Solution Manual for College Algebra, 4th Edition

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INSTRUCTOR’SSOLUTIONMANUALBEVERLYFUSFIELDCOLLEGEALGEBRAFOURTHEDITIONJ. S. RattiUniversityof South FloridaMarcus McWatersUniversity of South FloridaLeslaw A. SkrzypekUniversity of South Florida

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CONTENTSChapter PBasic Concepts of AlgebraP.1The Real Numbers and Their Properties......................................................1P.2Integer Exponents and Scientific Notation...................................................7P.3Polynomials................................................................................................13P.4Factoring Polynomials................................................................................20P.5Rational Expressions..................................................................................27P.6Rational Exponents and Radicals...............................................................37Chapter P Review Exercises....................................................................................46Chapter P Practice Test...........................................................................................51Chapter 1Equations and Inequalities1.1Linear Equations in One Variable..............................................................531.2Applications of Linear Equations: Modeling.............................................631.3Quadratic Equations...................................................................................741.4Complex Numbers:Quadratic Equationswith Complex Solutions...........891.5Solving Other Types of Equations.............................................................961.6Inequalities...............................................................................................1161.7Equations and Inequalities Involving Absolute Value.............................131Chapter1Review Exercises..................................................................................148Chapter1Practice TestA......................................................................................159Chapter 1 Practice Test B......................................................................................160Chapter 2GraphsandFunctions2.1The Coordinate Plane...............................................................................1632.2Graphs of Equations.................................................................................1722.3Lines.........................................................................................................1852.4Functions..................................................................................................2002.5Properties of Functions.............................................................................2102.6A Library of Functions.............................................................................2192.7Transformations of Functions..................................................................2302.8Combining Functions; Composite Functions...........................................2482.9Inverse Functions.....................................................................................263Chapter 2 Review Exercises..................................................................................275Chapter 2 Practice Test A......................................................................................285Chapter 2 Practice Test B......................................................................................286Cumulative Review Exercises (Chapters P−2)......................................................287Chapter 3Polynomial and Rational Functions3.1Quadratic Functions.................................................................................2913.2PolynomialFunctions...............................................................................3103.3Dividing Polynomials...............................................................................3233.4The RealZeros of a Polynomial Function................................................3343.5The Complex Zeros of a Polynomial Function........................................3533.6Rational Functions....................................................................................3633.7Variation...................................................................................................382Chapter 3 Review Exercises..................................................................................387Chapter 3 Practice Test A......................................................................................403Chapter 3 Practice Test B......................................................................................404Cumulative Review Exercises (ChaptersP−3)......................................................405

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Chapter 4Exponential and Logarithmic Functions4.1ExponentialFunctions..............................................................................4084.2Logarithmic Functions.............................................................................4204.3Rules of Logarithms.................................................................................4334.4Exponential and Logarithmic Equations and Inequalities........................4464.5Logarithmic Scales; Modeling.................................................................459Chapter4Review Exercises..................................................................................470Chapter4Practice Test A......................................................................................479Chapter4Practice Test B......................................................................................480Cumulative Review Exercises (ChaptersP−4)......................................................480Chapter5Systems of Equations and Inequalities5.1Systems of Linear Equations in Two Variables.......................................4835.2Systems of Linear Equations in Three Variables.....................................5015.3Partial-Fraction Decomposition...............................................................5225.4Systems of Nonlinear Equations..............................................................5455.5Systems of Inequalities.............................................................................5595.6Linear Programming.................................................................................572Chapter5Review Exercises..................................................................................587Chapter5Practice Test A......................................................................................600Chapter5Practice Test B......................................................................................603Cumulative Review Exercises (ChaptersP−5)......................................................605Chapter6Matrices and Determinants8816.1Matrices and Systems of Equations..........................................................6086.2Matrix Algebra.........................................................................................6296.3The Matrix Inverse...................................................................................6496.4Determinants and Cramer’s Rule.............................................................670Chapter6Review Exercises..................................................................................683Chapter6Practice Test A......................................................................................694Chapter6Practice Test B......................................................................................695Cumulative Review Exercises (ChaptersP−6)......................................................696Chapter7The Conic Sections7.2The Parabola.............................................................................................6997.3The Ellipse................................................................................................7147.4The Hyperbola..........................................................................................732Chapter7Review Exercises..................................................................................756Chapter7Practice Test A......................................................................................765Chapter7Practice Test B......................................................................................767Cumulative Review Exercises (ChaptersP−7)......................................................768Chapter8FurtherTopics in Algebra8.1Sequences and Series................................................................................7718.2Arithmetic Sequences; Partial Sums........................................................7828.3Geometric Sequences and Series..............................................................7908.4Mathematical Induction............................................................................7998.5The Binomial Theorem............................................................................8108.6Counting Principles..................................................................................8188.7Probability................................................................................................825Chapter8Review Exercises..................................................................................829Chapter8Practice Test A......................................................................................833Chapter8Practice Test B......................................................................................833Cumulative Review Exercises (ChaptersP−8)......................................................834

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1ChapterP Basic Concepts of AlgebraP.1The Real Numbers and TheirPropertiesP.1 Practice Problems1.Letx= 2.132132132….Then, 1000x= 2132.132132…10002132.1321322.13213299921302130710999333xxxx=====KK2.a.Natural numbers: 2, 7b.Whole numbers: 0, 2, 7c.Integers:216,3, 0, 2, 77--= -d.Rational numbers:21146,3,, 0,, 2, 7723--= --e.Irrational numbers:3,17f.Real numbers: the setB3.a.328=b.()()()223339==aaaac.41111112222216æ ö=× × ×=ç÷èø4.a.Trueb.Truec.False5.{}{}3,1, 0, 1, 3 ,4,2, 0, 2, 4= --= --AB{ }{}0 ,4,3,2,1, 0, 1, 2, 3, 4==----ABABIU6.a.()12,II= - ¥¥Ub.[)122, 5II= -I7.a.1010-=b.3411-= -=c.()23711-+==8.()7, 27299-= --= -=d9.a.()352015205-× += -+=b.5126 252 2541-¸× =-× =-=c.9185 75 72353344--× =-× =-= -d.()234x-+-forx= 6()2236432341-+-= -+= -+=10.a.731431748888+=+=b.824063435151515-=-=c.979143×=31427×13132=d.55155 1658158168 1516=¸=×=18116×215323=11.a.()()233233110133333xx-¸+=-¸+=¸+=+=b.1122777333xy--=-=+=12.39C413417 C3°=+=+=°P.1Concepts andVocabulary1.Whole numbers are formed by adding thenumberzeroto the set of natural numbers.2.The number −3 is an integer, but it is also arational numberand areal number.3.Ifa<b, thenais to theleftofbon thenumber line.4.If a real number is not a rational number, it isanirrationalnumber.

