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# Recent problems solved by 'mananth'

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 Percentage-and-ratio-word-problems/547498: A coin bank contains only dimes and quarters. The ToTal value of The coins in The bank is \$3.70 . If the dimes were quarters and quarters were dimes, the total value of the coIns would be \$2.95 . Find the number of quarters in the bank.1 solutions Answer 356399 by mananth(12270)   on 2011-12-14 19:31:03 (Show Source): You can put this solution on YOUR website!dimes = x numbers quarters = y numbers convert \$ to cents 10x+25y=370 25x+10y=295 dimes x Quarters y 10 x + 25 y = 370 .............1 25 x + 10 y = 295 .............2 Eliminate y multiply (1)by 2 Multiply (2) by -5 20 x 50 y = 740 -125 x + -50 y = -1475 Add the two equations -105 x = -735.00 / -105 x = 7 plug value of x in (1) 10 x + 25 y = 370 70 + 25 y = 370 25 y = 370 -70 25 y = 300 y = 12 dimes = 7 Quarters= 12 m.ananth@hotmail.ca
 Travel_Word_Problems/547494: When Amy rollerskates, she moves 120 yards per minute. What is her speed in miles per hour?1 solutions Answer 356396 by mananth(12270)   on 2011-12-14 19:18:55 (Show Source): You can put this solution on YOUR website!120 yards/minute =120 yards/60 seconds = 2 yards/second 1 yard = 1760 mile 1second = 1/3600 hours 2 yards/ second ==> (2/1760)/(1/3600)= (2/1760)*(3600/1) =4.09 mph
 Travel_Word_Problems/547493: Kendra bikes to work. She travels at a rate of 12 miles per hour. How long will it take her to bike 8 miles1 solutions Answer 356394 by mananth(12270)   on 2011-12-14 19:13:10 (Show Source): You can put this solution on YOUR website!Time = distance / speed distance == 8 miles speed = 12 mph time = 8/12 = 3/4 hour =45 minutes
 test/547490: -1/3p + 3/8p= -21 solutions Answer 356393 by mananth(12270)   on 2011-12-14 19:11:42 (Show Source): You can put this solution on YOUR website! Multiply by the LCD 24 -8p+9p=-48 -p=48 /-1 p=-48
 Percentage-and-ratio-word-problems/547100: aling martha invested part of her P20,000 at 8% interest and the remaining at 7%. If the total earnings for the investment is P1520, how much did she invest at 8%?1 solutions Answer 356261 by mananth(12270)   on 2011-12-14 09:18:26 (Show Source): You can put this solution on YOUR website!Fund A 8.00% per annum ---x Fund B 7.00% per annum ---y x + y= 20000 ------------------------1 8.00% x + 7.00% y= = \$1,520.00 Multiply by 100 8 x + 7 y= = \$152,000.00 --------2 Multiply (1) by -8 we get -8 x -8 y= = -160000.00 Add this to (2) 0 x -1 y= = -P8,000.00 divide by -1 y = P8,000.00 investment at 7.00% Balance P12,000.00 investment at 8.00% CHECK \$12,000.00 --------- 8.00% ------- P960.00 \$8,000.00 ------- 7.00% ------- P560.00 Total -------------- P1,520.00
 Linear-equations/547145: find the equation of the line that is perpendicular to 9x-3y=-2 and contains the point (0,4). i know the answer is y=-1/3x+4 but i don't know how to get it.1 solutions Answer 356259 by mananth(12270)   on 2011-12-14 09:07:14 (Show Source): You can put this solution on YOUR website!9 x -3 y = -2 Find the slope of this line -3 y = -9 x -2 Divide by -3 y = 3 x + 0.67 Compare this equation with y=mx+b, m= slope & b= y intercept slope m = 3 The slope of a line perpendicular to the above line will be the negative reciprocal m1*m2=-1 The slope of the required line will be - 1/3 m= - 1/3 ,point ( 0 , 4 ) Find b by plugging the values of m & the point in y=mx+b 4 = 0.00 + b b= 4 m= - 1/3 The required equation is y =- 1/ 3x+4 m.ananth@hotmail.ca
