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# Recent problems solved by 'mananth'

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 Sequences-and-series/716105: 15th term of the A.P. x-7, x-2, x+3, ........ is : (A) x+63 (B) x+73 (C) x+83 (D) x+531 solutions Answer 439733 by mananth(12270)   on 2013-02-19 08:12:04 (Show Source): You can put this solution on YOUR website!first term a = x-7 d = common difference= x-2-(x-7) = 5 t15 = (x-7) +(15-1)5 t15= x-7 +70 = x+63
 Age_Word_Problems/715609: the ratio of the ages of a husband and his wife is 4:3. after 4 years this ratio will be 9:7. if at the time of the marriage the ratio was 5:3, then how many years ago thy got married?1 solutions Answer 439507 by mananth(12270)   on 2013-02-18 01:25:01 (Show Source): You can put this solution on YOUR website!husband --------- x wife = y 3x-4y=0...................(1) after 4 years (x+4)/(y+4) =9/7 7(x+4)=9(y+4) 7x+28=9y+36 7x-9y=8..............(2 x= husband's age y= wife's age 3 x -4 y = 0 .............1 Total value 7 x -9 y = 8 .............2 Eliminate y multiply (1)by -9 Multiply (2) by 4 -27 x 36 y = 0 28 x -36 y = 32 Add the two equations 1 x = 32 / 1 x = 32 plug value of x in (1) 3 x -4 y = 0 96 -4 y = 0 -4 y = 0 -96 -4 y = -96 y = 24 x= 32 husband's age y= 24 wife's age ) let a be the years ago they married (x-a)/(y-a) =5/3 (32-a)/(24-a) =5/3 3(32-a)=5(24-a) 96-3a=120-5a 2a=24 a=12 They got married 12 years ago
 Linear-equations/715559: Y=5x-3 with y=2x find the solution of each system of simultaneous equations by graphing1 solutions Answer 439506 by mananth(12270)   on 2013-02-18 01:13:09 (Show Source): You can put this solution on YOUR website!-5 x + 1 y = -3 .............1 -2 x 1 y = 0 .............2 Find the x & y intercept points by plugging x=0,y=0 in both equations. equation I when x= 0 y= -3 ,( 0 , -3 ) when y = 0 x= -3 ,( 0.6 , 0 ) Equation 2 when x= 0 y= 0 ( 0 , 0 ) when y = 0 x= 0 ( 0 , 0 ) You will observe that the point of intersection is 1,2 The solution of the system is ( 1,2 )
 Money_Word_Problems/715564: If an investor invested \$1300 in two mutual funds, one was at 5% and the other at 2%, and a total of \$50 was the profit, how much was invested in each fund?1 solutions Answer 439505 by mananth(12270)   on 2013-02-18 00:59:46 (Show Source): You can put this solution on YOUR website!Part I 5.00% per annum ------------- Amount invested =x Part II 2.00% per annum ------------ Amount invested = y 1300 Interest----- 50 Part I 5.00% per annum ---x Part II 2.00% per annum ---y Total investment x + 1 y= 1300 -------------1 Interest on both investments 5.00% x + 2.00% y= 50 Multiply by 100 5 x + 2 y= 5000.00 --------2 Multiply (1) by -5 we get -5 x -5 y= -6500.00 Add this to (2) 0 x -3 y= -1500 divide by -3 y = 500 Part I 5.00% \$ 800 Part II 2.00% \$ 500 CHECK 800 --------- 5.00% ------- 40.00 500 ------------- 2.00% ------- 10.00 Total -------------------- 50.00 m.ananth@hotmail.ca
 Linear-equations/715572: find the equation of a line that is parallel to the line y=-9x and contains the point (3, -9)1 solutions Answer 439504 by mananth(12270)   on 2013-02-18 00:56:05 (Show Source): You can put this solution on YOUR website!y=-9x slope of line is -9 a parallel line will have same slope and passes through (3,-9) y-y1=m(x-x1) y-(-9)=-9(x-3) y+9=-9x+27 y+9x=18 OR y =-9x +18
