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# Recent problems solved by 'mananth'

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 Linear-equations/318456: Please help to solve this problem: x - 9/4 = 1/31 solutions Answer 227923 by mananth(12270)   on 2010-06-28 23:33:37 (Show Source): You can put this solution on YOUR website!x - 9/4 = 1/3 .. x=1/3 + 9/4 LCM =12 x=4+27 /12 x=31/12
 Linear-equations/318454: Please help me to solve for the unknown variable -5/12 = s - 7/241 solutions Answer 227921 by mananth(12270)   on 2010-06-28 23:30:54 (Show Source): You can put this solution on YOUR website!-5/12 = s - 7/24 .. s=-5/12 +7/24 LCM =24 s= -10+7 /24 s=-3/24 s=-1/8
 Circles/318452: A circle has a radius of 8 inches. Find the area of a sector of the circle if the sector has an arc that measures 45°.1 solutions Answer 227920 by mananth(12270)   on 2010-06-28 23:27:39 (Show Source): You can put this solution on YOUR website!area of sector = angle /360 * pi*r^2 angle = 45 radius r= 8 .. area of sector = 45/360 *pi*8^2 Area =25.1 sq. in.
 Miscellaneous_Word_Problems/318241: you are given 8 identical coins and a balance scale. seven of the coins weight the same, but the eighth is lighter. you many use the balcne three times to determine which coin is lighter. show how you do this.1 solutions Answer 227783 by mananth(12270)   on 2010-06-28 10:54:40 (Show Source): You can put this solution on YOUR website!FIRST weigh put 4 on each side. the lighter one -will go up. second weighment put 2 on each pan. the lighter one -pan will go up. third weighment put one on each the lighter one will go up. .. That's it.
 Triangles/318251: find the base of a triangle if its area is 766 sq. cm. and its altitude is 74 cm.1 solutions Answer 227782 by mananth(12270)   on 2010-06-28 10:45:17 (Show Source): You can put this solution on YOUR website!area of triangle = 1/2 *base * height area =766 height =74 .. 766=1/2 * base * 74 766*2/74=base base 20.7 cm
 Travel_Word_Problems/318242: a car travels 1 mile in 75 seconds, at this rate how many miles will the car travel in a one hour ?1 solutions Answer 227781 by mananth(12270)   on 2010-06-28 10:41:03 (Show Source): You can put this solution on YOUR website!in 75 seconds it travels 1 mile 1 hour = 3600 seconds 36000/75 =48 mph
 Miscellaneous_Word_Problems/318224: In a college there are 13 times as many students as professors. If together the students and professors number 28,000, how many students are there in the college1 solutions Answer 227778 by mananth(12270)   on 2010-06-28 09:50:54 (Show Source): You can put this solution on YOUR website!let the professors be x students will be 13x .. x+13x=28000 14x=28000 x=2000 the number of professors .. 26000 students
 Pythagorean-theorem/318210: a guy wire is necessary to support the telephone pole. If the height of the pole is 36 feet and the guy wire is to be placed 15 feet from the base of the pole how long a wire is needed?1 solutions Answer 227777 by mananth(12270)   on 2010-06-28 09:48:09 (Show Source): You can put this solution on YOUR website!pole height =46 horizontal distance from pole on ground to where it is pegged = 15 ft. they form the legs of a right triangle = let length of wire be l .. l^2=36^2+15^2 l^2=1521 l=39 feet
 Radicals/318213: Solve the equation. (x-5)2/3=91 solutions Answer 227776 by mananth(12270)   on 2010-06-28 09:30:44 (Show Source): You can put this solution on YOUR website!(x-5)2/3=9 .. 2(x-5)=9*3 x-5=9*3/2 x-5=27/2 x=27/2 +5 x=27+10 /5 x=37/2
 Exponential-and-logarithmic-functions/318214: Please show work: Divide (fraction 1) (3y^2-12)/(^2+4y+4) / (y^3-2y^2)/(y^2+2y) (fraction 2)1 solutions Answer 227775 by mananth(12270)   on 2010-06-28 09:23:15 (Show Source): You can put this solution on YOUR website!(3y^2-12)/(y^2+4y+4) / (y^3-2y^2)/(y^2+2y) .. 3(y^2-4)/(y+2)^2 / y^2(y-2)/y(y+2) .. 3(y+2)(y-2) /(y+2)^2 * y(y+2)/y^2(y-2) .. 3(y+2)(y-2)*y(y+2) / (y+2)^2*y^2(y-2) 3/y
 Rational-functions/318135: (7z+5)^2+2(7z+5)-15=01 solutions Answer 227765 by mananth(12270)   on 2010-06-28 03:41:10 (Show Source): You can put this solution on YOUR website!(7z+5)^2+2(7z+5)-15=0 let (7z+5)be =x x^2+2x-15=0 x^2+5x-3x-15=0 x(x+5)-3(x+5)=0 (x-3)(x+5)=0 replace the value of x (7z+5-3)(7z+5+5)=0 (7z+2)(7z+10)=0 z=-2/7 or z=-10/7
 Equations/318161: Soup Kitchen A soup kitchen is preparing a meal for a large number of people. The basic recipe for the sauce requires 15 ounces (oz) of crushed tomatoes to serve 8 people. The chefs expect to serve 100 people, and crushed tomatoes are sold in 24 oz cans. How many cans should the chefs purchase?1 solutions Answer 227755 by mananth(12270)   on 2010-06-28 01:45:24 (Show Source): You can put this solution on YOUR website!8 people 15 oz 100 people = 100*15 /8 = 187.5 oz. .. 24oz 1 can 187.5 oz = 187.5/24 =12.5 cans He has to open 13 cans.