 Travel_Word_Problems/547099: At his usual rate a man rows 15 miles downstream in five hours less time than it takes him to return. If he doubles his usual rate, the time downstream is only one hour less than the time upstream. Find the rate of the streams current?1 solutions Answer 356254 by mananth(12270)   on 2011-12-14 08:49:38 (Show Source): You can put this solution on YOUR website!let speed of boat be x speed of current be y downstream speed = x+y upstream speed = x-y 15/(x-y) -15/(x+y)=5 LCD = (x+y)(x-y) multiply by the LCD 15(x+y)-15(x-y)=5(x^2-y^2) 15x+15y-15x+15y=5(x^2-y^2) 30y=5(x^2-y^2) ---------------- Speed is doubled downstream speed = 2x+y upstream speed = 2x-y 15/(2x-y)-15/(2x+y)=1 LCD = (2x+y)(2x-y) multiply by the LCD 15(2x+y)-15(2x-y)=4x^2-y^2 30x+15y-30x+15y=4x^2-y^2 30y=4x^2-y^2 equate 30y from both equations 5x^2-5y^2=4x^2-y^2 x^2-4y^2=0 x=2y substitute x=2y in 15/(x-y) -15/(x+y)=5 15/(2y-y)-15/(2y+y)=5 15/y-15/3y=5 45-15=15y 30=15y 30/15=y y=2 the current speed x=4 mph boat speed m.ananth@hotmail.ca
 Exponents/547136: if x2+y2=85 and xy=9 what is (x+y)2 *the 2 behind means to the second power i couldn't get it 2 show properly1 solutions Answer 356246 by mananth(12270)   on 2011-12-14 08:21:50 (Show Source): You can put this solution on YOUR website!if x2+y2=85 and xy=9 what is (x+y)2 add 2xy to both sides x^2+2xy+y^2=85+2xy (x+y)^2= 85+2*9 (x+y)^2=103
 Radicals/547137: use the quadratic formula to solve the following equations (r-2)(r+6)=11 simplify your answer. type an exact answer using radicals as needed. use integers or fractions for any numbers in the expression. use a comma to seperate answers as needed. 1 solutions Answer 356243 by mananth(12270)   on 2011-12-14 08:16:36 (Show Source): You can put this solution on YOUR website!(r-2)(r+6)=11 r(r+6)-2(r+6)+11=0 r^2+6r-2r-12+11=0 r^2+4r-1=0 Find the roots of the equation by quadratic formula a= 1 ,b= 4 ,c= -1 b^2-4ac= 16 + 4 b^2-4ac= 20 x1=( -4 + 4.47 )/ 2 x1= 0.24 x2=( -4 -4.47 ) / 2 x2= -4.24 you can also work it out in fractions
 Radicals/547134: solve by completing the square x^2-6x-4=0 simplify your answer. type an exact answer using radicals as needed. use integers or fractions for any numbers in the expression. use a comma to seperate answers as needed. 1 solutions Answer 356242 by mananth(12270)   on 2011-12-14 08:12:15 (Show Source): You can put this solution on YOUR website!x^2-6x-4=0 x^2-6x-4+13=0+13 x^2+6x+9=13 (x+3)^2=13 Take the squareroot x+3= -+sqrt(13) x=3+sqrt(13) OR x=3-sqrt(13)
 Pythagorean-theorem/547020: if the length of a rectangle is √1o and width of 2, what is the length of the diagonal?1 solutions Answer 356214 by mananth(12270)   on 2011-12-14 04:51:07 (Show Source): You can put this solution on YOUR website!length = sqrt(10) width = 2 The diagonal of rectangle is the hypotenuse leg1^2+leg2^2=hyp^2 10+4 = hyp^2 hyp =
 Travel_Word_Problems/547092: A bucket of water is brought up from a well 9.68 m deep by a rope which winds round a drum 22 cm in diameter. How many turns of the handle are required to bring up a bucket from the bottom of the well?1 solutions Answer 356213 by mananth(12270)   on 2011-12-14 04:47:13 (Show Source): You can put this solution on YOUR website!drum diameter = 22 cm = 0.22 m radius = 0.22/2=0.11 m height = 9.68 m 2 * pi * 0.11=0.691 m Number of turns = 9.68/0.691 = 14 turns
