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# Recent problems solved by 'mananth'

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 Linear-systems/679506: Solving Linear Systems of equations The problem: one is 5% acid and one is 6.5% acid . You want to make 200ml of vinegar,with 6% acid. How many ml of each vinegar do you need to mix together? My question: With percents I get confused, and I am not sure which variables you would use to set this up into two equations? 1 solutions Answer 421967 by mananth(12270)   on 2012-11-12 20:58:17 (Show Source): You can put this solution on YOUR website!Let quantity of 5% acid required be x Let quantity of 6.5% acid required be y Mixture = 6% Equate percentages 5%x+6.5%y=6%*200 multiply by 100 5x+6.5y=1200................(1) Quantity x+y=200.....................(2) multiply equation (2) by -5 we get -5x-5y=-1000 Add this equation to (1) we get 1.5y=200 y= 200/1.5 y=133.3 ml x= balance amount= 66.67ml
 Travel_Word_Problems/678995: A jet can fly 550mph in calm air. Traveling with the wind, the jet can fly 2400 miles in the same amount of time it takes to fly 2000 miles against the wind. Find the rate of the wind. 1 solutions Answer 421750 by mananth(12270)   on 2012-11-12 05:01:06 (Show Source): You can put this solution on YOUR website!let rate of wind be x m/h speed against wind 550-x m/h----------- 2000 miles speed with wind = 550+x m/h------------2400 miles time = d/r time against = time with 2000/(550-x)= 2400/(550+x) 2000(550+x)=2400(550-x) 1100000+2000x=1320000-2400x 2400x+2000x=1320000-1100000 4400x=220000 x= 50 m/h
 Travel_Word_Problems/678318: A car and a motorcycle set off from the same point to travel the same journey. The car has a start of four minutes before the motorcycle sets off. If the car travels at 80km/h and the motorcycle travels at 90km/h, how many kilometres will be travelled when the two vehicles are level? 1 solutions Answer 421358 by mananth(12270)   on 2012-11-10 07:22:47 (Show Source): You can put this solution on YOUR website!Let the car and motorcycle meet after distance x car speed = 80 km/h motorcycle speed = 90 km/h They both travel the same distance The car takes 4 minutes more .= 4/60 = 1/15 hours time = distance /speed car time - motorcycle time = 1/15 hours (x/80)-(x/90) = 1/15 LCD = 720 multiply equation by 720 9x-8x= 720/15 x= 48 They will meet after 48 km
 Quadratic_Equations/678402: Solve the completing the square 6z^2=z+21 solutions Answer 421353 by mananth(12270)   on 2012-11-10 07:13:56 (Show Source): You can put this solution on YOUR website! /6 Find the last term of perfect square Last term = 1/2 the coefficient of 2nd. term squared (1/2*1/6)^2 (1/12)^2= 1/144 add (1/44) to both sides ( taking the LCD Take the square root of both sides (z+(1/12)) = +/- (7/12) z= -(1/12) +(7/12) --->1/2 OR z= -(1/12) -(7/12) ---> -2/3
 Linear-equations/674042: What's the answer to this question? Y=-1/2ax-5,m=5/21 solutions Answer 419002 by mananth(12270)   on 2012-10-30 20:54:36 (Show Source): You can put this solution on YOUR website!Y=-1/2ax-5,m=5/2 What is the question? Anyway I think we have to find a y= 1/2 ax compare with y= mx so m= 1/2a 5/2 = 1/2 a a= 5
 Linear-equations/674013: Write the equation of a line with a slope of 2 that passes through the point (3, 7).1 solutions Answer 418998 by mananth(12270)   on 2012-10-30 20:51:49 (Show Source): You can put this solution on YOUR website!(3,7) slope 2 equation of line = y-y1=m(x-x1) where (x1,y1) is the point on the line y-7=2(x-3) y-7=2x-6 y-2x=1 y-2x=1 is the required equation
