数学课补充习题

1.SolvingLinearEquations(解线性方程4|6+2𝑠|−27≤Which1.SolvingLinearEquations(解线性方程4|6+2𝑠|−27≤Whichofthefollowingbestdescribesthesolutionstotheinequalityshown−24≤s≤−6≤s≤s≤0ors≥No4(80+𝑛)=Intheequationabove,kisaconstant.Forwhatvalueofkaretherenosolutionstothe8−9𝑥+1=𝑎𝑥+Intheequationshownabove,aisaconstant.Whichofthefollowingvaluesofaresultsinanequationwithexactlyonesolution?98Bothvalues4−3𝑦=6𝑦+4−WhichofthefollowingbestdescribesthesolutionsettotheequationshownTheequationhasnoTheequationhasexactlyonesolution,y=Theequationhasexactlyonesolution,y=!Theequationhasinfinitelymany17+27=Giventheaboveequation,whatisthevalueof10(−21𝑤+2.Interpretinglinearfunctions(线性函数 𝐶=1.5𝑏+2.Interpretinglinearfunctions(线性函数 𝐶=1.5𝑏+Thetotalcost,C,indollars,toproducebbooksisgivenbytheequationbelow.Whatisthemeaningof1.5intheequation?1.5bookswillcost$67.50toItcostsanextra$1.50foreachbookIfyouproduceonebook,youtotalcostwillbeThereisaflatfeeof$1.50toproduceanynumberof𝐵=Jingismakinghomemadepeanutbutter.Theequationaboveshowstheamountofpeanutyielded,B,incups,forAcupsofpeanuts.Whatpercentageofthevolumeofpeanutsislostwhenprocessingthemintopeanutbutter?𝑃=Astoreishavingasaleoneveryitempurchased.Irinadecidestotakeadvantageofthesalepurchasesasweater.Theequationthatgivestheafter-saleprice,P,ofIrina’ssweaterwithanoriginalcost,c,isshownabove.WhatpercentofftheoriginalcostdidIrinasave?𝑇=1200−Aprintshopcopiesandprintsdocumentsinlargevolumeforitscustomers.Foraparticularcopymachine,theequationabovegivestheamountoftoner,T,ingrams,leftaftermakingccopies.Howmanygramsoftonerareusedper 16𝐵+3.5𝑊=Antoinebikes 16𝐵+3.5𝑊=Antoinebikespartofthewayona22miletrailandwalkstherestoftheway.IfhespendshoursbikingandWhourswalking,thetripismodeledbytheequationshownabove.Whatisthemeaningofthe16Bintheequation?Antoinetravelsatotalof16Bmiles.Antoinebikesforatotalof16Bmiles.Antoinebikesfor16BmilesbeforestartinghisAntoinerideshisbikeatanaveragespeedof16Bmileper0.30𝑃+0.25𝐺=AhomeownerusesGhourofnaturalgasheatandPhoursofheatfromapelletstovetoheathouseonemonth,withatotalof57thermsofoutput.Howmanythermsperhourdoesthepelletstoveoutput?$ 𝐶=40(5−AfterHiro'sfamilyphotoshootthephotographersellstheprintedphotosbythesheet.Hirohas＄200creditfromapriorsession,andtheaboveequationgivesthetotalcreditleft,C,indollars,ifhebuys𝒔sheets.HowmanysheetscanHiropurchasewithhiscredit?58352003.LinearEquationWordProblems线性方程应用题Ameteorologistestimatesthatonasunnyday,theairtemperaturedecreasesbyabout4°Fforevery1,000feet(ft)ofelevationgain.Onacertain3.LinearEquationWordProblems线性方程应用题Ameteorologistestimatesthatonasunnyday,theairtemperaturedecreasesbyabout4°Fforevery1,000feet(ft)ofelevationgain.Onacertainday,theairtemperatureoutsideanairplaneflyingaboveSeattleis−58°F,andthegroundleveltemperatureinSeattleis70°F.Ifxistheheight,infeet,atwhichtheplaneisflying,whichofthefollowingbestmodelsthe70= x−!70=!x−−58=−4x+−58=4x+Atautstringoflength10inchesispluckedatthecenter.Thevibrationtravelsalongthestringataconstantrateofcinchespermillisecondinbothdirections.Ifxrepresentsthepositiononthestringfromtheleft-mostend,sothat0≤x≤10,whichofthefollowingequationscanbeusedtofindthelocationxofthevibrationafter0.3!