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# Recent problems solved by 'mananth'

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 Quadratic_Equations/331938: the different between two positive integers is 36. one interger is three times as great as the other. Find the integers.1 solutions Answer 237929 by mananth(12270)   on 2010-08-15 08:06:24 (Show Source): You can put this solution on YOUR website!let integers be x &y .. x-y=36 x=3y .. plug the value of x in the first equation 3y-y=36 2y=36 y=18 x= 54
 Numbers_Word_Problems/331950: Find the three consecutive even numbers such that sum of the first and the last numbers exceeds the second number by 10 1 solutions Answer 237927 by mananth(12270)   on 2010-08-15 07:47:46 (Show Source): You can put this solution on YOUR website!Find the three consecutive even numbers such that sum of the first and the last numbers exceeds the second number by 10 .. let the numbers be x,x+2,x+4 .. x+x+4 = x+2+10 2x+4 = x+12 2x-x 12-4 x=8 .. the numbers are 8,10,12 CHECK 8+12= 10+10
 Bodies-in-space/331947: The diameter of Cylinder I is 5 and its height is 9.The diameter of Cylinder II is 10 and its height is 9.What is the ratio of the volume of Cylinder I to Cylinder II? (A) 1 : 2 (B) 1 : 4 (C) 1 : 5 (D) 1 : 8 (E) 1 : 251 solutions Answer 237926 by mananth(12270)   on 2010-08-15 07:44:49 (Show Source): You can put this solution on YOUR website!The diameter of Cylinder I is 5 and its height is 9. The diameter of Cylinder II is 10 and its height is 9. What is the ratio of the volume of Cylinder I to Cylinder II? .. Volume of cylinder I = pi*(2.5)^2*9 Volume of cylinder II = pi*(5)^2*9 Ratio = pi*(2.5)^2*9/ pi*(5)^2*9 Ratio = 6.25/25 Ratio =1/4
 Linear-equations/331943: (5x+1)/6=(4x-1)/2 1 solutions Answer 237925 by mananth(12270)   on 2010-08-15 07:39:47 (Show Source): You can put this solution on YOUR website!(5x+1)/6=(4x-1)/2 .. 2*(5x+1)=6*(4x-1) 10x+2=24x-6 24x-10x=6+2 14x= 8 x= 8/14 x=4/7
 Polynomials-and-rational-expressions/331870: w^2 + 2w -8/6w^2 + 36w -48=1 solutions Answer 237924 by mananth(12270)   on 2010-08-15 06:05:23 (Show Source): You can put this solution on YOUR website!w^2 + 2w -8/6w^2 + 36w -48= ..
 Quadratic_Equations/331856: 13x^2+8x-14=0 value of the discriminate1 solutions Answer 237923 by mananth(12270)   on 2010-08-15 05:59:22 (Show Source): You can put this solution on YOUR website!13x^2+8x-14=0 .. a=13,b=8,c=-14 .. b^2-4ac =64-4*13*(-14) =792
 Money_Word_Problems/331859: roberto invested some money at 7%, and then invested \$3000 more than twice this ammount at 9%. his total annual income for two investments was \$3200. how much was invested at 9%1 solutions Answer 237922 by mananth(12270)   on 2010-08-15 05:54:26 (Show Source): You can put this solution on YOUR website!amount invested be x at 7% 2x+3000 @ 9% total interest for 1 year =3200 0.07x+0.09*(2x+3000)=3200 0.07x+0.18x+270=3200 0.25x=3200-270 0.25x=2930 x=2930/0.25 \$11,720 at 7% .. 2x+3000 2*11720+300 23,440+300 =\$23,740 @ 9%
 Equations/331883: Simplify. sq rt 6/2 multiplied by 1/sq rt 31 solutions Answer 237921 by mananth(12270)   on 2010-08-15 04:51:12 (Show Source): You can put this solution on YOUR website!sq rt 6/2 multiplied by 1/sq rt 3 .. =1
 Numbers_Word_Problems/331865: the sum of three consecutive integers is sixteen less then five times the middle integers1 solutions Answer 237920 by mananth(12270)   on 2010-08-15 04:39:28 (Show Source): You can put this solution on YOUR website!the sum of three consecutive integers is sixteen less then five times the middle integers. .. x, x+1,x+2 are the integers x+x+1+x+2=5(x+1)-16 3x+3=5x+5-16 5x-3x=3-5+16 2x=14 x= 7 the integers are 7,8,9. ..