 Travel_Word_Problems/674031: When the wind is blowing at 25 mph, a plane flying at a constant speed can travel 700 miles with the wind in the same about of time it can fly 600 miles against the wind. Find the speed of the plane. please and thanks1 solutions Answer 418995 by mananth(12270)   on 2012-10-30 20:47:45 (Show Source): You can put this solution on YOUR website!plane speed x mph wind speed 25 mph Distance with wind 700 miles Distance against wind 600 miles speed with wind x + 25 mph speed against x -25 mph Time with wind= 700 /( x + 25 ) time against wind 600 / ( x -25 ) Time with wind = time against 700/(x+25)=600/(x-25) divide by 100 7/(x+25)=6/(x-25) 7(x-25)=6(x+25) 7x-175=6x+150 7x-6x=175+150 x=325 speed of plane = 325 mph
 Miscellaneous_Word_Problems/674044: I need help solving this problem: a couple wishes to rent a car for one day while on vacation. ford automobile rental want \$26 per day and \$0.16 per mile, while chevrolet for a day wants \$23 per day and \$0.18 per mile. after how many miles would the price to rent the chevrolet exceed the price to rent a ford?1 solutions Answer 418990 by mananth(12270)   on 2012-10-30 20:36:07 (Show Source): You can put this solution on YOUR website!Let x be the number of miles Ford 26 + 0.16 x chevrolet 23 + 0.18 x Ford > chevrolet 26 + 0.16 x > 23 + 0.18 x add -26 to both sides 26+0.16n-26>23 +0.18x-26 0.16 n- -23 > > 0.18 x -3 add -0.18 x -0.02 x > -3 / -0.02 x < 150 x should be less than 150 for Ford to be a better deal OR Chevrolet will be expensive after 150 miles
 Graphs/674036: is y=-2x,2y=x,4y=2x+4 a perpendicular or parallel 1 solutions Answer 418985 by mananth(12270)   on 2012-10-30 20:24:58 (Show Source): You can put this solution on YOUR website!y=-2x,2y=x,4y=2x+4 Line l, y=-2x,slope (m) = -2 line p, 2y=x, slope (m) = 1/2 line n, 4y=2x+4 slope (m) = 1/2 line l is perpendicular line p & n line p & line n are parallel If the slopes are equal with different y intercepts then the lines are parallel. if the product of the slopes is = -1 then the lines are peripendicular.
 test/673131: The manager of a trust account invests 25% of a client's account in a money market fund which earns 8% annual simple interest, 40% in bonds which earn 10.5% annual simple interest, and the remainder in trust deeds which earn 13% annual simple interest. How much should be invested in each type of investment so that the total interest earned is \$4300? 1 solutions Answer 418497 by mananth(12270)   on 2012-10-29 02:31:31 (Show Source): You can put this solution on YOUR website!let the total investment be x 25x% @ 8% 40% @ 10.5% bonds (x-(0.25x+0.4x) @ 13% 0.25x**8%+0.4x*10.5%+ (1-0.25x+0.4x)*0.13% = 4300 multiply by 100 8*0.25x+10.5*0.4x+0.35x*13=4300*100 2x+4.2x+4.55x=430000 10.75x=430000 x=430000/10.75 = 40,000 Total invested = \$40,000 25% of 40,000@ 8% --> \$10,000 40% of 40,000 @ 10.5% bonds ----->\$ \$16000 35% of 40,000 @ 13%---->\$14000
 Polynomials-and-rational-expressions/673107: How do you factor 12x³ -15x² - 18x by grouping?1 solutions Answer 418484 by mananth(12270)   on 2012-10-28 22:51:50 (Show Source):
 Equations/673074: Find the slope-intercept form for the line satisfying the following conditions x-intercept3, y-intercept 4/5 1 solutions Answer 418483 by mananth(12270)   on 2012-10-28 22:49:35 (Show Source): You can put this solution on YOUR website!using the formula (y-y1)=m(x-x1) where (x1,y1) are the co ordinates of the point on the line The point is (3,0)--- (x1,y1) slope = 4/5 y-0= 4/5(x-3) multiply by 5 5y=4(x-3) 5y=4x-12 /5 y=(4/5)x-(12/5)
