ϩ 3y ϭ Ϫ13 63 x ϩ 4y ϭ Ϫ12 64 x 53 60 x (0, 0) 65 11, Ϫ226 68 e a , 3b f 67 1Ϫ6, 1226 71 556 75 5536 79 5296 72 eϪ 76 eϪ f 80 5276 81 5n 0n Ն Ϫ56 or 3Ϫ5, q 73 e 19 f 10 69 5176 47 f 77 5Ϫ6, 26 82 e n n Ͼ 1 f or a , qb 4 2 83 e x 0x Ͼ Ϫ f or a Ϫ , q b 5 55 84 5n 0n Ͼ 66 or 16, q y 56 (3, 0) x 92 (0, −6) y 57 85 e x 0x Ͻ 5 f or aϪq, b 16 16 86 e x 0x Ն Ϫ 88 90 95 16 16 f or cϪ , qb 87 65° and 115° 3 13 and 37 89 7, nickels, 15 dimes, and 25 quarters 91 $3780 $48 93 hours 94 12.5 milliliters 91 or better 96 More than 11 97 12 minutes y 58 (0, 3) (−4, 0) (−2, 0) x (0, −2) x Chapter 10 Problem Set 10.1 (page 424) 5Ϫ15, 06 50, 126 50, 56 51, 86 11 5Ϫ6, 16 13 e- , f 2 15 e , f 19 5Ϫ8, 86 5 21 eϪ , f 3 23 5Ϫ4, 46 25 5Ϫ 214, 2146 29 5Ϫ4 22, 226 33 eϪ 322 322 , f 2 5Ϫ2, 76 17 e f 27 No real number solutions 31 5Ϫ3 22, 226 35 eϪ 22 22 , f 4 37 5Ϫ1, 36 39 5Ϫ8, 26 41 eϪ , f 43 5Ϫ6 Ϫ 25, Ϫ6 ϩ 256 45 51 Ϫ 222, ϩ 2226 Ϫ3 Ϫ 25 Ϫ3 ϩ 225 , f 2 49 No real number solutions 47 e 51 e 533 Ϫ 210 ϩ 210 , f 3 55 5Ϫ8 Ϫ 522, Ϫ8 ϩ 5226 53 eϪ , f 7 57 522 inches 59 227 meters 61 2211 feet 534 Answers to Odd-Numbered Problems 25 eϪ1, 63 a ϭ inches and b ϭ 23 inches 65 c ϭ 12 feet and b ϭ 23 feet 67 a ϭ 23 meters and c ϭ 23 meters 69 a ϭ 10 inches and c ϭ 10 22 inches 22 meters 73 8.2 feet 75 30 meters 77 35 meters 81 5.2 centimeters 83 10.8 centimeters 71 a ϭ b ϭ Problem Set 10.2 (page 430) 5Ϫ4 Ϫ 217, Ϫ4 ϩ 2176 52 Ϫ 22, ϩ 2226 5Ϫ5 Ϫ 223, Ϫ5 ϩ 2236 No real number solutions 5Ϫ1 Ϫ 22, Ϫ1 ϩ 226 f 5 27 eϪ , Ϫ f 29 e Ϫ5 Ϫ 273 Ϫ5 ϩ 273 f , 4 31 e Ϫ2 Ϫ 27 Ϫ2 ϩ 27 f , 3 35 e Ϫ2 Ϫ 25 Ϫ2 ϩ 25 f , 2 37 e Ϫ9 Ϫ 257 Ϫ9 ϩ 257 f , 12 12 33 e Ϫ f Ϫ 233 ϩ 233 f , 4 41 No real number solutions 39 e 11 e Ϫ1 Ϫ 213 Ϫ1 ϩ 213 , f 2 13 e Ϫ 233 ϩ 233 , f 2 Ϫ4 Ϫ 222 Ϫ4 ϩ 222 , f 15 e 2 43 e Ϫ5 Ϫ 2137 Ϫ5 ϩ 2137 f , 14 14 45 e Ϫ 285 ϩ 285 , f 6 47 5Ϫ14, Ϫ96 53 5Ϫ2.52, 7.526 55 5Ϫ8.10, 2.106 61 5Ϫ1.95, 2.156 17 e Ϫ6 Ϫ 242 Ϫ6 ϩ 242 , f 3 59 5Ϫ1.33, 3.586 19 e Ϫ 22 ϩ 22 , f 2 Problem Set 10.4 (page 439) 5Ϫ9, 56 21 No real number solutions e f 23 e Ϫ 265 ϩ 265 , f 2 25 e Ϫ3 Ϫ 217 Ϫ3 ϩ 217 , f 4 15 eϪ1, eϪ 11 e 0, f Ϫ1 Ϫ 27 Ϫ1 ϩ 27 , f 29 5Ϫ14, 126 3 31 5Ϫ11, 156 33 5Ϫ6, 26 35 5Ϫ9, Ϫ36 21 5Ϫ12, 76 37 5Ϫ5, 86 31 e 27 e 45 e 39 e , f 43 e Problem Set 10.3 (page 435) 5Ϫ1, 66 e 5Ϫ9, 46 51 Ϫ 26, ϩ 266 Ϫ 233 ϩ 233 , f 2 11 5Ϫ2 Ϫ 22, Ϫ2 ϩ 226 17 516, 186 19 5Ϫ10, 86 21 5Ϫ26 15 e 0, 22 f 13 57 Ϫ 2217, ϩ 22176 17 eϪ , Ϫ f 23 e 19 22 Ϫ 3, 22 ϩ 36 Ϫ 233 ϩ 233 , f 4 29 516, 306 39 e 33 e , f 3 Ϫ 23 ϩ 23 , f 2 Ϫ5 Ϫ 2193 Ϫ5 ϩ 2193 , f 6 25 5Ϫ1, 46 35 5Ϫ13, 16 41 eϪ1, Ϫ f 45 5Ϫ5, 36 Problem Set 10.5 (page 444) No real number solutions 13 50, 66 5Ϫ1, 26 Ϫ1 Ϫ 213 Ϫ1 ϩ 213 , f 2 37 511, 176 Ϫb ϩ 2b2 Ϫ 4ac Ϫb Ϫ 2b2 Ϫ 4ac , f 2a 2a e 0, f 13 , f 5 27 No real number solutions 41 eϪ , f 2 57 5Ϫ3.55, 1.226 f 2 23 eϪ , f 17 and 18 19 and 25 ϩ 25 and Ϫ 25 22 12, 14, and 16 11 Ϫ8 or 13 meters by 12 meters 15 15 centimeters by 25 centimeters 22 or 17 27 feet by 78 feet 19 15 rows and 20 seats per row 21 feet by feet 23 inches and inches Answers to Odd-Numbered Problems 25 inches 27 30 students 29 24 inches and 32 inches 31 18 miles per hour Chapter 10 Review Problem Set (page 449) 5Ϫ6, Ϫ16 50, 176 e 5Ϫ4 Ϫ 213, Ϫ4 ϩ 2136 5Ϫ4, 16 511, 156 Ϫ7 Ϫ 261 