Algebra and Trigonometry, 9th Edition Solution Manual

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C H A P T E RPPrerequisitesSection P.1Review of Real Numbers and Their Properties.....................................2Section P.2Exponents and Radicals .........................................................................5Section P.3Polynomials and Special Products.......................................................10Section P.4Factoring Polynomials..........................................................................16Section P.5Rational Expressions ............................................................................24Section P.6The Rectangular Coordinate System and Graphs ...............................32Review Exercises..........................................................................................................38Problem Solving...........................................................................................................45Practice Test...............................................................................................................49

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2C H A P T E RPPrerequisitesSection P.1Review of Real Numbers and Their Properties1.irrational2.origin3.absolute value4.composite5.terms6.Zero-Factor Property7.72239,, 5,,2, 0, 1,4, 2,11−−−−(a) Natural numbers: 5, 1, 2(b) Whole numbers: 0, 5, 1, 2(c) Integers:9, 5, 0, 1,4, 2,11−−−(d) Rational numbers:72239,, 5,, 0, 1,4, 2,11−−−−(e) Irrational numbers:28.75345,7,, 0, 3.12,,3, 12, 5−−−(a) Natural numbers: 12, 5(b) Whole numbers: 0, 12, 5(c) Integers:7, 0,3, 12, 5−−(d) Rational numbers:75347,, 0, 3.12,,3, 12, 5−−−(e) Irrational numbers:59.2.01, 0.666 . . .,13, 0.010110111 . . ., 1,6−−(a) Natural numbers: 1(b) Whole numbers: 1(c) Integers:13, 1,6−−(d) Rational numbers:2.01, 0.666 . . .,13, 1,6−−(e) Irrational numbers:0.010110111 . . .10.1215225,17,,9, 3.12,, 7,11.1, 13π−−−(a) Natural numbers:25,9, 7, 13(b) Whole numbers:25,9, 7, 13(c) Integers:25,17,9, 7, 13−(d) Rational numbers:12525,17,,9, 3.12, 7,11.1, 13−−−(e) Irrational numbers:12π11.(a)(b)(c)(d)12.(a)(b)(c)(d)13.48−> −14.1631<15.5263>16.8377−< −17.(a) The inequality5x≤denotes the set of all realnumbers less than or equal to 5.(b)(c) The interval is unbounded.

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Section P.1Review of Real Numbers and Their Properties318.(a) The inequality0x<denotes the set of all realnumbers less than zero.(b)(c) The interval is unbounded.19.(a) The interval[)4,∞denotes the set of all realnumbers greater than or equal to 4.(b)(c) The interval is unbounded.20.(a)(), 2−∞denotes the set of all real numbers lessthan 2.(b)(c) The interval is unbounded.21.(a) The inequality22x−<<denotes the set of allreal numbers greater than2−and less than 2.(b)(c) The interval is bounded.22.(a) The inequality 06x<≤denotes the set of all realnumbers greater than zero and less than or equal to 6.(b)(c) The interval is bounded.23.(a) The interval[)5, 2−denotes the set of all realnumbers greater than or equal to5−and less than 2.(b)(c) The interval is bounded.24.(a) The interval(]1, 2−denotes the set of all realnumbers greater than1−and less than or equal to 2.(b)(c) The interval is bounded.25.[)0; 0,y≥∞26.(]25;, 25y≤−∞27.[]1022; 10, 22t≤≤28.[)35;3, 5k−≤<−29.()65; 65,W>∞30.[]2.5%5%; 2.5%, 5%r≤≤31.()101010−= − −=32.00=33.()38555−=−= − −=34.4133−==35.12121−− −=−= −36.( )33336−− −= −−= −37.()5551555−−−=== −−− −38.( )333 39−−= −= −39.If2,x< −then2x+is negative.So,()221.22xxxx+−+== −++40.If1,x>then1x−is positive.So,111.11xxxx−−==−−41.44−=because44−=and44.=42.55−= −since55.−= −43.66− −<−because66−=and( )666.− −= −= −44.22− −= −because22.−= −45.()126, 757512651d=−=46.()()126,757512651d−−=−−=47.()()555222, 00d−=−−=48.()511111144442,d=−=49.()161612811211257575575,d=−=50.()9.34,5.655.659.3414.99d−=−−=51.(), 55d xx=−and(), 53,d x≤so53.x−≤iection P.1Review of Real Numbers and The

