See tutors' answers!

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


   
By Tutor
 | By Problem Number | 

Tutor:
New! Get regular updates about newly solved problems via algebra.com's RSS system.

Recent problems solved by 'jim_thompson5910'

jim_thompson5910 answered: 28583 problems
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

Inequalities/539545: 2(-3m-5)>= -28
1 solutions

Answer 353455 by jim_thompson5910(28595) About Me  on 2011-11-30 19:52:54 (Show Source):
You can put this solution on YOUR website!

2%28-3m-5%29%3E=-28 Start with the given inequality.


-6m-10%3E=-28 Distribute.


-6m%3E=-28%2B10 Add 10 to both sides.


-6m%3E=-18 Combine like terms on the right side.


m%3C=%28-18%29%2F%28-6%29 Divide both sides by -6 to isolate m. note: Remember, the inequality sign flips when we divide both sides by a negative number.


m%3C=3 Reduce.


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

Answer:

So the solution is m%3C=3


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Inequalities/539549: -6(w+1)<2(w+5)
Thank you so much!
1 solutions

Answer 353454 by jim_thompson5910(28595) About Me  on 2011-11-30 19:51:42 (Show Source):
You can put this solution on YOUR website!

-6%28w%2B1%29%3C2%28w%2B5%29 Start with the given inequality.


-6w-6%3C2w%2B10 Distribute.


-6w%3C2w%2B10%2B6 Add 6 to both sides.


-6w-2w%3C10%2B6 Subtract 2w from both sides.


-8w%3C10%2B6 Combine like terms on the left side.


-8w%3C16 Combine like terms on the right side.


w%3E%2816%29%2F%28-8%29 Divide both sides by -8 to isolate w. note: Remember, the inequality sign flips when we divide both sides by a negative number.


w%3E-2 Reduce.


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

Answer:

So the solution is w%3E-2


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Inequalities/539508: 2p + 5 > 3p - 10
1 solutions

Answer 353439 by jim_thompson5910(28595) About Me  on 2011-11-30 19:19:14 (Show Source):
You can put this solution on YOUR website!

2p%2B5%3E3p-10 Start with the given inequality.


2p%3E3p-10-5 Subtract 5 from both sides.


2p-3p%3E-10-5 Subtract 3p from both sides.


-p%3E-10-5 Combine like terms on the left side.


-p%3E-15 Combine like terms on the right side.


p%3C%28-15%29%2F%28-1%29 Divide both sides by -1 to isolate p. note: Remember, the inequality sign flips when we divide both sides by a negative number.


p%3C15 Reduce.


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

Answer:

So the solution is p%3C15


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Polynomials-and-rational-expressions/539493: THE factor polynomial problem is 15x2−84x−36
I know the answer to the polynomial is 3(5x+2)(x−6)but i dont understand how you get from
3(5x2−28x−12)to 3(5x+2)(x−6)<----the answer
can you please show me how you get it STEP BY STEP

1 solutions

Answer 353432 by jim_thompson5910(28595) About Me  on 2011-11-30 19:08:05 (Show Source):
You can put this solution on YOUR website!

15x%5E2-84x-36 Start with the given expression.


3%285x%5E2-28x-12%29 Factor out the GCF 3.


Now let's try to factor the inner expression 5x%5E2-28x-12


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


Looking at the expression 5x%5E2-28x-12, we can see that the first coefficient is 5, the second coefficient is -28, and the last term is -12.


Now multiply the first coefficient 5 by the last term -12 to get %285%29%28-12%29=-60.


Now the question is: what two whole numbers multiply to -60 (the previous product) and add to the second coefficient -28?


To find these two numbers, we need to list all of the factors of -60 (the previous product).