Ϫ7 ϩ 261 f , 6 e f 10 5Ϫ5, Ϫ16 No real number solutions 11 52 Ϫ 22, ϩ 226 12 5Ϫ2 Ϫ 322, Ϫ2 ϩ 226 13 5Ϫ325, 256 16 52 Ϫ 213, ϩ 2136 14 5Ϫ3, 96 15 50, 16 17 520, 246 18 52 Ϫ 22, ϩ 226 20 e e , f Ϫ1 Ϫ 273 Ϫ1 ϩ 273 f , 12 12 19 eϪ , f 21 e , f 22 eϪ , Ϫ1 f 23 inches by 12 inches 24 18 and 19 25 7, 9, and 11 26 25 meters and 325 meters 27 yards and yards 28 40 shares at $20 per share 29 10 meters 30 Jay’s rate was 45 miles per hour and Jean’s rate was 48 miles per hour; or Jay’s rate was miles per hour and Jean’s rate was 10 miles per hour 31 622 inches 32 1623 centimeters Chapter 10 Test (page 450) 2213 inches 13 meters inches 423 centimeters eϪ3, f 3 e , f e 5Ϫ4, 46 Ϫ 229 ϩ 229 f , 2 5Ϫ1 Ϫ 210, Ϫ1 ϩ 2106 10 No real number solutions 12 e Ϫ 241 ϩ 241 , f 4 13 e Ϫ 257 ϩ 257 , f 2 16 e , f 19 e 17 e 0, f 11 5Ϫ12, 26 14 e , f 15 513, 156 18 eϪ1, f Ϫ 23 ϩ 323 , f 4 20 No real number solutions 22 14 miles per hour 21 15 seats per row 23 15 and 17 24 feet 25 20 shares Chapter 11 Problem Set 11.1 (page 455) 5Ϫ4, 46 −4 5x x Ͼ Ϫ1 and x Ͻ 16 or 1Ϫ1, 12 −1 5x x Յ Ϫ2 or x Ն 26 or 1Ϫq, Ϫ2 ഫ 32, q 5Ϫ3, Ϫ16 5Ϫ1, 36 11 5x 0x Ն and x Յ 46 or 30, 4 −3 −2 13 5x 0x Ͻ Ϫ4 or x Ͼ 26 or 1Ϫq, Ϫ42 ഫ 12, q 15 5Ϫ2, 16 −4 −2 17 eϪ , f 5 −1 −1 −− − 535 536 Answers to Odd-Numbered Problems 19 5x 0x Յ or x Ն 26 or 1Ϫq, ഫ 32, q 15 29 5 21 e x x Ͼ Ϫ and x Ͻ Ϫ f or a Ϫ , Ϫ b 4 4 27 41 27 −− −− 4 23 5Ϫ26 17 16 19 16 31 21 32 35 Ϫ32 33 625 43 1 45 47 14 14 and x Ͻ f or aϪ , 8b 3 35 e x x Ն Ϫ6 and x Յ 19 19 f or cϪ6, d 2 21 21 or x Ն f or aϪq, Ϫ d ഫ 33, q 5 45 5x 0x is any real number6 47 л 53 5x 04 Ͻ x Ͻ 146 or 14, 142 61 10n4 3 67 64x4y2 69 2x y 63 71 4x15 61 5x 0Ϫ1 Ͻ x Ͻ 66 or 1Ϫ1, 62 125x 79 216y 13, 1, Ϫ22 1Ϫ1, 3, 42 15, Ϫ3, 12 1Ϫ2, 3, 52 13, Ϫ2, Ϫ42 11 1Ϫ1, 3, 12 13 13, 0, Ϫ22 11, 4, 22 17 10 quarters, dimes, nickels ЄA ϭ 120°, ЄB ϭ 24°, ЄC ϭ 36° 21 Plumber ϭ $50 per hour; Apprentice ϭ $20 per hour; Laborer ϭ $10 per hour 23 Peaches ϭ $1.29 per pound; Cherries ϭ $.99 per pound; Pears ϭ $.69 per pound 25 Helmet ϭ $250, Jacket ϭ $350, Gloves ϭ $50 29 Infinitely many solutions 31 л Problem Set 11.3 (page 469) Ϫ4 i i 211 5i22 4i23 11 3i26 13 ϩ 17i 15 10 Ϫ 10i 17 ϩ 2i 19 Ϫ2 Ϫ 6i 21 Ϫ5 ϩ 3i 23 Ϫ12 Ϫ 16i 25 Ϫ10 Ϫ 4i 8i 11 13 Ϫ3 5 ϩ i 12 ϩ i 35 Ϫ56 ϩ 0i 37 Ϫ6 ϩ 12i 15 12 39 Ϫ24 ϩ 20i 41 Ϫ2 ϩ 23i 43 59 Ϫ 17i 45 Ϫ21 Ϫ 12i 47 Ϫ26 ϩ 15i 49 Ϫ9 ϩ 40i 51 61 ϩ 0i 53 ϩ 0i 33 Ϫ Problem Set 11.5 (page 477) 5Ϫ8i, 8i6 52 Ϫ i, ϩ i6 5Ϫ5 Ϫ i213, Ϫ5 ϩ i2136 17 52 Ϫ 4i, ϩ 4i6 Problem Set 11.2 (page 463) 5 77 73 b12 eϪ , f 5 13 5Ϫ3 Ϫ i 23, Ϫ3 ϩ i236 59 5x 0Ϫ7 Ͻ x Ͻ Ϫ16 or 1Ϫ7, Ϫ12 Ϫ10 17 53 a12 59 2y12 53 Ϫ 3i22, ϩ 3i226 57 5x Ϫ11 Ͻ x Ͻ 76 or 1Ϫ11, 72 51 x4 11 27 Ϫ1 ϩ 12i 29 Ϫ20 Ϫ 8i 31 55 5x 0Ϫ1 Յ x Յ 46 or Ϫ1, 44 15 19 39 Problem Set 11.4 (page 473) 7 41 e x x Ͻ Ϫ or x Ͼ f or aϪq, Ϫ b ഫ a , qb 2 2 49 5Ϫ66 4x3 83 (a) 28 (b) 35 (c) 17 (d) 42 85 (a) 11.18 (b) 5.28 (c) 3.11 (d) 1573.56 (e) 6.45 (f) 5.81 39 5x 0x Ͼ Ϫ6 and x Ͻ 26 or 1Ϫ6, 22 43 506 49 49 57 24x12 75 16 27 eϪ , f 29 5x x Ͻ Ϫ5 or x Ͼ 46 or 1Ϫq, Ϫ52 ഫ 14, q 37 e x 0x Յ Ϫ 2 2 or a Ϫq, b ഫ a , qb 3 16 f 37 27 x6 − 33 eϪ6, 25 Ϫ3 65 25xy 31 e x x Ͼ Ϫ 55 15x12 −2 25 5x 0x 23 21 eϪ1, f 19 e 15 53 Ϫ 2i, ϩ 2i6 Ϫ i22 ϩ i 22 , f 3 23 51 Ϫ 3i22, ϩ 3i226 25 52 Ϫ i23, ϩ i236 29 e 11 5Ϫ1, 46 27 e Ϫ i 231 ϩ i231 , f 8 Ϫ1 Ϫ i25 Ϫ1 ϩ i25 , f 6 Problem Set 11.6 (page 482) 14% 480 66% Physics 21% 11 62% 13 1000 people 15 1500 people 17 Jan and Feb 19 Feb and March 21 0.4% 537 Answers to Odd-Numbered Problems (c) P(s) 20 23 $390 25 Monday or Wednesday 27 $580 29 2% 31 3% 33 2007 and 2008 35 (a) 12% (b) 12% (c) Neither, they are the same 39 Gold 15 10 Mutual Funds Annuities (d) 17 (2, 8) (1, 4) Bonds s Stocks Problem Set 11.7 (page 489) Domain: 54, 6, 8, 106 Range: {7, 11, 20, 28} It is a function Domain: 5Ϫ2, Ϫ1, 0, 16 Range: 51, 2, 3, 46 It is a function Domain: 54, 96 Range: 5Ϫ3, Ϫ2, 2, 36 It is not a function Domain: 53, 4, 5, 66 Range: 5156 It is a function Domain: 5Carol6 Range: 522400, 23700, 252006 It is not a function 11 Domain: 5Ϫ66 Range: 51, 2, 3, 46 It is not a function 13 Domain: 5Ϫ2, Ϫ1, 0, 1, 26 Range: 50, 1, 46 It is a function 15 All reals 17 All reals except Ϫ8 19 All reals 21 All reals except 23 All reals except 25 All reals 27 All reals except 29 All reals 31 4; 7; 1; 22 11 13 19 ; ; ;Ϫ 33 Ϫ16; 19; 24; Ϫ5t Ϫ 35 12 36 12 37 0; 0; 45; Ϫ4 39 0; Ϫ3; Ϫ3; Ϫ8 41 23; Ϫ21; 3; 43 8; 48; 8; Ϫ7 21 (a) $20,800 V(t) (c) 35,000 (b) $14,950 (d) $13,000 (0, 32,500) 15,000 (10, 13,000) 5,000 (16.7, 0) 10 14 18 t 23 (a) ͉ 50 ͉ 41 ͉ Ϫ4 ͉ 212 ͉ 95 ͉ 77 ͉ 59 t ͉ 10 (b) f (t) f(t) ͉ ͉ 17 ͉ ͉ ͉ ͉ ͉ ͉ 10,000 ͉ 15,000 ͉ 20,000 ͉ 25,000 ͉ 30,000 f(n) 19 (a) 12 ͉ ͉ 4.5 ͉ ͉ (b) 20 3/10 7.5 ͉ n 1/5 ͉ ͉ 1/10 ͉ f(x) ͉ ͉ 2/5 100 ͉ 35 ͉ 25 ͉ 15 (c) Ϫ6.7ЊC (50, 10) 20 20 60 100 140 180 220 t Chapter 11 Review Problem Set (page 497) 55% 44% 52% 25 students Shopping and workout Dinner out, television, movie, shopping, workout, sports, study 2006 $1500 $5750 10 $5583 11 eϪ , f −− 12 5x 0x Ͼ and x Ͻ 56 or 13, 52 9; 289; 72.25; 430.56; 126.56 $464,500 $6.75; $10.13; $13.50; $24.60 $30; $15; $27 $4.00; $1.50; $0; $6.00 11 $367.50; $420; $577.50; $210 $118.50; $138.50; $98.50; $158.50 x 15 ͉ (212, 100) 100 60 Ϫ20 Problem Set 11.8 (page 492) 13 (f) 16.7 years 25,000 13 5x 0x Յ Ϫ1 or x Ն 26 or 1Ϫq, Ϫ1 ഫ 32, q −1 2 14 ex0 x Ն Ϫ and x Յ 2f or cϪ , d 3 15 5Ϫ4, 56 −4 −− 538 Answers to Odd-Numbered Problems 8 16 e x x Յ Ϫ or x Ն f or aϪq, Ϫ d ഫ c , qb 5 5 −− 17 18 Ϫ1 24 Ϫ32 31 3 19 16 25 − 26 20 Ϫ5 21 27 28 17 32 x3 33 6x20 34 36a 37 13n20 38 22 125 29 23 32 30 35 27xy2 36 5x2y3 39 8x3 40 { (0, 2, 5) } n4 41 { (2, 1, 3) } 45 49 53 57 71 Domain: 51, 2, 36 Range: 54, 8, 10, 156 It is not a function 72 All reals except 73 All reals 74 All reals 75 All reals except Ϫ4 1 76 All reals except 77 All reals except Ϫ 3 78 Ϫ14; Ϫ2; 13; 3a Ϫ 79 Ϫ ; ; Ϫ2; Ϫ3 3 ; 0; ; 5 82 (a) $.80 81 Ϫ6; Ϫ3; 2; 80 (b) $1.70 f(x) (c) 1.75 42 ϩ 2i 43 Ϫ7 Ϫ 5i 44 Ϫ 4i (d) $1.40 (5, 1.70) 1.25 Ϫ 4i 46 Ϫ1 ϩ 3i 47 Ϫ6 ϩ 10i 48 Ϫ34 ϩ 31i Ϫ2 Ϫ11i 50 Ϫ4 Ϫ 8i 51 Ϫ 45i 52 85 58 54 55 Ϫ 48i 55 Ϫ 15i 56 56 Ϫ 5i, ϩ 5i6 5Ϫ1 Ϫ i 26, Ϫ1 ϩ i 266 75 (1, 50) 25 58 51 Ϫ 4i, ϩ 4i6 59 e Ϫ 3i 23 ϩ 3i 23 , f 2 Ϫ i 223 ϩ i 223 , f 60 e 4 62 e x 83 (a) 22 gallons 61 e , f Ϫ i 23 ϩ i 23 , f 2 (b) 32 gallons (c) f(x) 40 (d) 28 gallons (100, 32) 20 (50, 22) Ϫ3 Ϫ i 239 Ϫ3 ϩ i239 63 e , f 4 50 64 e 65 e Ϫ1 Ϫ i 259 Ϫ1 ϩ i259 , f 6 Ϫ1 Ϫ i 247 Ϫ1 ϩ i247 , f 8 66 Domain: 5red, blue, green6 1 Range: e , , f 8 It is a function 