 Linear-systems/673106: An investor invested a total of \$1,400 in two mutal funds. One fund earned a 7% profit and the other earned a 2% profit. If the investors profit was \$58 how much was invested in each mutal fund? fund that earned 7%? fund that earned 2%?1 solutions Answer 418482 by mananth(12270)   on 2012-10-28 22:43:00 (Show Source): You can put this solution on YOUR website!Part I 7.00% per annum ------------- Amount invested =x Part II 2.00% per annum ------------ Amount invested = y = 1400 Interest----- 58 Part I 7.00% per annum ---x Part II 2.00% per annum ---y Total investment x + y= 1400 -------------1 Interest on both investments 7.00% x + 2.00% y= 58 Multiply by 100 7 x + 2 y= 5800.00 --------2 Multiply (1) by -7 we get -7 x -7 y= -9800.00 Add this to (2) 0 x -5 y= -4000 divide by -5 y = 800 Part I 7.00% \$ 600 Part II 2.00% \$ 800 CHECK 600 --------- 7.00% ------- 42.00 800 ------------- 2.00% ------- 16.00 Total -------------------- 58.00 m.ananth@hotmail.ca
 Money_Word_Problems/673087: An investor invested a total of \$2,300 in two mutual funds. one fund earned a 9% profit while the other earned a 2% profit was \$95. how much was invested in each mutual fund1 solutions Answer 418480 by mananth(12270)   on 2012-10-28 22:41:11 (Show Source): You can put this solution on YOUR website!Part I 9.00% per annum ------------- Amount invested =x Part II 2.00% per annum ------------ Amount invested = y = 2300 Interest----- 95 Part I 9.00% per annum ---x Part II 2.00% per annum ---y Total investment x + y= 2300 -------------1 Interest on both investments 9.00% x + 2.00% y= 95 Multiply by 100 9 x + 2 y= 9500.00 --------2 Multiply (1) by -9 we get -9 x -9 y= -20700.00 Add this to (2) 0 x -7 y= -11200 divide by -7 y = 1600 Part I 9.00% \$ 700 Part II 2.00% \$ 1600 CHECK 700 --------- 9.00% ------- 63.00 1600 ------------- 2.00% ------- 32.00 Total -------------------- 95.00 m.ananth@hotmail.ca
 Linear-systems/673099: solve system of linear equation by elimination a+9b=1 a+3b=-51 solutions Answer 418478 by mananth(12270)   on 2012-10-28 22:36:13 (Show Source): You can put this solution on YOUR website!a + 9 b = 1 .............1 a + 3 b = -5 .............2 Eliminate y multiply (1)by 1 Multiply (2) by -3 1 a 9 b = 1 -3 a -9 b = 15 Add the two equations -2 a = 16 / -2 a = -8 plug value of a in (1) 1 a + 9 b = 1 -8 + 9 b = 1 9 b = 1 + 8 9 b = 9 b = 1 a -8 b 1 m.ananth@hotmail.ca
 Exponential-and-logarithmic-functions/673067: How do I solve the equation 4^2X=64? The teacher gave us the answer, 3/2, but I don't know the steps to get to that answer.1 solutions Answer 418467 by mananth(12270)   on 2012-10-28 21:31:33 (Show Source): You can put this solution on YOUR website!4^2X=64 2x log 4 = log 64 2x= log 64/log4 2x=3 x= 3/2
 Exponential-and-logarithmic-functions/673045: Solve the equation 6^x=72. ROund the answer to four decimal places.1 solutions Answer 418466 by mananth(12270)   on 2012-10-28 21:29:17 (Show Source): You can put this solution on YOUR website!x = log72/log6 = 2.3869. x= 2.39
