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# Recent problems solved by 'mananth'

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 Inequalities/398256: Graph the inequality. 4x+3y>-3 1 solutions Answer 282218 by mananth(12270)   on 2011-01-22 20:41:46 (Show Source): You can put this solution on YOUR website!Graph the inequality. 4x+3y>-3 -4x 3y>-4x-3 /3 y>(-4x/3)-1 ... the boundary ... The inequality
 Graphs/398036: graph and check to solve the linear system. 3x+y=5 -x+y=-71 solutions Answer 282050 by mananth(12270)   on 2011-01-21 22:27:45 (Show Source): You can put this solution on YOUR website!graph and check to solve the linear system. 3x+y=5 -x+y=-7 ... 3x+5y=5................1 -x+y=-7................2 ... multiply (2) by 3 -3x+3y=-21 add to (1) 8y=-16 y=-2 .. plug value of y in 2 -x-2=-7 -x=-5 x=5 ...
 Travel_Word_Problems/398038: a train travels 20 feet in 1/5 seconds, at the same speed how many feet will it travel in three seconds1 solutions Answer 282045 by mananth(12270)   on 2011-01-21 22:17:30 (Show Source): You can put this solution on YOUR website!a train travels 20 feet in 1/5 seconds, at the same speed how many feet will it travel in three seconds 20 feet in 1/5 second so in 1 second it will travel 5 times the distance 5*20=100feet .. so in 3 seconds it will travel 300 feet
 Geometry_Word_Problems/398013: A rectangular plot of ground having dimensions 21 ft by 24 ft is surrounded by a walk of uniform width. If the area of the walk is 424 ft2, what is its width?1 solutions Answer 282043 by mananth(12270)   on 2011-01-21 22:13:55 (Show Source): You can put this solution on YOUR website!A rectangular plot of ground having dimensions 21 ft by 24 ft is surrounded by a walk of uniform width. If the area of the walk is 424 ft2, what is its width? .. area of ground = 21*24=504 ft^2 ... area of walk = 424 ft^2 .. let width of walk be x .. width of total area = 21+2x length of total area = 24+2x .. Area of total area = (21+2x)(24+2x) Total Area = 504+90x+4x^2 .. 4x^2+90x+504-504 = 424 4x^2+90x-424=0 Find the roots of the equation by quadratic formula a= 4 , b =90 , c = -424 . b^2-4ac=14884 x1= 4 x2= negative so ignore walk width = 4 feet ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/398019: Amount of an investment. The amount of an investment of P dollars for t years at simple interest rate r is given by A = P + Prt. a) Rewrite this formula by factoring out the greatest common factor on the right-hand side. b) Find A if \$8300 is invested for 3 years at a simple interest rate of 15%.1 solutions Answer 282035 by mananth(12270)   on 2011-01-21 21:52:48 (Show Source): You can put this solution on YOUR website!Amount of an investment. The amount of an investment of P dollars for t years at simple interest rate r is given by A = P + Prt. a) Rewrite this formula by factoring out the greatest common factor on the right-hand side. b) Find A if \$8300 is invested for 3 years at a simple interest rate of 15%. ... A=P+Prt A=P(1+rt) A=8300(1+0.15*3) A=8300(1.45) A=\$ 12035