67 Domain: 53, 4, 56 Range: 55, 7, 96 It is a function 68 Domain: 51, 26 Range: 5Ϫ16, Ϫ8, 8, 166 It is not a function 69 Domain: 52, 3, 4, 56 Range: 5106 It is a function 70 Domain: 5Ϫ2, Ϫ1, 0, 1, 26 Range: 50, 1, 46 It is a function 150 x 100 Chapter 11 Test (page 500) French fries; salad 30 60 11 Ϫ 13i 5i 23 216 10 5n10 11 52 Ϫ 4i, ϩ 4i6 35 11 27 10x12 12 51 Ϫ i 22, ϩ i226 13 {Ϫ3 Ϫ 2i23, Ϫ3 ϩ 2i 23} 14 e Ϫ i211 ϩ i211 , f 2 16 eϪ , Ϫ f 4 18 e 15 5Ϫ4, 86 17 л Ϫ i27 ϩ i27 , f 4 19 eϪ4, f 20 {x x Յ Ϫ5 or x Ն Ϫ1} or 1Ϫq, Ϫ5] ഫ [Ϫ1, q 21 {x x Ͼ Ϫ3 and x Ͻ 4} or 1Ϫ3, 42 23 4; Ϫ6; Ϫ21; 14 25 $11,550; $16,250 22 All real numbers except 24 $447 Answers to Odd-Numbered Problems 539 Appendix B Appendix B Answers (page 503) 6 33 and 34 Ϫ41 and Ϫ42 22, 24, and 26 47, 49, and 51 10 11 Ϫ3 12 19 and 20 13 49, 50, and 51 14 15 32 16 48 17 72 16 25 103 104 105 26 Ϫ or 5 27 Ϫ or 29 Ϫ or 30 36 and 42 31 14 and 41 33 32 and 67 34 40 and 96 35 ϩ 13; Ϫ 13 25 36 and 37 and 28 or 32 17 and 85 38 20 years 39 23 years 40 Kaitlin is 12 years old and Nikki is years old 41 Jessie is 18 years old and Annilee is 12 years old 42 Angie is 22 years old and her mother is 42 years old 13 43 All numbers greater than 44 All numbers less than or equal to 45 All numbers less than 47 100 or better 46 92 or better 48 77 or less 49 166 or better 50 10 centimeters 51 14 inches 52 35Њ and 70Њ 53 62Њ and 118Њ 54 24Њ and 66Њ 55 60Њ 56 A ϭ 32Њ, B ϭ 58Њ, and C ϭ 90Њ 57 55Њ 59 60 62 64 65 66 67 69 70 71 72 74 75 76 78 58 inches by 15 inches 14 centimeters by 21 centimeters yard, 12 yards, and 15 yards 61 12 inches centimeters 63 meters by meters Side is inches and altitude is inches inches and 12 inches Width is meters and length is 15 meters meter 68 inches by 14 inches units and 11 units $3000 at 5% and $4500 at 6% $1000 at 8% and $3000 at 9% $1000 73 $800 at 7% and $1200 at 8% 40 shares at $20 per share 40 shares at $15 per share 12 lots at $10,000 per lot 77 14 feet by 17 feet 130 miles 79 300 miles 80 $4000 81 25 pounds 82 feet and 14 feet 83 87 miles 5 99 101 18 and or Ϫ and Ϫ8 12 19 Ϫ2 and Ϫ12 or and 10 20 and or Ϫ5 and Ϫ6 21 and 22 18 and 39 23 and 56 24 84 86 92 97 106 107 109 110 113 116 $300 and $450 85 2750 females and 1650 males 30% 87 115% 88 75 89 55 90 90 91 $52 $60 93 40% 94 35% 95 $8 96 $36.25 $27.50 98 $1.60 per pound 58 mph and 65 mph 100 hours hour 102 hours Kaitlin at miles per hour and Kent at 12 miles per hour Simon walks hours at miles per hour and Dave walks hours at miles per hour 12 miles per hour out and miles per hour back or 16 mph out and 12 mph back Walks at miles per hour and jogs at miles per hour 55 miles per hour 108 20 miles per hour Lorraine at 20 mph and Charlotte at 25 mph, or Lorraine at 45 mph and Charlotte at 50 mph liters 111 cups 112 25 milliliters quarts 114 10 gallons 115 43 % 3 15 quarts of 30% and quarts of 70% 1 117 quarts 118 12 minutes 119 37 minutes 120 A in hours and B in hours 121 60 minutes 122 hours for Tom and hours for Terry 123 80 minutes 124 pennies, 15 nickels, and 20 dimes 125 14 nickels and 16 dimes 126 48 pennies, 24 nickels, 32 dimes 127 40 quarters, 20 dimes, 10 nickels 128 30 pennies, 20 nickels, 45 dimes 129 dimes and 15 quarters 130 