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# Recent problems solved by 'checkley71'

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 Percentage-and-ratio-word-problems/61065: if sally can paint a house in 4 hrs, and john can paint the asame house in 6 hrs, how long will it take for both of them to apint the house together?1 solutions Answer 41979 by checkley71(8403)   on 2006-11-12 20:49:02 (Show Source): You can put this solution on YOUR website!TO SOLVE THESE TYPE OF PROBLEMS WE MULTIPLY THE TIMES & THEN DIVIDE BY THE SUM OF THE TIMES THUS 4*6/(4+6)=24/10=2.4 HOURS TO PAINT THE HOUSE TOGETHER
 Equations/61041: 4-3x=16 is the answer 4 dont get this one -13(3x-11)+2=28 6-4(2-1/2x)+x=22 help me please1 solutions Answer 41978 by checkley71(8403)   on 2006-11-12 20:40:50 (Show Source): You can put this solution on YOUR website!4-3X=16 -3X=16-4 -3X=12 X-12/-3 X=-4 -------------------------------------- -13(3X-11)+2=28 -39X+143+2=28 -39X=28-2-143 -39X=-117 X=-117/-39 X=3 -------------------------------------------------------- 6-4(2-1/2X)+X=22 6-8+2X+X=22 3X=22-6+8 3X=24 X=24/3 X=8
 Graphs/61049: Determine the equattion of each line. write teh answer in standard form using only intergers as the coefficients. The line through (-2,4) that is perpendicular to the x-axis1 solutions Answer 41975 by checkley71(8403)   on 2006-11-12 20:33:32 (Show Source): You can put this solution on YOUR website!A PERPENDICULAR LINE THROUGH (-2,4) IS A VERTICLE LINE THROUGH THE POINTS (-2,4) X=-2 IS THE FORMULA FOR THIS LINE.
 Miscellaneous_Word_Problems/61060: At 1:00 p.m., a car leaves a city and travels north at a rate of 55 mi/h. An hour later, a second car leaves the city and travels south at a rate of 60 mi/hr. At what time will the two cars be 285 miles apart?1 solutions Answer 41974 by checkley71(8403)   on 2006-11-12 20:28:56 (Show Source): You can put this solution on YOUR website!285=(55T)+60(T-1) 285=55T+60T-60 285=115T-60 115T=285+60 115T=345 T=345/115 T=3 HOURS THEY WILL BE 285 MILES APART PROOF 285=55*3+60(3-1) 285=165+60*2 285=165+120 285=285
 Miscellaneous_Word_Problems/61058: If the perimeter of a rectangle is 36 ft and the width is 10 ft, find its length. [Hint: The perimeter of a rectangle is given by P = 2L + 2W.]1 solutions Answer 41967 by checkley71(8403)   on 2006-11-12 20:19:34 (Show Source): You can put this solution on YOUR website!36=2L+2*10 2L=36-20 2L=16 L=16/2 L=8 PROOF 36=2*8+2+10 36=16+20 36=36
 Linear-systems/61027: Instructions: Solve each system by the substitution method. What is the solution for 4x-y=-3 y=4x+31 solutions Answer 41948 by checkley71(8403)   on 2006-11-12 17:37:58 (Show Source): You can put this solution on YOUR website!Y=4X+3 4X-(4X+3)=-3 4X-4X-3=-3 4X-4X=-3+3 0=0 SHOWS THAT THESE TWO EQUATIONS ARE IDENTICAL PROOF 4X-Y=-3 -Y=-4X-3 Y=4X+3 & Y=4X+3
 Linear-systems/61020: Instructions: Solve each system by the elimination method. What is the solution for 5x-y=5 -5x+2y=01 solutions Answer 41946 by checkley71(8403)   on 2006-11-12 17:18:12 (Show Source): You can put this solution on YOUR website!5X-Y=5 -5X+2Y=0 ELIMINATE X BY ADDITION --------------------------------------------- Y=5 THEN 5X-5=5 5X=10 X=2 SOLUTION PROOF 5*2-Y=5 -Y=5-10 -Y=-5 Y=5 SOLUTION
 Rectangles/61017: I need help. I am lost on this algebra. The area of a rectangle is 119 m2. The base is four less than three times the height. What is the length of the base? 1 solutions Answer 41945 by checkley71(8403)   on 2006-11-12 17:12:45 (Show Source): You can put this solution on YOUR website!AREA=1/2BASE*HEIGHT BASE=3*H-4 119=1/2(3*H-4)H 119=1/2(3H-4)H 119=1/2(3H^2-4H) 119=1.5H^2-2H 1.5H^2-2H-119=0 USING THE QUADRATIC EQUATION X=(-B+-SQRT[B^@-4AC])/2A WE GET X=(2+-SQRT(4-4*1.5*-119])/2*1.5 X=(2+-SQRT[4+714])/3 X=(2+-SQRT[718])/3 X=(2+-26.8)/3 X=28.8/3 X=9.6 SOLUTION. THUS THE HEIGHT IS 9.6M 119=1/2(B*9.6) 119=9.6B/2 9.6B=2*119 9.6B=238 B=238/9.6 B=24.8 SOLUTION & THE LENGTH OF THE BASE. PROOF 119=1/2(9.6*24.8) 119=1/2(238) 119=119
 Miscellaneous_Word_Problems/60890: One pipe can fill a tank in 8 minutes and a second pipe can fill it in 12 minutes. If the tank is empty, how long will it take both pipes to fill it? Thank you for looking. 1 solutions Answer 41942 by checkley71(8403)   on 2006-11-12 16:51:13 (Show Source): You can put this solution on YOUR website!TWODIFFERENT ITEMS WORKING TOGETHER TO ACCOMPLISH A TASK IS GIVEN BY X*Y/(X+Y) THUS 8*12/(8+12) 96/20=4.8 MINUTES TO FILL THE TANK WHEN BOTH PIPES ARE USED
 Linear-systems/61015: A motorcycle manufacturer produces three different models: the Avalon, the Durango, and the Roadtripper. Production restrictions require it to make, on a monthly basis, 10 more Roadtrippers than the total of the other two models, and twice as many Durangos as Avalons. The shop must produce a total of 490 cycles per month. How many cycles of each type should be made per month? I just don't know how to set it up!!!! Thanks in advance!1 solutions Answer 41941 by checkley71(8403)   on 2006-11-12 16:46:58 (Show Source): You can put this solution on YOUR website!A+D+R=490 GIVEN R=10+(A+D) GIVEN D=2A GIVEN THEN R=10(A+2A) OR R=10+(A+2A) R=10+3A THEN A+(2A)+(10+3A)=490 A+2A+10+3A=490 6A=490-10 6A=480 A=480/6 A=80 AVALONS D=2*80 D=160 DURANGOS R=10+(80+160) R=10+240 PROOF R=250 A+D+R=490 80+160+250=490 490=490
 Travel_Word_Problems/61006: If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of the river and the rate of the boat in still water respectively are _______________? I have the answers, but want to know how to work it out, thanks.1 solutions Answer 41935 by checkley71(8403)   on 2006-11-12 16:01:45 (Show Source): You can put this solution on YOUR website!DISTANCE=RATE*TIME 72=3R OR R=72/3 OR R=24 MPH DOWNSTREAM 60=6R OR R=60/6 OR R=10 MPH UP STREAM TO FIND THE CURRENT WE ONLY NEED TO FIND 1/2 THE DIFFERENCE IN THE TWOSPEEDSUP & DOWN STREAM THUS (24-10)/2=14/2=7 MPH FOR THE CURRENT
 Polynomials-and-rational-expressions/60918: This question is from textbook solve each equation 36x^3-48x-12x^2=0 please help thank you1 solutions Answer 41933 by checkley71(8403)   on 2006-11-12 15:38:37 (Show Source): You can put this solution on YOUR website!36X^3-12X^2-48X=0 FACTOR OUT 12X FROM EACH TERM THEN WE HAVE 12X(3X^2-X-4)=0 12X(3X-4)(X+1)=0 12X=0 X=0/12 X=0 SOLUTION 3X-4=0 3X=4 X=4/3 SOLUTION X+1=0 X=-1 SOLUTION
 Miscellaneous_Word_Problems/61004: This question is from textbook Can somebody please help me! Find all real and imaginary solutions, b^4 + 13b^2 + 36 = 0 I have been working on this problems for a couple of days and I can't seem to understand, or even know what to do. Thank you 1 solutions Answer 41932 by checkley71(8403)   on 2006-11-12 15:31:05 (Show Source): You can put this solution on YOUR website!B^4+13B^2+36=0 (B^2+9)(B^2+4)=0 B^2+9=0 B^2=-9 B=3i B^2+4=0 B^2=-4 B=2i
 Geometry_Word_Problems/60957: A certain sum of money is invested at 10%. Twice that amount is invested at 8%. The total amount of interest from both investments is \$91.00. How much is invested at 8%. Can you show me how you work it out and solve it?1 solutions Answer 41931 by checkley71(8403)   on 2006-11-12 15:28:00 (Show Source): You can put this solution on YOUR website!.10X+.08*2X=9100 .10X+.16X=9100 .26X=9100 X=9100/.26 X=35000 AMOUNT INVESTED @ 10% 2*35000=70000 INVESTED @ 8% PROOF 35000*.10+70000*.08=9100 3500+5600=9100 9100=9100
 Geometry_Word_Problems/60959: The width of a retangle is 15 feet less than its length, and the perimeter is 210 feet. Can you show me how to find the width and the length.1 solutions Answer 41930 by checkley71(8403)   on 2006-11-12 15:23:40 (Show Source): You can put this solution on YOUR website!W=L-15 P=2L+2W 210=2L+2(L-15) 210=2L+2L-30 4L=210+30 4L=240 L=240/4 L=60 THEN W=60-15 W=45 PROOF 210=2*60+2*45 210=120+90 210=210
 Travel_Word_Problems/60966: Ching leaves San Francisco and travels toward Los Angeles at 50 mi/h. An hour later, Phil leaves Los Angeles and travels toward San Francisco at 60 mi/h. If the two cities are 380 miles apart, how many hours will it take for Ching to meet Phil1 solutions Answer 41929 by checkley71(8403)   on 2006-11-12 15:19:28 (Show Source): You can put this solution on YOUR website!380=50H+60(H-1) 380=50H+60H-60 50H+60H=380+60 110H=440 H=440/110 H=4 HOURS AFTER CHING LEFT THEY MEET PROOF 380=50*4+60(4-1) 380=200+60*3 380=200+180 380=380
 Evaluation_Word_Problems/60967: Sally bought three chocolate bars and a pack of gum and paid \$1.75. Jake bought two chocolate bars and four packs of gum and paid \$2.00. Find the cost of a chocolate bar and the cost of a pack of gum. 1 solutions Answer 41928 by checkley71(8403)   on 2006-11-12 15:11:59 (Show Source): You can put this solution on YOUR website!3B+G=175 OR G=175-3B 2B+4G=200 NOW SUBSTITUTE (175-3B) FOR G IN THE SECOND EQUATION WE GET 2B+4(175-3B)=200 2B+700-12B=200 -10B=-500 B=-500/-10 B=50 SOLUTION (\$.50 FOR THE BARS) G=175-3*50 G=175-150 G=25 SOLUTION (\$.25 FOR THE GUM) PROOF 2*50+4*25=200 100+100=200 200=200
 Polynomials-and-rational-expressions/60976: 1.) solve the following system by elimination 2x-4y=7 x-y=9 2.) the sum of two intergers, a and b (a>b), is 1,000. the smaller minus the larger is -746. find the value of the intergers a and b. 3.) factor completely. (a) w^3 - 1,000 (b) (w - x)^3 + z^3 4.) factor completely. c^2 - 11 solutions Answer 41927 by checkley71(8403)   on 2006-11-12 15:04:56 (Show Source): You can put this solution on YOUR website!x-y=9 or x=y+9 then 2(y+9)-4y=7 2y+18-4y=7 -2y=7-18 -2y=-11 y=-11/-2 y=5.5 solution then x=5.5+9 x=14.5 solution proof 2*14.5-4*5.5=7 29-22=7 7=7
 Inequalities/60996: x+5<181 solutions Answer 41926 by checkley71(8403)   on 2006-11-12 15:00:10 (Show Source): You can put this solution on YOUR website!x+5<18 x<18-5 x<13
 Expressions-with-variables/60997: Roland traveled from Nashville to St. Louis, a distance of 300 miles. If he had increased his speed by 10 mph he would have arrived at St. Louis an hour and 30 minutes sooner. What was his speed?1 solutions Answer 41925 by checkley71(8403)   on 2006-11-12 14:57:17 (Show Source): You can put this solution on YOUR website!300=rt or r=300/t 300=(r+10)(t-1.5) now substitute (300/t) for r in the second equation we get 300=(300/t+10)(t-1.5) 300=(300/t*t)+10*t+(300/t*-1.5)+(10*-1.5) 300=300+10t-450/t-15 0=10t-450/t-15 0=(10t^2-450-15t)/t 0=10t^2-15t-450 (5t+30)(2t-15)=0 5t+30=0 5t=-30 t=-30/5 t=-6 2t-15=0 2t=15 t=15/2 t=7.5 hours then 300=r*7.5 r=300/7.5 r=40 mph speed of trip
 Linear-systems/61001: This question is from textbook Algebra 1 Evaluate the function for the given value of x. then graph the function. 29. f(x)=x-7 when x=-2 30. f(x)=-x+4 when x=4 31. f(x)=2x+6 when x=-3 32. f(x)=1.5x-42 when x=-91 solutions Answer 41922 by checkley71(8403)   on 2006-11-12 14:26:23 (Show Source): You can put this solution on YOUR website!f(x)=x-7 x=-2 f(-2)=-2-7 f(-2)=-9 f(x)=-x+4 x=4 f(4)=-4+4 f(4)=0 f(x)=2x+6 x=-3 f(-3)=2*-3+6 f(-3)=-6+6 f(-3)=0 f(x)=1.5x-42 x=-9 f(-9)=1.5*-9-42 f(-9)=-13.5-42 f(-9)=-55.5 ----------------------------------------------------------------------------- sorry -- don't have graphing capabilities.
 Linear-systems/60950: Instructions: Solve each system by the substitution method. What is the solution for 6x+9y=6 2x=2-3y1 solutions Answer 41892 by checkley71(8403)   on 2006-11-11 22:17:09 (Show Source): You can put this solution on YOUR website!6x+9y=6 6x=6-9y x=6/6-9y/6 x=1-3y/2 substitute (1-3y/2) for z in the other equation 6*(1-3y/2)=6-9y 6-18y/2=6-9y 6-9y=6-9y 0=0 no solutions other than x & y=0
 Mixture_Word_Problems/60951: If you mix 140 mL of a 60% acid solution with 200 mL of a 30% solution you can get a 350 mL of a _____% solution. Help!1 solutions Answer 41890 by checkley71(8403)   on 2006-11-11 22:12:06 (Show Source): You can put this solution on YOUR website!140*.6+200*.3=350x 84+60=350x 140=350x x=140/350 x=.40 or 40% mix.
 Mixture_Word_Problems/60952: Mardi received an inheritance of \$50,000. She invested part at 8% and deposited the remainder in tax-free bonds at 12%. Her total annual income from the investments was \$4,800. What amount was invested at 8%?1 solutions Answer 41889 by checkley71(8403)   on 2006-11-11 22:08:19 (Show Source): You can put this solution on YOUR website!.08x+.12(50000-x)=4800 .08x+6000-.12x=4800 -.04x=4800-6000 -.04x=-1200 x=-1200/.04 x=30000 invested @ 8% proof .08*30000+.12*20000=4800 2400+2400=4800
 Money_Word_Problems/60948: I seem to have trouble when I am setting up for two unknowns. Can anyone help? Six cans of soda and two candy bars cost \$5.12. At the same prices, 8 cans of soda and 5 candy bars cost \$9.86. Find the price per can of soda and price per candy bar. Thanks for your efforts. 1 solutions Answer 41888 by checkley71(8403)   on 2006-11-11 21:53:37 (Show Source): You can put this solution on YOUR website!6s+2b=512 8s+5b=986 ------------------ multiply equation 1 by -2.5 & add to the second equation -15s-5b=-1280 8s+5b=986 ------------------ -7s=-294 s=-294/-7 s=42 ------------------ 6*42+2b=512 252+2b=512 2b=512-252 2b=260 b=260/2 b=130 proof 8*42+5*130=986 336+650=986 986=986
 Expressions-with-variables/60945: Can anyone help getting this set up and solved? Thanks Solve 5x^2 + 2x - 1 = 0 Thanks!1 solutions Answer 41881 by checkley71(8403)   on 2006-11-11 21:36:00 (Show Source): You can put this solution on YOUR website!5x^2+2x-1=0 using the quadratic equation we get x=(-b+-sqrt[b^2-4ac])/2a x=(-2+-sqrt[4-4*5*-1])/2*5 x=(-2+-sqrt[4+20])/10 x=(-2+-sqrt24)/10 x=(-2+-4.9)/10 x=(-2+4.9/10 x=2.9/10 x=.29 solution x=(-2-4.9)/10 x=-6.9/10 x=-.69 solution
 Quadratic_Equations/60937: A garden area is 30 ft long and 20ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^2, what is the width of the path?1 solutions Answer 41876 by checkley71(8403)   on 2006-11-11 20:57:40 (Show Source): You can put this solution on YOUR website!(30-2x)(20-2x)=400 600-40x-60x+4x^2=400 4x^2-100x+600-400=0 4x^2-100x+200=0 x^2-25x+50=0 using the quadratic equation x=(-b+-sqrt[b^2-4ac])/2a we get x=(-25+-sqrt[625-4*1*50])/2*1 x=(-25+-sqrt[625-200])/2 x=(-25+-sqrt425)/2 x=(-25+-20.6)/2 x=(-25+20.6)/2 x=-4.4/2 x=-2.2 solution x=(-25-20.6)/2 x=-45.6/2 x=-22.8 solution seeing as one of these sidesare only 20 ft we can ignore this solution proof using the first soluition we get (30-2*2.2)+(20-2*2.2)=400 (30-4.4)(20-4.4)=400 25.6*15.6=400 400=400
 Inequalities/60906: In which quadrants does the graph of the following inequality lie? 2x - y <= 4 a) I,II only b) I,II,III only c) I,III,IV only d) I,II,III,IV e) none of these1 solutions Answer 41874 by checkley71(8403)   on 2006-11-11 18:29:19 (Show Source): You can put this solution on YOUR website!2X-Y<=4 -Y=2X+4 Y=-2X-4 THEN THE Y INTERCEPT IS (0,-4)SETTING Y=0 WE FIND THE VALUE OF X 0=2X+4 2X=-4 X=-4/2 X=-2 OR (-2,0) ANSWER D) NONE OF THE ABOVE. THIS LINE FALLS WITH QUADRANTS II,III,& IV ONLY.
 Linear-systems/60922: This question is from textbook beginning algebra 21. 3x+5y=15 23. -4x+3y=12 25. x-7y=3 I am not sure how to solve with 2 variables. please help me!!!1 solutions Answer 41873 by checkley71(8403)   on 2006-11-11 18:11:23 (Show Source): You can put this solution on YOUR website!ONE EQUATION WITH TWO VARIABLES CANNOT BE UNIGUELY SOLVED BECAUSE THERE ARE MANY DIFFERWENT COMBINATIONS OF VALUES FOR EACH VARIABLE. EXAMPLE 3X+5Y=15 IF X=5 THEN Y=0 OR IF X=0 THEN Y=3 IF YOUR TRYING TO SOLVE FOR X OR Y THE 3X+5Y=15 3X=15-5Y X=15/3-5Y/3 X=5-5Y/3 OR SOLVING FOR Y THEN 3X+5Y=15 5Y=15-3X Y=15/5-3X/5 Y=3-3X/5
 Square-cubic-other-roots/60912: I am really having difficulty understanding this section of my algebra class. Solve: SQRT(3X+5)= SQRT(5X-7) Can anyone show me the steps the solve this?1 solutions Answer 41863 by checkley71(8403)   on 2006-11-11 15:03:23 (Show Source): You can put this solution on YOUR website!ignore the sqrt signs as the numbers under the radicals are equal thus -- 3x+5=5x-7 3x-5x=-7-5 -2x=-12 x=-12/-2 x=6 proof 3*6+5=5*6-7 18+5=30-7 23=23
 Quadratic_Equations/60913: Please, please help with this question. I do not know where to go. When a ball is thrown vertically upward, its height (h, in feet) above the ground after t seconds is described by the mathematical formula h = - 16t2 + 96t + 80. At what times is the ball 103 feet above the ground?1 solutions Answer 41862 by checkley71(8403)   on 2006-11-11 14:58:46 (Show Source): You can put this solution on YOUR website!103=-16t^2+96t+80 16t^2-96t-80+103=0 16t^2-96t+23=0 (4x-23)(4x-1)=0 4x-23=0 4x=23 x=23/4 x=5.75 solution 5.75 seconds 4x-1=0 4x=1 x=1/4 x=.25 solution .25 seconds