 Geometry_Word_Problems/398015: A farmer plans to enclose a rectangular region, using part of his barn for one side and fencing for the other three sides. If the side parallel to the barn is to be twice the length of an adjacent side, and the area of the region is to be 98 ft2, how many feet of fencing should be purchased?1 solutions Answer 282033 by mananth(12270)   on 2011-01-21 21:47:13 (Show Source): You can put this solution on YOUR website!A farmer plans to enclose a rectangular region, using part of his barn for one side and fencing for the other three sides. If the side parallel to the barn is to be twice the length of an adjacent side, and the area of the region is to be 98 ft2, how many feet of fencing should be purchased? ... let the adjacent side be x ft. the other side will be 2x ... The area = L*W Area = x*2x=2x^2 2x^2=98 x^2=49 x=7 feet .. the three sides to be fenced will be x+x+2x=4x x=7 so 7*4 = 28 feet of fencing will be required. ... m.ananth@hotmail.ca
 Linear-equations/398022: how do you this problem so can graph it 2x+y=11 solutions Answer 282031 by mananth(12270)   on 2011-01-21 21:37:45 (Show Source): You can put this solution on YOUR website!how do you this problem so can graph it 2x+y=1 .. 2x+y=1 y=-2x+1 .. generate values for y from various values of x x=0,y=1........(0,1) y=0,x=1/2.......(1/2,0) .. plot these points and draw the line graph. ... check to see whether the slope is -2 from the graph. ... m.ananth@hotmail.ca
 Rational-functions/398025: Solve (type an integer or a simplified fraction. Use a common to separate answers as needed. Type each solution only once) w^2+w-20=0 1 solutions Answer 282023 by mananth(12270)   on 2011-01-21 21:22:26 (Show Source): You can put this solution on YOUR website!w^2+w-20=0 ... w^2+5w-4w-20 w(w+5)-4(w+5)=0 (w+5)(w-4)=0 ... w= -5, 4
 Rational-functions/398028: Subtract. Simplify by collecting like radical terms if possible. 3√12-3√3 1 solutions Answer 282022 by mananth(12270)   on 2011-01-21 21:20:17 (Show Source): You can put this solution on YOUR website! .. ... ...
 Rational-functions/398027: Find a Polynomial for the perimeter and for the area. (Simplify, do not factor) N+2 n The perimeter is The area is 1 solutions Answer 282021 by mananth(12270)   on 2011-01-21 21:17:26 (Show Source): You can put this solution on YOUR website!length = n+2 width = n .... Perimeter = 2*(L+W)\ Perimeter = 2(n+n+2) =2*(2n+2) if n is not equal to N ( due a typo) then 2*(n+N+2)units .. Area = L*W n(N+2)sq.units
 Volume/397189: Harry has a large number of cubes, all with edges 3cm long.What is the greatest number of these cubes that he could fit into a) A Cubical box with all its internal edges 12cm long. b) A box in the shape of a cuboid with internal dimensions 17cm by 10cm by 8cm.1 solutions Answer 281573 by mananth(12270)   on 2011-01-20 08:34:54 (Show Source): You can put this solution on YOUR website!Harry has a large number of cubes, all with edges 3cm long.What is the greatest number of these cubes that he could fit into a) A Cubical box with all its internal edges 12cm long. b) A box in the shape of a cuboid with internal dimensions 17cm by 10cm by 8cm. volume of bigger cube/volume of smaller cube = number of cubes .. side = 12 v= 12*12*12 =1728cm^3 ... volume of small cube = 3*3*3=27cm^3 1728/27 =64 small cubes .. Volume of cuboid = 17*10*8 V=1360 cm^3 1360/27 50.3 50 small cubes can be placed , m.ananth@hotmail.ca
 Exponents/397214: i really dont understand the solving for y or x..1 solutions Answer 281572 by mananth(12270)   on 2011-01-20 08:27:16 (Show Source): You can put this solution on YOUR website!where is the problem?