12 nickels, 25 dimes, 35 quarters 131 $9.50 per hour 132 $20 133 $30 per hour 134 $3.69 135 $65 136 730 Democrats 137 360 girls 138 $23 per share 139 $12 per hour 140 $10.20 per hour 141 rows and 13 trees per row 142 rows and desks per row 143 $1.79 per pound for Gala apples and $.99 per pound for Fuji apples 144 $1.69 for tape 145 $2.29 for corn flakes and $2.98 for wheat flakes 146 30 hours 147 25 students at $4 each 148 people 149 12 mugs at $7 each 150 30 feet This page intentionally left blank Index Abscissa, 317 Absolute value equation, 452 Absolute value inequality, 453 Absolute value of a number, 16 Addition: of algebraic fractions, 279 of complex numbers, 471 of decimals, 63 of fractions, 51 of integers, 16 of polynomials, 186 of radicals, 388 Addition method of solving systems, 360 Addition property of equality, 93 Addition property of inequality, 122 Additive inverse, 15 Additive inverse property, 28, 62 Algebraic equation, 92 Algebraic expression, Algebraic fraction, 268 Algebraic inequality, 120 Analytic geometry, 315 Approximation of square roots, 383 Associative property: of addition, 27, 61 of multiplication, 27, 61 Axes of a coordinate system, 316 Bar graph, 479 Base of a power, 69 Binomial, 186 Cartesian coordinate system, 317 Circle, 160 Circle graph, 477 Circumference, 160 Common binomial factor, 231 Commutative property: of addition, 27, 61 of multiplication, 27, 61 Complementary angles, 107 Completing the square, 426 Complex fraction, 287 Complex number, 470 Composite number, Compound inequality, 129 Cone, right circular, 161 Conjugates, 399 Consecutive number problems, 106 Consistent system of equations, 352 Contradiction, 105 Coordinate geometry, 315 Coordinates of a point, 317 Cross products, 144 Cube root, 381, 466 Cylinder, right circular, 161 Decimals: basic operations, 62 nonrepeating, 59 repeating, 59 terminating, 59 Declaring the variable, 99 Degree: of a monomial, 186 of a polynomial, 186 Denominator: common, 51 least common, 52 rationalizing a, 399 Dependent equations, 352 Descartes, René, 315 Difference of two cubes, 241 Difference of two squares, 237 Discount, 153 Distributive property, 28, 62 Divisibility, rules of, 13 Division: definition of, of algebraic fractions, 275 of decimals, 64 of fractions, 46 of integers, 23 of monomials, 205 of polynomials, 208 of radicals, 399 of rational numbers, 46 Division property of equality, 94 Division property of inequality, 123 Domain of a relation, 486 Element of a set, Elimination-by-addition method, 360 Empty set, English system of measure, 78 Equal sets, Equations: absolute value, 452 dependent, 352 equivalent, 92 first-degree in one variable, 92 first-degree in two variables, 324 linear, 92 quadratic, 418 radical, 402 root of, 92 second-degree in one variable, 418 solution of, 92 I-1 I-2 Index Equivalent equations, 92 Equivalent fractions, 51 Equivalent inequalities, 120 Estimation, 173 Evaluating algebraic expressions, 5, 18 Exponents: definition of, 69 integers as, 214 negative, 214 positive integers as, 192 properties of, 213 rational numbers as, 467 zero as an, 213 Extraneous solution, 403 Factoring: common factor, 231 complete, 231, 237 composite numbers, difference of