New!
Get regular updates about newly solved problems
via algebra.com's RSS system.
Recent problems solved by 'jim_thompson5910'
jim_thompson5910 answered: 28703 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 , 28590..28619 , 28620..28649 , 28650..28679 , 28680..28709, >>Next
Polynomials-and-rational-expressions/412024: I am trying to factor this but I can't factor it?? Can you please help this is my problem 64c^2-80cx+25x^2 is this nonfactorable? THANK YOU!
1 solutions
Answer 289466 by jim_thompson5910(28715)   on 2011-02-21 13:06:27 (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 64 and 25 respectively.
Now multiply the first coefficient 64 and the last coefficient 25 to get 1600. Now what two numbers multiply to 1600 and add to the middle coefficient -80? Let's list all of the factors of 1600:
Factors of 1600:
1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,160,200,320,400,800
-1,-2,-4,-5,-8,-10,-16,-20,-25,-32,-40,-50,-64,-80,-100,-160,-200,-320,-400,-800 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 1600
1*1600
2*800
4*400
5*320
8*200
10*160
16*100
20*80
25*64
32*50
40*40
(-1)*(-1600)
(-2)*(-800)
(-4)*(-400)
(-5)*(-320)
(-8)*(-200)
(-10)*(-160)
(-16)*(-100)
(-20)*(-80)
(-25)*(-64)
(-32)*(-50)
(-40)*(-40)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -80? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -80
| First Number | Second Number | Sum | | 1 | 1600 | 1+1600=1601 | | 2 | 800 | 2+800=802 | | 4 | 400 | 4+400=404 | | 5 | 320 | 5+320=325 | | 8 | 200 | 8+200=208 | | 10 | 160 | 10+160=170 | | 16 | 100 | 16+100=116 | | 20 | 80 | 20+80=100 | | 25 | 64 | 25+64=89 | | 32 | 50 | 32+50=82 | | 40 | 40 | 40+40=80 | | -1 | -1600 | -1+(-1600)=-1601 | | -2 | -800 | -2+(-800)=-802 | | -4 | -400 | -4+(-400)=-404 | | -5 | -320 | -5+(-320)=-325 | | -8 | -200 | -8+(-200)=-208 | | -10 | -160 | -10+(-160)=-170 | | -16 | -100 | -16+(-100)=-116 | | -20 | -80 | -20+(-80)=-100 | | -25 | -64 | -25+(-64)=-89 | | -32 | -50 | -32+(-50)=-82 | | -40 | -40 | -40+(-40)=-80 |
From this list we can see that -40 and -40 add up to -80 and multiply to 1600
Now looking at the expression , replace  with  (notice adds up to . So it is equivalent to )
Now let's factor  by grouping:
 Group like terms
 Factor out the GCF of  out of the first group. Factor out the GCF of  out of the second group
 Since we have a common term of  , we can combine like terms
So factors to
So this also means that factors to (since is equivalent to )
note: is equivalent to  since the term occurs twice. So also factors to
------------------------------------------------------------
Answer:
So factors to
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/410763: I am totally lost please help. Solving by substitution or elimination
2x+y=6
x-y=3
1 solutions
Answer 288776 by jim_thompson5910(28715) on 2011-02-17 17:36:54 (Show Source):
You can put this solution on YOUR website!Basic outline:
Add the two equations to get:
2x+y=6
x-y=3
------
3x+0y=9
which gives us the new equation 3x=9
Next solve for x. Once you have the solution for x, use it to find y. You do this by plugging that value of x into either equation and solving for y.
|
Functions/409605: Find the domain and range of
{(-3,-7), (-1,-3), (0,-1), (2,3), (4,7)}
I don't understand this at all.
1 solutions
Answer 288275 by jim_thompson5910(28715) on 2011-02-15 17:37:56 (Show Source):
You can put this solution on YOUR website!The domain is the set of all inputs. In this case, this means that the domain is the set of all x coordinates.
So the domain is {-3, -1, 0, 2, 4} Notice how these values are all x coordinates.
In a similar fashion, the range is the set of all the y coordinates (since the range is the set of all outputs). So the range is {-7, -3, -1, 3, 7}
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/409514: Compute P9,9
1 solutions
Answer 288243 by jim_thompson5910(28715) on 2011-02-15 14:15:20 (Show Source):
You can put this solution on YOUR website!Use the formula P(n,r) = (n!)/((n-r)!) to get
P(9,9) = (9!)/((9-9)!)
P(9,9) = (9!)/(0!)
P(9,9) = (9!)/1
P(9,9) = 9!
P(9,9) = 9*8*7*6*5*4*3*2*1
P(9,9) = 362880
Note: P(x,x) = x! for all nonnegative integers x
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/409296: how do you factor y2+2xy+x2
1 solutions
Answer 288151 by jim_thompson5910(28715) on 2011-02-15 01:11:45 (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 2? 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 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2
| First Number | Second Number | Sum | | 1 | 1 | 1+1=2 | | -1 | -1 | -1+(-1)=-2 |
From this list we can see that 1 and 1 add up to 2 and multiply to 1
Now looking at the expression , replace  with  (notice adds up to . So it is equivalent to )
Now let's factor  by grouping:
 Group like terms
 Factor out the GCF of  out of the first group. Factor out the GCF of  out of the second group
 Since we have a common term of  , we can combine like terms
So factors to
So this also means that factors to (since is equivalent to )
note: is equivalent to  since the term occurs twice. So also factors to
------------------------------------------------------------
Answer:
So factors to
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/409257: Hi, I am solving with the quadraic formula and would like you to check my work and answer please.
3n^2-2n+5=0
-2 sqrt ((-2)^2-4(3)(5))/(2(3))
-2 sqrt (4-60)/(2)
-2 sqrt (60)/(2)
-2 sqrt ((4)(15))/(2)
-2 +- 2 sqrt (15)/(2) is this final answer?
1 solutions
Answer 288148 by jim_thompson5910(28715) on 2011-02-15 01:02:52 (Show Source):
You can put this solution on YOUR website!
 Start with the given equation.
Notice we have a quadratic equation in the form of  where  ,  , and 
Let's use the quadratic formula to solve for n
 Start with the quadratic formula
 Plug in , , and
 Negate  to get  .
 Square to get  .
 Multiply  to get 
 Subtract from to get 
 Multiply and  to get  .
 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)
 or  Break up the expression.
 or  Reduce
So the answers are or
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/409103: I have the the first part to this problem, I think. The tree diagram I have drawn but have no idea if it is correct. I am completely stumped on the last 2 parts. I have read and reread the material and even looked at how some of the problems are done on here. But I am still lost on this one. PLEASE HELP! I have to turn it in this evening! Thanks...
Problem:
A mini license plate for a toy car must consist of a two letters followed by a one digit odd number. Each letter must be a P, Q or a R. Repetition of letters is not permitted.
• Use the counting principle to determine the number of points in the sample space.
• Construct a tree diagram to represent this situation.
• List the sample space.
• Determine the exact probability of creating a mini license plate with a Q. Give solution exactly in reduced fraction form.
A) P,Q, and R = 3 ways 1 digit odd # = 5 ways
3*5 = 15
B) tree diagram
1st column P, Q, R
2nd column 1,3,5,7,9 beside each letter
c) HELP!
D) Help!
1 solutions
Answer 288063 by jim_thompson5910(28715) on 2011-02-14 19:17:07 (Show Source):
You can put this solution on YOUR website!A)
# of letters possible * # of letters possible * # of odd digits
= 3 * 2 * 5
= 6 * 5
= 30
So there are 30 different license plates (you're missing half of them)
--------------------------------------
B)
I can't draw here.
--------------------------------------
C)
Sample Space
{PQ1, PQ3, PQ5, PQ7, PQ9,
PR1, PR3, PR5, PR7, PR9,
QP1, QP3, QP5, QP7, QP9,
QR1, QR3, QR5, QR7, QR9,
RP1, RP3, RP5, RP7, RP9,
RQ1, RQ3, RQ5, RQ7, RQ9}
--------------------------------------
D)
There are 20 license plates that have a Q in them, and they are
{PQ1, PQ3, PQ5, PQ7, PQ9,
QP1, QP3, QP5, QP7, QP9,
QR1, QR3, QR5, QR7, QR9,
RQ1, RQ3, RQ5, RQ7, RQ9}
There are 30 plates total. So the probability is 
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
|
Quadratic_Equations/408793: Can you help me with this problem? 2(a-6)^2-45=53
1 solutions
Answer 287908 by jim_thompson5910(28715) on 2011-02-14 00:00:21 (Show Source):
You can put this solution on YOUR website! Start with the given equation.
 FOIL
 Distribute.
 Subtract 53 from both sides.
 Combine like terms.
Notice we have a quadratic equation in the form of  where  ,  , and 
Let's use the quadratic formula to solve for a
 Start with the quadratic formula
 Plug in , , and
 Negate  to get  .
 Square to get  .
 Multiply  to get 
 Rewrite  as 
 Add to  to get 
 Multiply and to get .
 Take the square root of to get  .
 or  Break up the expression.
 or  Combine like terms.
 or  Simplify.
So the answers are or
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/408765: can you please show me how to solve this problem? -2|3x-4|<16
thank you
1 solutions
Answer 287891 by jim_thompson5910(28715) on 2011-02-13 22:22:38 (Show Source):
You can put this solution on YOUR website!If you divide both sides of the inequality by -2 you'll get
|3x-4| > -8
Note: remember that the sign will flip when you divide both sides by a negative number.
Now remember that the absolute value of ANY number is ALWAYS nonnegative. In other words, it will NEVER be negative.
Since 0 and every positive number is greater than any negative number, this means that the inequality |3x-4| > -8 is true for ALL values of x.
So there are an infinite number of solutions. Basically, any real number will work for x.
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
|
logarithm/408682: Solve the following exponential equations using logarithms:
2^(x) = 3^(x+1)
Feeling pretty lost on this one...
I've tried to google for similar examples, but when I do find a similar problem it's solves using a form like this: "xln(2)=(xln(3)+ln(3))" I think this is a little beyond where I am now :( Looking for a more basic algebra solution!
Appreciate any help!!
Thanks :)
1 solutions
Answer 287853 by jim_thompson5910(28715) on 2011-02-13 21:15:55 (Show Source):
You can put this solution on YOUR website!If something like "xln(2)=(xln(3)+ln(3))" scares you, then just replace each "ln" with "log" and you'll get
xlog(2)=xlog(3)+log(3)
Why can I replace "ln" with "log"? Because "ln" is actually a log that has base 'e' (2.718...). However you can use any log of any base. So you can use the default log of base 10 if you want.
If you need more help, email me at jim_thompson5910@hotmail.com
|
|
