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# Recent problems solved by 'mananth'

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 Equations/524746: Can you please help me with this problem? I have to find the equation of the line that passes through the point (2,5) and is perpendicular to the line x-2y=5 The final answer has to be in slope-intercept form.1 solutions Answer 347891 by mananth(12270)   on 2011-11-01 22:04:59 (Show Source): You can put this solution on YOUR website!1 x -2 y = 5 Find the slope of this line -2 y = -1 x + 5 Divide by -2 y = 1 x + -2.5 Compare this equation with y=mx+b slope m = 1/2 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 -2 m= -2 ,point ( 2 , 5 ) Find b by plugging the values of m & the point in y=mx+b 5 = -4.00 + b b= 9 m= -2 The required equation is y =-2 x + 9 m.ananth@hotmail.ca
 Linear_Equations_And_Systems_Word_Problems/524740: Hi anyone, Could you help me solve this problem...I keep getting an answer that does not make any sense to me...its the pennies that are confusing..I know they represent p=1 and d=10 but I am having trouble setting up the problem..please help!!! Chris Here is the problem: Josh has a change jar that contains only dimes and pennies. He has 32 coins which add up to a total of \$1.85. How many of each type of coin does he have?1 solutions Answer 347889 by mananth(12270)   on 2011-11-01 22:02:36 (Show Source): You can put this solution on YOUR website!Pennies =x dimes = y x+y=32.................(1) x+10y=185...............(2) subtract (2) from (1) -9y=-163 /-9 y=17 17 dimes and 15 pennies
 Quadratic_Equations/524741: 5k^2=1801 solutions Answer 347888 by mananth(12270)   on 2011-11-01 21:58:18 (Show Source): You can put this solution on YOUR website! /5 k=6
 Equations/524742: Can you please help me with this? I have to write this equation in slope-intercept form: y+12=-2(x+5/3)1 solutions Answer 347887 by mananth(12270)   on 2011-11-01 21:55:27 (Show Source): You can put this solution on YOUR website!y+12=-2(x+5/3) y+12= -2(3x+5)/3 multiply by 3 3(y+12)=-6x-10 3y+36=-6x-10 3y=-6x-36-10 3y=-6x-46 /3 y=-2x-(46/3)
 Rational-functions/524727: How do i write a quadratic function in standard formwith the zeros; -4 and -41 solutions Answer 347878 by mananth(12270)   on 2011-11-01 21:29:13 (Show Source): You can put this solution on YOUR website!(x+4)(x+4) x^2+8x+16
 Age_Word_Problems/524709: In 10 years, a child will be 3 years older than twice her current age. What is the current age of the child.1 solutions Answer 347877 by mananth(12270)   on 2011-11-01 21:27:45 (Show Source): You can put this solution on YOUR website!let the current age of child be x years After ten years x+10=2x+3 2x-x=10-3 x=7 years the child's age now
 Triangles/524722: The length of the base of a triangle is six times its height. If the area of the triangle is 75 square kilometers. find the height (A = 1/2 b h) I got the height = X and the base 6x every time i plug it in i am getting 75 = 1/2 (6x)(x) 75 = (3x)(x2) then 0 = x2 +3x-75 and now i am stuck on (x+ )(x- ) can you please tell me where i am messing up thank you1 solutions Answer 347876 by mananth(12270)   on 2011-11-01 21:25:08 (Show Source): You can put this solution on YOUR website!height =x base = 6x Area = 1/2 * base * height Area = 1/2 * x*6x 3x^2= 75 /3 x^2=25 x=5 km the height Base = 30 km
 Travel_Word_Problems/524698: A car travels 147 miles in 3 hours. It was driven at 24 mph in the city and 54 mph in the country. Find the number of hours that the car was driven at each rate.1 solutions Answer 347873 by mananth(12270)   on 2011-11-01 21:21:55 (Show Source): You can put this solution on YOUR website!City time + country time = 3 hours t=d/r D(city)=x speed = 24 D(country)=(147-x) speed = 54 LCD = 216 Multiply by LCD 9x+588-4x=648 5x=60 /5 x=12 miles in the city Balance =>147-12= 135 miles in country
