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# Recent problems solved by 'mananth'

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 Polynomials-and-rational-expressions/355708: Regarding Products of Sums and Differences Multiply and Simplify (2t+3)^2 - (t-1)(t+1) Please show me the steps to solving this. What form is used? How do I know what to do first? Thank you, Jill1 solutions Answer 253981 by mananth(12270)   on 2010-10-13 08:53:49 (Show Source): You can put this solution on YOUR website!(2t+3)^2 - (t-1)(t+1) (2t+3)^2-(t^2-1) .............( (a+b)(a-b)= a^2-b^2) here a =t & b =1) (4t^2+12t+9)-(t^2-1)...........( (a+b)^2 = a^2+2ab+b^2; a= 2t and b =3) 4t^2+12t+9-t^2+1 group the similar terms & simplify 4t^2-t^2+12t+9+1 3t^2+12t+10 ... In such problems first solve the terms in the brackets and then simplify .. m.ananth@hotmail.ca
 Volume/355669: The diameter of a circle whose area is approximately 113.04cm squared1 solutions Answer 253952 by mananth(12270)   on 2010-10-13 05:47:08 (Show Source): You can put this solution on YOUR website!area = 113.04 pi*r^2= 113.04 r^2=113.04/pi r = sqrt ( 113.04/pi) r=6 so diameter = 12 cm ... m.ananth@hotmail.ca
 Linear_Equations_And_Systems_Word_Problems/355671: If the numerator and denominator of a fraction is increased by 2 the fraction beomes 5/7 and if the denominator is decreased by 1 the fraction becomes 3/4. Find fraction.1 solutions Answer 253951 by mananth(12270)   on 2010-10-13 05:43:28 (Show Source): You can put this solution on YOUR website!let x be the numerator y the denominator x+2/y+2 =5/7 7(x+2)=5(y+2) 7x+14=5y+10 7x-5y=-4.....................1 .. x/y-1 = 3/4 4x=3(y-1) 4x=3y-3 4x-3y=-3.....................2 .. multiply equation1 by -4 and equation 2 by 7 and add them to eliminate x -28x+20y=16 28x-21y=-21 -y=-5 y=5 .. plug value of y in equation 1 7x-25=-4 7x=21 /7 x=3 so the fraction is 3/5 ... m.ananth@hotmail.ca
 Volume/355663: The surface area of a cube is 294 cm squared. What is the length of its side?1 solutions Answer 253950 by mananth(12270)   on 2010-10-13 05:36:04 (Show Source): You can put this solution on YOUR website!the cube has 6 faces let length of side be l area of one face = l^2 area of 6 faces = 6l^2 6l^2=294 l^2=294/6 l^2=49 l=7 cm .. m.ananth@hotmail.ca
 Age_Word_Problems/355636: Please Help me solve this problem. Maylen is 20 years older than her daughter Hazel. In ten years time she will be twice as old as her daughter. How old are Maylene and Hazel ? Thanks ~1 solutions Answer 253949 by mananth(12270)   on 2010-10-13 05:26:02 (Show Source): You can put this solution on YOUR website!let hazel be x years maylene = x+20 ... ten years later their ages will be hazel = x+10 Maylene = x+20+10=x+30 x+30=2(x+10) x+30 = 2x+20 2x-x=20-10 x=10 hazels age Maylene = x+20 Maylene will be 30 years ... m.ananth@hotmail.ca
 Angles/355656: What is the measure of an angle if the measure of its supplement is 39 degree more than twice the measure of its complement?1 solutions Answer 253948 by mananth(12270)   on 2010-10-13 05:06:42 (Show Source): You can put this solution on YOUR website!let the angle be x the complement will be 90-x deg the supplement = 180-x .. 180-x = 2(90-x)+39 180-x=180-2x+39 180-180-39=-2x+x -x=-39 x= 39 the measure of the angle .. m.ananth@hotmail.ca