 Travel_Word_Problems/673048: A passenger train's speed is 60mi/h and a freight trains speed is 40mi/h. the passenger train travels the same distance in 1.5 hour less time then the freight train. How long does each train take to make the trip? I know d= r*t and t=d/r, but no where in the problem does it say what the overall time of the trip was, just that one train was 1.5 hr less. Please help.1 solutions Answer 418460 by mananth(12270)   on 2012-10-28 21:20:28 (Show Source): You can put this solution on YOUR website!let distance be x passenger train speed = 60 mi/h time pasanger train = x/60 Similarly time freight train = x/40 Difference between the two timings is 1.5 x/40 -x/60 = 1.5 LCD = 120 3x-2x=120*1.5 x= 180 miles Passenger train takes 180/60 = 3 hours Freight tain takes 180/40 = 4.5 hours
 Graphs/672704: i need help with this question 3x-y=8 6x-2y=8 I have to solve the systems of equations by graphing1 solutions Answer 418277 by mananth(12270)   on 2012-10-27 23:27:53 (Show Source): You can put this solution on YOUR website!y= 3x -8 Assume values of x and plug in the equation to get values of y. Plot the points x 0 5 2 y= -8 7 -2 (x,y)(0,-8),(5, 7),(2-2) 6 x + -2 y = 8 y= 3 x -4 Assume values of x and plug in the equation to get values of y. Plot the points x 0 5 2 y= -4 11 2 (x,y) (0,-4),(5,11),( 2,2) The slopes are same. The lines are parallel. Hence no solution to the system of equations m.ananth@hotmail.ca
 Linear-equations/672514: Could you please help me to answer this eqution I have tried and tried? Find the slope of the line passing through the two given points of (-8,8) and (-3,-6)1 solutions Answer 418121 by mananth(12270)   on 2012-10-27 08:30:36 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 -8 8 -3 -6 slope m = (y2-y1)/(x2-x1) ( -6 - 8 )/( -3 - (-8) ) ( -14 / 5 ) m= -14/5
 Linear-equations/672515: Could you please help me to answer this eqution I have tried and tried? Find the slope of the line passing through the two given points of (-8,8) and (-3,-6)I need the answer in fractions1 solutions Answer 418119 by mananth(12270)   on 2012-10-27 08:29:46 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 -8 8 -3 -6 slope m = (y2-y1)/(x2-x1) ( -6 - 8 )/( -3 - (-8) ) ( -14 / 5 ) m= -14/5
 Polynomials-and-rational-expressions/672521: Solve the equation by completing the square. a^2-2a= 241 solutions Answer 418117 by mananth(12270)   on 2012-10-27 08:26:42 (Show Source): You can put this solution on YOUR website! Take the square root (a+1)=+/-5 a=-1+5=4 OR a=-1-5=-6 a=4OR-6
 Parallelograms/672501: are these vertices of a square A(-3,1)B(1,4)C(4,0) D(0,-3) JUSTIFY ANSWER AND SHOW WORK THANK YOU1 solutions Answer 418073 by mananth(12270)   on 2012-10-27 02:07:35 (Show Source): You can put this solution on YOUR website!A(-3,1)B(1,4)C(4,0) D(0,-3) Find the slopes of AB,BC,CD,DA Slope of AB x1 y1 x2 y2 -3 1 1 4 slope m = (y2-y1)/(x2-x1) ( 4 - 1 )/( 1 - -3 ) ( 3 / 4 ) m(AB)= 3/4 M(BC) x1 y1 x2 y2 4 0 1 4 slope m = (y2-y1)/(x2-x1) ( 4 - 0 )/( 1 - 4 ) ( 4 / -3 ) m= -4/3 m(CA) x1 y1 x2 y2 4 0 0 -3 slope m = (y2-y1)/(x2-x1) ( -3 - 0 )/( 0 - 4 ) ( -3 / -4 ) m= 3/4 m(AD) x1 y1 x2 y2 -3 1 0 -3 slope m = (y2-y1)/(x2-x1) ( -3 - 1 )/( 0 - -3 ) ( -4 / 3 ) m= -4/3 Two lines are having same slopes and two are having slopes negative reciprocal So the angles formed are 90 degrees. If the distances aer equal then the co ordinates form a square. l(AB) x1 y1 x2 y2 -3 1 1 4 d= d= d= d= d= 5 l(BC) x1 y1 x2 y2 4 0 1 4 d= d= d= d= d= 5 l(CD) x1 y1 x2 y2 4 0 0 -3 d= d= d= d= d= 5 l(DA) x1 y1 x2 y2 -3 1 0 -3 d= d= d= d= d= 5 The lengths are all 5 units. and they are at right angles. so it is a square.
 Mixture_Word_Problems/672461: How many liters of a 12% acid solution and a 20% acid solution should be mixed in order to obtain 4 liters of a 15% acid solution?1 solutions Answer 418064 by mananth(12270)   on 2012-10-26 23:43:30 (Show Source): You can put this solution on YOUR website! percent ---------------- quantity Acid solution I 12 ---------------- x liters Acid solution II 20 ------ 4 - x liters Mixture 15 ---------------- 4 12x+20(4-x)=15*4 1200x+2000(4-x) =6000 1200x+8000-2000 x=6000 1200x- 2000x=6000 -8000 -800 x = -2000 / -800 x=2.5 liters 12.00% Acid solution I 1.5 liters 20.00% Acid solution II m.ananth@hotmail.ca
 Money_Word_Problems/672467: An investment of \$4500 is made at an annual simple interest rate of 9.25%. How much additional money must be invested at an annual simple interest rate of 13.5% so that the total interest earned is 12% of the total investment?1 solutions Answer 418063 by mananth(12270)   on 2012-10-26 23:38:35 (Show Source): You can put this solution on YOUR website!\$4500--------------9.25% x............13.5% Total yield = 12% 4500*9.5%+13.5%(x)=12%*(4500+x) multiply by 100 4500*9.5+13.5(x)=12(4500+x) 42750+13.5x=154000+12x 13.5x-12x=54000-42750 1.5x=11250 x= 7500 \$ 7500 has to be invested to get a total return of 12%
 Money_Word_Problems/672474: An investment advisor invested \$18000 in two accounts.One investment earned 11.2% annual simple interest while the other investment lost 4.7%. The total earnings from both investments were \$1062. Find the amount invested at 11.2%. I understand these interest problems, but I do not understand how to represent the loss of 4.7% in an equation. Your help would be greatly appreciated! Thank you.1 solutions Answer 418058 by mananth(12270)   on 2012-10-26 23:17:00 (Show Source): You can put this solution on YOUR website!Part I 11.20% per annum ------------- Amount invested =x Part II -4.70% per annum ------------ Amount invested = y 18000 Interest----- 1062 Part I 11.20% per annum ---x Part II -4.70% per annum ---y Total investment x + 1 y= 18000 -------------1 Interest on both investments 11.20% x + -4.70% y= 1062 Multiply by 100 11.2 x + -4.7 y= 106200.00 --------2 Multiply (1) by -11.2 we get -11.2 x -11.2 y= -201600.00 Add this to (2) 0 x -15.9 y= -95400 divide by -15.9 y = 6000 Part I 11.20% \$ 12000 Part II -4.70% \$ 6000 CHECK 12000 --------- 11.20% ------- 1344.00 6000 ------------- -4.70% ------- -282.00 Total -------------------- 1062.00 m.ananth@hotmail.ca
 Complex_Numbers/672484: Please help me solve this equation: x^2+16=-49 I have tried adding positive 16 to -49 to get -33 but i can't get past square routing the plus, minus ( -33 ). Thank You1 solutions Answer 418057 by mananth(12270)   on 2012-10-26 23:13:47 (Show Source): You can put this solution on YOUR website! we solve by the squaring method When we add 64 then we get a perfect square on the left side of the equation Take the square root on both sides (x+8) = +/- x= -8+ OR x=-8-