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2Chapter PBasic Concepts of Algebra5.True6.False.51222-= -7.True8.False. An example is()()22224,++-=which is rational.P.1 Building Skills9.0.3, repeating10.0.6, repeating11.0.8-,terminating12.0.25-,terminating13.0.27, repeating14.0.3, repeating15.3.16, repeating16.2.73, repeating17.375153.751004==18.235472.3510020-= -= -19.1053.35.3948481693165.33xxxx=====-= -20.1096.69.6987872993xxxx=====21.100213.132.139921121199xxxx====22.100323.233.239932032099xxxx====23.100452.3234.52399447.8447.84478223999990495xxxx======24.100142.35351.423599140.93140.9314, 093999900xxxx=====25.Rational26.Rational27.Rational28.Rational29.Rational30.Rational31.Irrational32.IrrationalExercises 33-38 refer to the set1217A19,,3, 0, 2,10,, 1134ìü=---íýîþ33.Natural numbers:2, 1134.Whole numbers: 0, 2, 1135.Integers:1219,4, 0, 2, 113--= -36.Rational numbers:121719,, 0, 2,, 1134--37.Irrational numbers:3,10-38.Real numbers: All numbers in setAare realnumbers.39.310base: 10; exponent: 331010 10 101000=××=40.45base: 5; exponent: 4455 5 5 5625=× × × =41.323æ öç÷èøbase:2 ;3exponent: 3322228333327æ ö=× ×=ç÷èø42.452æ öç÷èøbase:5 ;2exponent: 44555556252222216æ ö=× × ×=ç÷èø

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Section P.1The Real Numbers and Their Properties343.()32-base:–2; exponent: 3()() () ()322228-= -× -× -= -44.412æö-ç÷èøbase:1 ;2-exponent: 441111112222216æöæöæöæöæö-=----=ç÷ç÷ç÷ç÷ç÷èøèøèøèøèø45.42 3×base: 3; exponent: 442 32 3 3 3 32 81162×=× × × × =×=46.3153æ ö×ç÷èøbase:1 ;3exponent: 3311111555533332727æ ö×=× × ×=×=ç÷èø47.42 3-×base: 3; exponent: 442 32 3 3 3 32 81162-×= -× × × × = -×= -48.()432-× -base:–2; exponent: 4()()()()()432322223 1648-× -= -----= -×= -49.()532-× -base:–2; exponent: 5()()()()()()()53232222233296-× -= ------= -× -=50.()253-× -base:–3; exponent: 2()()()2535335 945-× -= ---= -× = -51.32> -52.32-< -53.1122³54.1<+xx55.52£x56.12->x57.0x->58.0x<59.2714+£x60.235+£x61.2446=62.52-< -63.40-<64.91422-= -65.{}4,3,2, 0, 1, 2, 3, 4= ---ABU66.{}0, 2, 4=ABI67.{}4,2, 0, 2AC= --I68.{}4,3,2,1, 0, 1, 2, 3, 4BC= ----U69.(){}{}3, 0, 24,3,2, 0, 2, 4BCAA=-=---IUU70.(){}{}4,3,2,1, 0, 2, 43, 0, 2, 4ACBB=----=-UII71.(){}{}4,3,2, 0, 1, 2, 3, 44,3,2, 0, 2ABCC=---=---UII72.(){}{}4,3,2, 0, 1, 2, 3, 44,3,2,1, 0, 1, 2, 3, 4ABCC=---=----UUU73.()[]12122, 5 ;1, 3IIII= -=UI74.[]()12121, 7 ;3, 5IIII==UI75.()12126, 10 ;IIII= -= ÆUI76.()1212,;IIII= - ¥¥= ÆUI77.()[)1212,;2, 5IIII= - ¥¥=UI78.()()12122,;0,IIII= -¥=¥UI79.()[)[]1212,;1, 35, 7IIII= - ¥¥= -UIU80.(]()[]1212, 26,;3, 0IIII= - ¥¥= -UUI81.44-=82.1717- -= -83.5577=-84.3355-=85.5252-=-86.2552-=-87.3223-=-88.33pp-=-89.88188==-90.88188--== -

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4Chapter PBasic Concepts of Algebra91.575722- -=-= -=92.474733-=-= -=93.(3,8)3855=-= -=d94.(2,14)2141212=-= -=d95.( 6,9)691515-= --= -=d96.( 12,3)1231515-= --= -=d97.( 20,6)20( 6)1414--= ---= -=d98.( 14,1)14( 1)1313--= ---= -=d99.2242242626,777777æöæö-=--==ç÷ç÷èøèød100.1631631919,555555æöæö-=--==ç÷ç÷èøèød101.31-<£x102.62-£< -x103.3³ -x104.0³x105.5£x106.1£ -x107.3944-<<x108.132-<< -x109.4(1)44+=+xx110.( 3)(2)63--= -+xx111.5(1)555-+=-+xyxy112.2(35)6102+-=+-xyxy113.Additive inverse:5-; reciprocal:15114.Additive inverse:23; reciprocal:32-115.Additive inverse:0;no reciprocal116.Additive inverse:1.7-; reciprocal:1017117.Additive inverse118.Additive inverse119.Multiplicative identity120.Multiplicative identity121.Associative property of multiplication

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Section P.1The Real Numbers and Their Properties5122.Associative property of multiplication123.Multiplicative inverse124.Multiplicative inverse125.Additive identity126.Additive identity127.Associative property of addition128.Commutativeandassociative propertiesofaddition129.349202953151515+=+=130.73141529104202020+=+=131.6542256757353535+=+=132.9554559212121212+=+=133.53259341761030303015+=+==134.82241034159454545+=+=135.59253611810404040-=-= -136.713582785404040-=-=137.5755638911999999-=-= -138.5715141812242424-=-=139.2145152101010-=-= -140.1132146121212-=-=141.3824279×=142.91427273×=143.88168 1535165155 16215=¸=×=144.5515561615666 1536=¸=×=145.77217162821816821316=¸=×=146.337315910710151071415=¸=×=147.3131251102222×-=-==148.73143112 22222×-=-=149.21216513 15353151515×-=-=-=150.53103209112 3232666×-=-=-=151.2()32(3( 5))3( 5)2( 2)( 15)41511+-=+ ---=---= -+=xyy152.2()52(3( 5))5( 5)2( 2)( 25)4( 25)21-++= -+ -+-= --+ -=+ -= -xyy153.323 3253(3)2(5)9101-=--=-=-= -xy154.77 3( 5)7 87(8)56-=--===xy155.333( 5)3( 5)223( 15)( 15)218( 15)9( 15)62---+=+---=+ -=+ -=+ -= -xyxy156.3533( 5)3243( 15)33+-+-=---=--=yxyx157.2(12 )2(12(3))()( 3)( 5)52( 5)15215135xx yy----=-----=-=-= --

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6Chapter PBasic Concepts of Algebra158.3(2)3(23)(1)(13( 5))53( 1)(1( 15))53771655----=-----=----=-= -xxyy159.14114131 462232( 5)651544++==×=-- -xy160.4848482( 5)355352252210415575++---æö æö==+× -ç÷ ç÷-èø èøæö=× -= -ç÷èøyxy161.333xxxxyyy++=162.()()222332656xxxxxxx++=+++=++163.()( )5355 3515xxx+=+=+.164.()()2254100xxx=165.()3232xyxy-+=--166.()245245xyxy--=-+167.1xyxyyxxxx+=+=+168.xyxyxzxzxz+=++++169.()()111xyxyxy++=+++170.111111yyxxyxxy=¸=×=171.()()2,2222,222ababaabd P Maabbabbad Q Mb++--+=-==+-+-=-==Since()(),,,22abbad P Md Q M-+-===Misthe midpoint of the line segmentPQ.172.Answers may vary. Using the hint, we have44013130-= -and770 .13130=Therefore,40313001301301301106970 .130130130130-< -< -<<<<<<<<P.1Applying the Concepts173.a.people who own either MP3 players orpeople who own DVD players.b.people who own both MP3 players andDVD players.174.a.A= {LexusLS460}b.B= {LexusLS 460, LincolnContinental}c.C= {LexusLS 460, LincolnContinental,Audi A4}d.ABI= {LexusLS 460}e.BCI= {LexusLS 460, LincolnContinental}f.ABU= {LexusLS 460, LincolnContinental}g.ACU= {LexusLS 460, LincolnContinental, Audi A4}175.119.5134.5££x176.30107££x177.a.1241204-=b.13712017-=c.11412066-= -=178.a.15141-=b.1517.52.5-=c.1596-=179.Letx= the number of calories from broccoli.Then we have522.5550522.5559.5-=Þ=Þ=xxxThe number of grams of broccoli is9.5 × 100 = 950 grams.

