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# Recent problems solved by 'mananth'

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 Miscellaneous_Word_Problems/380158: Gerald and John agreed to start from the same point and go in opposite directions every morning for a jog. If Gerald runs at a speed of 3km/hr ans John has a speed of 4km/hr,in how many hrs. will they be 14 km apart?1 solutions Answer 269817 by mananth(12270)   on 2010-12-03 00:57:44 (Show Source): You can put this solution on YOUR website!Gerald runs at a speed of 3km/hr John has a speed of 4km/hr, in how many hrs. will they be 14 km apart .. they are running in opposite directions add up speeds 4+3=7 km/hr .. distance = 14 km ... t= d/r t= 14/7 t= 2 After 2 hours they will be 14 km apart ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/380148: (x2+26x-87)/(x-3)1 solutions Answer 269816 by mananth(12270)   on 2010-12-03 00:54:52 (Show Source): You can put this solution on YOUR website! ... ... ... ... ... x+29 .. m.ananth@hotmail.ca
 Travel_Word_Problems/380152: two cars start from points 420 miles apart and travel toward each other. They meet after 3. 5hours. Find the average speed of each car if one travels 30 mph slower than the other1 solutions Answer 269815 by mananth(12270)   on 2010-12-03 00:47:50 (Show Source): You can put this solution on YOUR website!Distance = 420 miles .. speed of 1 car = x speed of other car = x-30 ... time they meet = 3.5 hours ... since they are travelling towards each other add up the speeds x+x-30= 2x-30 .. t= d/r 3.5=420/(2x-30) multiply by (2x-30) 3.5(2x-30)=420 7x-105=420 +105 7x=420+105 7x=525 /7 x=75 mph ....speed of one car speed of other car = 75 -30 = 45 mph ... m.ananth@hotmail.ca
 Mixture_Word_Problems/380155: A chemist needs 12 liters of a 40% alcohol solution. She must mix a 20% solution and a 50% solution. How many liters of each well be required to obtain what she needs?1 solutions Answer 269814 by mananth(12270)   on 2010-12-03 00:42:01 (Show Source): You can put this solution on YOUR website!A chemist needs 12 liters of a 40% alcohol solution. She must mix a 20% solution and a 50% solution. How many liters of each well be required to obtain what she needs? ... 20% solution .............x liters 50% solution.............12-x liters 40%.......................12 liters (requirement) ... I have not converted the percentage to 0.2,0.5,0.4.as generally done. Even if we convert it, we again multiply by 100 for easy calculation .. 20*x+50*(12-x)=40*12 20x+600-50x=480 20x-50x=480-600 -30x=-120 /-30 x= 4 liters 20% solution 12-x = 8 liters of 50% solution. ... m.ananth@hotmail.ca
 Graphs/380089: y=3x+2 6x-2y=-4 pick between (3,0),(-3,1),infinitely many solutions, or no solution 1 solutions Answer 269785 by mananth(12270)   on 2010-12-02 22:55:36 (Show Source): You can put this solution on YOUR website!y=3x+2 ..... 6x-2y=-4 /2 3x-y=-2 y=3x+2 .. the equations are of the same line. so there are infintely many solutions ... m.ananth@hotmail.ca