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4Chapter PPrerequisites52.(),1010 ,d xx−=+and(),106,d x−≥so106.x+≥53.(),d y aya=−and(),2,d y a≤so2.ya−≤54.602337 F−=°Receipts, RExpenditures, E−RE55.$1880.1$2292.81880.12292.8$412.7 billion−=56.$2406.9$2655.12406.92655.1$248.2 billion−=57.$2524.0$2982.52524.02982.5$458.5 billion−=58.$2162.7$3456.22162.73456.2$1293.5 billion−=59.74x+Terms:7 , 4xCoefficient: 760.365xx−Terms:36,5xx−Coefficient:6,5−61.3452xx+−Terms:34,,52xx−Coefficients:14, 262.2331x+Terms:233, 1xCoefficients:3363.46x−(a)()4164610−−= −−= −(b)( )4 06066−=−= −64.97x−(a)()97392130−−=+=(b)( )97 392112−=−= −65.254xx−+−(a)()()2151415410− −+−−= −−−= −(b)( )( )215 141540−+−= −+−=66.11xx+−(a)112110+=−Division by zero is undefined.(b)1100112−+==−−−67.()()161,66hhh+=≠ −+Multiplicative Inverse Property68.()()330xx+−+=Additive Inverse Property69.()23223xx+=⋅+⋅Distributive Property70.()202zz−+=−Additive Identity Property71.()()()33Associative Property of Multiplication3Commutative Property of Multiplicationxyxyx y=⋅=72.()()11777127 12Associative Property of Multiplication112Multiplicative Inverse Property12Multiplicative Identity Property⋅=⋅=⋅=requisitesrequisites

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Section P.2Exponents and Radicals573.55151093148126242424248−+=−+==74.()4182663−⋅= −⋅= −75.283534121212xxxxx−=−=76.52515693927xxx⋅=⋅=77.(a) Because0,0.AA>−<The expression is negative.(b) Because,0.BA BA<−<The expression is negative.(c) Because0,0.CC<−>The expression is positive.(d) Because,0.ACAC>−>The expression is positive.78.The types of real numbers that may be used in a range ofprices are nonnegative rational numbers because a priceis neither negative nor irrational. For example, a priceof1.80−or$2would not be reasonable. The typesof real numbers to describe a range of lengths arenonnegative and rational because lengths are often not inwhole unit amounts but in parts, such as 2.3 centimetersor34inch.79.False. Because 0 is nonnegative but not positive, notevery nonnegative number is positive.80.False. Two numbers with different signs will alwayshave a product less than zero.81.(a)(b) (i) Asnapproaches 0, the value of5nincreaseswithout bound (approaches infinity).(ii) Asnincreases without bound (approachesinfinity), the value of5napproaches 0.Section P.2Exponents and Radicals1.exponent; base2.scientific notation3.square root4.index; radicand5.like radicals6.conjugates7.rationalizing8.power; index9.(a)3433381⋅==(b)22423113339−===10.(a)()0331=(b)239−= −11.(a)()2323 22 26423232364815184⋅⋅⋅=⋅=⋅=⋅=(b)()3232332233213535113553533355−−−§· §·−=−⋅= −⋅⋅¨¸ ¨¸©¹ ©¹= −⋅= −12.(a)45433332433−=⋅==(b)()()33484834846444−−== −= −−13.(a)()22121214316423443233−−− −−−−⋅=⋅⋅=⋅⋅=⋅(b)()021−=14.(a)12371143412121232−−+=+=+=(b)()22411481333−−===15.When2,x=( )3333 224.x−= −= −16.When4,x=( )2227777 4.416x−−===17.When10,x=()( )0066 106 16.x===18.When3,x= −()()3322322754.x=−=−= −n0.00010.01110010,0005n50,00050050.050.0005ection P.2Exponents aSection P.2Exponents3555()())(