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Section P.2Integer Exponents and Scientific Notation7180.Letx= the number of orders offrench fries.The number of calories lost from broccoli is6×55 = 330. Then we have16533001653302-=Þ=Þ=xxxSo, Carmen will have to eat 2 orders of frenchfries.P.1 Beyond the Basics181.True182.True183.a.False. For example,020.×=b.The products of a nonzero rational numberand an irrational number is an irrationalnumber.184.False. For example,222.×=185.False. For example,()()23634.+-+= -186.False. For example,1242.3 ==187.True188.TrueFor exercises 189–190, use the following definition:An integerPisevenifp= 2nfor some integern. Anintegerqis odd ifq= 2k+ 1 for some integerk.189.a.Ifais odd, thena= 2m+ 1 for someintegerm.()()()()()()2222121214414112 211,ammmmmm mm m=+=++=++=++=++which is of the format 2k+1. Therefore,2ais an odd integer.b.Assume thatbis odd. Then, from part (a),2bis also odd. However,2bis an eveninteger, so, by contradiction,bmust be aneven integer.190.22qis evenbecause it is of the form 2n,soitfollows that2pis even. Then, from exercise189(b),pis also even. Therefore,p= 2n, forsome integern. Substituting, we have()222222222 2qpnqn==Þ=×Þ222,qn=and, thus,qis even using exercise189 (b).P.1 Getting Ready for the Next Section191.a.523aaa×=b.4711aaa×=c.mnmnaaa+×=192.a.32bbb=b.743bbb=c.mmnnbbb-=193.a.()362aa=b.()284aa=c.()nmmnaa=194.a.()222abab=b.()444abab=c.()nnnabab=P.2Integer Exponents and ScientificNotationP.2 Practice Exercises1.a.1122-=b.0415æ ö=ç÷èøc.22324239-æ öæ ö==ç÷ç÷èøèø2.a.27933×=xxxb.()()()332333302444161616 116xxxxxx+ ---=×===× =3.a.44040333813-===

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8Chapter PBasic Concepts of Algebrab.1( 2)325551255---===c.33( 4)74222333---==xxxx4.a.()05( 5)(0)07771--===b.()50(0)( 5)07771--===c.()81( 1)(8)881xxxx---===d.()52( 2)( 5)10----==xxx5.a.( )1111112222---æöæ öæ ö===ç÷ç÷ç÷èøèøèøxxxxb.()()221212(1)(2)225552525----====xxxxxc.()3232(3)36==xyx yx yd.()632( 2)( 3)33-----==xxyxyy6.a.222111393æ ö==ç÷èøb.222210774971010010-æöæö===ç÷ç÷èøèø7.a.()2244811224-æö==ç÷èøxxxb.()()3223336321--== -xyx yx yxyxy8.5732,0007.3210=´9.102282.910290100.8910$893253.2510´=´»´»´per personP.2Concepts andVocabulary1.In the expression27 ,the number 2 is calledtheexponent.2.In the expression73 ,-the base is3.3.The number214-simplifies to be the positiveinteger16.4.The power-of-a-product rule allows us torewrite()35aas335.a5.False.()10101111-=6.False. When()32xis simplified, theexpression becomes6.x7.True8.FalseP.2 Building Skills9.22111133339-æ öæ öæ ö===ç÷ç÷ç÷èøèøèø10.3311111222228-æ öæ öæ öæ ö===ç÷ç÷ç÷ç÷èøèøèøèø11.4412162-æ ö==ç÷èø12.()221242-æö-= -=ç÷èø13.071=14.()081-=15.()071--= -16.()021=17.()233 2622264×===18.()322 36333729×===19.()()22224411333813---====20.()()12122211777497---====

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Section P.2Integer Exponents and Scientific Notation921.()3332211152515, 6255-æöæö===ç÷ç÷èøèø22.()3331111555125-æ öæ ö===ç÷ç÷èøèø23.() ()35( 35)2444416--+×===24.() ()23( 23)177777--+×===25.()00310112+=+=26.()0059110-=-=27.22221111123333999-æ öæ öæ ö+=+=+=ç÷ç÷ç÷èøèøèø28.22221111125555252525-æ öæ öæ ö+=+=+=ç÷ç÷ç÷èøèøèø29.3311282--= -= -30.2211393--= -= -31.()()2211393--==-32.()()3311282--== --33.11(11 10)11022222-===34.6(68)28231133933--====35.()4312121255155==36.()2510(108)28899998199-====37.52(54)( 2( 3))1143232323623------×=×=×=×38.23( 2( 3))(3 1)312454545454 25100------×=××=×=×=39.2112511222252525---= -×= -× = -40.2112711333494937---= -×= -× = -41.12332-æ ö=ç÷èø42.1155-æ ö=ç÷èø43.222223393242-æ öæ ö===ç÷ç÷èøèø44.222232242393-æ öæ ö===ç÷ç÷èøèø45.22111149121712111497-æö===ç÷èøæöç÷èø46.22131125169516913255-æö===ç÷èøæöç÷èø47.40441=× =x yxx48.10111-=× =xyxx49.11-=×=yxyyxx50.2222221-=×=xx yxyy51.1221--=xyxy52.32321--=xyx y53.()4312121--==xxx54.()2510101--==xxx55.()311( 11) ( 3)33xxx---×-==56.()124( 4) ( 12)48xxx---×-==

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10Chapter PBasic Concepts of Algebra57.5553()3-= -xyx y58.6668()8-= -xyx y59.()221222444xxyx yy--==60.()331333666yxyxyx--==61.()551( 1) ( 5)55333xxyxyy---×--==62.()6616( 1) ( 6)6555yxyxyx----× --= -= -63.()()233 26610452 510421xxxxxxxxx×--×=====64.()2222 121043 4121031xxxxxxxxx--×=====65.33333336322 363333228888-×-æö===ç÷èø==xyx yx yxyxxxyxyx66.4444444 12433 412484855625625625625-×-æö===ç÷èø==xyx yx yxyxxxyxyx67.5252 55105551055553( 3)243243243×-æö---==ç÷èø= -= -xyxyxyxxxxyx y68.32332 33633363332( 2)888×-æö---==ç÷èø= -= -xyx yx yyyyx yx y69.22222221113( 3)2599115592525xxxxx----×--æö====ç÷èø70.4444444441115( 5)5625113381381625----×--æö===ç÷èø=yyyyy71.3232 36535 3315915446464xxxxyx yx yx y--×-×æö===ç÷èø72.5252 551051033 5151033243243××æö===ç÷èøx yxyxyxyyyy73.3353( 2)3 15424-------===x yxxyx yxyy74.2232( 1)2234124-------===x yxxyx yxyy75.353( 4)5712472273339-------===xyxxyx yxyy76.52572( 3)21732155553-------===x yyxyxyx yx77.()()()32432 343643364111xxxxxxxxxxxx--×----+--=====78.()()()()1212124343441243124121212341241212121212121241212121212412001616162288222222212aaa babbbababababaabbaba bbb-----------------+-+----æö=×ç÷èø=×=×=×××××=××===