 Linear_Equations_And_Systems_Word_Problems/380099: 10. You invested your money in a fixed interest junk bond that earns 8.35% per year interest. How many years with simple interest will it take to double your money?1 solutions Answer 269784 by mananth(12270)   on 2010-12-02 22:50:57 (Show Source): You can put this solution on YOUR website!Interest rate = 8.35% Let principal be \$ 100 double your money = \$200 So interest = \$200-100=\$100 n = number of years ... I= p*r*n 100=100*0.0835*n n= 100/100 *0.0835 n=1/0.0835 n= 11.97 years Say 12 years ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/380101: Micah paid \$1,080 for a new set of drums that were marked 20% off. What was the original price of the drums? 1 solutions Answer 269782 by mananth(12270)   on 2010-12-02 22:42:46 (Show Source): You can put this solution on YOUR website!20 % off so he paid 80 % of the price let x be the price .. cross multiply x= \$1350 ... m.ananth@hotmail.ca
 Rectangles/380100: A rectangle is 4 1/2 feet long and 1 3/4 feet wide. Find the area of the rectangle. 1 solutions Answer 269780 by mananth(12270)   on 2010-12-02 22:36:48 (Show Source): You can put this solution on YOUR website!Area = L*W Length = 4 1/2 feet = 9/2 Width = 1 3/4 feet = 7/4 .. Area = .. Area = .. area = 7 7/8 feet ... m.ananth@hotmail.ca
 Rectangles/380097: The area of a rectangle is 15 square feet. The width can be represented by x - 3.5 and the length by 'x'. What are the dimensions of the rectangle? I've tried this problem a dozen times. I don't know what it is I'm doing wrong.1 solutions Answer 269778 by mananth(12270)   on 2010-12-02 22:30:59 (Show Source): You can put this solution on YOUR website!wid th = x-3.5 length =x .. Area = l*w x(x-3.5)=15 x^2-3.5x=15 multiply by 2 2x^2-7x=30 -30 2x^2-7x-30=0 2x^2-12x+5x-30=0 2x(x-6)+5(x-6)=0 (2x+5)(x-6)=0 x= 6 feet, the length x-3.5 =6-3.5 = 2.5 feet, the width. ... CHECK Area = l*w 6*2.5 = 15 .. m.ananth@hotmail.ca ...
 Age_Word_Problems/380072: Sarah is two thirds as old as her cousin. The sum of their ages is 45. How old are Sarah and her cousin?1 solutions Answer 269763 by mananth(12270)   on 2010-12-02 22:00:22 (Show Source): You can put this solution on YOUR website!cousin = x years Sarah = 2x/3 years .. 2x/3 +x = 45 LCD = 3 multiply by 3 2x/3 * 3 +3*x=45*3 2x+3x=135 5x=135 /5 x= 135/5 x=27 years cousins age. .. Sarah = 2*27/3=18 years .. m.ananth@hotmail.ca
 Rectangles/380068: Shaunice has 36 feet of fence to put around her rectangular flowerbed. How long and how wide will the flowerbed have to be so that she has 72 square feet of area to plant flowers?1 solutions Answer 269760 by mananth(12270)   on 2010-12-02 21:55:07 (Show Source): You can put this solution on YOUR website!let length be l width be w .. 2(l+w)=36 /2 l+w=18 ... Area = l*w = 72 .. 12 & 6 are the factors .. The dimensiona are 12 feet by 6 feet ... CHECK Perimeter = 12+12+6+6=36 area = 12*6 = 72 .. m.ananth@hotmail.ca
 Graphs/380070: How do I Solve the inequality: -15<5x<20 (Negative Fifteen is less than or equal to five(x) less than twenty.) 1 solutions Answer 269757 by mananth(12270)   on 2010-12-02 21:48:56 (Show Source): You can put this solution on YOUR website! /5 .. ...
