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checkley77 answered: 12560 problems
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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 = 240 1 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=-3 1 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-12 1 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-5 1 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=5x 1 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^4 1 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 year 1 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 schools 1 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=1 1 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 x 1 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=11 1 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.