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Section P.2Integer Exponents and Scientific Notation1179.() ()()()()()()() ()()()32342224223324442232 3362 42 488386852522221616116111616xyxyxyxyxyxyxyx yxyx yxyxyx y-×××-------=--=--×-=== -= -= -80.()()()()()()()()()223242 334555261552651522266126222122xyyxy yx yxyx yx yxyxyxyyxyxyx---×----------------éùéù--êúêú=êúêúêúëûëûæö-=ç÷èø= -= -= -===81.() ()()()() ()() ()23227323273222232277327444x y zx y zx y zx y zxyzxyz-==3 22 226423 72 77211476214 142715105151051616161616xyzx y zxyzxyzxyzxyzxyz××××------=====82.()()()()2222222223 2211621113222212522521330332244444xyzx y zx y zxy xzx y xzx yxzx y zxyzx y zzxy zx×-----------======83.22241(3)22432464655551--------==× =abcabca bcbaba84.252522522324323423433122( 3)()998( 2)89988------== ---= -= -abca b cabca b ca b caa bcbc85.3323( 3)( 3)( 2)( 3)2432( 3)( 4)( 3)3( 3)39661293( 6)9126( 9)31533153-----------------------æö=ç÷èø====xyzxyzx yzxyzxy zxyzxyzx zx yzy86.1211( 2)( 1)( 1)( 1)58( 5)( 1)1( 8)( 1)121152( 1)1 8518363767xyzxyzxyzxyzxy zxyzx yzyxy zx z------------------------æö=ç÷èø====87.21251.2510=´88.22472.4710=´89.5850,0008.510=´90.5205,0002.0510=´91.30.0077.010-=´92.30.00191.910-=´93.60.000002752.7510-=´94.60.00000383.810-=´P.2 Applying the Concepts95.333135 ft21080 ft´=96.3331675 in.25 in.3æ ö´=ç÷èø97.a.222(2 )442===xxAAb.222(3 )993===xxAA

Solution Manual for College Algebra, 4th Edition - Page 16 preview image

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12Chapter PBasic Concepts of Algebra98.a.222224222pppæöæ ö===ç÷ç÷èøèødddAb.22223993222pppæöæ öæ ö===ç÷ç÷ç÷èøèøèødddA99.2225, 000(0.25)1562.5 lb===FSw100.221.510, 000(3.14)2217, 662.5 lbs.pæöæö==ç÷ç÷èøèø»dFS101.724 hr60 min60 sec365.25 daysdayhrmin365.25246060 sec31,557,600 sec3.1557610sec´´´=´´´==´102.724 hr60 min60 sec366 daysdayhrmin366246060 sec31,622,400 sec3.1622410sec´´´=´´´==´103.CelestialBodyEquatorialDiameter(km)ScientificNotationEarth12,7001.27×104kmMoon34803.48×103kmSun1,390,0001.39×106kmJupiter134,0001.34×105kmMercury48004.8×103km104.2237, 600, 000, 000, 000, 000, 000, 0003.7610atoms=´105.20602, 000, 000, 000, 000, 000, 0006.0210atoms=´106.200.00000000000000000002662.6610kg-=´107.210.000000000000000000001671.6710kg-=´108.8380,000,0003.810m=´109.245, 980, 000, 000, 000, 000, 000, 000, 0005.9810kg=´110.302, 000, 000, 000, 000, 000, 000, 000, 000, 000, 0002.010kg=´P.2 Beyond the Basics111.232x=a.2222232 4128xx+=×=× =b.11122232162xx--=×=×=112.381x=a.1133381 3243xx+=×=× =b.222113338181939xx--æ ö=×=×=×=ç÷èø113.511x=a.1155511 555xx+=×=× =b.2221111555111152525xx--æ ö=×=×=×=ç÷èø114.xab=a.2222xxaaab aa b+=×=×=b.111xxbaaabaa--=×=×=115.()()()2222222332 22233232332233393333333311393nnnnnnnnnnnnn----------××=×======116.()()()()122112211221123566101522335552 32 32 53 52233555232325352mmnmnnmnmnmmnmnmnmmmnmnnnmmnnmmm+-+++-+-++×××××××××××××=×××××××××××××=×××××=12×2335mnm-×××5n×252n××32nm×32mn××12×5n×1535mm×××22221213535533535mmmmm××===×××

Solution Manual for College Algebra, 4th Edition - Page 17 preview image

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Section P.3Polynomials13117.()()2222222222222222122zx yzyxyxzyzxxyyzxzy xzxyxzxzxyyzyzyzxzxzyz----æö¸=¸ç÷èø=×=×=118.1111111111xyzxyyzxzyzxyzxxyzaaaaaaaaaaaaæöæöæö××ç÷ç÷ç÷èøèøèø=××=P.2 Getting Ready for the Next Section119.a.25257xxxx+×==b.()()232510xxx-= -c.()()()235235102342424yyyyy+ +==120.a.222257xxx+=b.22234xxx-= -c.333335119xxxx-+=121.False.25xand33xarenot liketerms, sothey cannot be combined.122.()23232 12532253410681068xxxxxxxxx++-+=-+=-+P.3PolynomialsP.3 Practice Problems1.( )( )216 715 7889 ft+=2.()()32323272523215524+-+ -+++=++-xxxxxxxx3.()()4324243235272355512-++--++-=---+xxxxxxxxxx4.()3254324258410-+-= --+xxxxxx5.()()()()22222432324325227527227105354214103314+-+-=-+-+-+-= -+--+-= -+--xxxxxxxxxxxxxxxxxxxx6.a.()()2241742874277-+=+--=+-xxxxxxxb.()()22322561541061910--=--+=-+xxxxxxx7.()()()( )22223232 3229124+=++=++xxxxx8.()()()22212121214xxxx-+=-=-9.a.()()()22222224xyxyxyxy+-=-=-b.()()()()()3322332233223223 23 283 468126xyxxx yyxxxyyxxxyy-=-+-=-+-=-+-P.3Concepts andVocabulary1.The polynomial723294-+-+xxxhasleading coefficient−3and degree7.2.When a polynomial is written so that theexponents in each term decrease from left toright, it is said to be instandardform.3.When a polynomial inxof degree 3 is added toa polynomial inxof degree 4, the resultingpolynomialhas degree4.4.When a polynomial inxof degree 3 ismultiplied by a polynomial inxof degree 4, theresulting polynomial has degree7.5.True6.True. This is true ifAorBor both are zero.7.False. This is not a polynomial because the term3x-does not have an exponent that is either apositive integer or zero.8.TrueP.3 Building Skills9.Apolynomial;221++xx10.Not a polynomial11.Not a polynomial