 Linear-equations/379981: so im working on my homework and the equation is slope intercept and it's so confusing. i tried doing it okay, m=1/4 (-2,-3) than i got y-2=1/4(x--3) so you add two to three than 1/4 times x= 1/4x=14? than i can't figure out how to turn that into slope-intercept form.1 solutions Answer 269729 by mananth(12270)   on 2010-12-02 20:14:00 (Show Source): You can put this solution on YOUR website!m=1/4 (-2,-3) ... you have to write the equation in the form y= mx+b First you have to find the value of b .. plug value of m and the point(-2,-3)in the equation .. -3=(1/4 *-2)+b -3=-1/2 +b add 1/2 -3+1/2 =b -5/2 = b .. Now form the equation y = 1/4*x -5/2 OR in decimal form y = 0.25x-2.5 .. m.ananth@hotmail.ca
 Travel_Word_Problems/379974: A boat travels 20 miles upstream in 5hours. Going downstream, it can travel 50 miles in the same amount of time. Find the speed of the current and the speed of the boat in still water. 1 solutions Answer 269727 by mananth(12270)   on 2010-12-02 20:06:25 (Show Source): You can put this solution on YOUR website!A boat travels 20 miles upstream in 5hours. Going downstream, it can travel 50 miles in the same amount of time. Find the speed of the current and the speed of the boat in still water. ... speed of boat = x mph speed of current = y mph .. speed against current = 4 mph speed with current = x+y mph ... time downstream = time upstream .. t=d/r .. 5=50/(x+y) 5(x+y)=50 /5 x+y =10 x-y=4 add the equations 2x=14 /2 x=7 .. speed in still water = 7 mph speed of current = 3 mph .. m.ananth@hotmail.ca
 Quadratic_Equations/379966: I have to find the zeros or roots of each function or equation by factoring & graphing. g(x)= 2x^2 - 25x + 12 2(x ) (x ) I know that the multiples of 12 should add up to -25 but there are none so I do not understand how to find the zeros by factoring1 solutions Answer 269717 by mananth(12270)   on 2010-12-02 19:55:42 (Show Source): You can put this solution on YOUR website!g(x)= 2x^2 - 25x + 12 ... it is multiples of 24 and not 12. 2*12 .. 2x^2-24x-x+12=0 2x(x-12)-1(x-12)=0 (x-12)(2x-1)=0 x=12 OR 1/2 ... ... m.ananth@hotmail.ca
 Triangles/379565: If the longest side of a triangle is 10 centimeters, does the perimeter have to be bigger than 20 centimeters? I think the triangle perimeter has to be bigger than 20 centimeters because each side would be 10 centimeters and the perimeter would be 30. But my mom says it is possible for a triangle could be equal to 20 centimeters if two sides equal 5 centimeters and the longest side is 10 centimeters. Which is correct? Thank you!1 solutions Answer 269500 by mananth(12270)   on 2010-12-02 08:27:15 (Show Source): You can put this solution on YOUR website!If the longest side of the three sides is less than the sum of the other two sides, then a triangle could be formed. .. you should have sum of other two side greater than 10 then a triangle can be drawn. sum of the other two sides must be >10. .. It is not necessary that the triangle perimeter be more than 30 cm
 Polynomials-and-rational-expressions/379562: solve (4y/y-3) -2 = 1/y-3 thanks1 solutions Answer 269486 by mananth(12270)   on 2010-12-02 08:06:28 (Show Source): You can put this solution on YOUR website! .. .. LCD = (y-3) .. multiply by (y-3) 4y-1=2(y-3) 4y-1=2y-6 -2y 4y-2y-1=-6 2y-1=-6 +1 2y=-6+1 2y=-5 /2 y =-5/2 .. m.ananth@hotmail.ca
 percentage/379551: after adding a 4% sales tax, selling price of a lamp was 15.60. what was its price before tax?1 solutions Answer 269481 by mananth(12270)   on 2010-12-02 07:59:12 (Show Source): You can put this solution on YOUR website!sales tax 4% let original price = x 1.04x=15.60 /1.04 x=15.60/1.04 x= \$15 the price before tax. ... m.ananth@hotmail.ca