 Systems-of-equations/397216: Solve by elimination method 6x-9y=13.5 7y-2x=-6.51 solutions Answer 281571 by mananth(12270)   on 2011-01-20 08:26:12 (Show Source): You can put this solution on YOUR website!6x-9y=13.5................1 7y-2x=-6.5................2 ... multiply (2) by 3 21y-6x=-19.5 add to (1) 21y-9y=-19.5+13.5 12y=-6 /12 y=-1/2 ... plug value of y in 1 6x-9*1/2=13.5 6x=13.5-4.5 6x=9 x=1.5 ... m.ananth@hotmail.ca
 Travel_Word_Problems/397197: Beth was required to make a cross-country flight in training for her pilot's license. When she flew from her home airport, a steady 30 miles per hour wind was behind her, and the trip took 5 hours. When she returned against the wind, the flight took 7 hours. Find the plane's speed in still air and the distance traveled each way.1 solutions Answer 281569 by mananth(12270)   on 2011-01-20 08:18:24 (Show Source): You can put this solution on YOUR website!Beth was required to make a cross-country flight in training for her pilot's license. When she flew from her home airport, a steady 30 miles per hour wind was behind her, and the trip took 5 hours. When she returned against the wind, the flight took 7 hours. Find the plane's speed in still air and the distance traveled each way. plane's speed = x mph .. with wind speed = x+30 against wind = x-30 ... d=rt. d is same so equate the distance 5(x+30)=7(x-30) 5x+150=7x-210 7x-5x=210+150 2x=360 /2 x= 180 mph speed in still air .. m.ananth@hotmail.ca
 Mixture_Word_Problems/397207: A collection of nickels and dimes adds up to \$5.60. If the ratio of dimes to nickels is 3:2, how many of each coin is there?1 solutions Answer 281567 by mananth(12270)   on 2011-01-20 08:11:01 (Show Source): You can put this solution on YOUR website!nickels to dimes = 3/2 let the common factor be x 3x/2x= 5(3x)+10(2x)=560 15x+20x=560 35x=560 x= 560/35 x=16 ... nickels = 3*16=48 Dimes= 2*16=32 .. CHECK 48*5+10*32=240+320=560
 Linear-equations/397211: how would I solve x/2 + x/3= 3/4 I know the least common denominator is 12 but I am having trouble working the problem out.1 solutions Answer 281564 by mananth(12270)   on 2011-01-20 07:57:59 (Show Source): You can put this solution on YOUR website!how would I solve x/2 + x/3= 3/4 I know the least common denominator is 12 but I am having trouble working the problem out. . x/2 + x/3= 3/4 LCD =12 multiply each fraction by 12 12x/2 +12x/3=36/4 6x+4x=9 10x=9 divide by 10 x= 9/10
 Numbers_Word_Problems/397208: The sum of one-half, one-third and one-fourth of a number exceeds the number by 12. The number is1 solutions Answer 281561 by mananth(12270)   on 2011-01-20 07:49:55 (Show Source): You can put this solution on YOUR website!The sum of one-half, one-third and one-fourth of a number exceeds the number by 12. The number is let the number be x x/2 +x/3+x/4 = x+12 ... LCD = 12 (6x+4x+3x)/12=x+12 13x= 12(x+12) 13x=12x+144 13x-12x=144 x= 144 ..
 test/396592: The sum of 3 integers is 123. The second number is two more than twice the first number. The third number is five less than the product of three and the first number. Find the three numbers1 solutions Answer 281279 by mananth(12270)   on 2011-01-19 01:33:37 (Show Source): You can put this solution on YOUR website!The sum of 3 integers is 123. The second number is two more than twice the first number. The third number is five less than the product of three and the first number. Find the three numbers ... let the integers be x, y, z .. x+y+z=123...........................1 .. y=2x+2...............................2 ... z=3x-5...............................3 ... plug value of y & z in equation (1) x+2x+2+3x-5 =123 6x-3=123 6x=126 /6 x= 21 y= 2x+2= 44 z=58 .. 21+44+58=123 ... m.ananth@hotmail.ca
 Rate-of-work-word-problems/396577: Working together, two pipes can fill the tank in 2 hours and 6 minutes. Working alone, the larger pipe fills the tank in 4 hours less time than the smaller on. How long does the larger pipe take?1 solutions Answer 281278 by mananth(12270)   on 2011-01-19 01:09:01 (Show Source): You can put this solution on YOUR website!Working together, two pipes can fill the tank in 2 hours and 6 minutes. Working alone, the larger pipe fills the tank in 4 hours less time than the smaller on. How long does the larger pipe take? 6 minutes=6/60 = 1/10 hours both pipes 2 1/10 hours= 23/10 hours they do 10/23 of the filling in 1 hour ..... smaller pipe takes x hours it does 1/x of filling in 1 hour .... larger pipe takes x-4 hours it does1/(x-4) of the job in 1 hour ... 1/x + 1/(x-4)= 10/23 LCD = x(x-4) (x-4+x)/x(x-4)=10/23 cross ultiply 23(2x-4)=10x(x-4) 46x-92=10x^2-40x 10x^2-86x+92=0 /2 5x^2-43x+46=0 solve using quadratic formula Find the roots of the equation by quadratic formula a= 5 , b = -43 , c =46 b^2-4ac= 929 . 7.3 hours ... x2= (43-sqrt(929))/(10) x2=1.25 this is not possible since larger pipe takes four hours less. So larger pipe takes 7.34-4 = 3.3 hours m.ananth@hotmail.ca