 Geometry_Word_Problems/355651: PROBLEM 1. If the area of an equilateral triangle is 36 suare centimeter, find its side length and height. PROBLEM 2. If a gallon of paint covers 400 square feet, how much gallons are needed to paint two walls each having dimensions 38ft x 25ft.1 solutions Answer 253947 by mananth(12270)   on 2010-10-13 05:01:28 (Show Source): You can put this solution on YOUR website!the area of equilateral triangle = 36m^2 the area = sqrt3/4 * s^2=36 4*36/sqrt3=s^2 144/sqrt3 =s^2 83.13=s^2 s= 9.11 cm ... dimensions wall = 38 by 25 Area = 38*25= 950 ft^2 2 walls = 1900 ft^2 .. area = 1900 ft^2 400ft2 /gallon .. 1900/400 = 4.75 gallons m.ananth@hotmail.ca
 Percentage-and-ratio-word-problems/355644: A shirt is on sale at a 20% discount. The sales tax is 5%. A new sales clerk simply takes 15% off the original price. Is this correct? Why?1 solutions Answer 253946 by mananth(12270)   on 2010-10-13 04:41:46 (Show Source): You can put this solution on YOUR website!let the shirt cost \$x 20% discount so the shirt will cost 0.8x .. add 5%sales tax on 0.8x 0.05*0.8x=0.04x 0.8x+0.04x=0.84x is the price... ... price is \$x less 15% 0.15x is reduced. so the price will be x-0.15x =0.85x. This is incorrect. He will be charging more. ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/355645: The price of regular rice is \$1 per pound; that of premium rice is \$2. Mix 300 pounds of regular rice with 400 pounds of premium rice. What is the price of the mixture?1 solutions Answer 253945 by mananth(12270)   on 2010-10-13 04:32:28 (Show Source): You can put this solution on YOUR website!The price of regular rice is \$1 per pound; 300 pounds that of premium rice is \$2. :: 400 pounds ... 300*1 +400*2 = 700*x 300+800= 700x 1100=700x /700 1100/700 =x x=1.57 Mix cost = \$1.57 ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/355646: A car runs 30 miles per gallon of gasoline. How long can it run with \$40 worth of gasoline purchased at \$4 per gallon?1 solutions Answer 253944 by mananth(12270)   on 2010-10-13 04:24:23 (Show Source): You can put this solution on YOUR website!\$4 for 1 gallon \$40 you get 10 gallons .. 1 gallon 30 miles 10 gallons 10*30 = 300 miles ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/355647: Mary and Jane shop at an office supplies store. Mary spends \$20 on 10 pens and 10 notebooks. Jane spends \$15 on 5 pens and 8 notebooks. Find the prices of the stationery.1 solutions Answer 253943 by mananth(12270)   on 2010-10-13 04:20:29 (Show Source): You can put this solution on YOUR website!let price of pen be \$x price of notebook be \$y/10 ... 10x+10y=20 x+y=2.......................1 5x+8y=15....................2 multiply equation 1 by -5 and add it to equation2 -5x-5y=-10 add to 2 8y-5y=15-10 3y=5 /3 y = 5/3 ... plug value of y in equation 1 x+5/3 = 2 (3x+5)/3=2 3x+5 =6 3x=6-5 3x=1 x= 0.33 ... Pen costs 33 cents notebook costs \$1.67 ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/355648: A pizza restaurant wants to make a pizza that is 10% bigger than the current 8 inch pizza. What is the diameter of the new pizza?1 solutions Answer 253942 by mananth(12270)   on 2010-10-13 04:08:08 (Show Source): You can put this solution on YOUR website!present pizza = 8 % 10% more 10/100 * 8 = 0.8 8+0.8 =8.8 inches ... m.ananth@hotmail.ca