 Linear_Equations_And_Systems_Word_Problems/379553: what is twice a nnumber minus 4 is less than 3 times a number1 solutions Answer 269479 by mananth(12270)   on 2010-12-02 07:55:47 (Show Source): You can put this solution on YOUR website!let number be n 2n-4 < 3n +4 2n+4-4<3n+4 2n<3n+4 -3n 2n-3n<4 -n<4 /-1 n>-4 ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/379559: solve (w/w+2) - 5 = 2/w+2 thank you1 solutions Answer 269477 by mananth(12270)   on 2010-12-02 07:47:24 (Show Source): You can put this solution on YOUR website!(w/w+2) - 5 = 2/w+2 LCD = (w+2) ... .. w-2=5(w+2) w-2=5w+10 -w -2=4w+10 -10 -12=4w /4 -3=w ... w=-3 ... m.ananth@hotmail.ca
 Exponents/379549: I'm very much stuck on this problem. I'm not sure if this is in the right section, but I hope someone can help. (2^x)^(x+3)=1/4 If I try to simply this using the rules of exponents, I get.. 2^(x^2+3x)=1/4 How can I possibly simplify this since x^2 and 3x are not like terms? I thought about making it a logarithm to make it no longer an exponent, but I still can't figure out how I would solve for x. Please help! 1 solutions Answer 269471 by mananth(12270)   on 2010-12-02 06:21:32 (Show Source): You can put this solution on YOUR website!2^(x^2+3x)=1/4 2^(x^2+3x)=1/2^2 2^(x^2+3x)=2^-2 .. x^2+3x=-2 x^2+3x+2=0 x^2+2x+x+2=0 x(x+2)+1(x+2)=0 (x+2)(x+1)=0 x=-1 OR x=-2
 Linear_Equations_And_Systems_Word_Problems/379547: An airplane can fly 650 miles with the wind in the same amount of time as it can fly 475 miles against the wind. If the wind speed is 40mph, find the speed of the plane in still air.1 solutions Answer 269470 by mananth(12270)   on 2010-12-02 06:16:06 (Show Source): You can put this solution on YOUR website!An airplane can fly 650 miles with the wind in the same amount of time as it can fly 475 miles against the wind. If the wind speed is 40mph, find the speed of the plane in still air. ... wind speed = 40 mph let plane speed = xmph .. against wind speed = x-40 with wind speed = x+40 .. time with wind = time against wind t=d/r 650/(x+40)=475/(x-40) cross multiply 650(x-40)=475(x+40) 650x-26000=475x+19000 650x-475x=26000+19000 175x=45000 /175 x= 45000/175 257 mph the speed of plane ... m.ananth@hotmail.ca
 Linear_Equations_And_Systems_Word_Problems/379546: A repairman purchased some washing machine motors for a total of \$224. When the unit cost decreased by \$4, he was able to buy one extra motor for the same total price. How many motors did he buy originally?1 solutions Answer 269469 by mananth(12270)   on 2010-12-02 06:05:02 (Show Source): You can put this solution on YOUR website!let the number of motors he bought be x he paid \$224 so he paid 224/x for each motor. .. (224/x) -4 is the reduced price. he got (x+1) motors ((224/x)-4)(x+1)=224 ((224-4x)/x)(x+1)= 224 (224-4x)(x+1)/x=224 multiply by x (224-4x)(x+1)= 224x 224x+224-4x^2-4x=224x re write 224x-224x+224 -4x^2-4x=0 4x^2+4x-224=0 /4 x^2+x-56=0 x^2+8x-7x-56=0 x(x+8)-7(x+8)=0 (x+8)(x-7)=0 x= 7 The number of motors he bought originally = 7 .. m.ananth@hotmail.ca
 Expressions-with-variables/379541: Please help solve using the LCD to simplify complex fraction. 1/x + 1/y --------- 3/x + 3/y1 solutions Answer 269460 by mananth(12270)   on 2010-12-02 03:29:48 (Show Source): You can put this solution on YOUR website!1/x + 1/y --------- 3/x + 3/y .. .. .. ... ... m.ananth@hotmail.ca
 Geometry_Word_Problems/379443: write a system of two linear equations in two variables for:a plane flew with a tail wind from madrid to lima, a trip of 1054 km in 93 min, the return trip took 9 more mins. Let p be the air speed of the plane in km/h and w for the wind speed in km/h. solve the system and find the air speed of the plane1 solutions Answer 269456 by mananth(12270)   on 2010-12-02 01:32:05 (Show Source): You can put this solution on YOUR website!speed of plane = p kmph speed of wind = w kmph .. speed with wind = p+w speed against wind = p-w .. distance = 1054 km .. time with wind = 93 minutes = 1.55 hours time against wind = 102 minutes= 1.7 hours .. t=d/r 1054/p+w= 1.55 1054 =1.55p+1.55w...............1 ... 1054/(p-w)=1.7 1054 = 1.7p+1.7w................2 ... solve these equations (1) & (2) to get the value of p & w p= 650 km/h w = 30 km/h ... m.ananth@hotmail.ca
