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# Recent problems solved by 'mananth'

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 Linear_Equations_And_Systems_Word_Problems/734074: An investor invested a total of \$2200 in two mutual funds. One earned 5% profit while the other earned a 3% profit. If the investor's total profit was \$86, how much was invested in each mutual fund?1 solutions Answer 448705 by mananth(12270)   on 2013-04-05 02:07:17 (Show Source): You can put this solution on YOUR website! Part I 3.00% per annum ------------- Amount invested =x Part II 5.00% per annum ------------ Amount invested = y 2200 Interest----- 86.00 Part I 3.00% per annum ---x Part II 5.00% per annum ---y Total investment x + 1 y= 2200 -------------1 Interest on both investments 3.00% x + 5.00% y= 86 Multiply by 100 3 x + 5 y= 8600.00 --------2 Multiply (1) by -3 we get -3 x -3 y= -6600.00 Add this to (2) 0 x 2 y= 2000 divide by 2 y = 1000 Part I 3.00% \$ 1200 Part II 5.00% \$ 1000 CHECK 1200 --------- 3.00% ------- 36.00 1000 ------------- 5.00% ------- 50.00 Total -------------------- 86.00 m.ananth@hotmail.ca
 Quadratic_Equations/733212: how do i solve 3x^2-5x-8=0 using the quadratic formula1 solutions Answer 448309 by mananth(12270)   on 2013-04-03 00:44:21 (Show Source): You can put this solution on YOUR website! compare with equation a= 3 , b= -5 , c= -8 b^2-4ac= 25 + 96 b^2-4ac= 121 x1=( 5 + 11 )/ 6 x1= 2.67 x2=( 5 -11 ) / 6 x2= -1.00 2.67 , -1 m.ananth@hotmail.ca
 Quadratic_Equations/733129: We are learning this in class and my teacher goes way to fast. Could you please help me with the following question? Solve each equation symbolically. A. (X+3)^2=7 B. (X-2)^2-8=13 I honestly don't understand what "solve symbolically". If you would help me I would be extremely thankful. Dakota1 solutions Answer 448300 by mananth(12270)   on 2013-04-02 21:50:02 (Show Source): You can put this solution on YOUR website!Solve each equation symbolically. A. (X+3)^2=7 B. (X-2)^2-8=13 symbolically means using the quadratic formula compare this equation with ax^2+bx+c a=1, b=6, c=2 b^2-4ac= 36 -8 b^2-4ac= 28 x1=( -6 + 5.29 )/ 2 x1= -0.35 x2=( -6 -5.29 ) / 2 x2= -5.65 two values of x. -0.35 & -5.65
 Graphs/732835: How do I draw the graph of: ?1 solutions Answer 448083 by mananth(12270)   on 2013-04-02 08:10:59 (Show Source): You can put this solution on YOUR website!y=-3x+7 Generate values of x & y x=0,y=7 (0,7) x=2,y=1 (2,1) x=3, y=-2 (3,-2) Plot the points and the line
 Equations/732855: For some reason im really struggling with the equation (a-2)/3=(1-a)/2, could you possibly explain how i would work this out, thankyou Emma1 solutions Answer 448082 by mananth(12270)   on 2013-04-02 08:01:24 (Show Source): You can put this solution on YOUR website! Cross multiply 2(a-2)=3(1-a) 2a-4=3-3a 2a+3a=4+3 5a=7 a=7/5
 Linear-equations/732863: Find the intercepts of the equation. 4x-7y = 56 1 solutions Answer 448081 by mananth(12270)   on 2013-04-02 07:58:14 (Show Source): You can put this solution on YOUR website!4x-7y=56 7y=4x-56 /7 y=(4/7)x-8 X intercept plug y =0 (4/7)x-8=0 (4/7)x=8 4x=56 x=14 x intercept 14 Y intercept plug x=0 y =-8 y intercept -8
 Linear-equations/732868: help! Fractions yikes! Compleing ordered pairs for this equation. y = 1/4x -4 (4, ) and (0, )1 solutions Answer 448080 by mananth(12270)   on 2013-04-02 07:53:51 (Show Source): You can put this solution on YOUR website!y = (1/4)x -4 (4,-3) (0,-4)