|x-5|=0.!3!|x-0.3|=!|x-10|Intheyear2006,theaveragehomepricepersquarefootinacertaincountywas$98.Foreachyearbeforeorafter2006,theaveragepricepersquarefootincreasedbyapproximatelyInwhatyearscouldtheaveragehomepricepersquarefootbe2003and2002and2000and1999andOlivermowslawnsinhisneighborhood.Hecharges$10foreachregularyardhemows,andhechargesanextra$5foreachlargeyardthathemows.Inoneweekhemowed6morelargeyardsthanregularyardsandmade$265.IfrrepresentsthenumberofregularyardsthatOlivermowed,whichequationbestmodelsthesituation?10(r+6)+10r+Annaspent3hoursinhergardenplanting6rosebushes.Toplantarosebush,shefirstdugthehole,thenrefilledtheholewiththerootball,dirt,andcompost.Shespenttwiceas10r+Annaspent3hoursinhergardenplanting6rosebushes.Toplantarosebush,shefirstdugthehole,thenrefilledtheholewiththerootball,dirt,andcompost.Shespenttwiceaslongdiggingtheholeforeachplantasshedidrefillingit.Ifmrepresentstheminutesspentdiggingaholeforasinglerosebush,whichequationbestmodelsthesituation?!3!0!Apopularcandyismanufacturedtoweigh0.16ouncesperpiece.Thepiecesaresoldinpackagesof36.Iftheallowableamountofvariationinweightforonepieceofcandyis0.03ounces,whichofthefollowingequationscanbeusedtodeterminethehighestandlowestallowableweight,w,ofapackageof36pieces?AssumethattheweightofthepackagingisThemaximumactivitylevelofaparticularenzymeis60micromolarsperminute(!!)occursatatemperatureof20degreesCelsius(°C).Forevery2°Caboveorbelow20°C,enzymeactivitydecreasesby8!!.Whichofthefollowingequationscanbeusedtofindtemperatures,T,atwhichtheenzymeactivitylevelis40!!A．0B．0C．0D．08.Ucheisacartographer.HepicksascaletofitamapofIndiaontoapageofanatlas.Thepageis12by12inches,with0.75inchmarginsonall4sides.Indiameasures3,214kilometersfromnorthtosouthand2,933kilometersfromwesttoeast.UchewantsthelongestdimensionofIndiatofitexactlyinbetweenthemarginsofthepage.IfkisthenumberofkilometersinchinUche'sscale,whichequationbestmodelsthe!=12k=!=inchinUche'sscale,whichequationbestmodelsthe!=12k=!=AlmaandErikaworkparttimestockingshelvesatagrocerystore.At7:00a.m.onSaturday,Almabeginsunpackingboxesatarateof1boxevery6minutes.Erikajoinsherat7:45a.m.andunpacks1boxevery5minutes.Whenfinishedwiththistask,atotalof24boxeshavebeenunpackedsince7:00a.m.IfxrepresentsthenumberofminutesforwhichAlmahasbeenworking,whichofthefollowingequationsbestmodelsthex+(- x+(x− 6x+6x+5(x−!!Onahighway,driversarerequiredtomaintainaspeedofbetween55and65milesperhour(mph).A$7penaltyisassessedforeach1mphadriver’sspeedisoutsidethisrange.Ifadriverreceivesa$42penalty,whatarepossiblevaluesforhisspeed?49and49and54and54andOn 2014,approximately450thousandbuildingsintheUnitedStates(US)solarpanels.Thisnumberincreasedbyatotalofabout180thousandoverthenext12months.Assumingaconstantrateofchange,approximatelyhowmanymonthsafterJanuary1st,would900thousandbuildingsintheUShavesolarThegasmileageforacaris23milespergallonwhenthecartravelsat60milesperhour.Thecarbeginsatripwith13gallonsinitstank,travelsatanaveragespeedof60milesperhourforhhours,andendsthetripwith10gallonsinitstank.Whichofthefollowingequationsbestmodelsthis13−!"