Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

# Recent problems solved by 'jim_thompson5910'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 4740..4769 , 4770..4799 , 4800..4829 , 4830..4859 , 4860..4889 , 4890..4919 , 4920..4949 , 4950..4979 , 4980..5009 , 5010..5039 , 5040..5069 , 5070..5099 , 5100..5129 , 5130..5159 , 5160..5189 , 5190..5219 , 5220..5249 , 5250..5279 , 5280..5309 , 5310..5339 , 5340..5369 , 5370..5399 , 5400..5429 , 5430..5459 , 5460..5489 , 5490..5519 , 5520..5549 , 5550..5579 , 5580..5609 , 5610..5639 , 5640..5669 , 5670..5699 , 5700..5729 , 5730..5759 , 5760..5789 , 5790..5819 , 5820..5849 , 5850..5879 , 5880..5909 , 5910..5939 , 5940..5969 , 5970..5999 , 6000..6029 , 6030..6059 , 6060..6089 , 6090..6119 , 6120..6149 , 6150..6179 , 6180..6209 , 6210..6239 , 6240..6269 , 6270..6299 , 6300..6329 , 6330..6359 , 6360..6389 , 6390..6419 , 6420..6449 , 6450..6479 , 6480..6509 , 6510..6539 , 6540..6569 , 6570..6599 , 6600..6629 , 6630..6659 , 6660..6689 , 6690..6719 , 6720..6749 , 6750..6779 , 6780..6809 , 6810..6839 , 6840..6869 , 6870..6899 , 6900..6929 , 6930..6959 , 6960..6989 , 6990..7019 , 7020..7049 , 7050..7079 , 7080..7109 , 7110..7139 , 7140..7169 , 7170..7199 , 7200..7229 , 7230..7259 , 7260..7289 , 7290..7319 , 7320..7349 , 7350..7379 , 7380..7409 , 7410..7439 , 7440..7469 , 7470..7499 , 7500..7529 , 7530..7559 , 7560..7589 , 7590..7619 , 7620..7649 , 7650..7679 , 7680..7709 , 7710..7739 , 7740..7769 , 7770..7799 , 7800..7829 , 7830..7859 , 7860..7889 , 7890..7919 , 7920..7949 , 7950..7979 , 7980..8009 , 8010..8039 , 8040..8069 , 8070..8099 , 8100..8129 , 8130..8159 , 8160..8189 , 8190..8219 , 8220..8249 , 8250..8279 , 8280..8309 , 8310..8339 , 8340..8369 , 8370..8399 , 8400..8429 , 8430..8459 , 8460..8489 , 8490..8519 , 8520..8549 , 8550..8579 , 8580..8609 , 8610..8639 , 8640..8669 , 8670..8699 , 8700..8729 , 8730..8759 , 8760..8789 , 8790..8819 , 8820..8849 , 8850..8879 , 8880..8909 , 8910..8939 , 8940..8969 , 8970..8999 , 9000..9029 , 9030..9059 , 9060..9089 , 9090..9119 , 9120..9149 , 9150..9179 , 9180..9209 , 9210..9239 , 9240..9269 , 9270..9299 , 9300..9329 , 9330..9359 , 9360..9389 , 9390..9419 , 9420..9449 , 9450..9479 , 9480..9509 , 9510..9539 , 9540..9569 , 9570..9599 , 9600..9629 , 9630..9659 , 9660..9689 , 9690..9719 , 9720..9749 , 9750..9779 , 9780..9809 , 9810..9839 , 9840..9869 , 9870..9899 , 9900..9929 , 9930..9959 , 9960..9989 , 9990..10019 , 10020..10049 , 10050..10079 , 10080..10109 , 10110..10139 , 10140..10169 , 10170..10199 , 10200..10229 , 10230..10259 , 10260..10289 , 10290..10319 , 10320..10349 , 10350..10379 , 10380..10409 , 10410..10439 , 10440..10469 , 10470..10499 , 10500..10529 , 10530..10559 , 10560..10589 , 10590..10619 , 10620..10649 , 10650..10679 , 10680..10709 , 10710..10739 , 10740..10769 , 10770..10799 , 10800..10829 , 10830..10859 , 10860..10889 , 10890..10919 , 10920..10949 , 10950..10979 , 10980..11009 , 11010..11039 , 11040..11069 , 11070..11099 , 11100..11129 , 11130..11159 , 11160..11189 , 11190..11219 , 11220..11249 , 11250..11279 , 11280..11309 , 11310..11339 , 11340..11369 , 11370..11399 , 11400..11429 , 11430..11459 , 11460..11489 , 11490..11519 , 11520..11549 , 11550..11579 , 11580..11609 , 11610..11639 , 11640..11669 , 11670..11699 , 11700..11729 , 11730..11759 , 11760..11789 , 11790..11819 , 11820..11849 , 11850..11879 , 11880..11909 , 11910..11939 , 11940..11969 , 11970..11999 , 12000..12029 , 12030..12059 , 12060..12089 , 12090..12119 , 12120..12149 , 12150..12179 , 12180..12209 , 12210..12239 , 12240..12269 , 12270..12299 , 12300..12329 , 12330..12359 , 12360..12389 , 12390..12419 , 12420..12449 , 12450..12479 , 12480..12509 , 12510..12539 , 12540..12569 , 12570..12599 , 12600..12629 , 12630..12659 , 12660..12689 , 12690..12719 , 12720..12749 , 12750..12779 , 12780..12809 , 12810..12839 , 12840..12869 , 12870..12899 , 12900..12929 , 12930..12959 , 12960..12989 , 12990..13019 , 13020..13049 , 13050..13079 , 13080..13109 , 13110..13139 , 13140..13169 , 13170..13199 , 13200..13229 , 13230..13259 , 13260..13289 , 13290..13319 , 13320..13349 , 13350..13379 , 13380..13409 , 13410..13439 , 13440..13469 , 13470..13499 , 13500..13529 , 13530..13559 , 13560..13589 , 13590..13619 , 13620..13649 , 13650..13679 , 13680..13709 , 13710..13739 , 13740..13769 , 13770..13799 , 13800..13829 , 13830..13859 , 13860..13889 , 13890..13919 , 13920..13949 , 13950..13979 , 13980..14009 , 14010..14039 , 14040..14069 , 14070..14099 , 14100..14129 , 14130..14159 , 14160..14189 , 14190..14219 , 14220..14249 , 14250..14279 , 14280..14309 , 14310..14339 , 14340..14369 , 14370..14399 , 14400..14429 , 14430..14459 , 14460..14489 , 14490..14519 , 14520..14549 , 14550..14579 , 14580..14609 , 14610..14639 , 14640..14669 , 14670..14699 , 14700..14729 , 14730..14759 , 14760..14789 , 14790..14819 , 14820..14849 , 14850..14879 , 14880..14909 , 14910..14939 , 14940..14969 , 14970..14999 , 15000..15029 , 15030..15059 , 15060..15089 , 15090..15119 , 15120..15149 , 15150..15179 , 15180..15209 , 15210..15239 , 15240..15269 , 15270..15299 , 15300..15329 , 15330..15359 , 15360..15389 , 15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629 , 15630..15659 , 15660..15689 , 15690..15719 , 15720..15749 , 15750..15779 , 15780..15809 , 15810..15839 , 15840..15869 , 15870..15899 , 15900..15929 , 15930..15959 , 15960..15989 , 15990..16019 , 16020..16049 , 16050..16079 , 16080..16109 , 16110..16139 , 16140..16169 , 16170..16199 , 16200..16229 , 16230..16259 , 16260..16289 , 16290..16319 , 16320..16349 , 16350..16379 , 16380..16409 , 16410..16439 , 16440..16469 , 16470..16499 , 16500..16529 , 16530..16559 , 16560..16589 , 16590..16619 , 16620..16649 , 16650..16679 , 16680..16709 , 16710..16739 , 16740..16769 , 16770..16799 , 16800..16829 , 16830..16859 , 16860..16889 , 16890..16919 , 