Solution Manual for College Algebra, 4th Edition - Page 18 preview image

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14Chapter PBasic Concepts of Algebra12.Apolynomial;7543321++-+xxxx13.Not a polynomial14.Not a polynomial15.Apolynomial; in standard form16.Apolynomial; in standard form17.Degree: 1; terms: 7x, 318.Degree: 2; terms:23, 7-x19.Degree: 4; terms:42,, 2 ,9--xxx20.Degree: 7; terms:739, 2, ,21-xxx21.()()()()()()32333222532425234231+-++ -+-=+ -++ -++-=--xxxxxxxxxxxx22.()()()()()33233232313313222xxxxxxxxxxxxx-++-+-=+-+ -++-=---23.()()()()()()323332322543245358xxxxxxxxxxxxx-+---+=--+--+ --=-+-24.()()()()()()3323323224372327422396xxxxxxxxxxxxx-+--+-+= ---+--+ --= --+-25.()()()()()()4243244322432237869172876391710612717xxxxxxxxxxxxxxxx-+--+--= ----+----= --+-+26.()()222223222 54366102813814xxxxxxxxxx-++-+=-++-+=-+27.()()222222 316322622181212241414xxxxxxxxxx-+++---= ------= ---28.()()222222 534 3711026122842302xxxxxxxxxx-+-++=-+---= --+29.()()()33233232342214342214221yyyyyyyyyyyyy-+++--+=-+++-+-=+--30.()()()222222253123255312325661yyyyyyyyyyyyyy+---++++=+--+-+++=++31.26 (23)1218+=+xxxx32.27 (34)2128-=-xxxx33.()()()()22232232122221222222342xxxx xxxxxxxxxxxx+++=+++++=+++++=+++34.()()()()2223223252312315 2312310155213165xxxxxxxxxxxxxxxx--+=-+--+=-+-+-=-+-35.()()()()2223223232131213332223552xxxx xxxxxxxxxxxx--+=-+--+=-+-+-=-+-36.()()()()222322322134234134268342554xxxx xxxxxxxxxxxx+-+=-++-+=-++-+=-++37.22(1)(2)(2)1(2)2232++=+++=+++=++xxx xxxxxxx38.22(2)(3)(3)2(3)32656++=+++=+++=++xxx xxxxxxx39.22(32)(31)9362992++=+++=++xxxxxxx40.22(3)(25)2561521115++=+++=++xxxxxxx41.22( 45)(3)4125154715-++= --++= --+xxxxxxx

Solution Manual for College Algebra, 4th Edition - Page 19 preview image

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Section P.3Polynomials1542.22( 21)(5)21052115-+-= -++-= -+-xxxxxxx43.22(32)(21)6342672--=--+=-+xxxxxxx44.22(1)(53)5353583--=--+=-+xxxxxxx45.2222(23 )(25 )4106154415-+=+--=+-xaxaxaxaxaxaxa46.2222(52 )(5 )52521052310-+=+--=+-xaxaxaxaxaxaxa47.2222(2)4444+-=++-=+xxxxxx48.2222(3)6969--=-+-= -+xxxxxx49.22(41)1681+=++xxx50.22(32)9124+=++xxx51.2222333244439216xxxxxæöæ öæ ö+=++ç÷ç÷ç÷èøèøèø=++52.2222222255544525æöæ öæ ö+=++ç÷ç÷ç÷èøèøèø=++xxxxx53.()()()()()222223432 34492416xyxxyyxxyy-=-+=-+54.()()()()()222222522 25542025xyxxyyxxyy+=++=++55.()()()( )22222242222244xxxxx+=++=++56.()( )()()22222224332 396xxxxx-=-+=-+57.22222222222222442244xxxxxxxxxxæöæ öæ öæ öæ ö+=++ç÷ç÷ç÷ç÷ç÷èøèøèøèøèø=++=++58.22222223332333992299yyyyyyyyyyæöæöæöæöæö-=-+ç÷ç÷ç÷ç÷ç÷èøèøèøèøèø=-+=+-59.()( )( )32323322323226128xxxxxxx+=+++=+++60.()()() ( )()( )3323322123 213 21181261xxxxxxx-=-+-=-+-61.()333xx+-Note that this is the difference of cubes, withA=x+ 3 andB=x.()()()()()()332222222333336933 39992727xxxxxxxxxxxxxxxxx+-éù= é+-ù++++ëûëû=+++++=++=++62.()332xx--Note that this is the difference of cubes, withA=x–2 andB=x.()()()()()()332222222222224422 3646128xxxxxxxxxxxxxxxxx--éù= é--ù-+-+ëûëû= --++-+= --+= -+-63.()()()323233222323226128xyxxyxyxxyxy+=+++=+++64.()()() ()()()()3322332232323 233 2338365427xyxxyxyyxx yxyy+=+++=+++65.()()()222525252254xxxx+-=-=-66.()()()222343434916xxxx-+=-=-67.()()()()222223232349xyxyxyxy+-=-=-68.()()()()2222525252254xyxyxyxy-+=-=-

Solution Manual for College Algebra, 4th Edition - Page 20 preview image

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16Chapter PBasic Concepts of Algebra69.22221111xxxxxxxxæöæöæ ö+-=-=-ç÷ç÷ç÷èøèøèø70.222222222244yyyyyyyyæöæöæöæö-+=-ç÷ç÷ç÷ç÷èøèøèøèø=-71.()()()2222243339xxxx+-=-=-72.()()()2333262224xxxx-+=-=-73.()()()()22232232233523533526103915291915xxxx xxxxxxxxxxxx--+=-+--+=-+-+-=-+-74.()()()()222322322434324343286656xxxx xxxxxxxxxxxx---=-----=---++=-++75.()()()()2222233111 1111yyyyyyyyyyyyyy+-+=-++-+=-++-+=+76.()()()()2223223441641644164164166464yyyy yyyyyyyyyy+-+=-++-+=-++-+=+77.()()()()222322366366366636636636216216xxxx xxxxxxxxxx-++=++-++=++---=-78.()()()()22232231111111xxxx xxxxxxxxxx-++=++-++=++---=-79.2222(2 )(35 )3561031110++=+++=++xyxyxxyxyyxxyy80.2222(2)(72 )1447214112++=+++=++xyxyxxyxyyxxyy81.2222(2)(37 )614376117-+=+--=+-xyxyxxyxyyxxyy82.2222(3 )(25 )25615215-+=+--=--xyxyxxyxyyxxyy83.() ()()()()()()()()()()()22222242242xyxyxyxyxyxyxyxyxyxyxyxyxx yy-+=--++= é-+ùé-+ùëûëû=--=-+84.() ()()()()()()()()()()()2222224224222222222244168xyxyxyxyxyxyxyxyxyxyxyxyxx yy+-=++--= é-+ùé-+ùëûëû=--=-+85.()()()()()()22222223222233232444444444434xyxyxyxxyyx xxyyy xxyyxx yxyx yxyyxx yy+-=+-+=-++-+=-++-+=-+86.()()()()()()22222223222233232444444444434xyxyxyxxyyx xxyyy xxyyxx yxyx yxyyxx yy-+=-++=++-++=++---=+-87.() ()()()()()()()()()()323323223322332234322332234433422323222612826128261286128212241641616xyxyxxyxyyxyxx yxyyxyx xx yxyyy xx yxyyxx yx yxyx yx yxyyxx yxyy-+=+-+-+-×+=-+-+=-+-+-+-=-+-+-+-=-+-