#13−!"#Akilowatt(kW)isequalto1,000watts(W),andakilowatt-hour(kWh)isaunitofenergyequivalenttoonekilowattofpowerexpendedforonehour.For13−!"#Akilowatt(kW)isequalto1,000watts(W),andakilowatt-hour(kWh)isaunitofenergyequivalenttoonekilowattofpowerexpendedforonehour.Forexample,anelectricalloadratedat1kWthatoperatesfor1houruses1kWhofenergy.Electricityinacertaincitycosts$0.14perkilowatt-hour,andalightbulbratedat60Woperatesinthatcityforonehourdayfor200consecutivedays.Whichequationbestmodelsthecostindollars,c,ofthelightbulboverthistimeperiod?c=!"2!"!,!!!Erika'stimesforthe1-milerundecreasedconsistentlythroughouthertrackseason.Sheestimatesthathertimeforthe1-milerundecreasedbyabout15seconds(secs)forevery2weeksoftraining.IfErikaranamilein8minutes(mins)and20secsatthestartoftheseason,andxweeksintohertrainingranamilein7minsand5secs,whichofthefollowingequationsbestmodelsthe4.Linearinequalitywordproblems线性不等式应用题Membersofthewrestlingteamareplanningto4.Linearinequalitywordproblems线性不等式应用题Membersofthewrestlingteamareplanningtosellpre-orderedprogramsatmatches.Thecosttoprinttheprogramsis$150plus$0.50perprogram.Theyplantoselleachprogramfor$2.Ifprofitistheamountofmoneyearnedfromsellingprogramsminustheexpensesofprintingprograms,howmanyprogramsmusttheyselltomakeaprofitofatleastChristopherhasatmost$18.50tospendataconveniencestore.Hebuysonebagofbananas$1.50andabottleofapplejuicefor$1.55.Ifgasolineatthisstorecosts$2.35pergallon,ofthefollowingnumberofgallonscanhebuyforhiscarwithoutexceedinghisJonasistravelingbybustovisitafriendwholives300milesaway.ThefriendhasaskedJonastocallatleast30minutesbeforearriving,sohecanpickupJonas.Jonas'sbustravelsataconstantspeedof45milesperhour.Whichinequalityshowsthenumberoftravelhours,t,beforewhichJonasshouldcallhist≤6!t≥6!t≤6!t≥6!Oneparticularhotelinthedowntownareacosts$90anight.Anadditional10%taxisaddedtotheoriginalcostofthehotelroom.Thereisalsoaone-time$12parkingcharge,andafamilycanexpecttospend$30ontipsduringtheirstay.Howmanynightscanafamilyspendatthehotelwithoutexceedingtheirbudgetof56AnaudiologististestingapatienttodetermineAnaudiologististestingapatienttodeterminethesoftestsoundofaspecificfrequencythatthepatientreportshearing.Shebeginswitha10decibel(dB)soundfortrial1,thenincreasesthevolumeby2dBforeachtrialafterthat.Ifthepatientcanhearallsoundsofthatfrequencythathaveavolumelouderthan26dB,andtrepresentsthetrialnumbersthatthepatientcanwhichofthefollowinginequalitiesbestmodelsthesituationdescribed2t+10≥2t+10>2(t−1)+10≥2(t−1)+10>JoanneandRichardvolunteeratahospital.Joannevolunteers4hoursmoreperweekRicharddoes.Inagivenweek,theydonotvolunteerformorethanacombinedtotalof16hours.IfxisthenumberofhoursthatRichardvolunteers,whichinequalitybestmodelsthis𝑥+4≤2𝑥+4≤2𝑥+8≤2𝑥−4≤Mikalhasasummerprojectinwhichhemustcompleteatleast35hoursofcommunityserviceatacitypark.Eachdaythathegoestothepark,hevolunteersfor7hours.Ittakes1.5hourstogettotheparkeachway,whichalsocountstowardhiscommunityserviceWhichofthefollowinginequalitiescanbeusedtofindthenumberofdays,d,Mikalmustvolunteerattheparktocompletehissummerproject?7d>7d≥7d+3>7d+3d≥Aninsuranceagentsellsaninsurancepolicywithanout-of-pocketmaximumof$5,000.Out-of-pocketexpensesincludeanydeductiblesandcoinsurancethattheclientpaysbeyondthenormalmonthlypremium.Theclienthasadeductibleof$250.Thismeansthattheclienthastopayallofthefirst$250ofexpensesinsuredbythepolicy.Afterthat,theclienthasa20%co-insurance,meaningtheclientpays20%oftheinsuredexpensesandtheinsurancecompanypaystheremainder.Whichinequalityrepresentshowmuchthetotalinsuredexpenses,x,couldbeiftheclienthasnotyetreachedtheout-of-pocketx<x<x<x<5.Graphinglinearequations线性方程数形结合)1.Whichofthefollowingrepresents5.Graphinglinearequations线性方程数形结合)1.Whichofthefollowingrepresentsthegraphoftheequation3y-7=Theequationsx+y=3and-5x-5y=-15aregraphedinthexy-plane.Whichofthefollowingmustbetrueofthegraphsofthetwoequations?Theslopeofthegraphofx+y=3is11andtheslopeofthegraphof-5x-5y=-15isThegraphsofthetwoequationsareperpendicularThey-interceptofthegraphof-5x-5y=-15is-Thegraphsofthetwoequationsarethesame3.Whichofthefollowingrepresentsthegraphoftheequationx=−!!=4.Thelinerepresentedbytheequation −𝑥isgraphedin=4.Thelinerepresentedbytheequation −𝑥isgraphedinthexy-plane.WhichoffollowingstatementscorrectlydescribesthegraphoftheThelineisperpendiculartothegraphx+y=Thelinehasanegativeslopeandapositivey-Thelinehasapositiveslopeandanegativey-Thex-interceptisequaltothenegativeofthey-5.Ifkisarationalconstantnotequalto1,whichofthefollowinggraphsrepresentsthe6.Whatistheequationofthelinegraphedinthexy-planethatpassesthroughthepoint(-4,-5)isparalleltothelinewhoseequationis3x-4y=-A.y=−!𝑥+!B.y=!𝑥−!C.y=!𝑥−!D.y=−!𝑥−!7.Theequationsbelowaregraphedinthexy-plane.Whichequation'sgraphwillhaveaslope!anday-interceptof!A.B.7x-8y=-C.D.7x-8.TheequationD.7x-8.TheequationforthegravitationalpotentialenergyUofa1-kilogramobjectonEarthrestingmetersabovethegroundtsecondsafterplacementisU=9.8hjoules.WhichofthefollowingisagraphofUversustfora1-kilogramobject2metersabovetheground?6.LinearFunctionWordProblems线性函数应用题Mariaburnsabout600caloriesperhourjoggingandabout4506.LinearFunctionWordProblems线性函数应用题Mariaburnsabout600caloriesperhourjoggingandabout450caloriesperhourbiking.Mariaspendsxhoursperdaybiking,and!asmuchtimejogging,whichofthe!functionsbestmodelstheamountofcalories,C,thatMariaburnsinonedayfromjoggingA.B.C.D.Mikaylawalkedninemilesinthreehours.Shewalkedfmilesduringthefirsthourand!!theremainingdistanceduringthesecondhour.Whichofthefollowingfunctionsbestrepresentsthenumberofmilesinthethirdhour,t,shehadtowalkintermsofthenumberofmileswalkedinthefirsthour,fA.B.f!C.f!D.ThegastankinMs.Brown'scarholdsatotalof15gallons.Atanygiventime,howmanygallons,g,willMs.Brownhavetopumpintohercartofillhertankgiventhefractionofthetank,f,alreadyfilled?A.!C.D.!Sterlingsilverisanalloyofsilverthatis92.5%puresilver.Ifxgramsofsterlingsilveraremixedwithygramsofan88%silveralloytoproducea91%silveralloy,whichoffollowingequationscorrectlyrelatesxandA.B.C.D.C.D.Gustavisstartingaspecialsprintingregimeninoutdoortrack.Theregimensuggestssprintingforacertainnumberofseconds,s,atfirst.Thesecondtimehesprints,heshouldrun150moresecondsthanthefirsttime.Forthethirdtime,theregimensuggestssprintingtwicethenumberofsecondsasthefirsttime.Finally,theregimensuggestsan80-secondsprint.Whichofthefollowingfunctionscanbeusedtofindthetotalnumberofseconds,t,suggestedbytheentiresprintingA.B.C.!D.Correctanswer:In2007,approximately50%oftheworld'spopulationlivedinrural(definedasnon-urban)areas.From2005to2013,thepercentoftheworld'spopulationlivinginruralareasdecreasedbyabout0.5percentagepointsperyear.Iftrepresentsyearssince2005,whichofthefollowingequationsbestmodelsthepercentoftheworld'spopulationlivinginruralareas,r,from2005toA.B.C.D.7.Systemsoflinearinequalitieswordproblems不等式组线性规划应用题1.Atennisclubisorganizinggrouplessons.Theclubsupplies40newballsfor7.Systemsoflinearinequalitieswordproblems不等式组线性规划应用题1.Atennisclubisorganizinggrouplessons.Theclubsupplies40newballsforeachplayerwhichcost$1each.Eachplayerpays$300forthelessons.Theclubmustpayeachinstructor$1,000forconductingthelessons,andtheremustbeatleast1instructorforevery6players.Whichamountofplayersandinstructorsmeetstheserequirementsandstillgivestheclubanet6playersand210playersand313playersand216playersand32.Abottleweighs50gramsandholdsupto2litersofliquid.Achemistisfillingthebottlewithxgramsofliquidethanolandygramsofliquidwater.Ethanolhasadensityof789gramsperliterandwaterhasadensityof1,000gramsperliter.Thechemistwantsthemassofthefilledbottletobelessthan1,800grams.Whichofthefollowingsystemsofinequalitiesbestmodelsthedescribedxy789x1,000y789x1,000yxyxyyy 3.Derinistravellingabroadwitha$25callingcard,whichwasagiftfromhergrandmother.TheratetocallJapan,whereherboyfriendisliving,is$0.19perminute.HerfamilyisinTurkey,wherethecallingrateis$0.12perminute.Derinpromisedhergrandmothershewouldspendatleast30ofherminutesonkeepingintouchwithfamily.WhichofthefollowingsystemsofinequalitiesrepresentstherelationshipbetweenJ,thenumberofminutesDerincouldcallJapan,andT,thenumberofminutesDerincouldcallT208TJT208TT250.19T250.19TTJ4.Manojrunsabusinessatabaseballstadium.Thismonth,withabudgetof$17,000,Manojbuysppoundsofpeanutsat$1.10perpoundandpayshissalespeople$200each.Therearessalespeopleintotal,anditispredictedthateachcansellamaximumof1,875poundsofpeanutsthismonth.Manojwillnotbuymorepeanutsthanwhathepredictshissalespeoplecansell.WhichofthefollowingsystemsofinequalitiesrepresentsthisppA.C.＄1,7000ppA.C.＄1,70001,875ss1,875sD.＄1,70001,875s5.Ausedcardealerhas20vehicles,allcarsandtrucks.Hewouldliketopaintandclearcoatasmanyofthemaspossiblewiththe260litersofpaintand300litersofclearcoatthathehas.Ittakes13.2litersofpaintand9.5litersofclearcoatforonecar.Ittakes1.5timesthoseamountsforonetruck.Giventherelevantequationsgraphedatleft,whichofthefollowingcouldbetheamountofcarsandtrucksthatreceivedpaintandclear10carsand66carsand1014carsand1111carsand146.Somezoomonkeysareonadietoffruitandnuts.Fruithasabout13.3grams(g)ofsugarpercupand1.36gofproteinpercup.Nutshaveabout4.04gofsugarpercupand15.56gofproteinpercup.Eachmonkeymustgetbetween70gand90gofsugarperdayandatleast85gofperday.Whichofthefollowingdailydietsfitsthemonkeys'0cupsoffruitand16cupsof4cupsoffruitand8cupsof8cupsoffruitand4cupsofD.16cupsoffruitand0cupsof7.Amemorychipisbeingdesignedtoholdanumberoftransistorsandheatsinks.Theholdmemorywhiletheheatsinkscoolthechip.Theremustbeatleastoneheatsinkfor2,000transistorstopreventoverheating.Also,eachtransistorhasanareaof2.02,000transistorstopreventoverheating.Also,eachtransistorhasanareaof2.01010mm2(squaremillimeters),eachheatsinkhasanareaof3.6106mm2,andthetotalareaoftransistorsandheatsinksmustbeatmost2mm2.Whatistheapproximatemaximumnumberofthatthechipcanholdaccordingtothis2.78B.5.56C.1.0D.8.Abusinessanalystisdecidingtheamountoftimeallottedtoeachemployeeformeetingsandtraining.Hewantsthesumofmeetingandtrainingtimetobenomorethan16hourspermonth.Also,thereshouldbeatleastonetraininghourforeverytwomeetinghours.Finally,thereshouldbeatleast2meetinghourspermonthtodiscussshort-termgoals.WhatisthedifferencebetweenthemaximumandminimumnumberofmonthlytraininghoursthatcouldbeallottedtoanA.10B.13C.14D.169.ThesupplyanddemandcurvesforaproductaregivenbyfunctionsSandD,respectively.Foragivennumberofunits,Q,Sistheminimumprice,indollars,thatthesuppliershouldaccept.isthemaximumprice,indollars,whereconsumerswillpurchasethatnumberofS(Q)450.04QFortheaboveequations,whichofthefollowingcombinationsofpriceandquantitybetweenthemaximumconsumerpriceandminimumsupplier500unitsat1,000unitsat1,500unitsat2,450unitsat10.Abakery10.AbakeryneedstomakecakesforMother'sDay,andmustpreparebystoringingredients.Eachcakeismadefrom4cupsofbatterand7cupsoffrosting.Thebakeryhasstorageforupto2150cupsofingredients.Thetwoequationsrelatedtotheseconstraintsaregraphedatleft.Ifthebakerywantsnobatterleftover,whichofthefollowingcouldbethevolumeofbatterfrostingthatthey80cupsofbatterand60cupsof90cupsofbatterand70cupsof80cupsofbatterand80cupsof70cupsofbatterand70cupsof8.SolvingSystemsofLinearEquations(解线性方程组!𝑝+𝑘𝑞=𝑞=!8.SolvingSystemsofLinearEquations(解线性方程组!𝑝+𝑘𝑞=𝑞=!𝑝−!! Considerthesystemofequationsabove,wherekisaconstant.Forwhichvalueofkisno(p,q)-02NoneoftheForwhatvalueofcdoestheabovesystemoflinearequationsinthevariablesyandzinfinitelymanyWhichofthefollowingchoicesofbwillresultinasystemoflinearequationswithexactlyonesolution?bcanbeanybcanbeanynumberexcept1.2bcanbeanynumberexcept−1.2Considerthesystemofequationsabove,wherecisaconstant.Forwhichvalueofcarethereno(a,b)solutions?0!!!Noneofthep=2q−1Considerthesystemofequationsabove,whereaisaconstant.Forwhichvalueofais(p,q)=(1,1)asolution?012Noneofthe𝑎𝑦−!+!=2Noneofthe𝑎𝑦−!+!=3𝑦−𝑥−1= Considerthesystemofequationsabove,whereaisaconstant.Forwhichvalueofaareinfinitelymany(x,y)−!!!3NoneoftheConsiderthesystemofequationsabove,whereaisaconstant.Forwhatvalueofaareno(x,y)Forwhatvalueofkdoestheabovesystemoflinearequationsinthevariablesxandyhave9.SystemsofLinearEquationsWordProblems线性方程组应用题Jerryhasalargecarwhichholds22gallonsoffuelandget20milespergallon.Katehasasmallercarwhichholds16.59.SystemsofLinearEquationsWordProblems线性方程组应用题Jerryhasalargecarwhichholds22gallonsoffuelandget20milespergallon.Katehasasmallercarwhichholds16.5gallonsoffuelandgets30milespergallon.Ifbothcarshaveafulltankoffuelnowanddrivethesamedistance,inhowmanymileswilltheremainingineachtankbethePaulo'seconomicscourserequirestwopapers−−onelongandoneshort−−throughoutthesemester.Thenumberofpages,l,inthelongpaperisonemorethantwotimesthenumberofpages,s,intheshortpaper.Ifthetotalnumberofpagesforbothpapersis40,howmanypagesmustbeinthelongsAcharityisplanningaraffletoraisemoney.Thereare125regularticketsand50premiumtickets.Thecostofapremiumticketis25%morethanaregularticketplusanadditional$1.50.Theraffleorganizersexpecttosellallofthetickets,andtheywanttocollect$1,950fromtheticketsales.Whichofthefollowingsystemsofequationscanbeusedtotheprice,p,ofeachpremiumticketandtheprice,r,ofeachregularA.B.Thelengthofarectangularswimmingpoolistwicethewidth.Iftheperimeteris120thenwhatisthewidthinForahighschooldinnerfunctionforteachersandstudents,themathdepartmentbought6casesofjuiceand1caseofbottledwaterforatotalof$135.Thesciencedepartmentbought4casesofjuiceand2casesofbottledwaterforatotalof$110.Howmuchdidacaseofjuice10.SolvingQuadraticEquations解二次方程1.0!Intheequationabove,bisaconstant.If−!and!"aresolutionstotheequation,thenwhatis valueof−!!!−!!2.(v10.SolvingQuadraticEquations解二次方程1.0!Intheequationabove,bisaconstant.If−!and!"aresolutionstotheequation,thenwhatis valueof−!!!−!!2.(v+!)2−!Whatisthesumofthesolutionstotheequation−!−!0−! Intheequationabove,cisaTheequationhassolutionsat−!and−3.Whatisthevalueof!!!!!3D.Intheequationabove,bisaconstant.Iftheequationhasthesolutionsx=3±√5,whatistheof5.−(!"−b)=−!Ifb=sandb=tarethesolutionstotheequationabove,whatisthevalueof−!!!−!!! Intheequationabove,kisaconstant.Forwhatvalueofkdoestheequationhavenoreal−!!!−!!!!x2−!x−!= WhatarethesolutionstotheequationA.x=1andx=−C.x=2andx=−−!!!!x2−!x−!= WhatarethesolutionstotheequationA.x=1andx=−C.x=2andx=−!!−− andx=!D.x=!andx=! !!! Intheequationabove,cisaTheequationhassolutionsatt=!andt=−!.Whatisthevalueof!!−!–!D.––! Intheequationabove,kisaconstant.Theequationhassolutionsat7and−2.Whatisthevalueofk?5910.at2+!t−!Theaboveequationhassolutionsatt=−8andt=1.Whatisthevalueoftheconstant11.Intheequationabove,kisaconstant.Ifthesumofthesolutionstotheequationis0,whatisthevalueofk?012412.Letx=qandx=rbesolutionstotheequationshownabove,withq>r.Whatisthevalueof11.Interpretingnonlinearexpressions非线性表达式!1.F(11.Interpretingnonlinearexpressions非线性表达式!1.F(t)=5ThefunctionF(t)definedabovegivesthepercentageofinformationDiannaretainedtdaysaftermemorizinglinesforaplay.Assumingshedidnotworkonherlinesagain,whatisthebestdescriptionof0.95inthisDiannawillforget95%ofwhatsheretainedonedayago.Diannawillforget95%ofwhatsheretainedtwodaysago.Diannawillremember95%ofwhatsheretainedonedayago.Diannawillremember95%ofwhatsheretainedtwodaysTheamountofwatervapor,v(ingrams),thatwillsaturate1kilogramofdryairwhenthetemperatureisddegreesCelsiusisapproximatedbythefollowingequation.Foreachincreaseof1degree,whatisthepercentincreaseintheamountofwatervaportosaturatetheairaccordingtothis