16920..16949 , 16950..16979 , 16980..17009 , 17010..17039 , 17040..17069 , 17070..17099 , 17100..17129 , 17130..17159 , 17160..17189 , 17190..17219 , 17220..17249 , 17250..17279 , 17280..17309 , 17310..17339 , 17340..17369 , 17370..17399 , 17400..17429 , 17430..17459 , 17460..17489 , 17490..17519 , 17520..17549 , 17550..17579 , 17580..17609 , 17610..17639 , 17640..17669 , 17670..17699 , 17700..17729 , 17730..17759 , 17760..17789 , 17790..17819 , 17820..17849 , 17850..17879 , 17880..17909 , 17910..17939 , 17940..17969 , 17970..17999 , 18000..18029 , 18030..18059 , 18060..18089 , 18090..18119 , 18120..18149 , 18150..18179 , 18180..18209 , 18210..18239 , 18240..18269 , 18270..18299 , 18300..18329 , 18330..18359 , 18360..18389 , 18390..18419 , 18420..18449 , 18450..18479 , 18480..18509 , 18510..18539 , 18540..18569 , 18570..18599 , 18600..18629 , 18630..18659 , 18660..18689 , 18690..18719 , 18720..18749 , 18750..18779 , 18780..18809 , 18810..18839 , 18840..18869 , 18870..18899 , 18900..18929 , 18930..18959 , 18960..18989 , 18990..19019 , 19020..19049 , 19050..19079 , 19080..19109 , 19110..19139 , 19140..19169 , 19170..19199 , 19200..19229 , 19230..19259 , 19260..19289 , 19290..19319 , 19320..19349 , 19350..19379 , 19380..19409 , 19410..19439 , 19440..19469 , 19470..19499 , 19500..19529 , 19530..19559 , 19560..19589 , 19590..19619 , 19620..19649 , 19650..19679 , 19680..19709 , 19710..19739 , 19740..19769 , 19770..19799 , 19800..19829 , 19830..19859 , 19860..19889 , 19890..19919 , 19920..19949 , 19950..19979 , 19980..20009 , 20010..20039 , 20040..20069 , 20070..20099 , 20100..20129 , 20130..20159 , 20160..20189 , 20190..20219 , 20220..20249 , 20250..20279 , 20280..20309 , 20310..20339 , 20340..20369 , 20370..20399 , 20400..20429 , 20430..20459 , 20460..20489 , 20490..20519 , 20520..20549 , 20550..20579 , 20580..20609 , 20610..20639 , 20640..20669 , 20670..20699 , 20700..20729 , 20730..20759 , 20760..20789 , 20790..20819 , 20820..20849 , 20850..20879 , 20880..20909 , 20910..20939 , 20940..20969 , 20970..20999 , 21000..21029 , 21030..21059 , 21060..21089 , 21090..21119 , 21120..21149 , 21150..21179 , 21180..21209 , 21210..21239 , 21240..21269 , 21270..21299 , 21300..21329 , 21330..21359 , 21360..21389 , 21390..21419 , 21420..21449 , 21450..21479 , 21480..21509 , 21510..21539 , 21540..21569 , 21570..21599 , 21600..21629 , 21630..21659 , 21660..21689 , 21690..21719 , 21720..21749 , 21750..21779 , 21780..21809 , 21810..21839 , 21840..21869 , 21870..21899 , 21900..21929 , 21930..21959 , 21960..21989 , 21990..22019 , 22020..22049 , 22050..22079 , 22080..22109 , 22110..22139 , 22140..22169 , 22170..22199 , 22200..22229 , 22230..22259 , 22260..22289 , 22290..22319 , 22320..22349 , 22350..22379 , 22380..22409 , 22410..22439 , 22440..22469 , 22470..22499 , 22500..22529 , 22530..22559 , 22560..22589 , 22590..22619 , 22620..22649 , 22650..22679 , 22680..22709 , 22710..22739 , 22740..22769 , 22770..22799 , 22800..22829 , 22830..22859 , 22860..22889 , 22890..22919 , 22920..22949 , 22950..22979 , 22980..23009 , 23010..23039 , 23040..23069 , 23070..23099 , 23100..23129 , 23130..23159 , 23160..23189 , 23190..23219 , 23220..23249 , 23250..23279 , 23280..23309 , 23310..23339 , 23340..23369 , 23370..23399 , 23400..23429 , 23430..23459 , 23460..23489 , 23490..23519 , 23520..23549 , 23550..23579 , 23580..23609 , 23610..23639 , 23640..23669 , 23670..23699 , 23700..23729 , 23730..23759 , 23760..23789 , 23790..23819 , 23820..23849 , 23850..23879 , 23880..23909 , 23910..23939 , 23940..23969 , 23970..23999 , 24000..24029 , 24030..24059 , 24060..24089 , 24090..24119 , 24120..24149 , 24150..24179 , 24180..24209 , 24210..24239 , 24240..24269 , 24270..24299 , 24300..24329 , 24330..24359 , 24360..24389 , 24390..24419 , 24420..24449 , 24450..24479 , 24480..24509 , 24510..24539 , 24540..24569 , 24570..24599 , 24600..24629 , 24630..24659 , 24660..24689 , 24690..24719 , 24720..24749 , 24750..24779 , 24780..24809 , 24810..24839 , 24840..24869 , 24870..24899 , 24900..24929 , 24930..24959 , 24960..24989 , 24990..25019 , 25020..25049 , 25050..25079 , 25080..25109 , 25110..25139 , 25140..25169 , 25170..25199 , 25200..25229 , 25230..25259 , 25260..25289 , 25290..25319 , 25320..25349 , 25350..25379 , 25380..25409 , 25410..25439 , 25440..25469 , 25470..25499 , 25500..25529 , 25530..25559 , 25560..25589 , 25590..25619 , 25620..25649 , 25650..25679 , 25680..25709 , 25710..25739 , 25740..25769 , 25770..25799 , 25800..25829 , 25830..25859 , 25860..25889 , 25890..25919 , 25920..25949 , 25950..25979 , 25980..26009 , 26010..26039 , 26040..26069 , 26070..26099 , 26100..26129 , 26130..26159 , 26160..26189 , 26190..26219 , 26220..26249 , 26250..26279 , 26280..26309 , 26310..26339 , 26340..26369 , 26370..26399 , 26400..26429 , 26430..26459 , 26460..26489 , 26490..26519 , 26520..26549 , 26550..26579 , 26580..26609 , 26610..26639 , 26640..26669 , 26670..26699 , 26700..26729 , 26730..26759 , 26760..26789 , 26790..26819 , 26820..26849 , 26850..26879 , 26880..26909 , 26910..26939 , 26940..26969 , 26970..26999 , 27000..27029 , 27030..27059 , 27060..27089 , 27090..27119 , 27120..27149 , 27150..27179 , 27180..27209 , 27210..27239 , 27240..27269 , 27270..27299 , 27300..27329 , 27330..27359 , 27360..27389 , 27390..27419 , 27420..27449 , 27450..27479 , 27480..27509 , 27510..27539 , 27540..27569 , 27570..27599 , 27600..27629 , 27630..27659 , 27660..27689 , 27690..27719 , 27720..27749 , 27750..27779 , 27780..27809 , 27810..27839 , 27840..27869 , 27870..27899 , 27900..27929 , 27930..27959 , 27960..27989 , 27990..28019 , 28020..28049 , 28050..28079 , 28080..28109 , 28110..28139 , 28140..28169 , 28170..28199 , 28200..28229 , 28230..28259 , 28260..28289 , 28290..28319 , 28320..28349 , 28350..28379 , 28380..28409 , 28410..28439 , 28440..28469 , 28470..28499 , 28500..28529 , 28530..28559 , 28560..28589, >>Next