 Travel_Word_Problems/396554: Estimate the distance traveled when driving 48 miles per hour for 7 hours, 8 minutes 1 solutions Answer 281277 by mananth(12270)   on 2011-01-19 00:43:03 (Show Source): You can put this solution on YOUR website!7 hours 8 minutes 8 minutes = 8/60 = 2/15 hours .. 7+2/15 =107/15 hours .. d= rt d= 48 * 107/15 d= 342.4 miles
 Mixture_Word_Problems/396586: A chemist wants to dilute a 30% phosphoric acid solution to a 15% solution. He needs 10 liters of the 15% solution. How many liters of the 30% solution and water must the chemist use?1 solutions Answer 281276 by mananth(12270)   on 2011-01-19 00:40:59 (Show Source): You can put this solution on YOUR website!A chemist wants to dilute a 30% phosphoric acid solution to a 15% solution. He needs 10 liters of the 15% solution. How many liters of the 30% solution and water must the chemist use? 30% solution ------------- x liters 0%(water)-----------------------10-x liters 15%------------------------10 liters ... 30*x+0=15*10 30x=150 liters /30 x= 5 liters of water. 5 liters of 30% solution ..
 Evaluation_Word_Problems/396549: a freight train leaves the station 2 hours before a passenger train. There are two trains are traveling in the same direction on parallel tracks. If the rate of the passenger train is 11 mph faster than the Freight train, how fast is each train traveling if the passenger train passes the freight train in 10 hours?1 solutions Answer 281275 by mananth(12270)   on 2011-01-18 23:18:02 (Show Source): You can put this solution on YOUR website!a freight train leaves the station 2 hours before a passenger train. There are two trains are traveling in the same direction on parallel tracks. If the rate of the passenger train is 11 mph faster than the Freight train, how fast is each train traveling if the passenger train passes the freight train in 10 hours? .. freight train = x mph passenger train = x+11 mph ... freight train time = 10 +3 = 13 hours passanger train = 10 hours .. distance same. because they meet .. 13x=10(x+11) 13x=10x+110 13x-10x=110 3x= 110 /3 x= 36.66 mph speed of freight train passenger train speed = 36.66 +11 = 47.66 mph
 Age_Word_Problems/396548: Jack is 4 years older than Jill. Seven years from now the the sum of their ages will be 72. How old is Jill now?1 solutions Answer 281274 by mananth(12270)   on 2011-01-18 23:02:05 (Show Source): You can put this solution on YOUR website!jill = x years jack = x+4 ... after 7 years jill =x+7 jack = x+4+7=x+11 .. x+11+x+7= 72 2x+18=72 -18 2x=54 x= 23 years jill's age jack's age = 27
 Rate-of-work-word-problems/396484: Please show me how to solve this problem. I am sure that there is an equation to use but I do not know where to start. A backyard pool is being drained. The pool contains 9925 gallons of water. At 9am, Drain 1 is opened which drains at 175 gallons every 15 minutes. At 10am, Drain2 is opened (Drain 1 continues draining, too) and it drains 450 gallons every 30 minutes. At what time will the pool contain 0 gallons of water? THANK YOU!1 solutions Answer 281272 by mananth(12270)   on 2011-01-18 22:30:53 (Show Source): You can put this solution on YOUR website!A backyard pool is being drained. The pool contains 9925 gallons of water. At 9am, Drain 1 is opened which drains at 175 gallons every 15 minutes. At 10am, Drain2 is opened (Drain 1 continues draining, too) and it drains 450 gallons every 30 minutes. At what time will the pool contain 0 gallons of water? THANK YOU! ... let the total time to drain be x .. Drain 1 = 700 gallons /h Drain 2 = 900 gallons/h ... Drain 1 is open for x hours so it drained 700x gallons .. Drain 2 is open for (x-1) hours so it drains 900(x-1) gallons ... 700x+900(x-1)=9925 700x+900x-900=9925 1600x=9925+900 1600x= 10825 /2500 x= 6.765 hours x= 6hours 46 minutes Time it will empty = 3.46 pm ...