 Equations/331880: Simplify products. 2 sq rt 5 + sq rt 2 multiplied by 3 sq rt 5 - sq rt 21 solutions Answer 237919 by mananth(12270)   on 2010-08-15 04:31:18 (Show Source): You can put this solution on YOUR website!2 sq rt 5 + sq rt 2 multiplied by 3 sq rt 5 - sq rt 2 ..
 Equations/331879: Simplify products. Give exact answers. 2 sq rt 5 multiplied by 3 sq rt 101 solutions Answer 237918 by mananth(12270)   on 2010-08-15 04:18:14 (Show Source):
 Travel_Word_Problems/331874: Find two real numbers that have a sum of 8 and a product of 2.1 solutions Answer 237917 by mananth(12270)   on 2010-08-15 04:12:34 (Show Source): You can put this solution on YOUR website!x+y=8 xy=2 x= 2/y plug valu of x in the first equation 2/y + y =8 2+y^2 /y =8 2+y^2=8y y^2-8y+2=0 .. quadratic formula y1= (-(-8)+sqrt(64-8))/2a y1=(8+sqrt56)/2 y1=7.74 y2=(8-sqrt 56)/2 y2=0.26 the numbers are 7.74 & 0.26
 Graphs/331927: During the first 20 mi of a 50 mi bicycle race. Roger's average speed was 16 mi/h. what must his average speed be during the remainder of the race if he is to finish the race in less than 2.5h?1 solutions Answer 237916 by mananth(12270)   on 2010-08-15 04:01:59 (Show Source): You can put this solution on YOUR website!During the first 20 mi of a 50 mi bicycle race. Roger's average speed was 16 mi/h. what must his average speed be during the remainder of the race if he is to finish the race in less than 2.5h? First 20 mi. 16 mph time = 20/16 = 5/4 hours. .. he has to finish in less than 2.5 hours = 5/2 hours Balance time = 5/2 - 5/4 = 10-5 /4= 5/4 hours . He has to ride 30 more miles. in less than 5/4 hours speed > distance / time speed > 30/(5/4) speed > 30*4/5 speed > 24 mph he has to ride at speed > 24 mph
 Numbers_Word_Problems/331918: a two digit number is three times the sum of each digit. If 45 is addad to the number, the digit reverses. Find the number.1 solutions Answer 237909 by mananth(12270)   on 2010-08-15 02:03:01 (Show Source): You can put this solution on YOUR website!let the number be xy. 10x+y= 3(x+y) 10x+y=3x+3y 7x-2y=0...................1 .. 10x+y+45 = 10y+x 9x-9y=-45 x-y=-5....................2 .. multiply equation 2 by -2 and add to equation 1 -2(x-y)+7x-2y=10+0 -2x+2y+7x-2y=10 5x=10 x=2 .. x-y=-5 2-y=-5 y=7 the number is 27
 Finance/331910: please help me to solve this: A sum of rs24000 is lent out for 2 years at compound interest , the rates of interest being 10% for the first year and 12%for the second year. The borrower returns some money at the end of the first year and on paying rs12768 at the end of the second year the total debt is cleared.calculate the amount of returned at the end of the first year.1 solutions Answer 237908 by mananth(12270)   on 2010-08-15 01:52:02 (Show Source): You can put this solution on YOUR website!please help me to solve this: A sum of rs24000 is lent out for 2 years at compound interest , the rates of interest being 10% for the first year and 12%for the second year. The borrower returns some money at the end of the first year and on paying rs12768 at the end of the second year the total debt is cleared.calculate the amount of returned at the end of the first year. .. Amount at the end of 1 year = Principal + interest. interest = 24000*1*10 / 100 interest = 2400 Amount at the end of 1 year = 24000+2400=26400 .. Interest for second year = 26400*12*1/100 =3168 Amount to be paid at the end of 2 years = 3168+ 26400= 29568 He returned Rs x at the end of 1 year 29568-x= 12768 x= 29568-12768= 16800 He paid Rs. 16,800 after 1 year
 Equations/331886: Solve each equation using quadratic formula. x^2-3x+2=0 y^2+y=61 solutions Answer 237906 by mananth(12270)   on 2010-08-15 00:37:46 (Show Source): You can put this solution on YOUR website!x^2-3x+2=0 a=1,b=-3,c=2 y1=-1+sqrt(1+24)/2 y1=-1+5/2 y1=+2 .. y2= -1-sqrt(1+24)/2 y2=-6/2 y2=-3