Acertaintypeofmolluskhasashellintheshapeofaspiral,asshownbelow.Thedistance,r,fromtheorigintoapointonthespiralismodeledbytheequationabove,whereθistheangle,inradians,measuredcounterclockwisefromthepositivex-axistothesamepointonthespiral.Whatisthebestdescriptionof0.5inthisformula?0.5istherateofincreaseoftheradiusper2π0.5istheratioofradiithatdifferby2π0.5unitsisthelengthoftheradiuscorrespondingto0.5unitsisthelengthoftheradiuscorrespondingto AccordingtoBernoulli'sequationbelow,theproductofthearea,A1,ofacross-sectionofahoseataparticularpointandthevelocity,V1,ofwatertravelingthroughthehoseatthatpointwillbeequaltotheproductofthearea,A2,ofasecondcross-sectionofthesamehoseatasecondpointandthevelocity,V2,ofwatertravelingthroughthehoseatthesecondpoint.Ifsomeonecovers!oftheopeningofahose,howwillthevelocityofthewatercomingoutof!hoseThevelocityofIfsomeonecovers!oftheopeningofahose,howwillthevelocityofthewatercomingoutof!hoseThevelocityofthewaterthroughthepartiallycoveredopeningwillbe!ofthe!throughthefullThevelocityofthewaterthroughthepartiallycoveredopeningwillbe!ofthe!throughthefullThevelocityofthewaterthroughthepartiallycoveredopeningwillbe!ofthe!throughthefullThevelocityofthewaterthroughthepartiallycoveredopeningwillbe4timesthevelocitythroughthefullopening.Biologistsstockedalakewithanewspeciesoffish.Thenumberofthenewspeciesoffishinlake,P(t),tyearsafterbeingstocked,isshownabove.Howmanyfishdidthebiologistsinitiallyaddtothelake? A(x)!Adoughnutfranchisehasdeterminedthatitsaveragecostperunit(doughnut),A(x),isgivenbytheabovefunction,wherexisthenumberofunitsproduced,x>0.WhichofthefollowingbestdescribeswhathappenstotheaveragecostperdoughnutasthenumberofdoughnutsproducedTheaveragecostgetscloserandclosertoTheaveragecostgetscloserandcloserto$0.15perdoughnut.Theaveragecostis$0.15perdoughnut.Theaveragecostgetscloserandcloserto$20,000perReemisatestdriverforanautomobilecompany.Thefollowingformulagivesthetotaldistance,d,infeetthatReemdrovealuxurycarinthefirsttsecondsafteridlingataspeedof0milesperhour,uptothetimewhenshepassedaparticularsafetycone.ComparedtothetimeittookReemtopassthesafetycone,howlongdidittaketopassathatwas!ofthedistancefromthe!!"ofthetimeitrequiredtopassthe!ofthetimeitrequiredtopassthe!!ofthetimeitrequiredtopassthe!D.!oftheD.!ofthetimeitrequiredtopassthe! ThetemperatureTindegreesCelsiusofachilleddrinkaftermminutessittingonatableisgivenbythefollowingfunction.Whatisthebestinterpretationofthenumber32inthisThedrinkisoriginally32degreesEvery32minutes,thetemperaturewarmsby3degreesAfter32minutes,thedrinkwillfullywarmtotheambientAftersittingforaverylongtime,thedrinkwillwarmupto32degrees12Quadraticandexponentialwordproblems二次和指数函数应用题1.Theamountofcarbon-14ina12Quadraticandexponentialwordproblems二次和指数函数应用题1.Theamountofcarbon-14inasampledecreasesoncetheorganismfromwhichitcameisnolongeralive.Asampleofanancientfernfossilcontains42%oftheamountofcarbon-14inlivingferns.Thefractionofcarbon-14,F,leftinthefossilsampletyearsafteritdiedcanbemodeledbythefollowing!Approximatelyhowoldisthefern4,0005,0007,00010,000Aninvestment