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6Chapter PPrerequisites19.When2,x= −()()443323 1648.x−= −−= −= −20.When13,x= −()( )()331143279121212.x−===21.(a)()()333355125zzz−=−= −(b)()42426555xxxx+==22.(a)()2222339xxx==(b)()0300441,0xxx=⋅=≠23.(a)()()( )2220222626216424yyyyy=⋅==(b)() ()() ()33434347313133zzzzzz+−=−= −⋅⋅= −24.(a)223137777xxxxx−−===(b)()()()()33121244933xyxyxyxy−+=+=++25.(a)343434347434364815184yyyyyy+§· §·⋅=⋅==¨¸ ¨¸©¹ ©¹(b)22222221,0,0bbababaaba−−§·§·§·§·==≠≠¨¸¨¸¨¸¨¸©¹©¹©¹©¹26.(a)()()11122222222x yxyx yxy−−−−−−ªº=«»¬¼==(b)() ()()()()()()()()()( )( )( )33262636183618000555551 1 11x zx zxzxzxz−−−−====27.(a)()051,5xx+=≠ −(b)()()2224211242xxx−==28.(a)()()( )( )()24422484832yyyy−−==(b)()()()()314412222zzzz−−−++=+=+29.(a)33343441251255xyxxyy−−§·§·==¨¸¨¸©¹©¹(b)322352235abbbbbaaaa−−§·§·§·§·==¨¸¨¸¨¸¨¸©¹©¹©¹©¹30.(a)2233333nnnnn+⋅==(b)22231331nnnnnnxxxxxxxxx++−−−+⋅====⋅31.410,250.41.0250410=×32.40.0001251.2510−−= −×33.50.000039373.93710inch−=×34.757,300,0005.7310square miles=×35.51.80110180,100−×= −36.43.14100.000314−×=37.129.4610= 9,460,000,000,000 kilometers×38.59.0100.00009 meter−×=39.(a)()()9452.0103.4106.810−××=×(b)()()7341.2105.0106.010−××=×40.(a)81136.0102.0103.010−×=××(b)35622.5100.5105.0105.010−−−×=×=××41.(a)93=(b)33327273828==42.(a)3273=(b)()3336(6)216==43.(a)()555/512222===(b)555532(2 )2xxx==requisitesrequisites

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Section P.2Exponents and Radicals744.(a)123366⋅==(b)()4424842333xxx==45.(a)20454525=⋅==(b)3333312864264242=⋅==46.(a)3333331622222733⋅==(b)22755353422⋅==47.(a)327236262xxxxx=⋅=(b)2232218181818zzzzzzz===⋅48.(a)()24222546336xyxyyx=⋅⋅⋅=(b)()()22224222223242aabbab⋅⋅==49.(a)3353232168222xxxxx=⋅=(b)2244242757525353xx yyxyxy−=⋅==50.(a)()1 4424241 41 243333x yx yx yxy===(b)()()()1 5584841 555341 534534160160252525x zx zxxzxx zxx z==⋅⋅⋅==51.(a)()()10326181016269210 426 32402182222−=⋅−⋅=−=−=(b)()333333333331635422323223322292112+=⋅+⋅=+⋅=+=52.(a)532xxx−=(b)()29102 3106104yyyyyyy−+= −+= −+=53.(a)()()222222348775334735343753123353233xxxxxxxxx−+= −⋅⋅+⋅⋅= −⋅+⋅= −+=(b)()()7802125716522557 452 55285105185xxxxxxxxx−=⋅−⋅=−=−=54.(a)33375747xxx−−+−=−(b)()()3322221124594511579531175935775275505xxxxxxxxxxxxxxxx−=⋅⋅⋅−⋅⋅⋅=⋅−⋅=−=Section P.2Exponents aSection P.2ExponentsC50505xx55==

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8Chapter PPrerequisites55.11333333=⋅=56.333233333288284844422282=⋅===57.()()( )()()2251425142514255142142144102142142142142+++++=⋅====−−−+−58.()()()()3563563356356365561565656−−−=⋅=== −−=−−−++−59.84222222222122⋅===⋅=60.222233232=⋅=61.()()5353535323353353353++−−=⋅==−−−62.()()()73737379214473473473273−−+−−=⋅=== −++++63.3644,=Given1 3644,=Answer64.43334(2)8,aba b=Answer34(2),abGivenRadical FormRational Exponent Form65.323,0xx≠2 32 333xx−=66.2,xxGiven51222xxx=, Answer67.3,xxyGiven31111122222233xxyxy⋅=, Answer68.(a)23 21 243 231 243 21 2341(2)222222xxxxxxx−−−−−−−⋅⋅=⋅⋅⋅==⋅=69.(a)533 53 5311113232(2)8(32)−====(b)33 43 43416818132781161628−§·§·§·§·====¨¸¨¸¨¸¨¸¨¸©¹©¹©¹©¹70.(a)()33 231100100101000−−−===(b)1 21 294424939−§·§·===¨¸¨¸©¹©¹requisitesrequisites