 Rate-of-work-word-problems/317883: Marge worked 3 times as many hours as Sue. They worked a total of 32 hours. How many hours did Sue work?1 solutions Answer 227628 by mananth(12270)   on 2010-06-27 09:00:16 (Show Source): You can put this solution on YOUR website!let Sue work for x hours marge worked 3 times as Sue=3x .. total they worked for 32 hours .. x+3x=32 4x=32 x=32/4 x=8 .. Sue worked for 8 hours.
 Miscellaneous_Word_Problems/317885: If the perimeter of a rectangular courtyard is 36 yd, and the length is 3 yd longer than twice the width, then what are the length and width? 1 solutions Answer 227627 by mananth(12270)   on 2010-06-27 08:57:56 (Show Source): You can put this solution on YOUR website!If the perimeter of a rectangular courtyard is 36 yd, and the length is 3 yd longer than twice the width, then what are the length and width? .. widthe be x length = 2x+3 .. Perimeter = 2L+2W 2x+2(2x+3)=36 2x+4x+6=36 6x+6=36 6x=30 x=5 width = 5 length = 2*5 +3=13 .. CHECK 2*13+2*5=36
 Miscellaneous_Word_Problems/317886: Gwen mixes 5 pounds of dried cranberries that sell for \$4 per pound with some dried apples that sell for \$3 per pound. If she wants the mix to be worth \$3.25 per pound, then how many pounds of apples should she use? 1 solutions Answer 227626 by mananth(12270)   on 2010-06-27 08:54:36 (Show Source): You can put this solution on YOUR website!Gwen mixes 5 pounds of dried cranberries that sell for \$4 per pound with some dried apples that sell for \$3 per pound. If she wants the mix to be worth \$3.25 per pound, then how many pounds of apples should she use? .. apples be x lbs. cost = \$3 .. cranberries 5 lbs cost \$4 .. Mix x+5 lbs cost \$ 3.25 .. 3x+4*5=3.25(x+5) 3x+20=3.25x+16.25 0.25x=20-16.25 0.25x=3.75 x= 3.75/0.25 x=15 lbs of apples
 Percentage-and-ratio-word-problems/317890: John earns 3600 dollars per month. He spends 8 1/3% of his income towards house rent and 33 1/3% towards food. Find the amount he spends on rent.1 solutions Answer 227624 by mananth(12270)   on 2010-06-27 08:46:23 (Show Source): You can put this solution on YOUR website!John earns 3600 dollars per month. He spends 8 1/3% of his income towards house rent and 33 1/3% towards food. Find the amount he spends on rent. .. 8 1/3 on house = 25/3 % 25/3 % on on 3600 how much ? 25/3 * 3600/100 25*36 /3 12*25 =300 he spends \$ 300 on House rent
 Linear-equations/317862: what is the slope of y=2x y=3x-2?1 solutions Answer 227619 by mananth(12270)   on 2010-06-27 06:29:58 (Show Source): You can put this solution on YOUR website!what is the slope of y=2x compare the equation with y=mx +c where m is the slope here m =2 so slope =2 .. y=3x-2? slope =3
 Systems-of-equations/317854: Solve the system: 3c-d=1 3d+c=11 solutions Answer 227618 by mananth(12270)   on 2010-06-27 06:26:30 (Show Source): You can put this solution on YOUR website!1..3c-d=1 2..3d+c=1 .. multiply eq1 by 3 9c-3d=3 add to eq2 9c-3d+3d+c=4 10c=4 c=4/10 = 2/5 .. plug the value of c in eq1 3c-d=1 3*2/5-d=1 d=6/5 -1 d=6-5 / 5 d=1/5
 Polynomials-and-rational-expressions/317861: simplify the following: 1) -(-3x+y-5)+(7x+2y+9)-2(7x+3) 2) -(2x-5y)-{8-6y-[9x-(-11y+15)]-8x}1 solutions Answer 227617 by mananth(12270)   on 2010-06-27 06:20:48 (Show Source): You can put this solution on YOUR website!1) -(-3x+y-5)+(7x+2y+9)-2(7x+3) 3x-y+5+7x+2y+9-14x-6 -4x+3y+8 .. .. 2) -(2x-5y)-{8-6y-[9x-(-11y+15)]-8x} -2x+5y-{8-6y-[9x+11y-15]-8x} -2x+5y-{8-6y-9x-11y+15} -2x+5y-8+6y+9x+11y-15 7x+22y-23