 Rectangles/331890: A rectangular picture is 3 inches longer than it is wide. It has a frame 2 inches wide whose area is 92 square inches. Find the dimensions of the picture.1 solutions Answer 237905 by mananth(12270)   on 2010-08-15 00:24:25 (Show Source): You can put this solution on YOUR website!let width of picture be x length = x+3 .. width =2 inches width including frame = x+2 length including frame = x+3+2 .. Total area = (x+2)(x+5) =x^2+7x+10 .. area of picture alone = x(x+3) =x^2+3x .. x^2+7x+10-x^2-3x = area of frame 4x+10= 92 4x=92-10 4x=82 x=20.5 cm the width length = 20.5+2= 22.5 cm CHECK ((22.5)*(25.5))-(20.5*(20.5+3))=92
 Pythagorean-theorem/331894: the longer side of a rectangle is four times the length of the shorter side. if the diagonal is 17cm long, find the dimensions of the triangle 1 solutions Answer 237904 by mananth(12270)   on 2010-08-15 00:09:44 (Show Source): You can put this solution on YOUR website!shorter side =x longer side = 4x diagonal = 17 they form a right triangle 17^2=x^2+(4x)^2 17^2=x^2+16x^2 17^2=17x^2 x^2= 17 x= +/- sqrt17 ignore negative value x= root 17 shorter side longer side = 4sqrt17
 Travel_Word_Problems/331900: Distance word problem When Fritz drives to work, his trip takes 36 minutes. On days when he takes the train to work, his trip is only 20 minutes. What is the distance of Fritz's trip is the train travels 32 miles per hour faster than driving?1 solutions Answer 237902 by mananth(12270)   on 2010-08-14 23:48:23 (Show Source): You can put this solution on YOUR website!let driving speed =x train speed = x+32 .. time by drive = 36 minutes . 36/60 hours=3/5 hours time by train = 20 minutes. 20/60 hours = 1/3 hours .. the distance is the same to his work place .. distance = speed * time 3x/5 = 1/3 *(x+32) 3*3x=5*(x+32) 9x=5x+160 add -5x 9x-5x=5x-5x+160 4x= 160 divide by 4 x=40 miles.
 Graphs/331901: solve the following: (4x-5)/(2-x)= -(9/2) solve for x showing the steps. 1 solutions Answer 237901 by mananth(12270)   on 2010-08-14 23:40:39 (Show Source): You can put this solution on YOUR website! Add 18 Add -8x
 Linear-equations/331904: Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. The second angle of a triangle is 3 times as large as the first. The third angle is 55° more than the first. Find the measure of the smallest angle. 1 solutions Answer 237900 by mananth(12270)   on 2010-08-14 23:34:55 (Show Source): You can put this solution on YOUR website!let first angle = x second angle = 3x third angle = x+55 .. The sum of angles of triangle = 180(deg) x+3x+x+55=180 5x+55=180 add -55 5x+55-55=180-55 5x=125 divide by 5 5x/5=125/5 x=25 first angle 25 deg second angle = 3x= 75 deg third angle = x+55 = 25+55=80 deg. CHECK 80+75+25=180
 Graphs/331907: Given the linear equation: - Find the y-coordinates of the given points. Show your work. - Plot those points and graph the linear equation. Submit your graph through the dropbox. y = 4x - 1 (0, ), (1, ), (2, ) 1 solutions Answer 237899 by mananth(12270)   on 2010-08-14 23:28:43 (Show Source): You can put this solution on YOUR website!y = 4x - 1 Plug the values of 0,1,2 y=4*0-1 y=-1 .. y=4*1-1 y=3 .. y=4*2-1 y=7 (0,-1 ), (1,3 ), (2,7 ) .. plot the points on the graph
 Average/331906: Use an inequality and the five-step process to solve the problem. Show all steps necessary to arrive at your solution. One side of a rectangle is 12 inches and the other side is x inches. What values of x will make the perimeter at most 44? Use P = 2L + 2W. 1 solutions Answer 237898 by mananth(12270)   on 2010-08-14 23:23:06 (Show Source): You can put this solution on YOUR website!one side =x other side = 12 P=2x+2*12 p=2x+24 .. 2x+24<44 2(x+12)<44 divide by 2 2(x+12) /2 <44/2 x+12<22 add -12 x+12-12<22-12 x<10
 expressions/331909: can you please explain this? 58-2 [30-(7+5)]1 solutions Answer 237897 by mananth(12270)   on 2010-08-14 23:17:55 (Show Source): You can put this solution on YOUR website!58-2 [30-(7+5)] first you have to solve the innermost bracket always.(7+5) 58-2[30-(12)] then solve another bracket 58-2[30-12] 58-2[18] then multiply 2 by 18 58-36 22