 Miscellaneous_Word_Problems/715600: If two opposite sides of a square are increased by 10 meters and the other sides are decreased by 5 meters, the area of the rectangle that is formed is 76 square meters. Find the area of the original square.1 solutions Answer 439503 by mananth(12270)   on 2013-02-18 00:47:43 (Show Source): You can put this solution on YOUR website!let the side of square be x x+10 and x-5 are the sides of the rectangle (x+10)(x-5)= 76 x^2-5x+10x-50=76 x^2+5x-126=0 x^2+14x-9x-126=0 x(x+14)-9(x+14)=0 (x+14)(x-9)=0 x=-14 OR 9 ignore negative side of square is 9
 Angles/715592: I am trying to create an algebric expression from this worded problem One angle is 6 degrees less than twice a second angle. If the two angles are complementary, what are their measures?1 solutions Answer 439502 by mananth(12270)   on 2013-02-18 00:39:33 (Show Source): You can put this solution on YOUR website!let the angles be x & y x+y =90 x= 2y-6 substitute x in the first equation 2y-6+y = 90 3y=96 /3 y=32 now you know what x is
 Money_Word_Problems/715553: an investor invest 2500 in two mutual funds, he invest 5% in one and 2% in the other, both funds totaled an earning of \$95, how much did each fund earn?1 solutions Answer 439480 by mananth(12270)   on 2013-02-17 21:39:00 (Show Source): You can put this solution on YOUR website!Part I 5.00% per annum ------------- Amount invested =x Part II 2.00% per annum ------------ Amount invested = y 2500 Interest----- 95 Part I 5.00% per annum ---x Part II 2.00% per annum ---y Total investment x + 1 y= 2500 -------------1 Interest on both investments 5.00% x + 2.00% y= 95 Multiply by 100 5 x + 2 y= 9500.00 --------2 Multiply (1) by -5 we get -5 x -5 y= -12500.00 Add this to (2) 0 x -3 y= -3000 divide by -3 y = 1000 Part I 5.00% \$ 1500 Part II 2.00% \$ 1000 CHECK 1500 --------- 5.00% ------- 75.00 1000 ------------- 2.00% ------- 20.00 Total -------------------- 95.00 m.ananth@hotmail.ca
 Systems-of-equations/715480: In his motorboat, Bill travels upstream at top speed to his favorite fishing spot, a distance of 36 miles. It takes him 2 hours. Returning, he finds that the trip downstream, still at top speed, only takes 1.5 hours. Find the speed of Bill's boat and the speed of the current.1 solutions Answer 439479 by mananth(12270)   on 2013-02-17 21:36:49 (Show Source): You can put this solution on YOUR website!Boat speed speed =x mph current speed =y mph against current 2 hours with current 1.5 hours Distance with current 36 miles distance against current 36 t=d/r against current (x-y) 36.00 / ( x - y )= 2.00 2.00 x - -2.00 y = 36.00 ....................1 with current (x+y) 36.00 / ( x + y )= 1.50 1.50 ( x + y ) = 36.00 1.50 x + 1.50 y = 36.00 ...............2 Multiply (1) by 1.50 Multiply (2) by 2.00 we get 2.00 3.00 x + -3.00 y = 54.00 3.00 x + 3.00 y = 72.00 6.00 x = 126.00 / 6.00 x = 21 mph plug value of x in (1) y 2 x -2 y = 36 42 -2 -42 = 36 -2 y = 36 -2 y = -6 mph y = 3 Boat speed 21 mph current 3 mph
 Money_Word_Problems/715502: A student takes out two loans, totaling \$4000. One loan is at 6% interest, the other at 5% interest. the interest for one year is \$215. what is the amount of each loan?1 solutions Answer 439478 by mananth(12270)   on 2013-02-17 21:26:05 (Show Source): You can put this solution on YOUR website!Part I 6.00% per annum ---x Part II 5.00% per annum ---y Total investment x + y= 4000 -------------1 Interest on both investments 6.00% x + 5.00% y= 215 Multiply by 100 6 x + 5 y= 21500.00 --------2 Multiply (1) by -6 we get -6 x -6 y= -24000.00 Add this to (2) 0 x -1 y= -2500 divide by -1 y = 2500 Part I 6.00% \$ 1500 Part II 5.00% \$ 2500 CHECK 1500 --------- 6.00% ------- 90.00 2500 ------------- 5.00% ------- 125.00 Total -------------------- 215.00