cubes, 241 difference of squares, 237 by grouping, 232 sum of cubes, 241 trinomials, 242, 249 Factors, First-degree equations, 92 Formulas, 158 FOIL, 199 Fractional equation, 294 Fractions: addition of, 51 algebraic, 270 complex, 289 division of, 46 equivalent, 51 fundamental principle of, 43, 270 least common denominator of, 52 lowest terms of, 43 multiplication of, 43 reduced form of, 43 subtraction of, 51 Function, 487 Functional notation, 488 Fundamental principle of fractions, 43, 270 Geometric formulas, 160 Graphing method of solving systems, 351 Graph of an equation, 319 Graph of a solution set, 121 Graphs: bar, 479 circle, 477 line, 480 pie, 477 Greatest common factor, 9, 230, 256 Greatest common monomial factor, 230 Half-plane, 328 Hypotenuse, 246, 423 i, 470 Identity, 105 Identity element: for addition, 27, 61 for multiplication, 28, 61 Imaginary part of complex number, 471 Imaginary unit, 470 Inconsistent equations, 352 Index of a radical, 467 Inequalities: absolute value, 453 equivalent, 120 graphs of, 328 open sentences as, 120 properties of, 121, 122 solutions of, 120 Infinity symbol, 121 Integers, 14 Intercepts, 326 Interest, simple, 155 Intersection of sets, 129 Interval notation, 121 Irrational number, 60 Isosceles right triangle, 423 Least common denominator, 52 Least common multiple, 10 Like terms, 30 Line graphs, 480 Linear equations: definition of, 319 graph of, 319 slope-intercept form of, 343, 348 systems of, 351, 456 Linear inequalities of two variables, 328 Literal factors, 30 Lowest terms, 43 Metric system of measure, 78 Monomial, 186 Multiplication: of algebraic fractions, 274 of decimals, 63 of complex numbers, 472 of fractions, 43 of integers, 22 of monomials, 192 of polynomials, 197 of radicals, 397 Multiplication property of equality, 94 Multiplication property of inequality, 123 Multiplication property of negative one, 28, 62 Multiplication property of zero, 28, 62 Multiplicative inverse property, 62 Index Null set, Numbers: absolute value, 16 complex, 470 composite, imaginary, 471 integers, 14 irrational, 60 negative, 14 positive, 14 prime, rational, 42 real, 60 whole, Number line, 14 Numerical coefficient, 30 Numerical expression, Numerical statement, 92 Open sentence, 120 Operations, order of, 5, 72 Opposite of an integer, 15 Ordered pairs, 316 Ordered triples, 356 Ordinate, 317 Origin, 316 Parabola, 323 Parallelogram, 160 Percent, 148 Perfect squares, 255, 380 Perfect square trinomial, 255, 426 Pie chart, 477 Point-slope form, 342 Polynomials: addition of, 186 completely factored form of, 231 definition of, 186 degree of, 186 division of, 208 multiplication of, 197 subtraction of, 187 Power of a base, 69 Prime factor, Prime number, Principal cube root, 466 Principal square root, 380 Prism, 161 Problem-solving suggestions, 105, 167, 172 Profit, 154 Properties of equality, 92 Proportion, 144 Pyramid, 161 Pythagorean theorem, 246, 422 Quadrant, 316 Quadratic equations, 418 Quadratic formula, 432 Radicals: addition of, 382 definition of, 380 division of, 399 equation, 402 multiplication of, 397 simplest form of, 392 subtraction of, 382 Radical sign, 380 Radicand, 380 Range of a relation, 486 Ratio, 144 Rational approximation, 