Factors of -60:
1,2,3,4,5,6,10,12,15,20,30,60
-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to -60.
1*(-60) = -60
2*(-30) = -60
3*(-20) = -60
4*(-15) = -60
5*(-12) = -60
6*(-10) = -60
(-1)*(60) = -60
(-2)*(30) = -60
(-3)*(20) = -60
(-4)*(15) = -60
(-5)*(12) = -60
(-6)*(10) = -60

Now let's add up each pair of factors to see if one pair adds to the middle coefficient -28:


First NumberSecond NumberSum
1-601+(-60)=-59
2-302+(-30)=-28
3-203+(-20)=-17
4-154+(-15)=-11
5-125+(-12)=-7
6-106+(-10)=-4
-160-1+60=59
-230-2+30=28
-320-3+20=17
-415-4+15=11
-512-5+12=7
-610-6+10=4



From the table, we can see that the two numbers 2 and -30 add to -28 (the middle coefficient).


So the two numbers 2 and -30 both multiply to -60 and add to -28


Now replace the middle term -28x with 2x-30x. Remember, 2 and -30 add to -28. So this shows us that 2x-30x=-28x.


5x%5E2%2Bhighlight%282x-30x%29-12 Replace the second term -28x with 2x-30x.


%285x%5E2%2B2x%29%2B%28-30x-12%29 Group the terms into two pairs.


x%285x%2B2%29%2B%28-30x-12%29 Factor out the GCF x from the first group.


x%285x%2B2%29-6%285x%2B2%29 Factor out 6 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%28x-6%29%285x%2B2%29 Combine like terms. Or factor out the common term 5x%2B2


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


So 3%285x%5E2-28x-12%29 then factors further to 3%28x-6%29%285x%2B2%29


===============================================================


Answer:


So 15x%5E2-84x-36 completely factors to 3%28x-6%29%285x%2B2%29.


In other words, 15x%5E2-84x-36=3%28x-6%29%285x%2B2%29.


Note: you can check the answer by expanding 3%28x-6%29%285x%2B2%29 to get 15x%5E2-84x-36 or by graphing the original expression and the answer (the two graphs should be identical).


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Expressions-with-variables/539461: 6y^3+25y^2+14y
1 solutions

Answer 353428 by jim_thompson5910(28595) About Me  on 2011-11-30 18:34:42 (Show Source):
You can put this solution on YOUR website!

6y%5E3%2B25y%5E2%2B14y Start with the given expression.


y%286y%5E2%2B25y%2B14%29 Factor out the GCF y.


Now let's try to factor the inner expression 6y%5E2%2B25y%2B14


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


Looking at the expression 6y%5E2%2B25y%2B14, we can see that the first coefficient is 6, the second coefficient is 25, and the last term is 14.


Now multiply the first coefficient 6 by the last term 14 to get %286%29%2814%29=84.


Now the question is: what two whole numbers multiply to 84 (the previous product) and add to the second coefficient 25?


To find these two numbers, we need to list all of the factors of 84 (the previous product).


Factors of 84:
1,2,3,4,6,7,12,14,21,28,42,84
-1,-2,-3,-4,-6,-7,-12,-14,-21,-28,-42,-84


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to 84.
1*84 = 84
2*42 = 84
3*28 = 84
4*21 = 84
6*14 = 84
7*12 = 84
(-1)*(-84) = 84
(-2)*(-42) = 84
(-3)*(-28) = 84
(-4)*(-21) = 84
(-6)*(-14) = 84
(-7)*(-12) = 84

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 25:


First NumberSecond NumberSum
1841+84=85
2422+42=44
3283+28=31
4214+21=25
6146+14=20
7127+12=19
-1-84-1+(-84)=-85
-2-42-2+(-42)=-44
-3-28-3+(-28)=-31
-4-21-4+(-21)=-25
-6-14-6+(-14)=-20
-7-12-7+(-12)=-19



From the table, we can see that the two numbers 4 and 21 add to 25 (the middle coefficient).


So the two numbers 4 and 21 both multiply to 84 and add to 25


Now replace the middle term 25y with 4y%2B21y. Remember, 4 and 21 add to 25. So this shows us that 4y%2B21y=25y.