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Section P.2Exponents and Radicals971.(a)()()3 23 223 221 241 2433 23413 21 211 24222222222xxxxxxxxx−−−=====(b)()4 32 34 32 33 31 31 31 31 31 3xyxyxyxyxyxy===72.(a)31 21 213 213 231 21 3 23331 ,0xxxxxxxxxxxx−−+ −−−⋅⋅=⋅⋅===>(b)()1 25 21 25 23 23 23 21 25 213 23 255555555,055xxxxxxxxx−−−⋅⋅====>73.(a)422 41 23333===(b)()()()()44 62 32631111xxxx+=+=+=+74.(a)633 61 2xxxx===(b)()422433xx=75.(a)()1 21 24441 43232323216222====⋅=(b)()()()1 21 41 8842222xxxx===76.(a)()()()()()()()()1 21 21 444424312431243124313811331xxxxxxª+=+º«¼¬=+=+=⋅+=+(b)()()()1 21 33771 676661010101010a ba ba baabaab===⋅⋅=77.(a)1/ 32 / 33 / 3(1)(1)(1)(1)xxxx−−=−=−(b)1/ 34 / 33 / 311(1)(1)(1)(1)1xxxxx−−−−−=−=−=−78.(a)5 / 25 / 315 / 610 / 65 / 6(43)(43)(43)(43)3(43),4xxxxxx−−++=++=+≠ −(b)5 / 21/ 215 / 63 / 612 / 622(43)(43)(43)(43)(43)(43)13,(43)4xxxxxxxx−−−−++=++=+=+=≠ −+Section P.2Exponents aSection P.2Exponents

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10Chapter PPrerequisites79.()5 25 20.03 1212, 012thhªº=−−≤≤¬¼(a)(b) Ashapproaches 12,tapproaches()5 20.03 128.64314.96 seconds.==80.3500x=331 325022xx§·==¨¸©¹So, twice the length of a side of package B is32 31 3224 .2xxx§·==¨¸©¹Because34 ,xx<the length of a side of package A isless than twice the length of a side of package B.81.True. When dividing variables, you subtract exponents.82.False. When a power is raised to a power, you multiplythe exponents:().knnkaa=83.False. When a sum is raised to a power, you multiply thesum by itself using the Distributive Property.22222()2abaabbab+=++≠+84. False. To rationalize the denominator, multiply thefraction by1.bb=This does not change the value ofthe expression, but raising the numerator anddenominator to the second power does.Section P.3Polynomials and Special Products1.0;;nn aa2.monomial; binomial; trinomial3.like terms4.First terms; Outer terms; Inner terms; Last terms5.(a) Standard form:51214xx−+(b) Degree: 5Leading coefficient:12−(c) Binomial6.(a) Standard form: 7x(b) Degree: 1Leading coefficient: 7(c) Monomial7.(a) Standard form:63x−+(b) Degree: 6Leading coefficient:í1(c) Binomial8.(a) Standard form:2251yy−+(b) Degree: 2Leading coefficient: 25(c) Trinomial9.(a) Standard form: 3(b) Degree: 0Leading coefficient: 3(c) Monomial10.(a) Standard form:28t−(b) Degree: 2Leading coefficient: 1(c) Binomial11.(a) Standard form:54461xx−++(b) Degree: 5Leading coefficient:í4(c) Trinomial12.(a) Standard form: 23x+(b) Degree: 1Leading coefficient: 2(c) Binomialh(in centimeters)t(in seconds)0012.9325.4837.6749.53511.08612.32713.29814.00914.501014.801114.931214.96requisitesrequisitesc) Binomialc) Binomial