 Radicals/547087: 1/3of the principal square root of a number is 5. what is the number? 1 solutions Answer 356212 by mananth(12270)   on 2011-12-14 04:43:01 (Show Source): You can put this solution on YOUR website! square the equation multiply by 9 x= 9*25 x=225
 Coordinate-system/547011: Find slope and y intercept for: y=(2-a)x+a1 solutions Answer 356211 by mananth(12270)   on 2011-12-14 04:39:30 (Show Source): You can put this solution on YOUR website!slope = (2-a) y intercept =a point =(0,a)
 Travel_Word_Problems/547041: a train travels 100km in the same time that a plane covers 450 km. if the speed of the plane is 30km per hr less than 5 times the speed of the train , find both speeds..1 solutions Answer 356210 by mananth(12270)   on 2011-12-14 04:31:29 (Show Source): You can put this solution on YOUR website!train speed =x distance =180 plane speed = 5x-30 distance = 450 t=d/r 100/x = 450/(5x-30) time for both is same cross multiply 100(5x-30)=450x 500x-3000=450x 500x-450x=3000 50x=3000 /50 x=60 mph speed of car speed of plane = 5x-30 =5*60-30 =300-30 =270 mph speed of plane
 Numbers_Word_Problems/547086: find 2 numbers with a sum of 112 and a difference of 54 1 solutions Answer 356209 by mananth(12270)   on 2011-12-14 04:15:57 (Show Source): You can put this solution on YOUR website!let the numbers be x & y x+y =112 x-y =54 add the two equations 2x=166 x=83 one number is 83 x+y =112 so you can find the other number
 Travel_Word_Problems/547089: Find the number of 15-centimeter square tiles required to cover a rectangular floor 5.4 m long and 4.05 m wide.1 solutions Answer 356208 by mananth(12270)   on 2011-12-14 04:13:31 (Show Source): You can put this solution on YOUR website!Number of tiles required = area of floor/area of tile area of floor = 5.4*4.05=21.87 m^2 Area of tile = 0.15 *0.15 = 0.0625 m^2 21.87/0.0625=349.92 = 350 tiles
 Travel_Word_Problems/547082: the speed of air craft is 180 km/h.how much the aircraft travel in 20 min. 1 solutions Answer 356206 by mananth(12270)   on 2011-12-14 04:09:30 (Show Source): You can put this solution on YOUR website!speed = 180 km/h time = 20 minutes = 1/3 hours distance =180*1/3= 60 km
 Linear_Equations_And_Systems_Word_Problems/547085: Chemistry. E-Chem Testing has a solution that is 80% base and another that is 30% base. A technician needs 150 L of a solution that is 62% base. The 150 L will be prepared by mixing the two solutions on hand. How much of each should be used?1 solutions Answer 356205 by mananth(12270)   on 2011-12-14 04:07:22 (Show Source): You can put this solution on YOUR website!percent ---------------- quantity Base I 80 ---------------- x L Base II 30 ------ 150 - x L Mixture 62.00% ---------------- 150 80x+30(150-x)=62*150 80x+4500-30x=9300 80x-30x =9300-4500 50x=4800 / 50 x =96L 80.00% Base I 54L 30.00% Base II m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/547008: For each of the following polynomials, (a) list the degree of each term; (b) determine the leading term and the leading coefficient; and (c) determine the degree of the polynomial. 9x4 + x2 + x7 – 121 solutions Answer 356201 by mananth(12270)   on 2011-12-14 02:48:50 (Show Source): You can put this solution on YOUR website!leading term = 9x^4 leading coefficient;=9 and the degree=7 9x^4+ x2 + x7 – 12