 Linear-equations/174187: This question is from textbook algebra 1 Find the distance between the point (5,3)and(5,-3)1 solutions Answer 129127 by jim_thompson5910(28593)   on 2008-12-20 18:59:11 (Show Source): You can put this solution on YOUR website!You can simply count the spaces between the two points vertically to get 6 units, but here's the formal method to find the distance: Start with the distance formula. Plug in , , , and . Subtract from to get . Subtract from to get . Square to get . Square to get . Add to to get . Take the square root of to get . So our answer is So the distance between the two points is 6 units.
 Linear-equations/174188: This question is from textbook algebra 1 Find the distance between the point. (3,4)and(4,5)1 solutions Answer 129126 by jim_thompson5910(28593)   on 2008-12-20 18:57:51 (Show Source): You can put this solution on YOUR website! Start with the distance formula. Plug in , , , and . Subtract from to get . Subtract from to get . Square to get . Square to get . Add to to get . So our answer is Which approximates to So the distance between the two points is approximately 1.414 units.
 Radicals/174189: This question is from textbook beginning algebra sprt(w^22)1 solutions Answer 129125 by jim_thompson5910(28593)   on 2008-12-20 18:57:00 (Show Source): You can put this solution on YOUR website! Note: and
 absolute-value/174190: This question is from textbook algebra 1 solve each equation or inequality |x+142|=811 solutions Answer 129124 by jim_thompson5910(28593)   on 2008-12-20 18:55:59 (Show Source): You can put this solution on YOUR website! Start with the given equation Break up the absolute value (remember, if you have , then or ) or Set the expression equal to the original value 81 and it's opposite -81 Now lets focus on the first equation Subtract 142 from both sides Combine like terms on the right side Now lets focus on the second equation Subtract 142 from both sides Combine like terms on the right side So the solutions are: or
 absolute-value/174191: This question is from textbook algebra 1 solve each equation or inequality |2x-6|=811 solutions Answer 129123 by jim_thompson5910(28593)   on 2008-12-20 18:54:47 (Show Source): You can put this solution on YOUR website! Start with the given equation Break up the absolute value (remember, if you have , then or ) or Set the expression equal to the original value 81 and it's opposite -81 Now lets focus on the first equation Add 6 to both sides Combine like terms on the right side Divide both sides by 2 to isolate x Reduce Now lets focus on the second equation Add 6 to both sides Combine like terms on the right side Divide both sides by 2 to isolate x Reduce So the solutions are: and
 expressions/174180: if 5a=3a+10 evaluate -5a+3.1 solutions Answer 129116 by jim_thompson5910(28593)   on 2008-12-20 16:46:13 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ------------------------------------- Move onto the given expression Plug in Multiply Add So when
 Linear-equations/174179: What is the equation of the line that passes through the given points and is perpendicular to the given line? (3,3), 2y=3x-61 solutions Answer 129114 by jim_thompson5910(28593)   on 2008-12-20 16:31:07 (Show Source): You can put this solution on YOUR website! Start with the given equation. Divide both sides by to isolate y. Break up the fraction. Reduce. We can see that the equation has a slope and a y-intercept . Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is . Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope and the coordinates of the given point . Start with the point slope formula Plug in , , and Distribute Multiply Add 3 to both sides. Combine like terms. So the equation of the line perpendicular to that goes through the point is . Here's a graph to visually verify our answer: Graph of the original equation (red) and the perpendicular line (green) through the point .
 Equations/174178: please help me on 4/5n = 20. I got 1/2r= 3/8. i think it is r = 3 please tell me if im right1 solutions Answer 129113 by jim_thompson5910(28593)   on 2008-12-20 16:26:59 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by Multiply. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is
 expressions/174176: solve: 1. 2-8x+26-2x 2. 5/6x-1=1/6x+231 solutions Answer 129108 by jim_thompson5910(28593)   on 2008-12-20 15:54:30 (Show Source): You can put this solution on YOUR website!# 1 Cannot solve since is NOT an equation (it's missing an equals sign) # 2 Start with the given equation. Multiply EVERY term by the LCD to clear the fractions. Multiply. Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is
Graphs/174175: x^2 + 2x + 1= or something similar I need a three term polynomial with a graph???
1 solutions