 Angles/355631: A triangle has three angles A, B,C. Angle A is 38 less than three times angle C, and angle B is 14 more than twice angle C. Find the measures of all the angles.1 solutions Answer 253941 by mananth(12270)   on 2010-10-13 02:32:19 (Show Source): You can put this solution on YOUR website!let angle c be x deg Angle b =2x+14 Angle a= 3x-38 ... x+2x+14+3x-38=180 6x-24=180 6x=204 /6 x=34 deg. Angle C Angle b = 2x+14 = 68+14=82 deg Angle a =3x-38=102-38=64 deg ... m.ananth@hotmail.ca
 Linear_Algebra/355612: HARD!! algebra (Linear Systems) question? An Airplane cruises at 120km/h in still air. One day, when the wind was blowing steady rom the west, the airplane travelled west (flying into the wind) and landed at its desination after 1.5h. The airplane's return trip (flying with the wind) was only 1.0 h long. On both legs, the airplane travelled at its cruising speed. (meausred with respect to the air surrounding the airplane). Part A Write a System of equations that would allow you to determine the speed of the wind blowing that day and the distance traveled each way Part B When solving the system of equations graphically, what equations would you enter into the equation editor (to make graphs on your calculator) Part C Indicate what the X and the Y represent Well.... im stumpped... y=1.5(120 - x)= 180 -1.5x ?? then what y=1.0(120 + x)=120 + 1.0x ?? I'm so confused please can someone help me:(1 solutions Answer 253940 by mananth(12270)   on 2010-10-13 02:23:53 (Show Source): You can put this solution on YOUR website!speed of plane in still air = 120mph let speed of wind be x mph against wind the speed will be 120-x mph with wind the speed will be 120+x mph .. distance trraveled forward = (120-x)*1.5 distance traveled return = (120+x)*1 x+120 = 180-1.5x 2.5x=60 x=60/2.5 x= 24 mph the speed of wind ... the x axis represents the wind speed the y axis represents the cruising speed. Green line represents against wind red line represents with wind. they intesect at x = 24 the wind speed
 Percentage-and-ratio-word-problems/355613: whats the original price of a bike if the discounted price is \$91 and the dicsount is 30% off 1 solutions Answer 253928 by mananth(12270)   on 2010-10-13 00:16:36 (Show Source): You can put this solution on YOUR website!30% off on the cycle if the price is 100 the discounted price will be 70 if the discounted price = 91 then the original price will be 91/70*100==130 \$130 ... m.ananth@hotmail.ca
 Numbers_Word_Problems/355609: if the digits of a two digit number are reversed, the number is increased by 36. The sum of the digit in the number is three times their difference. What is the number?1 solutions Answer 253927 by mananth(12270)   on 2010-10-13 00:12:41 (Show Source): You can put this solution on YOUR website!let the digit in tens place be x & in the units place be y .. 10y+x=10x+y+36 9y-9x=36 /9 y-x=4.....................1 ... x+y=3(x-y) x+y=3x-3y 2x-4y=0 /2 x-2y=0....................2 Add equation1 & 2 -y=4 y=-4 plug value of y in 1 y-x=4 -4-x=4 x=-8 ... -84 is the number ... m.ananth@hotmail.ca
 Proportions/355610: I am having trouble getting the correct answer to this problem. The problem is 1/x+3 = -2x/x+5 This is how I worked it. The answer is -5/2, -1 but I keep getting -5/6 x+3(-2x) = x+5(1) x-6x = x+5 -6x = 5 divide through by -6 and get -5/6. What am I missing?1 solutions Answer 253924 by mananth(12270)   on 2010-10-13 00:04:17 (Show Source): You can put this solution on YOUR website!1/x+3 = -2x/x+5 .. x+5=-2x(x+3) x+5=-2x^2-6x -5 x+5-5 = -2x^2-6x-5 x=-2x^2-6x -5 2x^2+7x+5=0 2x^2+2x+5x+5=0 2x(x+1)+5(x+1)=0 (2x+5)(x+1)=0 x= -5/2 OR x=-1 ... m.ananth@hotmail.ca