 Inequalities/396509: -3x - 2 > x + 10 another iniquality i cannot solve 1 solutions Answer 281270 by mananth(12270)   on 2011-01-18 22:07:13 (Show Source): You can put this solution on YOUR website!-3x - 2 > x + 10 another iniquality i cannot solve add +2 to both sides -3x-2+2>x+10+2 -3x>x+12 add -x to both sides -3x-x>x-x+12 -4x>12 divide by -4 x<-3
 Inverses/396493: i = 30 p =_______ r=4% t =21 solutions Answer 281267 by mananth(12270)   on 2011-01-18 22:03:52 (Show Source): You can put this solution on YOUR website!i = 30 p =_______ r=4% t =2 ... i=p*r*t 30=p*0.04*2 p=30/(0.04*2) p= 375
 Rectangles/396508: if the perimeter of a rectangle is 150 find the area1 solutions Answer 281263 by mananth(12270)   on 2011-01-18 21:58:45 (Show Source): You can put this solution on YOUR website!Perimeter= 150 square edge be x all are equal so 4x=150 x=37.5 the side length .. Area = L*W But it is a square so Area = L*L Are = 37.5*37.5 Area = 1406.25
 Inequalities/396507: I cannot solve the inequality, can you help me step by step 3x-5<6-2x1 solutions Answer 281261 by mananth(12270)   on 2011-01-18 21:55:06 (Show Source): You can put this solution on YOUR website!3x-5<6-2x .. add 5 to both side 3x-5+5<6-5-2x 3x<1-2x add 2x to both sides 3x+2x<1-2x+2x 5x<1 divide by 5 x<1/5
 Rectangles/396506: if perimeter of a square is 150, find the area1 solutions Answer 281256 by mananth(12270)   on 2011-01-18 21:52:53 (Show Source): You can put this solution on YOUR website!Perimeter= 150 square edge be x all are equal so 4x=150 x=37.5 the side length .. Area = L*W But it is a square so Area = L*L Are = 37.5*37.5 Area = 1406.25
 Graphs/396501: Help please Find two consecutive integers that have a product of 201 solutions Answer 281253 by mananth(12270)   on 2011-01-18 21:49:28 (Show Source): You can put this solution on YOUR website!let one integer be x the other will be x+1 .. x(x+1)=20 x^2+x=20 -20 x^2+x-20=0 x^2+5x-4x-20=0 x(x+5)-4(x+5)=0 (x+5)(x-4)=0 x= -5 OR 4 -5+1=-4 (-5,-4) ... .. 4+1=5 (4,5)
 Linear_Equations_And_Systems_Word_Problems/396075: Joe and Sam have received walkie-talkies for their birthdays. If they leave from the same point at the same time, Joe walking north at 2.5 mph and Sam walking east at 3 mph, how long will they be able to talk to each other if the range of the walkie-talkies is 4 mi. Round your answer to the nearest minute.1 solutions Answer 281050 by mananth(12270)   on 2011-01-18 05:03:52 (Show Source): You can put this solution on YOUR website!Joe and Sam have received walkie-talkies for their birthdays. If they leave from the same point at the same time, Joe walking north at 2.5 mph and Sam walking east at 3 mph, how long will they be able to talk to each other if the range of the walkie-talkies is 4 mi. Round your answer to the nearest minute. .. Joe- 2.5 mph Sam - 3mph time they walk is the same let the time be t 2.5t -- joe distance 3t ----- same distance .. they are walking at right angles use pythagoras theorem (2.5t)^2 +(3t)^2=4^2 6.25t+9t=16 15.25t=16 t = 16/15.25 time = 1.08 hours ... m.ananth@hotmail.ca