Solution Manual for College Algebra, 4th Edition - Page 21 preview image

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Section P.3Polynomials1788.() ()()()()()()()3322332232223 23 2281262xyxyxxyx yyxyxx yxyyxy+-éù=+++ëû×-=+++-()()32233223432233223443342812681261624122812616164xxx yxyyyxx yxyyxx yx yxyx yx yxyyxx yxyy=+++-+++=+++----=+--For exercises89−94, use()()222222.ababababab+=+-=-+89.()22224,3242 316610xyxyxyxyxy+==+=+-=-× =-=90.()22223,2232 29413xyxyxyxyxy-==+=-+=+× =+=91.a.13xx+=Leta=xand1 .bx=Then11.abxxæ ö==ç÷èø2222111232927xxxxxxæöæ ö+=+-ç÷ç÷èøèø=-=-=b.Let2ax=and21 .bx=Using the resultfrom part a, we have2422422211127249247xxxxxxæöæö+=+-ç÷ç÷èøèø=-=-=92.a.12xx-=Leta=xand1 .bx=Then11.abxxæ ö==ç÷èø2222111222426xxxxxxæöæ ö+=-+ç÷ç÷èøèø=+=+=b.Let2ax=and21 .bx=Using the resultfrom part a, we have2422422211126236234xxxxxxæöæö+=+-ç÷ç÷èøèø=-=-=93.Leta= 3xandb= 2y. Thenab= 6xy.()()222294322 6122 6 61447272xyxyxy+=+-=-× × =-=94.Leta= 3xandb= 7y. Thenab= 21xy.()()()()2222949372 21102 2111004258xyxyxy+=-+=+-=-=P.3Applying the Concepts95.()( )20.025 60.44 64.28$6.02-++=in 2012(six years after 2006)96.()( )20.035 40.15 45.176.33++=In 2012 (four years after 2008), theater grosseswere 6.33 billion dollars.97.()20.1 404050$250.00++=98.()()2215105 155752575$100.00-+=+=+=99.()( )()216 520 516 25100500 feetd=+=+=100.()( )( )216 210 216 42084 feetd=+=+=101.a.22.50-+xb.()()()222301022.5030 22.5030225106751951010195675xxxxxxxxx+-=-+-=+-= -++102.a.10250+nb.22(502 )(10250)50(10 )50(250)2 (10 )2 (250)50012, 500205002012,500nnnnnnnnnn-+=+--=+--= -+

Solution Manual for College Algebra, 4th Edition - Page 22 preview image

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18Chapter PBasic Concepts of AlgebraP.3 Beyond the Basics103.()()()()()()2222222222abcabcabca abcb abcc abcaabacabbbcacbccabcabbcac++=++++=++++++++=++++++++=+++++104.()()( )( )222222224232432112212112222321xxxxx xxxxxxxxxxxx++=+++++=+++++=++++105.()()()()()()()2222222222 222 24424xyzxyzx yyzxzxyzxyyzxz+-=++ -++-+-=+++--()()()()()()()2222222222 222 24424xyzxyzxyy zx zxyzxyyzxz-+=+ -++-+-+=++--+()()()()22222222224424442488xyzxyzxyzxyyzxzxyzxyyzxzxyxz+---+=+++---++--+=-Alternatively, recognize the difference of two squares.()()()()()()()()2222222242288xyzxyzxyzxyzxyzxyzxyzxyxz+---+= é+-+-+ùé+---+ùëûëû=-=-106.8;12abcabbcac++=++=()()()22222222222222222222282 12642440abcabcabbcacabcabbcacabcabcabc++=+++++=+++++=+++=+++=++107.22212;44xyzxyz++=++=()()()()()22222222222212442144442100250xyzxyzxyyzxzxyzxyyzxzxyyzxzxyyzxzxyyzxzxyyzxz++=+++++=+++++=+++=+++=++=++108.22264;18xyzxyyzxz++=++=()()()()()2222222222222642 1810010010xyzxyzxyyzxzxyzxyyzxzxyzxyzxyz++=+++++=+++++++=+++=++==109.()()()()()2222222222223222223222223223333abcabcabbccaa abcabbccab abcabbccac abcabbccaaabaca babccaa bbbcabb cabca cb ccabcbcc aabcabc++++---=++---+++---+++---=++---+++---+++---=++-

Solution Manual for College Algebra, 4th Edition - Page 23 preview image

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Section P.4Factoring Polynomials19110.From exercise 109,( )()22233333333303033abcabbccaabcabcabcabcabcabc++---=++-Þ=++-Þ++=111.Leta=x–y,b=y–z, andc=z–x. Then()()()0.abcxyyzzx++=-+-+-=From exercise 110, if0,abc++=then3333.abcabc++=So,()()()()()()3333.xyyzzxxyyzzx-+-+-=---112.Leta= 2x–3y,b= 3y–5z, andc= 5z–3x. Then()()()2335530.abcxyyzzx++=-+-+-=From exercise 110, if0,abc++=then3333.abcabc++=So,()()()()()()3332335523 233552.xyyzzxxyyzzx-+-+-=---113.From exercise 109,()()2223333.abcabcabbccaabcabc++++---=++-If8abc++=and19,abbcca++=we have()()()()()()22222233322233338193(1)abcabcabbccaabcabcabbccaabcabcabcabcabc++++---=++++-++=++-Þ++-=++-From exercise 103,()()()22222222222222222222282 19643826abcabcabbcacabcabbccaabcabcabc++=+++++=+++++Þ=+++Þ=+++Þ++=Substituting into equation (1) gives us()3333338 26193563.abcabcabcabc-=++-Þ=++-114.From exercise 109,()()2223333.abcabcabbccaabcabc++++---=++-If9abc++=and11,abbcca++=we have()()()()()()22222233322233339113(1)abcabcabbccaabcabcabbccaabcabcabcabcabc++++---=++++-++=++-Þ++-=++-From exercise 103,()()()22222222222222222222292 11812259abcabcabbcacabcabbccaabcabcabc++=+++++=+++++Þ=+++Þ=+++Þ++=Substituting into equation (1) gives us()3333339 591134323.abcabcabcabc-=++-Þ=++-P.3 Getting Ready for the Next Sectionaba+bab115.34712116.–352–15117.4268118.3–5–2–15119.25710aba+bab120.35815121.–572–35122.5–7–2–35123.–2–3–56124.2356P.4Factoring PolynomialsP.4 PracticeProblems1.a.()5332614237+=+xxxxb.()54223272135735++=++xxxxxxc.()()()()225252xxyxyxyx-+-=-+2.a()()26842++=++xxxx

Solution Manual for College Algebra, 4th Edition - Page 24 preview image

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20Chapter PBasic Concepts of Algebrab.()()231052--=-+xxxx3.a.()22442xxx++=+b.()2296131xxx-+=-4.a.()()21644-=-+xxxb.()()24252525-=-+xxx5.()()()()()42228199339xxxxxx-=-+=-++6.a.()()321255525xxxx-=-++b.()()3227832964+=+-+xxxx7.Following the reasoning in Example 7, in fouryears, the company will have invested theintial 12 million dollars, plus an additional 4million dollars. Thus, the total investment is16 million dollars.To find the profit or losswith 16 million dollars invested, letx= 16 inthe profit-loss polynomial:()()()()()()220.01214141960.01216141614 1619616.224-++=-+×+=xxxThe company will have made a profit of16.224 million dollars in four years.8.a.()()()()32223331331xxxxxxxx+++=+++=++b.()()()()()()()3222282075475757541752121xxxxxxxxxxx--+=---=--=-+-c.()()()()()()()()222222212111111---=-++=-+=-+++=--++xyyxyyxyxyxyxyxy9.()()()()()42422422222222259696933333xxxxxxxxxxxxxxxxxx++=+-+=++-=+-éùéù=+++-ëûëû=++-+10.a.()()()()()()2225112510251025212512xxxxxxxxx xxxx++=+++=+++=+++=++b.()()()()()()22243443344334131431xxxxxxxxx xxxx+-=+--=+-+=+-+=-+P.4Concepts andVocabulary1.The polynomialsx+2 andx− 2 are calledfactorsof the polynomial24.-x2.The polynomial 3yisthegreatestcommonmonomialfactor of the polynomial236 .+yy3.The GCF of the polynomial321030+xxis210.x4.A polynomial that cannot be factored as aproduct of two polynomials (excludingconstant polynomials1)±is said to beirreducible.5.True6.True7.False. The polynomial24x-can be factoredas()()22 .xx+-Therefore, it is notirreducible.8.TrueP.4 Building Skills9.8248(3)xx-=-10.5255(5)xx+=+11.26126 (2)xxx x-+= --12.223213(7)xx-+= --