 Percentage-and-ratio-word-problems/715541: a large holding tank was three tenths filled.a worker then added two fifth of tank.after adding two fiths of, the tank contained 1,400 gallon.how many gallons will this tank contain when filled capacity1 solutions Answer 439475 by mananth(12270)   on 2013-02-17 21:17:53 (Show Source): You can put this solution on YOUR website!let capacity of tank be x (3/10)x +(2/5)x = 1400 LCD is 10 multiply equation by 10 3x+4x=1400*10 7x=14000 /7 x= 2000 gallons -the capacity of tank
 Linear-equations/715517: Find an equation in general form of the perpendicular bisector of the line segment with endpoints A(7,-1) and B(-4,2)1 solutions Answer 439462 by mananth(12270)   on 2013-02-17 20:01:19 (Show Source): You can put this solution on YOUR website!A(7,-1) and B(-4,2) mid point co-ordinates x=(7+(-4))/2=3/2 y=(-1+2)/2= =1/2 (3/2, 1/2) A(7,-1) and B(-4,2) slope = ((2-(-1))/(-4-7) slope=- 3/11 the slope of line perpendicular to this line will have slope of 11/3 m=11/3 , point (3/2, 1/2) y-(1/2) = 11/3( x-(3/2)) y-1/2 =11/3(2x-3)/2) simplify 2*3(y-1/2) = 11(2x-3) 6y-3=22x-33 6y=22x-30 y=(11/3)x -5
 Quadratic_Equations/715505: 1. Jake drives a tractor from one town to another, a distance of 120 kilometers. He drives 6 kilometers per hour faster on the return trip, cutting 1 hour off the time. How fast does he drive each way? Going?, Returning? 2.The oriental rug shown is 3 feet longer than it is wide. If the diagonal of the rug is 12 feet find its dimensions to the nearest tenth of a foot. width?, length? 3. A large rectangular movie screen in an IMAX theater has an area of 10,176 square feet. Find the dimensions of the screen if it is 10 feet longer than it is wide. Length?, Width? 4. 1 solutions Answer 439455 by mananth(12270)   on 2013-02-17 19:27:20 (Show Source): You can put this solution on YOUR website!Tie going - time returning = 1 hours let speed be x km/h time = d/r d=120 time going = 120/x time returning = 120/(x+6) multiply the equation by x(x+1) 120(x+1) -120x= x(x+1) 120x+120-120x=x^2+x x^2+x-120=0 Find the roots of the equation by quadratic formula a= 1 b= 1 c= -120 b^2-4ac= 1 - -480 b^2-4ac= 481 = 21.93 x1=( -1 + 21.93 )/ 2 x1= 10.47 x2=( -1 -21.93 ) / 2 x2= -11.47 Ignore negative value km/h x = 10.47 (going speed) add 6 for returning speed width =x length = x+3 Area = L * W Area = x(x+3) = 12 x^2+3x=12 x^2+3x-12=0 solve for x (x+4)(x-3)=0 x= 3 which is positive the dimensions are 4 ft by 3 ft
 Travel_Word_Problems/715283: Traveling by boat. Alonzo can travel from his camp downstream to the mouth of the river in 30 minutes. If it takes him 45 minutes to come back, then how long would it take him to go that same distance in the lake with no current?1 solutions Answer 439351 by mananth(12270)   on 2013-02-17 07:29:00 (Show Source): You can put this solution on YOUR website!let the distance be d d=rt d/t = r d/(1/2) = r r=2d ( downstream) d/(3/4) = r 4d/3 = r upstream let speed of boat in still water be b and speed of current be c b+c =2d b-c= 4d/3 add up 2b= 10d/3 b= 5d/3 speed of boat in still water in lake water t= d/r t= d/(5d/3) =3/5 hour if you want to convert to minutes multiply by 60
 Trigonometry-basics/715282: sec x + cos x = 3,then tan^2 x - sin^2 x is1 solutions Answer 439348 by mananth(12270)   on 2013-02-17 07:17:02 (Show Source): You can put this solution on YOUR website! secx +cosx =3 square both sides sec^2x= 1+tan^2x: cos^2x = 1-sin^2x