 Money_Word_Problems/732810: An investor invested a total of 2800 in two mutual funds. One fund earned a 6% profit while the other earned a 4% profit. If the investors total profit was \$152, how much was invested in each mutual fund?1 solutions Answer 448075 by mananth(12270)   on 2013-04-02 06:35:30 (Show Source): You can put this solution on YOUR website!Part I 6.00% per annum ------------- Amount invested =x Part II 4.00% per annum ------------ Amount invested = y 2800 Interest----- 152.00 Part I 6.00% per annum ---x Part II 4.00% per annum ---y Total investment x + 1 y= 2800 -------------1 Interest on both investments 6.00% x + 4.00% y= 152 Multiply by 100 6 x + 4 y= 15200.00 --------2 Multiply (1) by -6 we get -6 x -6 y= -16800.00 Add this to (2) 0 x -2 y= -1600 divide by -2 y = 800 Part I 6.00% \$ 2000 Part II 4.00% \$ 800 CHECK 2000 --------- 6.00% ------- 120.00 800 ------------- 4.00% ------- 32.00 Total -------------------- 152.00
 Sequences-and-series/732799: The sum of the first 100 terms of an arithmetic progression is 10000; the first, second and fifth terms of this progression are three consecutive terms of a geometric progression. Find the first term, a, and the non-zero common difference, d. of the arithmetic progression 1 solutions Answer 448074 by mananth(12270)   on 2013-04-02 06:31:58 (Show Source): You can put this solution on YOUR website!S 100 = 100/2[2a+99d] S100 =50[2a+99d] a, a+d, a+4d (a+d)^2=a(a+4d) a^2+2ad+d^2=a^2+4ad d^2=2ad d=2a S100 =50[2a+99d] S100= 50*100d S100=5000d 10,000=5000d d=2 Therefore a=1 Check s100 = 100/2[2+198] s100= 50*200 s100 = 10,000
 Rate-of-work-word-problems/732844: how to solve the sum of the digits of A 3-digit number is 16 if the digits are reversed and the resulting number added to the original number the sum is 1049 if the resulting number is subtracted from the original number the difference is 297 what is the number?1 solutions Answer 448072 by mananth(12270)   on 2013-04-02 06:20:29 (Show Source): You can put this solution on YOUR website!First condition x+y+z=16................................(1) Second condition 100x+10y+z+100z+10y+x=1049 101x+20y+101z=1049............................(2) third condition 100x+10y+z-(100z+10y+x)=297 99x-99z=297 /99 x-z=3 x=z+3.......................................(3) substitute x in (1) & (2) z+3+y+z=16 y+2z=13...................(4) 101(z+3)+20y+101z=1049 101z+303+20y+101z=1049 202z+20y=1049-303 202z+20y=746..................(5) 1.00 y + 2.00 z = 13.00 Total value 20.00 y + 202.00 z = 746.00 Eliminate y multiply (1)by 202.00 Multiply (2) by -2.00 202.00 y 404.00 z = 2626.00 -40.00 y -404.00 z = -1492.00 Add the two equations 162.00 y = 1134.00 / 162.00 y = 7 plug value of y in (1) 1.00 y + 2.00 z = 13.00 7.00 + 2.00 z = 13.00 2.00 z = 13.00 -7.00 2.00 z = 6.00 z = 3 y=7,z=3,therefore x= 6 100*6+70+3 673 is the number
 Sequences-and-series/732802: An arithmetic series has first term 1000 and common difference -1.4. calculate the value of the first negative term of the series, and the sum of all the positive terms1 solutions Answer 448070 by mananth(12270)   on 2013-04-02 04:22:34 (Show Source): You can put this solution on YOUR website!a= 1000 d= -1.4 1000/1.4 = 714.29 there are 714.29 =ve numbers add 1.4 you get 715.69 so 716th number will bwe negative t716 = 1000+(716-1)-1.4 t716 = -1 -1 is the first negative number. S715 will be the sum S715 = 715/2[2*1000+714*-1.4] S715 = 357643