Answer 129107 by jim_thompson5910(28593)   on 2008-12-20 15:54:23 (Show Source):
You can put this solution on YOUR website!
So you want to graph ?

Step 1: Finding the Vertex
Step 2: Finding two points to left of axis of symmetry
Step 3: Reflecting two points to get points right of axis of symmetry
Step 4: Plotting the Points (with table)
Step 5: Graphing the Parabola

In order to graph , we can follow the steps:

Step 1) Find the vertex (the vertex is the either the highest or lowest point on the graph). Also, the vertex is at the axis of symmetry of the parabola (ie it divides it in two).

Step 2) Once you have the vertex, find two points on the left side of the axis of symmetry (the line that vertically runs through the vertex).

Step 3) Reflect those two points over the axis of symmetry to get two more points on the right side of the axis of symmetry.

Step 4) Plot all of the points found (including the vertex).

Step 5) Draw a curve through all of the points to graph the parabola.

Let's go through these steps in detail

Step 1)

#### Finding the vertex:

In order to find the vertex, we first need to find the x-coordinate of the vertex.

To find the x-coordinate of the vertex, use this formula: .

From , we can see that , , and .

Plug in and .

Multiply 2 and to get .

Divide.

So the x-coordinate of the vertex is . Note: this means that the axis of symmetry is also .

Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the y-coordinate of the vertex is .

So the vertex is .

---------------------------------------------------------------------

Step 2)

#### Find two points to the left of the axis of symmetry:

Let's find the y value when

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the first point to the left of the axis of symmetry is (-3,4)

---------------------

Let's find the y value when

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the second point to the left of the axis of symmetry is (-2,1)

---------------------------------------------------------------------

Step 3)

#### Reflecting the two points over the axis of symmetry:

Now remember, the parabola is symmetrical about the axis of symmetry (which is )

This means the y-value for (which is one unit from the axis of symmetry) is equal to the y-value of (which is also one unit from the axis of symmetry). So when , which gives us the point (0,1). So we essentially reflected the point (-2,1) over to (0,1).

Also, the y-value for (which is two units from the axis of symmetry) is equal to the y-value of (which is also two units from the axis of symmetry). So when , which gives us the point (1,4). So we essentially reflected the point (-3,4) over to (1,4).

---------------------------------------------------------------------

Step 4)

#### Plotting the points:

Now lets make a table of the values we have calculated:

xy
-34
-21
-10
01
14

Now let's plot the points:

---------------------------------------------------------------------

Step 5)

#### Drawing a curve through all of the points:

Now draw a curve through all of the points to graph :