 Trigonometry-basics/715262: A man stands on a cliff and looks across the canyon in front of him. On the other side of the canyon, he sees a tree. The tree is 52 ft away from him. From where the man stands the angle of elevation to the top of the tree is32 degrees. From his position, the angle of depression to the bottom opposite side of the canyon is 67 degrees. What is the height of the tree? What is the distance from the bottom of the canyon to the top of the tree? Please help1 solutions Answer 439340 by mananth(12270)   on 2013-02-17 03:48:33 (Show Source): You can put this solution on YOUR website!Tan 32 = height of tree/ horizontal distance 52 * tan 32 = height of tree 0.62*52= 32.5 feet similarly Tan 67 * 52 = bottom of canyon to the foot of the tree =122.5 Add up both 32.5+122.5 =160 feet ---- from top of tree to bottom of canyon
 Percentage-and-ratio-word-problems/715268: out of his total income Hamza spend 20%on house rent and 70%of rest on household expenditure. if he saves Rs.1800, what is his total income 1 solutions Answer 439336 by mananth(12270)   on 2013-02-17 03:32:24 (Show Source): You can put this solution on YOUR website!Let income be x 0.2x on rent 0.7x on household expenditure saving = (1800) 0.2x+0.7x+1800=x 0.9x=x-1800 0.9x-x=-1800 -.1x=-1800 x=18000 the income
 Radicals/715242: ABCD is a square. The length of the diagonal is 10√ ̅2. Find the perimeter of the sqare.1 solutions Answer 439326 by mananth(12270)   on 2013-02-16 22:23:47 (Show Source): You can put this solution on YOUR website!ABCD is a square. The length of the diagonal is 10√ ̅2. Find the perimeter of the sqare. The area of square = 1/2 * (product of diagonals) Area = 1/2 * ( 10sqrt(2) * 10sqrt(2)}}} = 1/2 * 200 =100 area = 100 so side = sqrt(100) = 10 Perimeter = 4*10 = 40
 Quadratic_Equations/715247: The area of the rectangular plot is 140m^2. The length of the plot (in metres) is one less than three times its breadth. We have to find length & breadth pf the plot. 1 solutions Answer 439325 by mananth(12270)   on 2013-02-16 22:13:10 (Show Source): You can put this solution on YOUR website!The area of the rectangular plot is 140m^2. The length of the plot (in metres) is one less than three times its breadth. We have to find length & breadth pf the plot let breadth be x length is 3x-1 Area = Area of rectangle = L * B 140 =x(3x-1) Find the roots of the equation by quadratic formula -1 a= 3 b= -1 c= -140 -1680 b^2-4ac= 1 - b^2-4ac= 1681 = 41 41 x1=( 1 + )/ 6 x1= 7 ) / x2=( 1 -41 6 x2= -6.67 Ignore negative value mph x = 7 breadth = 7 length = 3(7) -1= 20 The dimensions are 7 & 20 m
 Trigonometry-basics/715244: Due to a storm, a flagpole broke at a certain point. The top part tipped over like a hinge, with the tip hitting the ground at a point 20 feet from the flagpole's base. The flagpole was rewelded, but another storm broke it again at a point 5 feet lower than the previous break. And, this time the tip hit the ground at a point 30 feet from the base. How tall was the flagpole?1 solutions Answer 439323 by mananth(12270)   on 2013-02-16 22:05:44 (Show Source): You can put this solution on YOUR website!Let the broken part length be y let the remaining lenngth be x distance from base of pole = 20ft they form a right triangle by Pythagoras theorem Second condition it breaks 5feet below The broken part length = y+5 The remaining part length =- x-5 distance from base of pole = 30 ft 10x+10y=500 /10 x+y= 50 But x+y is the length of the flag pole