6y%5E2%2Bhighlight%284y%2B21y%29%2B14 Replace the second term 25y with 4y%2B21y.


%286y%5E2%2B4y%29%2B%2821y%2B14%29 Group the terms into two pairs.


2y%283y%2B2%29%2B%2821y%2B14%29 Factor out the GCF 2y from the first group.


2y%283y%2B2%29%2B7%283y%2B2%29 Factor out 7 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%282y%2B7%29%283y%2B2%29 Combine like terms. Or factor out the common term 3y%2B2


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


So y%286y%5E2%2B25y%2B14%29 then factors further to y%282y%2B7%29%283y%2B2%29


===============================================================


Answer:


So 6y%5E3%2B25y%5E2%2B14y completely factors to y%282y%2B7%29%283y%2B2%29.


In other words, 6y%5E3%2B25y%5E2%2B14y=y%282y%2B7%29%283y%2B2%29.


Note: you can check the answer by expanding y%282y%2B7%29%283y%2B2%29 to get 6y%5E3%2B25y%5E2%2B14y or by graphing the original expression and the answer (the two graphs should be identical).


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Linear-equations/539450: Please help me solve 3(x+2)+4=5x+7
1 solutions

Answer 353422 by jim_thompson5910(28595) About Me  on 2011-11-30 18:24:47 (Show Source):
You can put this solution on YOUR website!
3%28x%2B2%29%2B4=5x%2B7 Start with the given equation.


3x%2B6%2B4=5x%2B7 Distribute.


3x%2B10=5x%2B7 Combine like terms on the left side.


3x=5x%2B7-10 Subtract 10 from both sides.


3x-5x=7-10 Subtract 5x from both sides.


-2x=7-10 Combine like terms on the left side.


-2x=-3 Combine like terms on the right side.


x=%28-3%29%2F%28-2%29 Divide both sides by -2 to isolate x.


x=3%2F2 Reduce.


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

Answer:

So the solution is x=3%2F2


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Linear-equations/539442: Use slope and y intercept to graph a line. y=2x-5
1 solutions

Answer 353417 by jim_thompson5910(28595) About Me  on 2011-11-30 18:13:27 (Show Source):
You can put this solution on YOUR website!
Looking at y=2x-5 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=2 and the y-intercept is b=-5


Since b=-5 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
slope=rise%2Frun

Also, because the slope is 2, this means:

rise%2Frun=2%2F1


which shows us that the rise is 2 and the run is 1. This means that to go from point to point, we can go up 2 and over 1



So starting at , go up 2 units


and to the right 1 unit to get to the next point



Now draw a line through these points to graph y=2x-5

So this is the graph of y=2x-5 through the points and


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Equations/538792: -9 -b +8b=-23
1 solutions

Answer 353361 by jim_thompson5910(28595) About Me  on 2011-11-30 13:11:27 (Show Source):
You can put this solution on YOUR website!
-9-b%2B8b=-23 Start with the given equation.


7b-9=-23 Combine like terms on the left side.


7b=-23%2B9 Add 9 to both sides.


7b=-14 Combine like terms on the right side.


b=%28-14%29%2F%287%29 Divide both sides by 7 to isolate b.


b=-2 Reduce.


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

Answer:

So the solution is b=-2


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Equations/539186: Do the equations x = 4y +1 and x = 4y -1 have the same solution?
1 solutions

Answer 353360 by jim_thompson5910(28595) About Me  on 2011-11-30 13:10:50 (Show Source):
You can put this solution on YOUR website!
x = 4y +1


4y - 1 = 4y +1


-1 = 1


Since the last equation is false, this means that there are no solutions.