383 Rational exponent, 467 Rational expression, 270 Rational number, 42 Rationalizing the denominator, 399 Real number, 60 Real number line, 61 Real part of a complex number, 471 Reciprocal, 62 Rectangle, 160 Rectangular coordinate system, 317 Rectangular prism, 160 Reflexive property of equality, 92 Relation, 486 Right triangle, 30°– 60°, 423 Root of an equation, 92 Root of a number, 382 Scientific notation, 215 Second-degree equation in one variable, 418 Set, Set-builder notation, 120 Similar terms, 30 Simplest radical form, 392 Simplifying algebraic fractions, 272 Simplifying numerical expressions, 3, 23 Simplifying radicals, 386 Slope, 333 Slope-intercept form, 343, 348 Solution of an equation, 92 Solution of an inequality, 120 Solution set, 92 Special product patterns, 200 Sphere, 160 Square root, 380, 465 Square-root property, 420 Standard form of a complex number, 491 Standard form of a quadratic equation, 418 Statement of inequality, 120 Substitution method of solving systems, 354 Substitution property of equality, 92, 122 Copyright 2009 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part I-3 I-4 Index Subtraction: of algebraic fractions, 279 of complex numbers, 471 of decimals, 63 of fractions, 51 of integers, 18 of polynomials, 186 of radicals, 51 Subtraction property of equality, 93 Subtraction property of inequality, 122 Suggestions for solving word problems, 105, 167, 172, 441 Sum of two cubes, 241 Supplementary angles, 107 Symmetric property of equality, 92 Systems of linear equations, 351 Systems of three equations, 456 Term, 30 Transitive property of equality, 92 Translating English phrases, 75 Trapezoid, 160 Triangle, 160 Trinomial, 186 Union of sets, 130 Value, absolute, 16 Variable, Whole numbers, x intercept, 326 y intercept, 326 Zero: addition property of, 27 as an exponent, 213 multiplication property of, 28 SOME APPROXIMATE COMPARISONS BETWEEN ENGLISH AND METRIC SYSTEMS (the symbol Ϸ means “is approximately equal to”) Length inch Ϸ 2.5 centimeters foot Ϸ 30.5 centimeters yard Ϸ 0.9 of a meter mile Ϸ 1.6 kilometers centimeter Ϸ 0.4 of an inch centimeter Ϸ 0.03 of a foot meter Ϸ 1.1 yards kilometer Ϸ 0.6 of a mile Volume pint Ϸ 0.5 of a liter quart Ϸ 0.9 of a liter gallon Ϸ 3.8 liters liter Ϸ 2.1 pints liter Ϸ 1.1 quarts liter Ϸ 0.3 of a gallon Mass ounce Ϸ 28.35 grams pound Ϸ 453.6 grams pound Ϸ 0.45 of a kilogram gram Ϸ 0.04 of an ounce gram Ϸ 0.002 of a pound kilogram Ϸ 2.2 pounds Simple Interest Temperature I ϭ Prt I P A r t A ϭ P ϩ Prt simple interest principal amount rate of interest time (in years) Distance-Rate-Time d ϭ rt d r t rϭ distance rate time d t tϭ d r 1F Ϫ 322 9 F ϭ C ϩ 32 F Fahrenheit degrees C Celsius degrees Cϭ SUBSETS OF THE REAL NUMBERS 51, 2, 3, p 50, 1, 2, 3, p p , Ϫ3, Ϫ2, Ϫ1, 0, 1, 2, 3, p a e ` a and b are integers and b f b 5x Ϳx is real number and x is not rational6 Natural numbers Whole numbers Integers Rational numbers Irrational numbers PROPERTIES OF REAL NUMBERS For real numbers a, b, and c, the following properties are true Commutative Property Associative Property Addition Multiplication aϩbϭbϩa 1a ϩ b2 ϩ c ϭ a ϩ 1b ϩ c2 ab ϭ ba 1ab2c ϭ a1bc2 aa b ϭ a a # 1ϭa Inverse Property a ϩ 1Ϫa2 ϭ Identity