Solution Manual for College Algebra, 4th Edition - Page 25 preview image

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Section P.4Factoring Polynomials2113.2327147(12 )xxxx+=+14.3439189(12 )xxxx-=-15.()43222221xxxxxx++=++16.()432225757xxxxxx-+=-+17.3223(31)xxxx-=-18.322222(1)xxxx+=+19.322844(21)axaxaxx+=+20.()423221axaxaxax xx-+=-+21.()()()()33x xyxyxxy-+-=+-22.()()()()2131231a aaaa+-+=-+23.()()()()3252352xxyyxyxyxy+++=++24.()()()()2537532753xxyyxyxyxy-+-=+-25.()()()()()()223222321yyyyyy+-+=++-=+-26.()()() ()()()()21111112yyyyyy+++=+++=++27.()()()()32223331331xxxxxxxx+++=+++=++28.()()()()32225551551xxxxxxxx+++=+++=++29.()()()()32225551551xxxxxxxx-+-=-+-=-+30.()()()()32227771771xxxxxxxx-+-=-+-=-+31.()()()()322264322321 323221xxxxxxxx+++=+++=++32.()()()()32223623212231xxxxxxxx+++=+++=++33.()()()()()()754252222522231243431313143141xxxxxxxxxxxxxx+++=+++=++=++34.()()()()()()754252222522233331113131xxxxxxxxxxxxxx+++=+++=++=++35.()()()()()()xyabbxayxybxabayx yba byxaby+++=+++=+++=++36.()()()()()222222222221121a xbbxaa xabbxaxbxabx--+=+-+=+-+=-+37.2712(3)(4)xxxx++=++38.2815(3)(5)xxxx++=++39.268(4)(2)xxxx-+=--40.2914(7)(2)xxxx-+=--41.234(4)(1)xxxx--=-+42.256(6)(1)xxxx--=-+43.Irreducible44.Irreducible45.2236(29)(4)xxxx+-=+-46.22327(29)(3)xxxx+-=+-47.261712(23)(34)xxxx++=++48.28103(23)(41)xxxx--=-+49.23114(31)(4)xxxx--=+-50.2572(52)(1)xxxx++=++51.Irreducible52.Irreducible53.()()222045xxyyxyxy--=+-

Solution Manual for College Algebra, 4th Edition - Page 26 preview image

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22Chapter PBasic Concepts of Algebra54.()()2282154523ppqqpqpq--=+-55.()()22152815283457xxxxxx-+=+-=-+56.()()2224354424352725yyyyyy++=++=++57.2269(3)xxx++=+58.22816(4)xxx++=+59.22961(31)xxx++=+60.2236121(61)xxx++=+61.2225204(52)xxx-+=-62.222643244(1681)4(41)xxxxx++=++=+63.2249429(73)xxx++=+64.2292416(34)xxx++=+65.264(8)(8)xxx-=-+66.2121(11)(11)xxx-=-+67.241(21)(21)xxx-=-+68.291(31)(31)xxx-=-+69.2169(43)(43)xxx-=-+70.22549(57)(57)xxx-=-+71.()()()()()4222111111xxxxxx-=-+=-++72.()()()()()42228199339xxxxxx-=-+=-++73.()()()44222055 415 2121xxxx-=-=-+74.()()()442212753 4253 2525xxxx-=-=-+75.()()33326444416xxxxx+=+=+-+76.()()333212555525xxxxx+=+=+-+77.()()3332273339xxxxx-=-=-++78.()()333221666636xxxxx-=-=-++79.()()333282242xxxxx-=-=-++80.()()3332273393xxxxx-=-=-++81.()()3332827(2 )323469xxxxx-=-=-++82.()()()33328125252541025xxxxx-=-=-++83.()()()()()333324055 815215 21421xxxxxx+=+=+=+-+84.()()()()3333275678727224xxxxxx+=+=+=+-+85.()()()()()()4242242222222222510925102595953533535xxxxxxxxxxxxxxxxxx++=+-+=++-=+-éùéù=+++-ëûëû=++-+86.()()()()()()4242242222222221212111111xxxxxxxxxxxxxxxxxx++=+-+=++-=+-éùéù=+++-ëûëû=++-+

Solution Manual for College Algebra, 4th Edition - Page 27 preview image

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Section P.4Factoring Polynomials2387.()()()()()()42422422222222215641664166488888xxxxxxxxxxxxxxxxxx++=+-+=++-=+-éùéù=+++-ëûëû=++-+88.()()()()()()42422422222222279696933333xxxxxxxxxxxxxxxxxx-+=--+=-+-=--éùéù=-+--ëûëû=+---89.()()()()()()42422422222222216891681694943433434xxxxxxxxxxxxxxxxxx-+=+-+=++-=+-éùéù=+++-ëûëû=++-+90.()()()()()()424224222222222163612436123646462622626xxxxxxxxxxxxxxxxxx-+=--+=-+-=--éùéù=-+--ëûëû=+---91.()()()()()()4422422222222244444442422222222xxxxxxxxxxxxxxxxx+=+-+=++-=+-éùéù=+++-ëûëû=++-+92.()()()()()()442242222222226416166416641681684844848xxxxxxxxxxxxxxxxx+=+-+=++-=+-éùéù=+++-ëûëû=++-+93.2116(14 )(14 )xxx-=+-94.2425(25 )(25 )xxx-=-+95.2269(3)xxx-+=-96.22816(4)xxx-+=-97.22441(21)xxx++=+98.221681(41)xxx++=+99.()2228102452(5)(1)xxxxxx--=--=-+100.()()()2251040528542xxxxxx--=--=-+101.22320(25)(4)xxxx+-=-+102.22730(25)(6)xxxx--=+-103.22436xx-+is irreducible.104.22025xx-+isirreducible.105.5433232312123(44)3(2)xxxxxxxx++=++=+106.5433232216322(816)2(4)xxxxxxxx++=++=+107.291(31)(31)xxx-=-+108.21625(45)(45)xxx-=-+109.2216249(43)xxx++=+110.2242025(25)xxx++=+111.215+xis irreducible.112.224+xis irreducible.113.()()()322458445845292xxxxxxxxx+-=+-=+-114.()()()32225409254095951xxxxxxxxx+-=+-=+-115.()()()2232278788axa xaa xaxaa xaxa--=--=-+

Solution Manual for College Algebra, 4th Edition - Page 28 preview image

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24Chapter PBasic Concepts of Algebra116.()()()2232210241024122axa xaa xaxaa xaxa--=--=-+117.()()()()22222216816816164164444xaxxxaxaxaxa-++=++-=+-=+-++118.()()()()222222366969363363636xaxxxaxaxaxa-++=++-=+-=+-++119.()()5432322233121234432xx yx yxxxyyxxy++=++=+120.()()5432322234243646943xx yx yxxxyyxxy++=++=+121.()()()()222222254444252252525xaxxxaxaxaxa-++=++-=+-=+-++122.()()()()222222164444162162424xaxxxaxaxaxa-++=++-=+-=+-++123.()()6542422241812229623xx yx yxxxyyxxy++=++=+124.()()6542422241212334432xx yx yxxxyyxxy++=++=+P.4Applying the Concepts125.If one side of the garden isxfeet, and theperimeter is 16 feet, then16282xx-=-gives the other dimension of the rectangle. So,the area of the garden is(8).xx-126.If one side of the tray isxinches, and theperimeter is 42 inches, then422212xx-=-gives the other dimension of the tray. So, thearea of the tray is(21).xx-Use the figure below for exercises 127and 128.127.Ifx= the length of the cut corner, then36–2x= the length of the box, and16–2x= the width of the box. The height of thebox isx. So,(362 )(162 )(2(18))(2(8))4 (18)(8)vxxxxxxxxx=--=--=--128.22222. .(362 )(162 )2 (362 )2 (162 )576104472432457644(144)4(12)(12)=--+-+-=-++-+-=-=-=-+S Axxxxxxxxxxxxxxxx129.The area of the outside circle =24cm .pThearea of the inside circle =22cm .xpSo thearea of the disk = area of outside circle–areaof inside circle =224(4)xxppp-=-=2(2)(2) cm .xxp-+130.The volume of the insidecylinder is238p× =372ftp,and the volume of the outsidecylinder is22388ft .xxpp× =So the volume between thecylinders is228728(9)xxppp-=-38(3)(3) ft .xxp=-+

Solution Manual for College Algebra, 4th Edition - Page 29 preview image

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Section P.4Factoring Polynomials25131.If one side of the fence isxfeet, and the rancher needs a total of 2800 feet of fencing, then the width of thefence is 2800–2x. So, the area of the pen is2(28002 )28002xxxx-=-=22 (1400) ft .xx-132.The area of the figure = the area of the rectangle plus the area of the circle. Find the length of the rectangle asfollows: The circumference of the circle =22xxppæ ö=ç÷èø. The perimeter of the figure is 48, so the length ofthe rectangle is48.2xp-The area of the circle is24xpand the area of the rectangle is242xxpæö-=ç÷èø224.2xxp-So.the area of the figure is222124(96)424xxxxxpppæö+-=-=ç÷èø21(96) in.4xxp-P.4 Beyond the Basics133.()()()()3322221xyxyxyxxyyxyxyxxyy+++=+-+++=+-++134.()()()()()2424222222221112191913133131xxxxxxxxxxxxxxx-+=-+-=--=---+=--+-135.()()()()()244224224222222222222222xyx yxx yyx yxyx yxyxyxyxyxxyyxxyy++=++-=+-=+-++=-+++136.()()()()()()()()()224422222222222222222222222222242444242422222222xyxyx yx yxx yyx yxyx yxyxyxyxyxxyyxxyy+=++-=++-=+-=+-++=-+++137.()()()()()()()()()()()26323364888224224222424xxxxxxxxxxxxxxxx-=-=-+=-+++-+=-+++-+138.()()()()()()633322262727133911xxxxxxxxxx--=-+=-+++-+

Solution Manual for College Algebra, 4th Edition - Page 30 preview image

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26Chapter PBasic Concepts of Algebra139.()()()()()()()()()()222222233838034032340328521xxxxxxxxxxxxxxxxéùéù----=---+ëûëû=---+=-+--140.()()()()()()()()()2222222222242424242222xyzyzxyzyzxyyzzxyzxyzxyzxyzxyz--+=-+-=--+=--=--+-=-++-141.From exercise 109 in Section P.3, we have()()2223333.abcabcabbccaabcabc++++---=++-Then,()()()()()()()()()()()() ()()()3332222222222222222223122122222221222212abcabcabcabcabbccaabcabcabbccaabcabcabbccaabcaabbbbccccaaabcabbcca++-=++++---=++×++---=++++---=++-++-++-+éù=++-+-+-ëûIf33330,abcabc++-=then either0abc++=or()()()2220.abbccaabc-+-+-=Þ==142.See exercise 111 in section P.3.()()()()()()3333xyyzzxxyyzzx-+-+-=---143.Let()(),,az xyxzyz bx yzxyxz=-=-=-=-and().cy zxyzxy=-=-Then0,abcxzyzxyxzyzxy++=-+-+-=and we can apply Section P.3 exercise 110.()()()()()()3333333zxyxyzyzxxyz xyyzzx-+-+-=---144.()()()()()()333222222333xyyzzxxyyzzx-+-+--+-+-In the numerator, let2222,,axybyz=-=-and22.czx=-Thena+b+c= 0, and we can applySection P.3 exercise 111. Use the result from exercise 142 above for the denominator.()()()()()()()()()()()()()()()()()()()()()()()()33322222222222233333xyyzzxxyyzzxxyyzzxxyyzzxxyxyyzyzzxzxxyyzzxxyyzzx-+-+----=----+-+-+-+-+-=---=+++P.4 Getting Ready for the Next Section145.1132546121212+=+=146.31927812242424-=-=147.9120516×4273415=148.21536×359=

Solution Manual for College Algebra, 4th Edition - Page 31 preview image

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Section P.5Rational Expressions27149.()22462 2323xxxxxx==+++150.()()232223232311xxxxxx xxxx+++==+++151.()()()()221232213343xxxxxxxxxx+++++==+++++152.()()()()2232632224xxxxxxxxx-+---==-+--P.5Rational ExpressionsP.5 Practice Problems1.()()()()0.05 10.10.320.95 0.10.0510.1-»+-The likelihood that a student who testspositive is a nonuser when the test that is usedis 95% accurate is about 32%.2.a.()()232224282343312xxxxxx xxx++==++b.()()()22222422442xxxxxxxx-+--==++++3.()()()()()()2232324343243323223234472844728282823284472831244174314xxxxxxxxxxxxxxxxxxxxxxxxxxxxx x----++=¸++++--+=×++-++=×++-=4.a.()()()()222221052252222036363674236767666xxxxxxxxxxxxx++++++=---+=-+==-+-b.()()()()22224134413412121231234314xxxxxxxxxxxxxxxxx+-+++-=+-+-+--=+--=+-=+5.a.()()()()()()232525322525++--+=++-+-xxxxx xx xxxxx()()()()()()()222210365425255425-++-==+-+--=+-xxxxxxxxxxxxxxb.()()()()()()()()()()()()()22252435324434351528323434332343xxxxx xx xxxxxxxxxxxxxxxxxxx--++-=--+-++-++==-+-++=-+6.a.() ()()22222341,2232xxxxxxx x+++--() ()222LCD322xxx=+-b.2222137,2545xxxxx---+-()()()()()()()2225554515LCD155xxxxxxxxxx-=-++-=-+=--+7.a.()()()()() ()()() ()()()() ()() ()222222222444442224222222482282222xxxxxxxxxx xxxxxxxxxxxxxx+-+-=+-+-+-=+-+-+++-++==-+-+

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