 Linear-systems/715238: Hi, how do you solve x+2/2 - y+4/3=3 and x+y/5=x - y/2 - 5/21 solutions Answer 439321 by mananth(12270)   on 2013-02-16 21:41:28 (Show Source): You can put this solution on YOUR website! LCD = 6 multiply equation by 6 3(x+2)-6(y+4) = 18 3x+6-6y-24=18 3x-6y = 36 /3 x-2y=12.......................(1) . LCD = 10 multiply eauation by 10 we get 2(x+y)= 5(x-y)-25 2x+2y=5x-5y-25 7y-3x=-25.......................(2) Solve equation (1) & (2) 1 x -2 y = 12 .............1 Total value -3 x + 7 y = -25 .............2 Eliminate y multiply (1)by 7 Multiply (2) by 2 7 x -14 y = 84 -6 x + 14 y = -50 Add the two equations 1 x = 34 / 1 x = 34 plug value of x in (1) 1 x -2 y = 12 34 -2 y = 12 -2 y = 12 -34 -2 y = -22 y = 11 x= 34 y= 11 (34,11) is the solution m.ananth@hotmail.ca
 Mixture_Word_Problems/715173: Premium coffee sells for \$6.00 per pound, and regular coffee sells for \$4.00 per pound. How many pounds of each type of coffee should be blended to obtain 100 pounds of a blend that sells for \$4.64 per pound?1 solutions Answer 439318 by mananth(12270)   on 2013-02-16 21:30:20 (Show Source): You can put this solution on YOUR website! Price ---------------- quantity Premium coffee \$6 ---------------- x pounds Regular coffee \$4 ------ 100 - x pounds Mixture \$4.64 ---------------- 100 6 x + 4 ( 100 - x ) = 4.64 * 100 600 x + 400 ( 100 - x ) = 46400 600 x + 40000 - 400 x = 46400 600 x - 400 x = 46400 - -40000 200 x = 6400 / 200 x = 32 pounds \$6.00 Premium coffee 68 pounds \$4.00 Regular coffee m.ananth@hotmail.ca
 Linear-equations/715241: find an equation of the line satisfying the conditions given. express in standard form. parallel to x-y=4 and passing through (-3,2)1 solutions Answer 439314 by mananth(12270)   on 2013-02-16 21:22:13 (Show Source): You can put this solution on YOUR website!1 x -1 y = 4 Find the slope of this line make y the subject -1 y = - x + 4 Divide by -1 y = x -4 Compare this equation with y=mx+b slope m = 1 The slope of a line parallel to the above line will be the same The slope of the required line will be 1 m= 1 ,point ( -3 , 2 ) Find b by plugging the values of m & the point in y=mx+b 2 = -3 + b b= 5 m= 1 Plug value of the slope and b in y = mx +b The required equation is y = x + 5 m.ananth@hotmail.ca
 Coordinate-system/715182: Find the slope-intercept equation of the line with slope -3, passing through the point (1,-5).1 solutions Answer 439313 by mananth(12270)   on 2013-02-16 21:19:48 (Show Source): You can put this solution on YOUR website!The equation of line in slope point form is (y-y1)=m(x-x1) (x1,y1) = (1,-5) m= -3 plug the values 9(y-(-5)=(-3)(x-1) 9(y+5)=-3x+3 9y+45=-3x+3 9y= -3x-42 /9 y= (-1/3)x -(14/3)
 Money_Word_Problems/715197: Suppose that john invested a certain amount of money at 3% interest, and he invested \$750 more than that amount at 5%. His total yearly interest was \$157.50. How much did he invest at each rate?1 solutions Answer 439312 by mananth(12270)   on 2013-02-16 21:13:00 (Show Source): You can put this solution on YOUR website!Amount @ 3.00% x Amount @ 5.00% 1 x + 750 Total interest earned = 157.50 3.00% x+ 5.00% ( 1 x + 750 )= 157.5 3.00% x+ 5.00% * 1 x + 37.5 = 157.5 3.00% x+ 5.00% x + 37.5 = 157.5 0.03 x+ 0.05 x = 120 0.08 x = 120 x= 1500 Amount @ 3.00% = Amount @ 5.00% = 1 * 1500 + 750 = 2250 CHECK Total interest 45 + 112.5 = 157.5