Property aϩ0ϭa a1b ϩ c2 ϭ ab ϩ ac Distributive Property INEQUALITIES Statement Set Notation xϾa 5x Ϳx Ͼ a6 xϽa Graph Interval Notation ( a 5x Ϳx Ͻ a6 a xՆa 5x Ϳx Ն a6 a xՅa 5x Ϳx Յ a6 a aϽxϽb 5x Ϳ a Ͻ x Ͻ b6 a aՅxՅb 5x Ϳ a Յ x Յ b6 0 a PROPERTIES OF EXPONENTS AND RADICALS n bn # bm ϭ bnϩm 1bn m ϭ bn ϫ m 2ab ϭ 2a 2b a n an a b ϭ n b b a 2a ϭ n Bb 2b n n n b 1Ϫq, a2 [ 3a, q ] 1Ϫq, a ( ) 1a, b2 ] a, b4 b [ b FACTORING PATTERNS 1a ϩ b2 ϭ a ϩ 2ab ϩ b a2 Ϫ b2 ϭ 1a ϩ b21a Ϫ b2 2 1a Ϫ b2 ϭ a2 Ϫ 2ab ϩ b2 1ab2 n ϭ a nbn n 1a, q MULTIPLICATION PATTERNS b ϭ bnϪm bm ) b n 1a ϩ b21a Ϫ b2 ϭ a2 Ϫ b2 1a ϩ b2 ϭ a3 ϩ 3a2b ϩ 3ab2 ϩ b3 1a Ϫ b2 ϭ a3 Ϫ 3a2b ϩ 3ab2 Ϫ b3 a3 Ϫ b3 ϭ 1a Ϫ b21a2 ϩ ab ϩ b2 a3 ϩ b3 ϭ 1a ϩ b21a2 Ϫ ab ϩ b2 ... 268 Algebraic Fractions 269 7.1 Simplifying Algebraic Fractions 7.2 Multiplying and Dividing Algebraic Fractions 7.3 Adding and Subtracting Algebraic Fractions 7.4 Addition and Subtraction of Algebraic... surface area radius altitude (height) slant height ELEMENTARY ALGEBRA NINTH EDITION This page intentionally left blank NINTH EDITION ELEMENTARY ALGEBRA Jerome E Kaufmann Karen L Schwitters Seminole... students who have never had an elementary algebra course and for those who need a review before taking additional mathematics courses The basic concepts of elementary algebra are presented in a simple,
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Xem thêm: Elementary algebra , Elementary algebra , 1: Numerical and Algebraic Expressions, 2: Prime and Composite Numbers, 3: Integers: Addition and Subtraction, 4: Integers: Multiplication and Division, 1: Rational Numbers: Multiplication and Division, 2: Addition and Subtraction of Rational Numbers, 3: Real Numbers and Algebraic Expressions, 5: Translating from English to Algebra, 2: Equations and Problem Solving, 3: More on Solving Equations and Problem Solving, 4: Equations Involving Parentheses and Fractional Forms, 6: Inequalities, Compound Inequalities, and Problem Solving, 1: Ratio, Proportion, and Percent, 2: More on Percents and Problem Solving, 5: More about Problem Solving, 1: Addition and Subtraction of Polynomials, 6: Integral Exponents and Scientific Notation, 1: Factoring by Using the Distributive Property, 2: Factoring the Difference of Two Squares, 3: Factoring Trinomials of the Form x2 + bx + c, 4: Factoring Trinomials of the Form ax2 +bx + c, 5: Factoring, Solving Equations, and Problem Solving, 2: Multiplying and Dividing Algebraic Fractions, 3: Adding and Subtracting Algebraic Fractions, 4: Addition and Subtraction of Algebraic Fractions and Simplifying Complex Fractions, 5: Fractional Equations and Problem Solving, 6: More Fractional Equations and Problem Solving, 2: Graphing Linear Equations and Inequalities, 3: Slope of a Line, 4: Writing Equations of Lines, 5: Systems of Two Linear Equations, 3: More on Simplifying Radicals, 4: Products and Quotients Involving Radicals, 4: Solving Quadratic Equations—Which Method?, 5: Solving Problems Using Quadratic Equations, 1: Equations and Inequalities Involving Absolute Value, 2: 3 x 3 Systems of Equations, 5: Quadratic Equations: Complex Solutions, 6: Pie, Bar, and Line Graphs

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