 Money_Word_Problems/524707: Shannon deposited \$12000 at 6% compounded annually l. How long will it take Shannon to double her money?1 solutions Answer 347870 by mananth(12270)   on 2011-11-01 21:04:53 (Show Source): You can put this solution on YOUR website!Principal P = 12000 Amount= 24000 years=n compounded (t) 1 Rate = 6 0.06 Amount = P*((n+r)/n)^n 24000 = 12000 *( 1 + 0.06 )^ n*t 2 = *( 1 + 0.06 )^ n* 1 ln 2 = 1 n *ln 1.06 0.69 = 1 0.06 *n 11.9 = n 11.9 years m.ananth@hotmail.ca
 Expressions-with-variables/524711: My homework is Adding and Subtracting Expressions. I have this problem on my homework 8x + 5x and I put 13. I don't know do they what the answer to the poblem or just tell them what x is? I'm so lost on this.1 solutions Answer 347868 by mananth(12270)   on 2011-11-01 21:02:40 (Show Source): You can put this solution on YOUR website!When adding or subtracting you have to add or subtract the coefficients and write the answer with the variable. The variables have to be the same. 8x+5x = (8+5)x=13x
 test/524714: Write a simplified expression for the sum of three and three times the reciprocal of a number1 solutions Answer 347866 by mananth(12270)   on 2011-11-01 20:59:22 (Show Source): You can put this solution on YOUR website!let the number be x reciprocal = (1/3)x => x/3 3 times reciprocal = 3x/3 LCD =3 =2x
 Length-and-distance/524712: the coordinate (-7,0) lies in which quadrant? 1 solutions Answer 347865 by mananth(12270)   on 2011-11-01 20:56:28 (Show Source): You can put this solution on YOUR website!It lies on the X - axis between quadrant II & III
 Polynomials-and-rational-expressions/524708: what is (4a^2+12ab+9b^2-25c^2) factored? and I know the answer is (2a+3b+5c)(2a+3b-5c) I just dont understand how to get there....thanks 1 solutions Answer 347863 by mananth(12270)   on 2011-11-01 20:54:41 (Show Source): You can put this solution on YOUR website! Use identity
 test/524705: y=8x+6?y=8x? are they parallel, perpendicular. or neither1 solutions Answer 347861 by mananth(12270)   on 2011-11-01 20:51:03 (Show Source): You can put this solution on YOUR website!y=8x+6 y=8x when you compare bothequations with y=mx+b m=slope =8 for both equations Hence the lines are paralle m.ananth@hotmail.ca
 Travel_Word_Problems/524176: A person has two choices for his salary. Plan A. A salary of \$900 per month plus a commission of 10% of sales OR Plan B A salary of \$1,200 per month plus a commission of 15% of sales in excess of \$8,000. For what amount of monthly sales is plan B better than plan A?1 solutions Answer 347688 by mananth(12270)   on 2011-11-01 06:21:26 (Show Source): You can put this solution on YOUR website!Plan A 900 + 0.1*x Plan B 1200 + 0.15(x-8000) Plan B < Plan A 1200+0.15(x-8000)<900+0.1x 1200+0.15x-1200<900+0.1x 0.15x-0.1x<900 0.05x<900 x<18000
 Travel_Word_Problems/524179: George leaves his house on his bike at 7:30 AM and averages 5 miles per hour. His wife leaves at 8 AM following the same path averaging 8 miles per hour. At what time will his wife catch George?1 solutions Answer 347687 by mananth(12270)   on 2011-11-01 06:13:28 (Show Source): You can put this solution on YOUR website!George speed 5 mph Wife speed 8 mph George speed 07:30 Wife speed 08:00 Difference in time= 00:30 => 0.5 hours George speed will have covered 2.5 miles before wife starts catch up distance= 2.5 miles catch up speed = 8 -5 mph catch up speed = 3 mph Catchup time = catchup distance/catch up speed catch up time= 2.5 / 3 catch up time= 5/6 hours =50 minutes she will catch up at 8:50 AM
 Graphs/524204: Please help me with this. I have no idea what I am doing. 1+√3 divided by -1-√2.1 solutions Answer 347686 by mananth(12270)   on 2011-11-01 05:54:11 (Show Source): You can put this solution on YOUR website! Multiply by the conjugate (-1+sqrt(2)) m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/524205: A coffee counter charges \$9.00 per pound for french roast, \$8.00 a pound for sumantra. How much of each type should be used to make a 20 pound blend that sells for \$8.65 per pound?1 solutions Answer 347685 by mananth(12270)   on 2011-11-01 05:44:12 (Show Source): You can put this solution on YOUR website!---------price ---------------- quantity French roast 9 ---------------- x pounds sumantra 8 ------ 20 - x pounds Mixture 8.65% ---------------- 20 9 x + 8 ( 20 - x ) = 8.65 * 20 9x+160-8x=173 9x-8x=173-160 x = 13 x = 13pounds \$9.00 French roast 7 pounds \$8.00 sumantra