 Quadratic_Equations/355587: 9.yto the power 4 +20 = 29 y square1 solutions Answer 253915 by mananth(12270)   on 2010-10-12 23:26:02 (Show Source): You can put this solution on YOUR website!9y^4+20=29y^2 9y^4-29Y^2+20=0 9y^4-20y^2-9y^2+20=0 y^2(9y^2-20)-1(9y^2-20) (9y^2-20)(y^2-1) (9y^2-20)(y+1)(y-1) (3y+sqrt20)(3y-sqrt20)(y+1)(y-1) ... m.ananth@hotmail.ca
 Numeric_Fractions/355593: 1. solve 20= t/15 2. a/6= -108 1 solutions Answer 253913 by mananth(12270)   on 2010-10-12 23:19:55 (Show Source): You can put this solution on YOUR website!20=t/15 multiply by 15 2*15=t/15 * 15 t=300 ... a/6=-108 multiply by 6 a/6 * 6 = -108*6 a=-648 ... m.ananth@hotmail.ca
 Travel_Word_Problems/355504: two motorcycles travel toward each other from Chicago and Indianapolis, which are about 350 km apart, at rates of 110 and 90 km/h. They started at the same time. in how many hours will they meet?1 solutions Answer 253912 by mananth(12270)   on 2010-10-12 23:17:16 (Show Source): You can put this solution on YOUR website!speed of A = 110 speed of B = 90 ... they are travelling towards each other. add the speeds 110+90 =200 km/h ... distance = 350 km .. time = distance/speed time = 350/200 =1.75 hours mananth@hotmail.ca
 Linear_Algebra/355553: What is the equation of the line that passes through the points (−2, 2) and (0, 5)?1 solutions Answer 253908 by mananth(12270)   on 2010-10-12 23:03:44 (Show Source): You can put this solution on YOUR website!points (-2,2) (0,5) slope m = y2-y1/x2-x1 slope = 5-2/0+2 = 3/2 ... equation = (y-y1)=m(x-x1) use the first point (y-2)=3/2(x+2) 2(y-2)=3(x+2) 2y-4 = 3x+6 2y= 3x+10 y = 3/2 *x +5is the equation of the line
 Equations/355530: A side of a square is 10 meters longer than the side of an equilateral triangle. The perimeter of the square is 3 times the perimeter of the triangle. Find the length of each side of the triangle.1 solutions Answer 253886 by mananth(12270)   on 2010-10-12 21:29:53 (Show Source): You can put this solution on YOUR website!square side = 10 meters perimeter of square = 4*L = 40 meters ... let side of triangle be x perimeter of triangle = 3x ... 40 = 3x *3 9x =40 x= 40/9 x= 4.44 meters length of side of triangle .. m.ananth@hotmail.ca
 Mixture_Word_Problems/355521: a painter needs to have 24 gallons of paint that contains 30% solvent. how many gallons of paint containing 20% solvent ahd how many gallons containing 60% solvent should be mixed to obtain the desired paint?1 solutions Answer 253884 by mananth(12270)   on 2010-10-12 21:24:57 (Show Source): You can put this solution on YOUR website! paint containing 20% solvent :let this be x gallons paint containing 60% solvent :this will be 24-x gallons Mixture : 24 gallons of paint that contains 30% solvent. ... 0.2x+0.6(24-x) = 24*0.3 0.2x+14.4-0.6x=7.2 -0.4x=-7.2 divide by -0.4 x= -7.2/0.4 x=18 18 gallons of 20% 6 gallons of 60% will be required. ... m.ananth@hotmail.ca