 Money_Word_Problems/715200: A sum of \$2300 is invested, part of it at 5% interest and the remainder at 6%. If the interest earned by the 6% investment is \$50 more than the interest earned by the 5% investment, find the amount invested at each rate.1 solutions Answer 439307 by mananth(12270)   on 2013-02-16 20:56:29 (Show Source): You can put this solution on YOUR website!\$ 2300 let x be part I..............5% (2300-x) = Part II............6% Interest earned by 5% investment = 0.05x Interest earned by 6% investment = 0.06(2300-x) 0.06(2300-x) -0.05x= 50 138- 0.06x-0.05x= 50 -0.11x= 50-138 -0.11x= - -88 x= -88/-0.11 x=800 ---------- investment at 5% invetment at 6% = 2300-800= 1500 at6%
 Money_Word_Problems/715198: Tyler received \$1200 from his parents as a graduation present. He invested part of it at 4% interest, and he invested the remainder at 6%. If the total yearly interest amounted to \$62, how much did he invest at each rate? 1 solutions Answer 439304 by mananth(12270)   on 2013-02-16 20:46:09 (Show Source): You can put this solution on YOUR website!Part I 4.00% per annum ------------- Amount invested =x Part II 6.00% per annum ------------ Amount invested = y 1200 Interest----- 62 Part I 4.00% per annum ---x Part II 6.00% per annum ---y Total investment x + 1 y= 1200 -------------1 Interest on both investments 4.00% x + 6.00% y= 62 Multiply by 100 4 x + 6 y= 6200.00 --------2 Multiply (1) by -4 we get -4 x -4 y= -4800.00 Add this to (2) 0 x 2 y= 1400 divide by 2 y = 700 Part I 4.00% \$ 500 Part II 6.00% \$ 700 CHECK 500 --------- 4.00% ------- 20.00 700 ------------- 6.00% ------- 42.00 Total -------------------- 62.00 m.ananth@hotmail.ca
 Linear-equations/715217: How do I solve 4x+3y=9 plus 4x+3y=2 with relation to whether they are parallel perpendicular or neither? I need to see the steps for solving if possible please. Thank you 1 solutions Answer 439302 by mananth(12270)   on 2013-02-16 20:42:11 (Show Source): You can put this solution on YOUR website!4x+3y=9 write the equation in slope intercept form 3y= -4x+9 /3 y= (-4/3)x+3 . 4x+3y=2 3y= -4x+2 y=(-4/3)x+(2/3) y= mx +b is the equation in slope intercept form where m is the slope. m in both the above lines is (-4/3) so the lines are parallel. Parallel lines have same slopes but different y intercepts
 Rectangles/715224: ABCD is a rectangle. The area of the rectangle is 40 square feet. The length is 3 more than the width. A) Find the measure of each length and each width B) Find the length of the diagonal, rounded to the nearest tenth1 solutions Answer 439300 by mananth(12270)   on 2013-02-16 20:36:56 (Show Source): You can put this solution on YOUR website!Area of rectangle = l*w Width be x Length = x+3 x(x+3) =40 x^2+3x=40 x^2+3x-40=0 x^2+8x-5x-40=0 x(x+8)-5(x+8)=0 (x+8)(x-5)=0 Therefore x= -8 OR x=5 Ignore negative x=5 is the width width = 5 feet Length = x+3----> 8feet
 Polynomials-and-rational-expressions/715226: completely factor the polynomial 3x^3+15x^2+3x+151 solutions Answer 439299 by mananth(12270)   on 2013-02-16 20:32:28 (Show Source): You can put this solution on YOUR website!3x^3+15x^2+3x+15
 Polynomials-and-rational-expressions/714966: Can anyone simplify this? [4y-[5z+1)][4y+(5z+1)] thanks!1 solutions Answer 439114 by mananth(12270)   on 2013-02-15 19:48:04 (Show Source): You can put this solution on YOUR website![4y-[5z+1)][4y+(5z+1)] use the identity (a+b)(a-b)= a^2-b^2 a= 4y b=(5z+1) (4y)^2-(5z+1)^2 16y^2-(25z^2+10z+1) 16y^2-25z^2-10z-1