 Equations/331878: Factor completely. if a polynomial is prime, state this. 12a^2+84ab+147b^21 solutions Answer 237887 by mananth(12270)   on 2010-08-14 21:34:54 (Show Source): You can put this solution on YOUR website!12a^2+84ab+147b^2 3(4a^2+28ab+49b^2) 3(2a+7b)^2
 Triangles/331766: we have a pile of dirt with the measurements of 26 ft wide base, 100 ft long, and 8 ft high, how do we measure this and turn it into cubic yards, this is more of a right triangle than triangle1 solutions Answer 237821 by mananth(12270)   on 2010-08-14 09:36:05 (Show Source): You can put this solution on YOUR website!we have a pile of dirt with the measurements of 26 ft wide base, 100 ft long, and 8 ft high, how do we measure this and turn it into cubic yards, this is more of a right triangle than triangle 3 feett = 1yard 26 feet = 26/3 = 8.66 yards .. 100 feet = 100/3= 33.33 yards .. 8 feet = 8 / 3 = 2.66 yards .. Volume = 8.66*33.33*2.66 = 767.77 cu. yards .. This cannot be a triangle . triangle is two dimensional. this can be represented as a cuboid
 Expressions-with-variables/331756: Please show me how to use substitution to solve the system of equations; 5x+5y=-30 and 2x-y=15. Thank you1 solutions Answer 237818 by mananth(12270)   on 2010-08-14 09:30:20 (Show Source): You can put this solution on YOUR website!5x+5y=-30 divide by 5 x+y=-6 y= -6-x .. and 2x-y=15 plug the value of y in the equation 2x-(-6-x)=15 2x+6+x=15 3x+6=15 3x=15-6 3x=9 x=3 .. plug value of x in the equation x+y=-6 3+y=-6 y=-6-3 y=-9
 Geometry_Word_Problems/331762: The perimeter of the state of Wyoming is 1280 mi. The width is 90 mi less than the length. Find the width and the length.1 solutions Answer 237816 by mananth(12270)   on 2010-08-14 09:25:21 (Show Source): You can put this solution on YOUR website!let length be x mi width = x-90 mi .. perimeter = 2*(L+W) 1280 = 2*(x+x-90) 1280=2*(2x-90) 1280/2 = 2x-90 640 = 2x-90 640+90=2x 730=2x x= 365 miles the length .. width = 365 -90 = 275 miles CHECK 275*2+365*2=550+730=1280
 Polynomials-and-rational-expressions/331764: The mainsail of a Lightning sailboat is a right triangle in which the hypotenuse is called the leech. If a 24-ft tall mainsail has a leech length of 26 ft and if Dacron sailcloth costs \$10 per square foot, find the cost of a new mainsail. 1 solutions Answer 237815 by mananth(12270)   on 2010-08-14 09:21:37 (Show Source): You can put this solution on YOUR website!height 24-ft leech length 26 ft \$10 per square foot, find .. base b^2 = 26^2-24^2 b=sqrt 100 b=10 .. Area of right triangle = 1/2 * base * height = 1/2 * 10*24 area = 120 square ft. .. cost \$ 10 / sq. ft 120 sq. ft cost = \$1200
 Travel_Word_Problems/331763: Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling 80 mph and train b is traveling 100 mph. Train A passes a station at 6:15 am. If train B passes the same station at 6:27 am, at what time will train B catch up to train A?1 solutions Answer 237812 by mananth(12270)   on 2010-08-14 09:11:43 (Show Source): You can put this solution on YOUR website! train B passes the station after 12 minutes Train A speed is 80mph so in 12 minutes Train A travels 12/60 *80 =16 miles. .. train B speed = 100 mph. Train A speed speed 80 mph so it catches up 20 miles per hour ( 100-80) 20 miles it catches up in 1 hour 16 miles it will catch up in ? 16/20 hours 4/5 hours. 4/5 * 60 minutes =48 minutes. .. Train B passes the station at 6.27 am add 48 minutes to 6.27 am it catches up at 7.15 am
 Rational-functions/331660: Hello,Can someoe help me solve by multiplying and simplify by factoring assuming that all expressions under radicals represent non-negetive numbers ∛y^4∛81y^5 Thank you 1 solutions Answer 237803 by mananth(12270)   on 2010-08-14 07:06:53 (Show Source): You can put this solution on YOUR website!cuberoot(y^3*y)*cuberoot ((3^3)*3*(y^3)*y^2) y * cuberoot(y)*3y(cuberoot(3y^2) 3y^2*cuberoot(3y^3) 3y^3cuberoot(3)