 Travel_Word_Problems/547081: two cars leave delhi at the same time travelling in opposite directions. if the average speed of one car is 5 km/hr more than that of the other and they are 425 km apart at the end of 5 hrs, what is the average speed of each?1 solutions Answer 356199 by mananth(12270)   on 2011-12-14 02:43:00 (Show Source): You can put this solution on YOUR website!Car I x kmph Car II x+ 5 kmph .. They are moving away from each other So add up their speed. combined speed = x+x+5 (2x+5) Time = 5 hours Distance = 425 km Distance = speed * time (2x+5 )* 5 = 425 10 x + 25 = 425 10 x = 425 + -25 10 x = 400 / 10 x= 40 kmph Car I Car II 40 + 5 = 45 kmph m.ananth@hotmail.ca
 Travel_Word_Problems/547045: a cheetah was timed running 200 yards in 6 seconds. What was its average speed in miles per hour? I am a mom trying to help my daughter with her math homework. Not sure where to begin with this. Do I divide 200 by 6? but then what? I need help!! Could you show me what the problem should look like? Thanks!! Amy1 solutions Answer 356196 by mananth(12270)   on 2011-12-14 02:36:51 (Show Source): You can put this solution on YOUR website!a cheetah was timed running 200 yards in 6 seconds. What was its average speed in miles per hour? you must first do the conversion from yards/second to miles/hour. Then your problem is solved. 1 yard = 3 feet 600 yards=1800feet 1800 feet in 6 seconds so in 1 second the cheetah runs 1800/6 = 300 feet /second .... convert 300 feet/second to miles /hour 1 mile = 5280 feet 1 second = 1/3600 hour ( 3600 seconds ,ake an hour) 300 feet = 300/5280 miles 1 second = 1/3600 hour =204.5 mph
 Finance/547066: how can 56000 be invested part at 4% annual simple interest ant the remainder at 10% annual simple interest so that the interest erned by the two accounts is equal at the end if the year1 solutions Answer 356194 by mananth(12270)   on 2011-12-14 02:24:57 (Show Source): You can put this solution on YOUR website!x+y=56000 x@ 4% y@10% 0.04x = 0.1y 0.04x-0.1y=0 x+y=56000 .............1 0.04x-0.1y=0 .............2 Eliminate y multiply (1)by 1 Multiply (2) by 10 1 x 1 y = 56000 0.4 x + -1 y = 0 Add the two equations 1.4 x = 56000.000 / 1.4 x = 40000 plug value of x in (1) 1 x + 1 y = 56000 40000 + 1 y = 56000 1 y = 56000 -40000 1 y = 16000 y = 16000 4000@4% 16000@10%
 Mixture_Word_Problems/547076: how many pounds of peanuts at php 80.00 per pound should be added to 200 pounds of cashew nuts at php 200.00 per pound of the mixture is to be worth php 120.00 per pound?1 solutions Answer 356193 by mananth(12270)   on 2011-12-14 02:19:59 (Show Source): You can put this solution on YOUR website! --------price ---------------- quantity cashew 200 ---------------- 200 lb peanuts 80 ---------------- x lb Mixture 120 ---------------- 200 + x lb 200*200 +80x=120(200+x) 40000+80x=24000 +120x 80x+(-120x)=24000 -(-40000) -40 x = -16000 /-40 x=400 400 lb of peanuts
 Evaluation_Word_Problems/547078: which point lies on the line represented by the equation below? 15=3y-6x1 solutions Answer 356192 by mananth(12270)   on 2011-12-14 02:15:09 (Show Source): You can put this solution on YOUR website!x=-1 & y=3 satisfy the equation (-1,3) lies on the line
 Linear-systems/547050: 2y=2x-2 x=y+11 solutions Answer 356191 by mananth(12270)   on 2011-12-14 02:12:21 (Show Source): You can put this solution on YOUR website!-2 x + 2 y = -2 .............1 1 x -1 y = 1 .............2 Eliminate y multiply (1)by 1 Multiply (2) by 2 -2 x 2 y = -2 2 x + -2 y = 2 Add the two equations 0 x = 0 there are infinite solutions if you draw the graph of the lines the lines coincide.