Graph of

 expressions/174174: find the celsius temperature when the fahrenheit is -50degrees. Using the formula F=1.8C+32 round your answer to the nearest tenth. 1 solutions Answer 129105 by jim_thompson5910(28593)   on 2008-12-20 15:44:52 (Show Source): You can put this solution on YOUR website! Start with the given equation Plug in Subtract 32 from both sides. Combine like terms. Divide both sides by 1.8 to isolate C Divide (and round to the nearest tenth) So the answer is approximately So this means that -50 F is approximately -45.6 C
 Linear_Equations_And_Systems_Word_Problems/174173: a theather sold 478 tickets for a play . thickets cost $20 for adults and$13 for senior citizens.,if the total sreceips were $6970, how many senior citizen tickets were sold?1 solutions Answer 129103 by jim_thompson5910(28593) on 2008-12-20 15:33:12 (Show Source): You can put this solution on YOUR website!Let x=# of adult tickets and y=# of senior tickets "a theater sold 478 tickets for a play" translates to and "thickets cost$20 for adults and $13 for senior citizens.,if the total receipts were$6970" translates to So we have the system of equations: Let's solve the system by substitution Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y. So let's isolate y in the first equation Start with the first equation Subtract from both sides Rearrange the equation --------------------- Since , we can now replace each in the second equation with to solve for Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown. Distribute to Multiply Combine like terms on the left side Subtract 6214 from both sides Combine like terms on the right side Divide both sides by 7 to isolate x Divide -----------------First Answer------------------------------ So the first part of our answer is: Since we know that we can plug it into the equation (remember we previously solved for in the first equation). Start with the equation where was previously isolated. Plug in Multiply Combine like terms -----------------Second Answer------------------------------ So the second part of our answer is: -----------------Summary------------------------------ So our answers are: and So this means that 108 adult tickets and 370 senior tickets were sold.
 Miscellaneous_Word_Problems/174169: A house had two rooms of equal area. One room is square and the other roon is a rectangle 4ft narrower and 5ft longer than the square one. Find the area of each room.1 solutions Answer 129100 by jim_thompson5910(28593)   on 2008-12-20 15:20:21 (Show Source): You can put this solution on YOUR website!Let x=side length of square Since "A house had two rooms of equal area. One room is square and the other room is a rectangle 4ft narrower and 5ft longer than the square one.", this means that Start with the given equation. FOIL Subtract from both sides. Combine like terms. Add 20 to both sides. So the answer is which means that the side length of the square is 20 ft. So the area of the square is square feet. So the length of the rectangle is ft and the width is ft. So the area of the rectangle is square feet.
 expressions/174168: if 10x-8=-28, evaluate 8x+101 solutions Answer 129097 by jim_thompson5910(28593)   on 2008-12-20 15:09:39 (Show Source): You can put this solution on YOUR website!First solve for "x": Start with the given equation. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. Now plug the given value of "x" into the expression Start with the given expression Plug in Multiply Add So if
 Inequalities/174159: This question is from textbook algebra concepts and applications I am trying to help my son with his algebra and am unable to figure out how to work the inequalities. I am actually having problems with all equations with fractions. Could you please help? When I type in the inequality all I get is unable to solve??? -n/3>_-3????1 solutions Answer 129084 by jim_thompson5910(28593)   on 2008-12-20 11:42:38 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Multiply both sides by Multiply. Divide both sides by to isolate . Note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the answer is
 Linear-equations/174157: graph by using the slope and y intercept 5x+2y=-61 solutions Answer 129083 by jim_thompson5910(28593)   on 2008-12-20 11:28:56 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is -5 and the run is 2. This means that to go from point to point, we can go down 5 and over 2 So starting at , go down 5 units and to the right 2 units to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 Linear-systems/174146: 2x-5y=-6 8x+3y=68 solve the system of equations and enter the solution as an ordered pair. 1 solutions Answer 129066 by jim_thompson5910(28593)   on 2008-12-19 21:13:06 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Multiply the both sides of the first equation by -4. Distribute and multiply. So we have the new system of equations: Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Notice how the x terms cancel out. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So our answer is and . Which form the ordered pair . This means that the system is consistent and independent. Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer. Graph of (red) and (green)
 Polynomials-and-rational-expressions/174076: how do you solve 10x^2-30x+20/x^2-11 solutions Answer 129012 by jim_thompson5910(28593)   on 2008-12-19 14:14:07 (Show Source): You can put this solution on YOUR website!Note: factors to and factors to So where or
 Equations/173997: 5n+24-12n=-25 solve for n.1 solutions Answer 128906 by jim_thompson5910(28593)   on 2008-12-18 18:39:00 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is
Expressions-with-variables/173986: Okay, this is just part of an equation involving fractions that i am doing, but i was wondering,can you factor u^2+u^2v^2+v^2 into two binomials? Thats all i really need for the problem.
thank you :)
1 solutions

Answer 128897 by jim_thompson5910(28593)   on 2008-12-18 17:30:52 (Show Source):
You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 1 and 1 respectively.