 Problems-with-consecutive-odd-even-integers/379526: lea has 5 more 5 peso coins than 10 peso coins.the total number of coins she have 15.how much is her money.1 solutions Answer 269455 by mananth(12270)   on 2010-12-02 01:13:16 (Show Source): You can put this solution on YOUR website!10 peso coins = x 5 peso coins x+5 .. Total coins = 15 x+x+5 =15 2x+5=15 -5 2x=15-5 2x=10 /2 x=5 she has 5, 10 peso coins so she has 10 , 5peso coins. .. 5*10+ 10*5 = 100 pesos. ... m.ananth@hotmail.ca
 Rational-functions/379489: we are graphing quadratic equations and the teacher isn't explaining it in simpler terms it is a function and i need help with the steps to solve the fuction is y=-2x^2-2x+3 and we have to graph it. can you help me and give me the steps? 1 solutions Answer 269453 by mananth(12270)   on 2010-12-02 00:09:33 (Show Source): You can put this solution on YOUR website!y=-2x^2-2x+3 ... first find the x intercepts. plug y =0 -2x^2-2x+3=0 ... Find the root of the equation using quadratic formula. discriminant b^2-4ac= 28 x1=(2+sqrt(28))/-4 x1=-1.82 ... x2=(2-sqrt(28))/-4 x2=0.82 ... The x intercepts are (0,-1.8) & (0,0.82) .. Using the equation y = -2x^2-2x+3 find the vertex of the parabola a=-2, b=-2 h=(-b/2a) h=(2/-4) h=-1/2 plug the value of (-1/2) in the equation to get the y value of the vertex y= -2*(1/4)-2*-1/2+3 y=-0.5+1+3 y=3.5 Vertex ( -1/2 , 3.5) .. since x^2 is negative the parabola opens downwards . generate various value of y for different values of x x=-1, y=3 x=1,y=-1 x=-2,y=3 x=2,y=-9 x=2,y=-9 ... use a calculator or plot points and join the curve.
 Equations/379490: IN 1912, an order by President Taft fixed the width and length of the U.S. flag in the ration 1 to 1.9. If 100 square feet of cloth are to be used to make a U.S. flag, estimate its dimensions to the nearest 1/4 foot. How can I solve this?1 solutions Answer 269444 by mananth(12270)   on 2010-12-01 23:30:44 (Show Source): You can put this solution on YOUR website!Ratio of width to length = 1:1.9 area of flag = 100 sq. ft ... Let the constant factor be x (1*x)*(1.9*x)=100 1.9x^2=100 x^2=100/1.9 x= sqrt(100/1.9) x= 7.25 feet ... length = 7.25 *1.9 = 13.77 ... The dimensions are 7.25 feet by 13.75 feet .. m.ananth@hotmail.ca
 Quadratic_Equations/379484: solve by completing the square. m^2- 9/2m=3/21 solutions Answer 269438 by mananth(12270)   on 2010-12-01 23:16:34 (Show Source): You can put this solution on YOUR website! ... ... ... .. take the square root m-(9/4)= +/- 2.561 ... m1= +(2.561)+2.250 m1= 4.811 ......... m2= -2.561+2.250 m2=-0.311 ....... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/379474: Im stumped! Essay; show all work. Find the product: (5/6x^2-2/3)(1/2x-1/3)1 solutions Answer 269405 by mananth(12270)   on 2010-12-01 22:51:46 (Show Source): You can put this solution on YOUR website!(5/6x^2-2/3)(1/2x-1/3) rationalize the denominators in each parenthesis LCD is = 6 for both .. ... FOIL ... ... m.ananth@hotmail.ca
 Quadratic_Equations/379470: Give exact and approximate solutions to three decimal places. y^2-16y+64=361 solutions Answer 269391 by mananth(12270)   on 2010-12-01 22:38:09 (Show Source): You can put this solution on YOUR website!y^2-16y+64=36 -36 y^2-16y+64-36=0 .. y^2-16y+28 ... y^2-14y-2y+28=0 y(y-14)-2(y-14)=0 (y-14)(y-2)=0 y = 2, 14 ... m.ananth@hotmail.ca