Vectors/539229: Find the magnitude and direction (in degrees) of the vector.
v = 3i +√7j
1 solutions

Answer 353359 by jim_thompson5910(28595) About Me  on 2011-11-30 13:08:09 (Show Source):
You can put this solution on YOUR website!
If v = ai+bj, then ||v|| = sqrt(a^2+b^2)


In this case, a = 3 and b = sqrt(7)


||v|| = sqrt(a^2+b^2)


||v|| = sqrt(3^2+(sqrt(7))^2)


||v|| = sqrt(9+7)


||v|| = sqrt(16)


||v|| = 4


So the magnitude of v is 4


To find the direction or angle, we use the idea that theta = arctan(b/a)


theta = arctan(b/a)


theta = arctan(sqrt(7)/3)


theta = 41.409622 (note: this is approximate)


So the direction is roughly 41.409622 degrees.


Exponents/539231: how do you simplify 15 with the power of -4 over 15 with the power of 5
1 solutions

Answer 353357 by jim_thompson5910(28595) About Me  on 2011-11-30 13:02:47 (Show Source):
You can put this solution on YOUR website!
%2815%5E%28-4%29%29%2F%2815%5E5%29+=+15%5E%28-4-5%29+=+15%5E%28-9%29+=+1%2F%2815%5E9%29


So %2815%5E%28-4%29%29%2F%2815%5E5%29+=+1%2F%2815%5E9%29


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Complex_Numbers/539205: n^7÷n^3
1 solutions

Answer 353353 by jim_thompson5910(28595) About Me  on 2011-11-30 12:14:26 (Show Source):
You can put this solution on YOUR website!
n^7÷n^3 = n^(7-3) = n^4


So n^7÷n^3 = n^4


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Distributive-associative-commutative-properties/539142: 2x(5x1)=(7x5)x1 what property is this
1 solutions

Answer 353352 by jim_thompson5910(28595) About Me  on 2011-11-30 12:13:56 (Show Source):
You can put this solution on YOUR website!
Assuming you meant to write 2x(5x1)=(2x5)x1, this is the associative property of multiplication.


Linear-equations/539066: What is the slope of the line that passes through the pair of points?
(1, 7), (10, 1)
1 solutions

Answer 353321 by jim_thompson5910(28595) About Me  on 2011-11-30 08:24:22 (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=1 and y%5B1%5D=7.
Also, is the second point . So this means that x%5B2%5D=10 and y%5B2%5D=1.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%281-7%29%2F%2810-1%29 Plug in y%5B2%5D=1, y%5B1%5D=7, x%5B2%5D=10, and x%5B1%5D=1


m=%28-6%29%2F%2810-1%29 Subtract 7 from 1 to get -6


m=%28-6%29%2F%289%29 Subtract 1 from 10 to get 9


m=-2%2F3 Reduce


So the slope of the line that goes through the points and is m=-2%2F3


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-7=%28-2%2F3%29%28x-1%29 Plug in m=-2%2F3, x%5B1%5D=1, and y%5B1%5D=7


y-7=%28-2%2F3%29x%2B%28-2%2F3%29%28-1%29 Distribute


y-7=%28-2%2F3%29x%2B2%2F3 Multiply


y=%28-2%2F3%29x%2B2%2F3%2B7 Add 7 to both sides.


y=%28-2%2F3%29x%2B23%2F3 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation that goes through the points and is y=%28-2%2F3%29x%2B23%2F3


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Linear-equations/538942: Find an equation of the line containing the given pair of points (-2,-8), (-5,-9)?
the equation of the line in slope-intercept form is y=
1 solutions

Answer 353292 by jim_thompson5910(28595) About Me  on 2011-11-29 22:55:41 (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=-2 and y%5B1%5D=-8.
Also, is the second point . So this means that x%5B2%5D=-5 and y%5B2%5D=-9.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28-9--8%29%2F%28-5--2%29 Plug in y%5B2%5D=-9, y%5B1%5D=-8, x%5B2%5D=-5, and x%5B1%5D=-2


m=%28-1%29%2F%28-5--2%29 Subtract -8 from -9 to get -1


m=%28-1%29%2F%28-3%29 Subtract -2 from -5 to get -3


m=1%2F3 Reduce


So the slope of the line that goes through the points and is m=1%2F3


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--8=%281%2F3%29%28x--2%29 Plug in m=1%2F3, x%5B1%5D=-2, and y%5B1%5D=-8


y--8=%281%2F3%29%28x%2B2%29 Rewrite x--2 as x%2B2


y%2B8=%281%2F3%29%28x%2B2%29 Rewrite y--8 as y%2B8


y%2B8=%281%2F3%29x%2B%281%2F3%29%282%29 Distribute


y%2B8=%281%2F3%29x%2B2%2F3 Multiply


y=%281%2F3%29x%2B2%2F3-8 Subtract 8 from both sides.


y=%281%2F3%29x-22%2F3 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation that goes through the points and is y=%281%2F3%29x-22%2F3


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Linear_Algebra/538943: Find the slope-intercept form of the line that passes through the points (2,-1)and (-3,4).

1 solutions

Answer 353290 by jim_thompson5910(28595) About Me  on 2011-11-29 22:54:22 (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=2 and y%5B1%5D=-1.
Also, is the second point . So this means that x%5B2%5D=-3 and y%5B2%5D=4.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%284--1%29%2F%28-3-2%29 Plug in y%5B2%5D=4, y%5B1%5D=-1, x%5B2%5D=-3, and x%5B1%5D=2


m=%285%29%2F%28-3-2%29 Subtract -1 from 4 to get 5


m=%285%29%2F%28-5%29 Subtract 2 from -3 to get -5


m=-1 Reduce


So the slope of the line that goes through the points and is m=-1


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--1=-1%28x-2%29 Plug in m=-1, x%5B1%5D=2, and y%5B1%5D=-1


y%2B1=-1%28x-2%29 Rewrite y--1 as y%2B1


y%2B1=-1x%2B-1%28-2%29 Distribute


y%2B1=-1x%2B2 Multiply


y=-1x%2B2-1 Subtract 1 from both sides.


y=-1x%2B1 Combine like terms.


y=-x%2B1 Simplify


So the equation that goes through the points and is y=-x%2B1


Notice how the graph of y=-x%2B1 goes through the points and . So this visually verifies our answer.
Graph of y=-x%2B1 through the points and


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


test/538946: How do you solve A= LW , for W in algebra 1
1 solutions

Answer 353289 by jim_thompson5910(28595) About Me  on 2011-11-29 22:49:42 (Show Source):
You can put this solution on YOUR website!
A=LW Start with the given equation.


A%2FL=W Divide both sides by L


W=A%2FL Flip the equation


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Equations/538936: 9-y=5
over
44=22
1 solutions

Answer 353287 by jim_thompson5910(28595) About Me  on 2011-11-29 22:46:47 (Show Source):
You can put this solution on YOUR website!
%289-y%29%2F44=5%2F22 Start with the given equation.


22%289-y%29=44%2A5 Cross multiply


22%289-y%29=220 Multiply 44 and 5 to get 220


198-22y=220 Distribute.


-22y=220-198 Subtract 198 from both sides.


-22y=22 Combine like terms on the right side.


y=%2822%29%2F%28-22%29 Divide both sides by -22 to isolate y.


y=-1 Reduce.


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

Answer:

So the solution is y=-1


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Equations/538933: How do I work this sentence into an equation: Twice a number is 12 more than five times the number.
1 solutions

Answer 353285 by jim_thompson5910(28595) About Me  on 2011-11-29 22:26:58 (Show Source):
You can put this solution on YOUR website!
" Twice a number is 12 more than five times the number" translates to 2x=5x%2B12 where 'x' is the unknown number


Radicals/538928: (2x-5)^2= 81
1 solutions

Answer 353284 by jim_thompson5910(28595) About Me  on 2011-11-29 22:25:43 (Show Source):
You can put this solution on YOUR website!

%282x-5%29%5E2=81 Start with the given equation.


2x-5=%27%27%2B-sqrt%2881%29 Take the square root of both sides.


2x-5=sqrt%2881%29 or 2x-5=-sqrt%2881%29 Break up the "plus/minus" to form two equations.


2x-5=9 or 2x-5=-9 Take the square root of 81 to get 9.


2x=5%2B9 or 2x=5-9 Add 5 to both sides.


2x=14 or 2x=-4 Combine like terms.


x=7 or x=-2 Divide both sides by 2 to isolate x.


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


Answer:


So the solutions are x=7 or x=-2.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Numeric_Fractions/538923: HI
Can someone please help me with this question? My mom as tried and she is stuck to
n/3 = 2+n/5
1 solutions

Answer 353281 by jim_thompson5910(28595) About Me  on 2011-11-29 22:15:34 (Show Source):
You can put this solution on YOUR website!

n%2F3+=+%282%2Bn%29%2F5 Start with the given equation.


5n+=+3%282%2Bn%29 Cross multiply


5n=6%2B3n Distribute.


5n-3n=6 Subtract 3n from both sides.


2n=6 Combine like terms on the left side.


n=%286%29%2F%282%29 Divide both sides by 2 to isolate n.


n=3 Reduce.


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

Answer:

So the solution is n=3


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Equations/538903: Please help me factor +9x%5E2%2B89x%2B40+
I know that the first number in the bracket will probably have to be 9 or 3 but I'm not sure about how about the other numbers since 89 and 40 do not have a common multiple.
Thanks!
1 solutions

Answer 353279 by jim_thompson5910(28595) About Me  on 2011-11-29 21:51:28 (Show Source):
You can put this solution on YOUR website!

Looking at the expression 9x%5E2%2B89x%2B40, we can see that the first coefficient is 9, the second coefficient is 89, and the last term is 40.


Now multiply the first coefficient 9 by the last term 40 to get %289%29%2840%29=360.


Now the question is: what two whole numbers multiply to 360 (the previous product) and add to the second coefficient 89?


To find these two numbers, we need to list all of the factors of 360 (the previous product).


Factors of 360:
1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
-1,-2,-3,-4,-5,-6,-8,-9,-10,-12,-15,-18,-20,-24,-30,-36,-40,-45,-60,-72,-90,-120,-180,-360


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to 360.
1*360 = 360
2*180 = 360
3*120 = 360
4*90 = 360
5*72 = 360
6*60 = 360
8*45 = 360
9*40 = 360
10*36 = 360
12*30 = 360
15*24 = 360
18*20 = 360
(-1)*(-360) = 360
(-2)*(-180) = 360
(-3)*(-120) = 360
(-4)*(-90) = 360
(-5)*(-72) = 360
(-6)*(-60) = 360
(-8)*(-45) = 360
(-9)*(-40) = 360
(-10)*(-36) = 360
(-12)*(-30) = 360
(-15)*(-24) = 360
(-18)*(-20) = 360

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 89:


First NumberSecond NumberSum
13601+360=361
21802+180=182
31203+120=123
4904+90=94
5725+72=77
6606+60=66
8458+45=53
9409+40=49
103610+36=46
123012+30=42
152415+24=39
182018+20=38
-1-360-1+(-360)=-361
-2-180-2+(-180)=-182
-3-120-3+(-120)=-123
-4-90-4+(-90)=-94
-5-72-5+(-72)=-77
-6-60-6+(-60)=-66
-8-45-8+(-45)=-53
-9-40-9+(-40)=-49
-10-36-10+(-36)=-46
-12-30-12+(-30)=-42
-15-24-15+(-24)=-39
-18-20-18+(-20)=-38



From the table, we can see that there are no pairs of numbers which add to 89. So 9x%5E2%2B89x%2B40 cannot be factored.


===============================================================



Answer:


So 9x%5E2%2B89x%2B40 doesn't factor at all (over the rational numbers).


So 9x%5E2%2B89x%2B40 is prime.


If you need more help, email me at
jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Probability-and-statistics/538891: Please help me solve this :
Find the mean for the following probability distribution, where x = number of hurricanes that hit a certain coast area in any given year and P(x) = the corresponding probabilities.
x P(x)
0 .15
1 .4
2 .3
3 .15
I think I would go X = 4 and P(x)=.37 q= 1-.37 =.63
and .63 would be my mean but im not sure if i have to find mean that is
0+.15 /2 = .075
1+.4=.7 and so on
Thanks for you help
1 solutions

Answer 353275 by jim_thompson5910(28595) About Me  on 2011-11-29 21:38:50 (Show Source):
You can put this solution on YOUR website!
Mean = sum of the x*P(x) terms


Mean = 0*0.15 + 1*0.4 + 2*0.3 + 3*0.15


Mean = 0 + 0.4 + 0.6 + 0.45


Mean = 1.45


So the mean is 1.45


Inequalities/538703: can you please help me solve:3(x-2)>21
1 solutions

Answer 353233 by jim_thompson5910(28595) About Me  on 2011-11-29 19:07:01 (Show Source):
You can put this solution on YOUR website!

3%28x-2%29%3E21 Start with the given inequality.


3x-6%3E21 Distribute.


3x%3E21%2B6 Add 6 to both sides.


3x%3E27 Combine like terms on the right side.


x%3E%2827%29%2F%283%29 Divide both sides by 3 to isolate x.


x%3E9 Reduce.


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

Answer:

So the solution is x%3E9


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Radicals/538704: help me solve +sqrt%286y%2B4%29%2B6=y+
1 solutions

Answer 353232 by jim_thompson5910(28595) About Me  on 2011-11-29 19:05:03 (Show Source):
You can put this solution on YOUR website!

+sqrt%286y%2B4%29%2B6=y+ Start with the given equation.

+sqrt%286y%2B4%29=y-6+ Subtract 6 from both sides.

+%28sqrt%286y%2B4%29%29%5E2=%28y-6%29%5E2+ Square both sides

+6y%2B4=y%5E2-12y%2B36+ Square and FOIL

+0=y%5E2-12y%2B36-6y-4+ Get everything to one side

+0=y%5E2-18y%2B32+ Combine like terms.

+y%5E2-18y%2B32=0+ Flip the equation


Notice that the quadratic y%5E2-18y%2B32 is in the form of Ay%5E2%2BBy%2BC where A=1, B=-18, and C=32


Let's use the quadratic formula to solve for "y":


y+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


y+=+%28-%28-18%29+%2B-+sqrt%28+%28-18%29%5E2-4%281%29%2832%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-18, and C=32


y+=+%2818+%2B-+sqrt%28+%28-18%29%5E2-4%281%29%2832%29+%29%29%2F%282%281%29%29 Negate -18 to get 18.


y+=+%2818+%2B-+sqrt%28+324-4%281%29%2832%29+%29%29%2F%282%281%29%29 Square -18 to get 324.


y+=+%2818+%2B-+sqrt%28+324-128+%29%29%2F%282%281%29%29 Multiply 4%281%29%2832%29 to get 128


y+=+%2818+%2B-+sqrt%28+196+%29%29%2F%282%281%29%29 Subtract 128 from 324 to get 196


y+=+%2818+%2B-+sqrt%28+196+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


y+=+%2818+%2B-+14%29%2F%282%29 Take the square root of 196 to get 14.


y+=+%2818+%2B+14%29%2F%282%29 or y+=+%2818+-+14%29%2F%282%29 Break up the expression.


y+=+%2832%29%2F%282%29 or y+=++%284%29%2F%282%29 Combine like terms.


y+=+16 or y+=+2 Simplify.


So the possible solutions are y+=+16 or y+=+2


However, when doing the check (which I'll let you do), you'll find that only y=16 works.