Now multiply the first coefficient 1 and the last coefficient 1 to get 1. Now what two numbers multiply to 1 and add to the middle coefficient 1? Let's list all of the factors of 1:

Factors of 1:
1

-1 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 1
1*1
(-1)*(-1)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1

First NumberSecond NumberSum
111+1=2
-1-1-1+(-1)=-2

None of these pairs of factors add to 1. So the expression cannot be factored

 Miscellaneous_Word_Problems/173975: How do you simplify the fraction 3a+b/6a+2b1 solutions Answer 128877 by jim_thompson5910(28593)   on 2008-12-18 16:11:36 (Show Source): You can put this solution on YOUR website! So where
 Miscellaneous_Word_Problems/173976: How do you simplify the fractions 2x+8/x+41 solutions Answer 128876 by jim_thompson5910(28593)   on 2008-12-18 16:10:57 (Show Source): You can put this solution on YOUR website! Note: factors to So where
 Miscellaneous_Word_Problems/173978: How do you solve x^2-y^2/x+y1 solutions Answer 128874 by jim_thompson5910(28593)   on 2008-12-18 16:08:09 (Show Source): You can put this solution on YOUR website!Take note that factors to So Note:
 Miscellaneous_Word_Problems/173980: How do you solve a^2-2ab+b^2/a-b1 solutions Answer 128872 by jim_thompson5910(28593)   on 2008-12-18 16:06:40 (Show Source): You can put this solution on YOUR website! Note: factors to So where
 Equations/173967: This question is from textbook Algebra structure and method book 1 can you please help me solve: (((24/x-3 = 72/x+3)))1 solutions Answer 128871 by jim_thompson5910(28593)   on 2008-12-18 15:41:23 (Show Source): You can put this solution on YOUR website! Start with the given equation Cross Multiply Distribute. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is
 Equations/173972: y=x-151 solutions Answer 128869 by jim_thompson5910(28593)   on 2008-12-18 15:33:28 (Show Source): You can put this solution on YOUR website!Do you want to graph? Please post full instructions. Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 1 and the run is 1. This means that to go from point to point, we can go up 1 and over 1 So starting at , go up 1 unit and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 Expressions-with-variables/173968: This question is from textbook Algebra structure and method book 1 can you please help me simplify: (((3a+b/6a+2b)))1 solutions Answer 128867 by jim_thompson5910(28593)   on 2008-12-18 15:31:59 (Show Source): You can put this solution on YOUR website!Note: you must surround the expression by three curly braces (not parenthesis) to make the expression show up the way you want it. Also, use parenthesis to show grouping. So write the expression as (3a+b)/(6a+2b) So where
Polynomials-and-rational-expressions/173971: This question is from textbook
Can someone please be nice and show me step by step on this thank you so much
x^2-5x+4
Polynomial equation
x + 7x^2 + 5
1 solutions

Answer 128865 by jim_thompson5910(28593)   on 2008-12-18 15:28:21 (Show Source):
You can put this solution on YOUR website!

In order to graph , we need to plot some points.

Let's find y when

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Let's find y when :

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Let's find y when :

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Let's find y when :

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Let's find y when :

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Let's find y when :

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So when , then .

So we have the point .

----------------------------------------------------

Now let's make a table of the values we just found.

#### Table of Values:



xy04
10
2-2
3-2
40
54



Now let's plot the points: