Solution Manual for College Algebra, 4th Edition

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Solution Manual for College Algebra, 4th Edition - Page 1 preview image

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

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

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××===×××

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

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

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

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

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

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-+=-=-

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

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++=

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