 Expressions-with-variables/547071: Solve using two equations in two variables. Kathleen invested \$5000, some at 6% and the rest at 5%. Her annual income from the investments is \$280. How much is invested at 5%?1 solutions Answer 356190 by mananth(12270)   on 2011-12-14 01:42:46 (Show Source): You can put this solution on YOUR website!Fund A 5.00% per annum ---x Fund B 6.00% per annum ---y x+y=5000 ------------------------1 5.00% x + 6.00% y= = \$280.00 Multiply by 100 5x+6y= \$28,000.00 --------2 Multiply (1) by -5 we get -5x-5y= -25000.00 Add this to (2) y =\$3,000.00 investment at 6.00% Balance \$2,000.00 investment at 5.00% CHECK \$2,000.00 --------- 5.00% ------- \$100.00 \$3,000.00 ------- 6.00% ------- \$180.00 Total -------------- \$280.00
 Expressions-with-variables/547075: A grocer makes a natural breakfast cereal by mixing oat cereal costing \$2 per kilogram with dried fruits costing \$9 per kilogram. How many kilograms of each are needed to make 60 kg of cereal costing \$3.75 per kilogram?1 solutions Answer 356189 by mananth(12270)   on 2011-12-14 01:36:20 (Show Source): You can put this solution on YOUR website!price ---------------- quantity Oat cereal 2 ---------------- x lb dry fruits 9 ------ 60 - x lb Mixture 3.75% ---------------- 60 2 x + 9 ( 60 - x ) = 3.75 * 60 2 x + 540 - 9 x = 225 2 x - 9 x = 225 - 540 -7 x = -315 / -7 x=45 45 lb \$ 2.00 Oat cereal 15 lb \$ 9.00 dry fruits m.ananth@hotmail.ca
 Linear-equations/546864: Find the slope and y-intercept of the line that is perpendicular to y=1/3x-3 and passes through the point (-4, 3). 1 solutions Answer 356130 by mananth(12270)   on 2011-12-13 20:11:07 (Show Source): You can put this solution on YOUR website! y = 1/ 3 x + -3 Compare this equation with y=mx+b, m= slope & b= y intercept slope m = 1/3 The slope of a line perpendicular to the above line will be the negative reciprocal -3 m1*m2=-1 The slope of the required line will be -3 m= -3 ,point ( -4 , 3 ) Find b by plugging the values of m & the point in y=mx+b 3 = 12.00 + b b= -9 m= -3 The required equation is y =-3x-9 m.ananth@hotmail.ca
 Angles/546924: the complement of a 35 degree angle is an angle with a measure of?1 solutions Answer 356128 by mananth(12270)   on 2011-12-13 20:07:07 (Show Source): You can put this solution on YOUR website!sum of complementary angles = 90 if one angle is 35 other is 90-35 =55
 Graphs/546903: write an equation of the line that passes through the point (3,-2) with slope of 31 solutions Answer 356126 by mananth(12270)   on 2011-12-13 20:05:58 (Show Source): You can put this solution on YOUR website!m= 3 Plug value of the slope and point ( 3,-2 ) in Y = m x + b -2.00 = 9 + b b= -2 - 9 b= -11 So the equation will be Y = 3 x -11 m.ananth@hotmail.ca