 Numbers_Word_Problems/355483: three times the greater of two consecutive odd integers is twice the least by 371 solutions Answer 253883 by mananth(12270)   on 2010-10-12 20:54:11 (Show Source): You can put this solution on YOUR website!let the numbers be x & x+2 3 times greater = 3(x+2) twice the least = 2x ... 3(x+2)=2x+37 ( i have presumed it is +37) 3x+6=2x+37 3x-2x=37-6 x= 31 .. the numbers are 31 & 33 ... m.ananth@hotmail.ca
 Equations/355481: steps to 0.5n +17 + n=201 solutions Answer 253879 by mananth(12270)   on 2010-10-12 20:21:39 (Show Source): You can put this solution on YOUR website!0.5n +17 + n=20 multiply by 10 to remove the decimal 5n+170+10n=200 15n+170=200 add -170 to both sides 15n+170-170 = 200 -170 15n = 30 divide by 15 n=2 ... m.ananth@hotmail.ca
 Equations/355476: 14+6a-8=8 1 solutions Answer 253877 by mananth(12270)   on 2010-10-12 20:18:30 (Show Source): You can put this solution on YOUR website!14+6a-8 =8 ... 6a+6 = 8 add -6 to both sides 6a=8-6 6a=2 divide by 6 a=2/6 a=1/3 .... m.ananth@hotmail.ca
 Geometry_Word_Problems/355471: If the sides of a square are decreased by 2cm, the area is decreased by 36cm2. What were the dimensions of the original square?1 solutions Answer 253876 by mananth(12270)   on 2010-10-12 20:15:21 (Show Source): You can put this solution on YOUR website!let side of square be x Area = x^2 it is decreased by 2 so new length = x-2 area = (x-2)^2 .. The area decreases by 36 m^2 x^2-(x-2)^2=36 x^2-x^2+2x-4=36 2x-4 = 36 2x=40 x= 20 m ... side = 20m ... m.ananth@hotmail.ca
 Problems-with-consecutive-odd-even-integers/355146: How do you find a set of four consecutive odd integers that are positive and whose sum is at most 25?1 solutions Answer 253685 by mananth(12270)   on 2010-10-12 09:39:28 (Show Source): You can put this solution on YOUR website!let the numbers be x,x+2,x+4,x+6 ... x+x+2+x+4+x+6<=25 4x+12,=25 4x<=25-12 4x<=13 x<=13/4 x<=3.2 you need odd +ve integers 1,3,5,7 sum <25 3,5,7,9 sum <24 ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/355113: An inlet pump can fill a reservoir in 10 hours. An outlet pump can drain the same reservoir in 30 hours. How long would it take to fill the reservoir if both pumps were in use at the same time? Thank You1 solutions Answer 253684 by mananth(12270)   on 2010-10-12 09:33:18 (Show Source): You can put this solution on YOUR website!inlet pump fills in 10 hours so it does 1/10 of the job in 1 hour. outlet pump takes 30 hours so it can do 1/30 of the job in 1 hour. .. when both are open they will do 1/10 -1/30 of the job in 1 hour =2/30 = 1/15 of the job in one hour. so the tank will fill in 15 hours when both are on. .... m.ananth@hotmail.ca
 Geometry_Word_Problems/355144: If the measure of an angle is twice the measure of its complement, what is the measure of an angle?1 solutions Answer 253682 by mananth(12270)   on 2010-10-12 09:26:07 (Show Source): You can put this solution on YOUR website!let the angle be x complement = 90-x .. x=2(90-x) x=180-2x 3x=180 x= 60 .. the angles are 60,30 .... m.ananth@hotmail.ca
 Graphs/355142: please explain how you get the answer find the slope and the y-intercept of the line 4x=-2y+7 thank you1 solutions Answer 253679 by mananth(12270)   on 2010-10-12 09:23:33 (Show Source): You can put this solution on YOUR website!4x=-2y+7 rewrite the equation in the slope intercept form y =mx+b 2y=-4x+7 /2 y=-2x +7/2 ... m is the slope so m= -2 .. to get the y intercept plug x=0 so y = -2*0+7/2 y= 7/2 7/2 is the intercept. ... m.ananth@hotmail.ca