So y=16 is the only solution.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Equations/538683: 3Y+1=13
1 solutions

Answer 353225 by jim_thompson5910(28595) About Me  on 2011-11-29 18:35:48 (Show Source):
You can put this solution on YOUR website!
3y%2B1=13 Start with the given equation.


3y=13-1 Subtract 1 from both sides.


3y=12 Combine like terms on the right side.


y=%2812%29%2F%283%29 Divide both sides by 3 to isolate y.


y=4 Reduce.


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

Answer:

So the solution is y=4


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Radicals/538685: help me solve +sqrt%28x%2B4%29=x%2B2+
1 solutions

Answer 353224 by jim_thompson5910(28595) About Me  on 2011-11-29 18:29:55 (Show Source):
You can put this solution on YOUR website!
+sqrt%28x%2B4%29=x%2B2+

+%28sqrt%28x%2B4%29%29%5E2=%28x%2B2%29%5E2+

+x%2B4=x%5E2%2B4x%2B4+

+0=x%5E2%2B4x%2B4-x-4+

+0=x%5E2%2B3x+

+x%5E2%2B3x=0+

+x%28x%2B3%29=0+

+x=0 or x%2B3=0+

+x=0 or x=-3+

When doing the check (which I'll let you do), you'll find that only x=0 works.


So x=0 is the only solution.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Polynomials-and-rational-expressions/538464: Find the LCM of 7(x-2)and 14(x-2). Please tell me if my solution to this is correct and if not why?
My solution: 7(x-2)


1 solutions

Answer 353188 by jim_thompson5910(28595) About Me  on 2011-11-29 13:03:29 (Show Source):
You can put this solution on YOUR website!
You're close, the LCM is really 14(x-2) since the LCM of 7 and 14 is 14.


test/538466: How do I calculate 1/5 to the third?
1 solutions

Answer 353187 by jim_thompson5910(28595) About Me  on 2011-11-29 13:02:19 (Show Source):
You can put this solution on YOUR website!
%281%2F5%29%5E3=%281%5E3%29%2F%285%5E3%29=1%2F125


So %281%2F5%29%5E3=1%2F125


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Numbers_Word_Problems/538461: five times a number subtracted from 40 is the same as three times the number. find the number
1 solutions

Answer 353186 by jim_thompson5910(28595) About Me  on 2011-11-29 12:56:08 (Show Source):
You can put this solution on YOUR website!
"five times a number subtracted from 40 is the same as three times the number. " translates to 40-5x=3x



40-5x=3x Start with the given equation.


-5x=3x-40 Subtract 40 from both sides.


-5x-3x=-40 Subtract 3x from both sides.


-8x=-40 Combine like terms on the left side.


x=%28-40%29%2F%28-8%29 Divide both sides by -8 to isolate x.


x=5 Reduce.


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

Answer:

So the solution is x=5


So the number is 5


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim


Equations/537737: What is the factor of 16x^2- 25y^2=
1 solutions

Answer 353183 by jim_thompson5910(28595) About Me  on 2011-11-29 12:28:05 (Show Source):
You can put this solution on YOUR website!

16x%5E2-25y%5E2 Start with the given expression.


%284x%29%5E2-25y%5E2 Rewrite 16x%5E2 as %284x%29%5E2.


%284x%29%5E2-%285y%29%5E2 Rewrite 25y%5E2 as %285y%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=4x and B=5y.


So let's use the difference of squares formula A%5E2-B%5E2=%28A%2BB%29%28A-B%29 to factor the expression:


A%5E2-B%5E2=%28A%2BB%29%28A-B%29 Start with the difference of squares formula.


%284x%29%5E2-%285y%29%5E2=%284x%2B5y%29%284x-5y%29 Plug in A=4x and B=5y.


So this shows us that 16x%5E2-25y%5E2 factors to %284x%2B5y%29%284x-5y%29.


In other words 16x%5E2-25y%5E2=%284x%2B5y%29%284x-5y%29.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim