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# Recent problems solved by 'checkley77'

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 Reduction-of-unit-multipliers/249439: use three unit multipliers to convert 5016 cubic inches to cubic feet.1 solutions Answer 181679 by checkley77(12569)   on 2009-12-13 20:13:08 (Show Source): You can put this solution on YOUR website!12*12*12=1,728 INCHES^3 = 1 FT^3 5,016/1,728=2.903 FT^3
 Travel_Word_Problems/249444: Mrs. Smith drove at a rate of 45 mph from her home to her sisters house. she spent 1.5 hrs having lunch with her sister. She then drove back home at a rate of 55 mph. The entire trip, including lunch, took 4 hrs. How far does Mrs. Smith live from her sister? 1 solutions Answer 181677 by checkley77(12569)   on 2009-12-13 20:08:14 (Show Source): You can put this solution on YOUR website!D=RT D=45T THE TRIP TO HER SISTER'S HOME. D=55(4-T-1.5) THE RETURN TRIP 45T=55(2.5-T) 45T=137.5-55T 45T+55T=137.5 100T=137.5 T=137.5/100 T=1.375 HOURS FOR THE TO TO HER SISTER'S HOUSE. 4-1.5-1.375=1.125HOURS FOR THE RETURN TRIP. PROOF: 45*1.375=55(4-1.375-1.5) 61.875=55*1.125 61.875=61.875
 Money_Word_Problems/249445: find P when R = 8 1/2%, T = 4 months, I = 2401 solutions Answer 181673 by checkley77(12569)   on 2009-12-13 19:54:29 (Show Source): You can put this solution on YOUR website!I=PRT I=P(.085)1/3 240=P*.02833 P=240/.02833 P=8,471.58 AMOUNT OF THE PRINCIPAL.
 Quadratic_Equations/249377: a rectangle is 6 feet long and 4 feet wide. if each dimension is increased by the same number of feet, a new rectangle is formed whose area is 39 square feet more then the area of the original rectangele. by how many feet was each dimension increased?1 solutions Answer 181671 by checkley77(12569)   on 2009-12-13 19:42:44 (Show Source): You can put this solution on YOUR website!AREA=6*4=24 FT^2 39+24=(6+X)(4+X) 63=24+10X+X^2 X62+10X+24-63 X^2+10X-39=0 (X+13)(X-3)=0 X-3=0 X=3 FT. ANS. FOR THE INCREASE IN LENGTH & WIDTH. pROOF: 63=(6+3)(4+3) 63=9*7 63=63
 Travel_Word_Problems/249387: Trains A and B are traveling int he same direction on parallel tracks. Train A is traveling at 80 mph and train B is traveling at 90 mph. Train A passes a station at 2:20 a.m. If train B passes the same station at 2:50 a.m., at what time will train B catch up to train A?1 solutions Answer 181669 by checkley77(12569)   on 2009-12-13 19:30:00 (Show Source): You can put this solution on YOUR website!D=RT FOR TRAIN A D=80T FOR TRAIN B D=90(T-.5) SET THE 2 DISTANCE EQUATION EQUAL & SOLVE FOR T. 80T=90(T-.5) 80T=90T-45 80T-90T=-45 -10T=-45 T=-45/-10 T=4.5 HOURS AFTER TRAIN A LEAVE THE STATION THEY WILL MEET. PROOF: 80*4.5=90(4.5-.5) 360=90*4 360=360
 Matrices-and-determiminant/249401: I need help solving this problem using cramer's rule -3x-4y=9 9x+10y=-31 solutions Answer 181667 by checkley77(12569)   on 2009-12-13 19:23:30 (Show Source): You can put this solution on YOUR website!-3x-4y=9 9x+10y=-3 ****************** 9/-3 -4/10 ----------- = x -3/9 -4/10 ******************** 9*10-(-3)(-4) --------------- = x -3(10)-(9*-4) **************** =78/6=13 ans. for x. (90-12)/(-30+36) ********************* -3/9 9/-3 ---------- = y -3/9 -4/10 ******************** -3*-3-9*9 ----------- = 9-81/-30+36=-72/6=-12 ans for y -3*10-9*-4 *********** Proof: -3*-13-4*12=9 -39+48=9 9=9 9*13+10*-12=-3 117-120=-3 -3=-3
 Quadratic_Equations/249403: The diagonal of a television set is 52 inches long. Its length is 28 inches more than its height. Find the dimensions of the television set.1 solutions Answer 181661 by checkley77(12569)   on 2009-12-13 18:58:20 (Show Source): You can put this solution on YOUR website!(28+x)^2+x^2=52^2 784+56x+x^2+x^2=2,704 2x^2+56x+784-2,704 2x^2+56x-1,920=0 2(x^2+28x-960)=0 2(x-20)(x+48)=0 x-20=0 x=20 inches for the height 20+28=48 inches for the length. Proof: 48^2+20^2=52^2 2,304+400=2,704 2,704=2,704
 Linear-systems/249406: solve the equation. 3/y=y/5y-121 solutions Answer 181647 by checkley77(12569)   on 2009-12-13 18:35:14 (Show Source): You can put this solution on YOUR website!3/y=y/(5y-12) cross multiply. y^2=3(5y-12) y^2=15y-36 y^2-15y+36=0 (y-12)(y-3)=0 y-12=0 y=12 ans. y-3=0 y=3 ans.
 Travel_Word_Problems/249358: a driver averaged 52 miles per hour and took 9 hours to travel between two cities. What is the distance between the two cities?1 solutions Answer 181644 by checkley77(12569)   on 2009-12-13 18:31:24 (Show Source): You can put this solution on YOUR website!52*9=468 MILES IS THE DISTANCE.
 Probability-and-statistics/249375: one professor grades homework by randomly choosing 5 out of 15 homework problems to grade. How many different groups of 5 problems can be choosen from the 15 problems?1 solutions Answer 181637 by checkley77(12569)   on 2009-12-13 18:20:04 (Show Source): You can put this solution on YOUR website!(15) (5 ) THIS IS A COMBINATION PROBLEM. 15 ITEMS TAKEN 5 AT A TIME OR: 15!/[5!(15-5)!] 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1/[(5*4*3*2*1)(10*9*8*7*6*5*4*3*2*1] NOW CANCEL OUT TO GROUP (10*9*---*2*1) 15*14*13*12*11/5*4*3*2*1 360,360/120=3,003 GROUPS OF 5 PROBLEMS CAN BE CHOSEN.
 Quadratic_Equations/249368: okay so it says factor completely and it is 2x^3+40x^2+220x . I'm so confused about the cubing part of it, I've never seen it before. I've only factored squared numbers. Can you please help me and show work so i can understand it better? thank you! ;)1 solutions Answer 181614 by checkley77(12569)   on 2009-12-13 17:36:59 (Show Source): You can put this solution on YOUR website!2x^3+40x^2+220x EXTRACT A 2 AND THE X TERM. 2X(X^2+20X+110) NOW FACTOR USING THE QUADRATIC EQUATION BELOW. X=(-20+-SQRT[20^2-4*1*110])/2*1 X=(-20+-SQRT[400-440])/2 X=(-20+-SQRT-40)/2 X=(-20+-6.32455i)/2 X=-20/2+-6.32455i/2 X=-10+-3.16228i ANS.
 Quadratic_Equations/249348: the length of a rectangle is three times its width. if the width is diminished by 1 inch and the length is increased by 3 inches, the area of the new rectangle is 72 square inches. find the dimensions of the original rectangle.1 solutions Answer 181613 by checkley77(12569)   on 2009-12-13 17:28:17 (Show Source): You can put this solution on YOUR website!L=3W AREA=LW FOR THE NEW RECTANGLE: L=L+3 W=W-1 (L+3)=3(W-1) L+3=3W-3 L=3W-3-3 L=3W-6 LW=72 (3W+6)W=72 3W^2+6W-72=0 3(W^2+2W-24)=0 3(W+6)(W-4)=0 W-4=0 W=4 ANS. FOR THE NEW WIDTH. 4-1=3 FOR THE ORIGINAL WIDTH. L*4=72 L=72/4 L=18 ANS. FOR THE NEW LENGTH. 18+3=21 ANS. FOR THE ORIGINAL LENGTH. PROOF: 4*18=72 72=72
 Travel_Word_Problems/249352: flying with the wind a plane went 408 mph. flying into the same wind the plane only went 330mph. find the speed of the wind and the speed of the plane in still air.1 solutions Answer 181608 by checkley77(12569)   on 2009-12-13 17:11:59 (Show Source): You can put this solution on YOUR website!(408-330)/2=78/2=39 mph. was the wind speed. 408-39=369 mph. for the plane. 330+39=369 ditto.
 Expressions-with-variables/249317: 0.3x - 2y = 4 0.4x + 0.5y = 63/19 (fraction) Solve by elimination. Solution is an ordered pair. Use an integers or fractions for any real numbers in the expression. Please help,I don't understand it. 1 solutions Answer 181606 by checkley77(12569)   on 2009-12-13 17:08:49 (Show Source): You can put this solution on YOUR website!0.3x - 2y = 4 0.4x + 0.5y = 63/19 multiply by 4 & add. 1.6x+2y=252/19 0.3x-2y=4 ---------------------- 1.9x=4+252/19 1.9x=(4*19+252)/19 1.9x=(76+252)/19 1.9x=328/19 x=(328/19)/1.9 x=328/19*1.9 x=328/36.1 ans. .3*328/36.1-2y=4 98.4/36.1-2y=4 -2y=4-98.4/36.1 -2y=(4*36.1-98.4)/36.1 -2y=(144.4-98.4)36.1 -2y=46/36.1 y=(46/36.1)/-2 y=-46/36.1*1/2 y=-46/72.2 ans.
 Graphs/249323: Find three different ordered pairs that are solutions of the equation, y=3x-51 solutions Answer 181594 by checkley77(12569)   on 2009-12-13 16:36:13 (Show Source): You can put this solution on YOUR website!y=3x-5 y=0 3x-5=0 or 3x=5 or x=5/3 (5/3,0) y=-3 3x-5=-3 or 3x=-3+5 or 3x=2 or x=2/3 (2/3,-3) y=5 3x-5=5 or 3x=5+5 or 3x=10 or x=10/3 (10/3,5) y=-5 3x-5=-5 or 3x=5-5 or 3x=0 (0,-5)
 Quadratic_Equations/249326: If one side of a square is increased by 2 inches and an adjacent side is decreased by 2 inches, the area of the resulting rectangle is 32 square inches. Find one side of the square.1 solutions Answer 181590 by checkley77(12569)   on 2009-12-13 16:30:16 (Show Source): You can put this solution on YOUR website!(x+2)(x-2)=32 x^2+2x-2x-4=32 x^2-4-32=0 x^2-36=0 (x+6)(x-6)=0 x-6=0 x=6 the length of the original side of the square. Proof: (6+2)(6-2)=32 8*4=32 32=32
 Mixture_Word_Problems/249334: How many gallons of a 10% salt solution should be added to 20 gallons of a 60% salt solution to obtain a 50% salt solution?1 solutions Answer 181586 by checkley77(12569)   on 2009-12-13 16:23:50 (Show Source): You can put this solution on YOUR website!.60*20+.10x=.50(20+x) 12+.10x=10+.50x .10x-.50x=10-12 -.4x=-2 x=-2/-.40 x=5 gallons of 10% salt solution is added. Proof: .60*20+.10*5=.5(20+5) 12+.5=.5*25 12.5=12.5
 Coordinate-system/249330: what are the intercepts of 5y-15=5x1 solutions Answer 181584 by checkley77(12569)   on 2009-12-13 16:19:10 (Show Source): You can put this solution on YOUR website!5y-15=5x 5y=5x+15 5y=5x+15 y=5x/5+15/5 y=x+3 The y intercept=3. Setting y=0 & solving for x 0=x+3 x=-3 Intercepts are: (-3,3) (graph 300x200 pixels, x from -6 to 5, y from -6 to 5, x +3).
 Rectangles/249097: The width of a rectangle is 5 meters less than twice its length. If its area is 88 square meters, find the dimensions of the rectangle. I appreciate your help!1 solutions Answer 181550 by checkley77(12569)   on 2009-12-13 10:14:35 (Show Source): You can put this solution on YOUR website!W=L-5 LW=88 L(L-5)=88 L^2-5L-88=0 (L-11)(L+8)=0 L=11=0 L=11 ANS. FOR THE LENGTH. W=11-5=6 ANS. FOR THE WIDTH. PROOF: 8*11=88 88=88
 Linear-equations/249114: write the equation of a line that is prependicular to the given line and that passes throught the given point. 4x-12y=2;(10,-1)1 solutions Answer 181549 by checkley77(12569)   on 2009-12-13 10:11:24 (Show Source): You can put this solution on YOUR website!Perpendicular to 4x-12y=2 & passing through (10,-1) 4x-12y=2 -12y=-4x+2 y=-4x/-12+2/-12 y=x/3-1/6 this line has a slope=1/3. (red line) Thus a perpendicular line would have a slope=-3 -1=-3*10+b -1=-30+b b=-1+30 b=29 ans. for the y intercept. y=-3x+29 (green line). (graph 300x300 pixels, x from -6 to 25, y from -10 to 30, of TWO functions x/3 -1/6 and -3x +29).
 Square-cubic-other-roots/249125: sqrt 49y^6/36x^41 solutions Answer 181544 by checkley77(12569)   on 2009-12-13 09:39:53 (Show Source): You can put this solution on YOUR website!sqrt(49y^6/36x^4) [7y^3/6x^2] ans.
 Linear-equations/249131: The price of an item was \$30 its first year,\$66 in its 4th year, and it can be assumed that its price will continue to increase linearly. Write a simplified equation describing the relationship between cost and year. find the cost for the 7th year1 solutions Answer 181543 by checkley77(12569)   on 2009-12-13 09:37:29 (Show Source): You can put this solution on YOUR website!(66-30)/4=36/4=9 dollars per year is the increase. c=9x+30 x being the year. Example: c=(9*7+30)=(63+30)=\$93 would be the cost in the 7th. year.
 Geometry_Word_Problems/249155: A cylinder has a radius of 3 cm and a height of 8 cm. What is the longest segment, in centimeters, that would fit inside the cylinder?1 solutions Answer 181542 by checkley77(12569)   on 2009-12-13 09:31:51 (Show Source): You can put this solution on YOUR website!What you have is a right triangle with a base=2*3=6cm & a height=8cm. The longest segment would be the hypotenuse of this triangle thus. a^2+b^2=c^2 [c being the hypotenuse) 6^2+8^2=c^2 36+64=c^2 100=c^2 c=sqrt100 c=10 ans. for the longest segment that would fit inside the cylinder.
 Functions/249172: i am solving the question "find the slope of the graph of the linear function f" and so far i got to 1=8m+2b and i dont know what to do next. 1 solutions Answer 181540 by checkley77(12569)   on 2009-12-13 09:26:12 (Show Source): You can put this solution on YOUR website!Y=mX+b 1=8m+2b If you mean Y=1, m=8, & b=2 Then y=8X+2 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, 8x +2).
 Travel_Word_Problems/249024: 80 miles per hour = how many feet per sec?1 solutions Answer 181459 by checkley77(12569)   on 2009-12-12 19:16:10 (Show Source): You can put this solution on YOUR website!80*5280=264,000 FT PER HOUR 264,000/60*60=73.33 FT PER SEC.
 Equations/249032: What volumes of 60% hydrocloric acid solution and 30% hydrocloric acid solution must be mixed to make 125 ml of 36% hydrocloric acid solution.1 solutions Answer 181456 by checkley77(12569)   on 2009-12-12 19:10:55 (Show Source): You can put this solution on YOUR website!.60X+.30(125-X)=.36*125 .60X+37.5-.30X=45 .30X=45-37.5 .30X=7.5 X=7.5/.3 X=25 ML. OX 60% ACID IS USED. 125-25=100 ML. OF 30% ACID IS USED. .60*25+.30*100=.368125 15+30=45 45=45
 Proportions/249043: determine if the quantities in each pair of ratios are proportional. 34 students from 8 schools and 25 students from 6 schools1 solutions Answer 181455 by checkley77(12569)   on 2009-12-12 19:04:07 (Show Source): You can put this solution on YOUR website!34/8=25/6 CROSS MULTIPLY 8*25=34*6 200=204 THESE RATIOS ARE NOT EQUAL.
 Numbers_Word_Problems/249047: 1) Two consecutive integers are added. The square of their sum is 361. What are the integers ? 2) The product of two consecutive even numbers is 288. What are the numbers ?1 solutions Answer 181453 by checkley77(12569)   on 2009-12-12 19:01:46 (Show Source): You can put this solution on YOUR website!LET X & X+1 ARE THE 2 INTEGERS. (X+X+1)^2=361 (2X+1)^2=361 4X^2+4X+1=361 4X^2+4X+1-361=0 4(X^2+X-90)=0 4(X+10)(X-9)=0 X+10=0 X=-10 ANS & -9 X-9=0 X=9 ANS & 10 PROOF: (9+10)^2=361 19^2=361 361=361
 Systems-of-equations/248961: m-2n=16 4m+n=11 solutions Answer 181451 by checkley77(12569)   on 2009-12-12 18:43:56 (Show Source): You can put this solution on YOUR website!m-2n=16 4m+n=1 MULTIPLY BY 2 & ADD 8M+2N=2 M-2N=16 --------------- 9M=18 M=18/9 M=2 ANS. 2-2N=16 -2N=16-2 -2N=14 N=14/-2 N=-7 ANS. PROOF: 2-2*-7=16 2+14=16 16=16
 Systems-of-equations/248963: 2.5(x-3)+1.7x=10.8(x+1.5) what is x1 solutions Answer 181447 by checkley77(12569)   on 2009-12-12 18:29:41 (Show Source): You can put this solution on YOUR website!2.5(x-3)+1.7x=10.8(x+1.5) 2.5X-7.5+1.7X=10.8X+16.2 2.5X+1.7X-10.8X=16.2+7.5 -6.6X=23.7 X=23.7/-6.6 OR -23.7/6.6 ANS. PROOF: 2.5(-23.7/6.6-3)+1.7*-23.7/6.6=10.8(-23.7/6.6+1.5) 2.5[(-23.7*-3*6.6)/6.6]-40.29/6.6=10.8[(-23.7+1.5*6.6)/6.6] 2.5[-23.7-19.8)/6.6]-40.29/6.6=10.8[(-23.7+9.9)/6.6] 2.5[-43.5)/6.6]-40.29/6.6=10.8[-13.8/6.6] -108.75/6.6-40.29/6.6=-149.04/6.6 149.04/6.6=149.04/6.6
 Systems-of-equations/248964: Solve this equation by elimination 5x+3y=19 2x-5y=111 solutions Answer 181442 by checkley77(12569)   on 2009-12-12 18:00:14 (Show Source): You can put this solution on YOUR website!5x+3y=19 MULTIPLY BY 5 2x-5y=11 MULTIPLY BY 3 & ADD 25X+15Y=95 6X-15Y=33 ------------------ 31X=128 X=128/31 ANS. 2*128/31-5Y=11 256/31-5Y=11 -5Y=11-256/31 -5Y=(11*31-256)/31 -5Y=(341-256)/31 -5Y=85/31 Y=(85/31)/-5 Y=(85/31)*1/-5 Y=-85/155 Y=-17/31 ANS.