 Systems-of-equations/317833: A cyclist travels 54 miles in 6 hours going against the wind and 52 miles in 4 hours with the wind. What is the rate of the cyclist in still air and what is the rate of the wind? 1 solutions Answer 227615 by mananth(12270)   on 2010-06-27 04:19:50 (Show Source): You can put this solution on YOUR website!let speed of cycle be x in still air speed of wind =y .. 6(x-y)=54 4(x+y)52 .. 6x-6y=54 x-y=9 4x+4y=52 x+y=13 .. add the two equations x-y+x+y=22 2x=22 x=11 mph. speed of cycle x-y=9 11-y=9 y=2 speed of wind = 2 mph
 Systems-of-equations/317840: A motorboat takes 4 hours to travel 192 miles going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? 1 solutions Answer 227614 by mananth(12270)   on 2010-06-27 04:14:40 (Show Source): You can put this solution on YOUR website!let speed of boat be x mph speed of current be y mph .. speed * time = distance 4(x-y)=192 x-y=48 .. 2(x+y)=192 x+y=96 add both the equations x-y+x+y=96+48 2x=144 x=72 mph. speed of boat .. x-y=48 72-y=48 y=72-48 24 mph speed of current
 Travel_Word_Problems/317855: A student walks and jogs to college each day. she averages 5km/h walking and 9km/h jogging. The distancefrom home to college is 8km and she makes the trip in 1 hour. How far does the student jog? I can't seem to get it set up right to get the correct calculation. I used 5km(X) +9 km(y) = 8km. 1 solutions Answer 227613 by mananth(12270)   on 2010-06-27 04:04:49 (Show Source): You can put this solution on YOUR website!let her walk x km. she will jog 8-x km .. walking speed = 5km/hr jogging speed = 9km/hr .. distance to college 8km. walking time + jogging time = total time x/5+ 8-x /9 =1 9x+40-5x /45=1 4x+40=45 4x=5 x= 5/4 km she walks 5/4 km 1.25 km so she jogs 8-5/4 32-5 /4 27/4 6.75 km
 Travel_Word_Problems/317841: how much tme it will take to travel 400 feet distance at road at a speed of 45mph. 1 solutions Answer 227612 by mananth(12270)   on 2010-06-27 03:49:19 (Show Source): You can put this solution on YOUR website!1 mile = 5280 feet 45 mph= 45 * 5280 / 3600 feet /sec = 66 ft/s .. 400 feet at 66ft/s 400/66=6.06 seconds
 Angles/317851: The measure of an angle is 8 degrees less than three times the measure of the angle's suplement. Find the measure of the angle.1 solutions Answer 227611 by mananth(12270)   on 2010-06-27 00:26:22 (Show Source): You can put this solution on YOUR website!let the angle be x the other angle is 3x-8 .. x+3x-8=180 4x-8=180 4x=188 x=47 deg the other angle is 3*47-8 =141-8 =133 deg CHECK 133+47=180
 Systems-of-equations/317849: Solve using the Addition/Elimination Method 6x + 8y = 18 -3 -4y = -9 The answer I got was 0=0 always true. I'm needing a second opinion. Thank you! It's greatly appreciated.1 solutions Answer 227610 by mananth(12270)   on 2010-06-27 00:21:33 (Show Source): You can put this solution on YOUR website!6x + 8y = 18 -3 -4y = -9 -4y=-9+3 -4y=-6 y=-6/-4 y=3/2 .. 6x+8* 3/2 =18 6x+12=18 6x=18-12 6x=6 x=1
 Numeric_Fractions/317847: kevin is driving 100km/hr on the freeway if the speed limit is 65 mph is 65 mph , is he speeding 1 solutions Answer 227609 by mananth(12270)   on 2010-06-27 00:18:19 (Show Source): You can put this solution on YOUR website!1 km = 0.6214 miles 100km = 100*0.6214 =62.14 miles < 65 mph He is not speeding
 Probability-and-statistics/317842: Ray Bond sells handcrafted yard decorations at county fairs. The variable cost to make these is \$20 each, and he sells them for \$50. The cost to rent a booth at the fair is \$150. How many of these must Ray sell to break even? 1 solutions Answer 227608 by mananth(12270)   on 2010-06-27 00:09:36 (Show Source): You can put this solution on YOUR website!Let the break even quantity be x \$20 s cost for each . Total cost = 20x Booth rent = 150 sales will be 50x 20x+150=50x 30x=150 x=5 Numbers CHECK 5*20+150=250
 Expressions-with-variables/317843: The sum of the angles of every triangle in a plane is 180 degrees. The measure of the largest angle of the triangle is 10 degrees more than one angle and 20 degrees more than the other. What is the measure of the largest angle?1 solutions Answer 227600 by mananth(12270)   on 2010-06-26 23:45:53 (Show Source): You can put this solution on YOUR website!the largest angle be x deg one angle = x-10 second angle = x-20 .. x+x-10+x-20=180 3x-30=180 3x=180+30 3x=210 x=70 deg the other angle will be 70-10=60deg third angle = 70-20=50deg
 Miscellaneous_Word_Problems/317724: When Dave walks to school, he averages 90 steps per minute, each of his steps are 75 cm long. It takes him 16 minutes to get to school. His brother, Jack, going to school by the same route,averages 100 steps per minute, but his steps are only 60 cm long. How long does it take Jack to get to school?1 solutions Answer 227559 by mananth(12270)   on 2010-06-26 19:07:55 (Show Source): You can put this solution on YOUR website!dave takes 90 steps /minute , length of each step = 75 cm, walks for 16 minutes Total distance walked = 16*75*90=108 000 cm .. jack takes 100 steps of 60 cm each = 6000 cm /minute distance = 108 000 cm rate = 6000 steps/minute .. distance / rate = time 108 000 / 6000 =18 minutes
 Travel_Word_Problems/317793: a motorboat can maintain a constant speed of 16 mile per hour relative to the water. the boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. what is the speed of the current?1 solutions Answer 227556 by mananth(12270)   on 2010-06-26 19:00:09 (Show Source): You can put this solution on YOUR website!a motorboat can maintain a constant speed of 16 mile per hour relative to the water. the boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. what is the speed of the current? .. upstream in 20 minutes = 1/3 hours Down stream in 15 minutes = 1/4 hours .. let speed of current = x mph upstream speed will be 16-x down stream speed will be 16+x .. distance is same to & fro distance= rate * time .. 1/3 * (16-x) = 1/4*(16+x) 4*(16-x)=3*(16+x) 64-4x=48+3x 7x=16 x=2.28 mph
 Equations/317736: Simplify: x^2+3x-4 division sign X^2+5x-6 X^2+6x+8 x^2+7x+6 the problem should be the first row on top with the division sign in the middle1 solutions Answer 227555 by mananth(12270)   on 2010-06-26 18:47:41 (Show Source): You can put this solution on YOUR website!X^2+6x+8 / x^2+7x+6 x^2+4x+2x+8 / x^2+6x+x+6 x(x+4)+2(x+4) / x(x+6)+1(x+6) (x+6)(x+2) / (x+1)(x+6) =(x+2) / (x+1) .. x^2+3x-4 / X^2+5x-6 x^2+4x-x-4 / x^2+6x-x-6 x(x+4)-1(x+4) / x(x+6)-1(x+6) (x-1)(x+4) / (x-1)(x+6) (x-4) / (x+6)