 Miscellaneous_Word_Problems/524207: Alvin paddled for 5 hours with a 2-km/h current to reach a campsite. The return trip against the same current took 7 hours. What is the speed of the boat in still water?1 solutions Answer 347684 by mananth(12270)   on 2011-11-01 05:39:02 (Show Source): You can put this solution on YOUR website!Boat speed =x kmph current speed 2 kmph Time with current= 5 hours time against current 7 hours Distance = same d=rt 5(x+2)= 7(x-2) 5x+10=7 x-14 7x-5x = 10+ 14 2 x= 24 x = 12 kmph Boat speed
 Word_Problems_With_Coins/524222: You have 5 less than twice as many dimes than quarters. You have \$4.90 in all. How many of each coin do you have?1 solutions Answer 347683 by mananth(12270)   on 2011-11-01 05:28:10 (Show Source): You can put this solution on YOUR website!Quarters =x dimes = 2x-5 \$4.90 = 490 cents 25x+10(2x-5)=490 25x+20x-50=490 45x=540 /45 x=12 quarters dimes = 2x-5 =2*12-5 =19 dimes check 19*10+25*12 190+300 =490
 Word_Problems_With_Coins/524223: Nicole has one less than one-fifth as many dimes as quarters. She has \$8.00 worth of coins. How many of each coin does she have?1 solutions Answer 347682 by mananth(12270)   on 2011-11-01 05:23:56 (Show Source): You can put this solution on YOUR website!quarters =x dimes= (1/5)x-1 she has 800 cents 25x+10((1/5)x-1) = 800 25x+2x-10=800 27x=810 /27 x=30 quarters dimes = (1/5)*30 -1 dimes= 5 CHECK 5*10 + 30*25 50+750=800
 Money_Word_Problems/524225: A company obtained two loans totaling \$30,000. The interest rate for one loan was 16 percent, and for the other loan it was 12 percent. The total annual interest for the two loans was equal to the interest the company would have paid if the entire amount had been borrowed at 15 percent. What was the amount of each loan?1 solutions Answer 347681 by mananth(12270)   on 2011-11-01 05:15:59 (Show Source): You can put this solution on YOUR website!15% of 30,000= 4500 Investment I 16.00% per annum ---x Investment II 12.00% per annum ---y x + y= 30000 ------------------------1 16.00% x + 12.00% y= = \$4,500.00 Multiply by 100 16 x + 12 y= = \$450,000.00 --------2 Multiply (1) by -16 we get -16 x -16 y= = -480000.00 Add this to (2) -4 y= = -30,000.00 divide by -4 y = \$7,500.00 investment at 12.00% Balance \$22,500.00 investment at 16.00% CHECK \$22,500.00 --------- 16.00% ------- \$3,600.00 \$7,500.00 ------- 12.00% ------- \$900.00 Total -------------- \$4,500.00 m.ananth@hotmail.ca
 Linear-equations/524247: Given the linear equation y=-3/5x-4, find the y-coordinates of the points (-5, ), (0, ), and (5, ). Please show all of your work. Plot those points and graph the linear equation. 1 solutions Answer 347679 by mananth(12270)   on 2011-11-01 05:07:09 (Show Source): You can put this solution on YOUR website!y= - 3/ 5 x + -4 Plot the points x -5 0 5 y= -1 -4 -7 (x,y) ( -5 , -1 ),( 0 , -4 ),( 5 , -7 )
 test/524182: You sell 310 pumpkins for \$1950.00. Small pumpkins are \$3.00 and large are \$9.00. How many of each size did you sell1 solutions Answer 347678 by mananth(12270)   on 2011-11-01 04:53:03 (Show Source): You can put this solution on YOUR website!small pumpkin x numbers , Price = \$3.00 large pumkin y numbers , Price = \$9.00 Total 345 1 x + 1 y = 310 .............1 3 x + 9 y = 1950 .............2 Eliminate y multiply (1)by -9 Multiply (2) by 1 -9 x -9 y = -2790 3 x 9 y = 1950 Add the two equations -6 x = -840 / -6 x = 140.00 plug value of x in (1) 1 x + 1 y = 310 140 + 1 y = 310 1 y = 310 -140 1 y = 170 y = 170.00 small pumpkin 140 numbers large pumkin 170 numbers m.ananth@hotmail.ca