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Section P.3Polynomials and Special Products1113.(a) Standard form:34xy(b) Degree: 4 (add the exponents onxandy)Leading coefficient: 4(c) Monomial14.(a) Standard form:52242xyx yxy−++(b) Degree: 6Leading coefficient:í1(c) Trinomial15.3238xx−+isa polynomial.Standard form:3328xx−++16.42252xxx−−+isnota polynomial because it includesa term with a negative exponent.17.1344334xxxx−+=+=+isnota polynomialbecause it includes a term with a negative exponent.18.2232xx+−isa polynomial.Standard form:21322xx+−19.243yyy−+isa polynomial.Standard form:432yyy−++20.4yy−isnota polynomial because it includes a termwith a square root.21.()()()()658156581568515210xxxxxxx+−+=+−−=−+−= −−22.()()()()22222222121212122112xxxxxxxxxxx+−−+=+−+−=−++−=+23.()()()3333333165165651551ttttttttttt−−+−= −++−=−+−+=−+24.()()()()222222251355135531524xxxxxxx−−−−+= −++−=−++−= −−25.()()()()232232322321568.314.7171568.314.7178.31514.76178.329.711xxxxxxxxxxx−−−−−=−+++=+++−+=++26.()()()()()444444415.61417.416.99.21315.61417.416.99.21315.616.9149.217.4131.34.830.4wwwwwwwwwwwwww−−−−+=−−−+−=−+−++−−= −−−27.()()()53108531085310853108128zzzzzzzzzzzzz−ª−+º=−−−¬¼=−++=−++=+28.()()()()()()3232323232113711371137311737yyyyyyyyyyyyyyyªº+−++−=+−+−−¬¼=+−−−+=−−+−+=−−+29.()()()( )223232133231363xxxx xxxxxxx−+=+−+=−+30.()()()()222222432423423423yyyyyyyyyyy+−=++−=+−31.()()()()25315351155zzzzzzz−−= −+−−= −+32.()()()()( )23523532156xxxxxxx−+= −+−= −−Section P.3Polynomials and SpecSection P.3Polynomials and Spe

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12Chapter PPrerequisites33.()()()()3344141 444444xxxxxxxxx−=−=−= −+34.()( )()()334443434124412xxxxxxxxx−−= −+−−= −+=−35.()()()()( )()2231.5531.53534.515ttttttt+−=−+−= −−36.()()()()()333344323.522 23.524774yyyyyyyyy−=+−=−= −+37.()()()()()220.11720.12170.234xxxxxxx−+=−+−= −−38.()()( )()()2233889944656563030yyyyyyyyy−=−=−= −+39.()()()()()322332327283473284424xxxxxxxx−++−−=−+−+−=−+40.()()()()()53353353232346234236233xxxxxxxxxxxxx−++++−=+−++++−=++−41.()()()()22225383538353835411xxxxxxxxxxx−+−−=−+−+=+−−++=−+42.()()()()424242424422420.620.55.60.620.55.60.620.55.61.62.55.6ttttttttttttt−−−+−=−+−+=++−−+=−+43.()()22723231421FOIL21721xxxxxxx++=+++=++44.()()2421xxxx+−−+Multiply:2243232243242142284594xxxxxxxxxxxxxxxx+−−++−−−++−−−+−45.()()22344312FOIL712xxxxxxx++=+++=++46.()()2251010550FOIL550xxxxxxx−+=+−−=+−47.()()22352163105FOIL675xxxxxxx−+=+−−=−−48.()()227243282186FOIL28296xxxxxxx−−=−−+=−+49.()()2211xxxx−+++Multiply:22432322432421110011xxxxxxxxxxxxxxxxxx−+++−+−+−+−+++=++50.()()222432xxxx−+++Multiply:224323224322432246312428255108xxxxxxxxxxxxxxxx−+++−+−+−+++++requisitesrequisites

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Section P.3Polynomials and Special Products1351.()()222101010100xxxx+−=−=−52.()()()22223232349xxxx+−=−=−53.()()()22222224xyxyxyxy+−=−=−54.()()()()22224545451625abababab+−=−=−55.()()()( )22222322 2334129xxxxx+=++=++56.()( )( )()()22225852588258064xxxxx−=+−+−=−+57.()()()( )( )222333634342 43316249xxxxx−=−+=−+58.()()()( )22228382 83364489xxxxx+=++=++59.()( )()3322332131311331xxxxxxx+=+++=+++60.()( )( )32323322323226128xxxxxxx−=−+−=−+−61.()()()()332233223223 23 28126xyxxyx yyxx yxyy−=−+−=−+−62.()()() ()()()()3322332233233 323 3222754368xyxxyxyyxx yxyy+=+++=+++63.()()()( )2222223336969mnmnmnmmnmnmª−+ºª−−º=−−¬¼¬¼=−+−=−−+64.()()()( )2222233369xyzxyzxyzxxyyzª−+ºª−−º=−−¬¼¬¼=−+−65.()()()2222222332369262669xyxy xyxxxyyyxxyyxyª−+º=−+−+¬¼=−++−+=++−−+66.()()()()()2222222112121222221xyxxyyxxxyyyxxyyxyª+−º=+++−+−¬¼=++−−+=−++−+67.()()()( )2221115551253339xxxx−+=−=−68.()()()( )2221116661363339xxxx+−=−=−69.()()()( )2221.54 1.541.542.2516xxxx−+=−=−70.()()()()2232323264343434916abababab−+=−=−71.()()()( )()222211144451162525525xxxxx−=−+−=−+72.()()()( )( )22222.432.42 2.4335.7614.49xxxxx+=++=++73.()()()251312122x xx xx xxx+−+=+=+74.()()()()()22213332232626FOIL286xxxxxxxxxx−+++=++=+++=++75.()()()()()22242244416uuuuuu+−+=−+=−76.()()()()()()()222222222244xyxyxyxyxyxyxy+−+=−+=−=−77.()()()()22xyxyxyxy+−=−=−78.()()( )()2255525xxxx+−=−=−79.()( )()()22225255255xxxxx−=−+=−+80.()()22223233233xxxxx+=++=++Section P.3Polynomials and SpecSection P.3Polynomials and Speyy33x232==x232

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14Chapter PPrerequisites81.(a)()ProfitRevenueCostProfit957325,000957325,0002225,000xxxxx=−=−+=−−=−(b)For5000:x=()Profit22 500025,000110,00025,000$85,000=−=−=82.(a)()()()2222500 15001500215001000500rrrrrr+=+=++=++(b)(c) Asrincreases, the amount increases.83.()()221821425218282246252Axxxxxxx=++=+++=++84.()()21444xxxxx++=+++This illustrates the Distributive Property.85.Area of shaded regionArea of outer rectangleArea of inner rectangle=−()()2222264412438Axxx xxxxxxx=+−+=+−−=+86.Area of shaded regionArea of outer triangleArea of inner triangle=−()()()()222112291268542430Axxxxxxx=−=−=87.The area of the shaded region is the difference between the area of the larger triangle and the area of the smaller triangle.()()()()222112210104450842Axxxxxxx=−=−=88.The area of the shaded region is one-half the area of the rectangle.()()()()()()21122lengthwidth42321 363Axxxxxx==−=−=−89.The area of the shaded region is the difference between the area of the larger square and the area of the smaller square.()()()22222421161642115183Axxxxxxxx=+−−=++−−+=++90.The area of the shaded region is the difference between the area of the larger triangle and the area of the smaller triangle.()()()()222222311112222228443264816324481224Axxxxxxxxxxªº=+−+=++−++=++=++¬¼91.(a)()()( )()( )()( )()()()()()()322621822 13294113194139488468Vlwhxxxxxxxxxx xxxxx=⋅⋅=−−=−−=−−−−=−−=−+(b)r122 %3%4%124 %5%()2500 1r+$525.31$530.45$540.80$546.01$551.25()cmx123()3cmV384616720requisitesrequisites

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Section P.3Polynomials and Special Products1592.(a)()()()()22233212121212Volumelengthwidthheight453152453152675904566135675xx xxxxxxxxxxx=××=−−=−−ªº=−−+¬¼ªº=−+¬¼(b) When( )( )( )()[]()33112211223:6 3135 3675 36271359202516212152025972486 cubic centimetersxVªº==−+=⋅−⋅+¬¼=−+==When( )( )( )[][]()32112211225:6 5135 5675 5612513525337575033753375750375 cubic centimetersxVªº==−+=⋅−⋅+¬¼=−+==When( )( )( )[][]()32112211227:6 7135 7675 7634313549472520586615472516884 cubic centimetersxVªº==−+=⋅−⋅+¬¼=−+==93.(a) Estimates will vary. Actual safe loads for12 :x=()()()2260.06 122.42 1238.71335.2561(using a calculator)S=−+=()()()2280.08 123.30 1251.93568.8225(using a calculator)S=−+=Difference in safe loads568.8225335.2561233.5664 pounds=−=(b) The difference in safe loads decreases in magnitude as the span increases.94.(a)()221.10.04750.0010.230.04751.0990.23TRBxxxxx=+=+−+=++.(b)(c) Stopping distance increases at an accelerating rate as speed increases95.False.()()23241 3112431xxxxx++=+++96.False.()()43464346369xxxx++−+=+−+=+=97.Because,mnmnxxx+=the degree of the product is.mn+98.If the degree of one polynomial ismandthe degree ofthe second polynomial isn(andnm>), the degree ofthe sum of the polynomials isn.99.()2239xx−=+/The student did not remember the middle term whensquaring the binomial. The correct method for squaringthe binomial is:()( )( )( )( )2222323369xxxxx−=−+=−+()cmx357()3Volumecm48637584mi hrx304055feetT75.95120.19204.36Section P.3Polynomials and SpecSection P.3Polynomials and Spe

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