 Money_Word_Problems/672476: An investment advisor invested \$18000 in two accounts. One investment earned 11.2% annual simple interest while the other investment lost 4.7%. The total earnings from both investments were \$1062. Find the amount invested at 11.2%.1 solutions Answer 418056 by mananth(12270)   on 2012-10-26 23:03:35 (Show Source): You can put this solution on YOUR website!Part I 11.20% per annum ------------- Amount invested =x Part II -4.70% per annum ------------ Amount invested = y 18000 Interest----- 1062 Part I 11.20% per annum ---x Part II -4.70% per annum ---y Total investment x + 1 y= 18000 -------------1 Interest on both investments 11.20% x + -4.70% y= 1062 Multiply by 100 11.2 x + -4.7 y= 106200.00 --------2 Multiply (1) by -11.2 we get -11.2 x -11.2 y= -201600.00 Add this to (2) 0 x -15.9 y= -95400 divide by -15.9 y = 6000 Part I 11.20% \$ 12000 Part II -4.70% \$ 6000 CHECK 12000 --------- 11.20% ------- 1344.00 6000 ------------- -4.70% ------- -282.00 Total -------------------- 1062.00 m.ananth@hotmail.ca
 Money_Word_Problems/672425: A man invests \$5500 dollars in three accounts that pay 5%, 8%, and 9% in annual interest respectively. He has two times as much money invested at 9% as he does at 8%. If the total interest earned for the year is \$449, how much is invested at 5%?1 solutions Answer 418037 by mananth(12270)   on 2012-10-26 20:32:07 (Show Source): You can put this solution on YOUR website!8%-------------------x 9%-------------------2x Balance @ 5%-------------------(5500-3x) Interest = 449 0.08x+0.09(2x)+0.05(5500-3x)=449 Multiply by 100 8x+18x+27500-15x=44900 11x=44900-27500 11x=17400 x= 1581.82................8% 2x=3163.64.................9% 754.55.....................5%
 test/672207: A boat travels upstream 60 miles in 4 hours. The return trip going downstream takes 2 hours. Find the rate of the boat in still water and the rate of the current?1 solutions Answer 417840 by mananth(12270)   on 2012-10-26 08:26:23 (Show Source): You can put this solution on YOUR website!Boat speed =x mph current speed =y mph againstcurrent x-y 4 hours with current x+y 2 hours Distance = 60 miles distance= 60 t=d/r against current 60.00 / ( x - y )= 4.00 4.00 x -4.00 y = 60.00 ....................1 downstream 60.00 / ( x + y )= 2.00 2.00 ( x + y ) = 60.00 2.00 x + 2.00 y = 60.00 ...............2 Multiply (1) by 1.00 Multiply (2) by 2.00 we get y 4.00 x -4.00 y = 60.00 4.00 x + 4.00 = 120.00 8.00 x = 180.00 / 8.00 x = 22.5 mph plug value of x in (1) y 4 x -4 y = 60 90 -4 -90 = 60 -4 y = 60 -4 y = -30 mph y = 7.5 Boat 22.5 mph current 7.5 mph
 Graphs/672217: I seem to be stuck and I know it is exhaustion. Please help I need to graph an inequality 2y<41 solutions Answer 417837 by mananth(12270)   on 2012-10-26 08:13:25 (Show Source): You can put this solution on YOUR website!2y<4 First the equality 2y=4 y=2 It is a line parallel to the x axis The equality Since y is < than something the line will be dotted one.the shaded portion will be below the line The inequality