 Graphs/524208: please help me solve this. I am not so good at word problems. The monthly profit in dollars that Carla makes on the sale of x automobiles is determined by the formula p=x^2 -4x-5. What values of x is her profit positive?1 solutions Answer 347676 by mananth(12270)   on 2011-11-01 04:45:02 (Show Source): You can put this solution on YOUR website!p=x^2-4x-5 find the roots equate to 0 x^2-4x-5=0 x^2-5x+x-5=0 x(x-5)+1(x-5)=0 (x-5)(x+1)=0 x= 5 OR -1 -1 is not possible so she has to sell more than 5 cars to make a profit
 Travel_Word_Problems/524213: A plane flies 300 km due north, 400 km due east, and then 500 km due south. How far is the plane from its starting point? State to the nearest km. My answer is approximately 860 km. Please confirm if this is correct. Using Distance Formula: D2 = (x2-x1)+(y2-y1) Starting Point: 0 East: positive x West: negative x North: positive y South: negative y Start: (0,0) 300 N: (0,0)+(300,0)=(300,0) 400 E: (300,0)+(400,0)=(700,0) 500 S: (700,0)+(0,-500)=(700,-500) The plane is 700km east and -500km south of starting point. D2= (700-0)2+ (0-500)2 D2= (700)2 + (-500)2 D2= 490,000 + 250,000 D2= 740,000 D = 860km The plane is approximately 860km from its starting point. Thank you, in advance, for your assistance. 1 solutions Answer 347675 by mananth(12270)   on 2011-11-01 04:41:27 (Show Source): You can put this solution on YOUR website!The plane has taken a rectangular path 300 North Turn right to east 400 then down south 500 it is 200 miles more south than the starting point the horizontal distance is 400 km Apply Pythagoras theorem 400^2+200^2= distance ^2 160000+40000=d^2 200000= d^2 d= sqrt (400000) d= 447.2 km from starting point
 Linear-systems/524215: solve the system of equations by graphing. 3x-18=9y 2x-6y=-121 solutions Answer 347674 by mananth(12270)   on 2011-11-01 04:30:11 (Show Source): You can put this solution on YOUR website!3x-18=9y /9 1/3 x -2=y.............................(1) 2x-6y=-12 -6y=2x-12 /-6 y=1/3 x+2............................(2) equation1 when x= 0 y= -2 ( 0 , -2 ) when y = 0 x= 6 ( 6 , 0 ) Equation 2 when x= 0 y= 2 ( 0 , 2 ) when y = 0 x= -6 ( -6 , 0 ) The lines are parallel hence NO SOLUTION m.ananth@hotmail.ca
 Rectangles/524243: The area of a rectangle is 14 square meters. Find the length and width of the rectangle if its length is 5 meters greater than its width.1 solutions Answer 347673 by mananth(12270)   on 2011-11-01 04:14:22 (Show Source): You can put this solution on YOUR website!width =x length = x+5 Area = L*W Area = x(x+5) x(x+5)=14 x^2+5x=14 x^2+5x-14-0 x^2+7x-2x-14=0 x(x+_7)-2(x+7)=0 (x-2)(x+7)=0 x= 2 the positive value width = 2 m length = 2+5=7 m
 Travel_Word_Problems/524220: A car travels 40 miles an hour and a plane travels 10 miles in a minute. How far will the car travel while the plane travels 450 miles?1 solutions Answer 347672 by mananth(12270)   on 2011-11-01 04:08:55 (Show Source): You can put this solution on YOUR website!Plane 10 miles a minute=10*60=600 mph t(plane)=d/r 450/600 = 3/4 hours D(car)= 40*3/4= 30 miles
 Linear-equations/524231: Given the linear equation y = 4x + 2, find the y-coordinates of the points (-2, ), (1, ), and (-3, ). Please show all of your work. Plot these points and graph the linear equation. 1 solutions Answer 347671 by mananth(12270)   on 2011-11-01 04:06:00 (Show Source): You can put this solution on YOUR website!y= 4 x + 2 plugvalues of x in the equation to get values of y. x -2 1 -3 y= -6 6 -10 (x,y) (-2, -6),(1 ,6),(-3 ,-10) m.ananth@hotmail.ca
 Quadratic_Equations/524242: The base of a 20 foot ladder is 15 feet from a house. How far up the house does the ladder reach?1 solutions Answer 347669 by mananth(12270)   on 2011-11-01 03:51:49 (Show Source): You can put this solution on YOUR website!The ladder,the floor & the wall form a right triangle. The ladder acts as the hypotenuse Pythagoras theorem (Hyp)^2= (leg1)^2+ Hypotenuse = 20 leg1= 15 Leg2= ? leg2^2=hyp^2-leg1^2 Leg2^2= 20 ^2 Leg2^2= 400 - Leg2^2= 175 Leg2= Leg2= 13.23 The ladder touches the wall at a height of 13.23 ft m.ananth@hotmail.ca