 Miscellaneous_Word_Problems/732769: \$6,000 dollars is invested in two different accounts earning 3% and 5% interest. At the end of one year, the two accounts earned \$220 in interest. How much money was invested at 5%? 1 solutions Answer 448034 by mananth(12270)   on 2013-04-01 21:24:23 (Show Source): You can put this solution on YOUR website! Part I 5.00% per annum ------------- Amount invested =x Part II 3.00% per annum ------------ Amount invested = y 6000 Interest----- 220.00 Part I 5.00% per annum ---x Part II 3.00% per annum ---y Total investment x + 1 y= 6000 -------------1 Interest on both investments 5.00% x + 3.00% y= 220 Multiply by 100 5 x + 3 y= 22000.00 --------2 Multiply (1) by -5 we get -5 x -5 y= -30000.00 Add this to (2) 0 x -2 y= -8000 divide by -2 y = 4000 Part I 5.00% \$ 2000 Part II 3.00% \$ 4000 CHECK 2000 --------- 5.00% ------- 100.00 4000 ------------- 3.00% ------- 120.00 Total -------------------- 220.00 m.ananth@hotmail.ca
 Travel_Word_Problems/732448: A certain aircraft can fly 630 miles with the wind in 3 hours and travel the same distance against the wind in 7 hours. What is the speed of the wind?1 solutions Answer 447850 by mananth(12270)   on 2013-04-01 00:46:41 (Show Source): You can put this solution on YOUR website!630 miles in 3 hours with wind speed = 210 mph 630 in 7 hours against wind speed = 630/7 = 90 mph plane speed = x wind speed = y x+y = 210 x-y=90 add up the equations 2x=300 /2 x= 150 mph so wind speed = 60 mph
 Travel_Word_Problems/732447: A private plain traveled from Seattle to the rugged wilderness, at an average speed of 156 mph.on the return trip the average speed was 182 mph if the total traveling time was 9 hours, how far was Seattle from the wilderness?1 solutions Answer 447849 by mananth(12270)   on 2013-04-01 00:37:10 (Show Source): You can put this solution on YOUR website!let distance be x miles time going + time return = 9 x/156 + x/182=9 182x+156x= 9 *182*156 338x=25528 x=756 miles
 Coordinate-system/732433: what is the equation of the line that is parallel to the line that has equation y=2x-3 and with y-intercept of 5.How do you solve the inequality of 8(2-x)-9>2x+5?Thank you.1 solutions Answer 447848 by mananth(12270)   on 2013-04-01 00:27:30 (Show Source): You can put this solution on YOUR website!y= mx +b is the equation in slope intercept form where b is the y intercept y=2x-3 slope = 2 a parallel line will have same slope which is =2 m=2 , point(0,5) y=2x+5
 Sequences-and-series/732158: The tickets in a raffle are numbered 1, 2, 3, and so on. The price of a ticket is the number of cents equal to the number of the ticket. If the raffled article cost \$100, what is the least number of tickets that must be sold so that those conducting the raffle will not lose money?1 solutions Answer 447575 by mananth(12270)   on 2013-03-31 07:00:48 (Show Source): You can put this solution on YOUR website!It is an AP a=1 d=1 Sn=\$100= 10000 cents Sn=n/2[2a+(n-1)d] 10000=n/2[2+n-1] 20000=n^2+n n^2+n-20000=0 Find the roots of the equation by quadratic formula a= 1 , b= 1 , c= -20000 b^2-4ac= 1 + 80000 b^2-4ac= 80001 x1=( -1 + 282.84 )/ 2 x1= 140.92 x2=( -1 -282.84 ) / 2 x2= -141.92 Ignore negative value Minimum tickets to be sold = 141 tickets m.ananth@hotmail.ca
 Sequences-and-series/732150: a particle sliding down an inclined plane travels 2 feet the first second. In any second after the first it slides 4 feet farther than it did in the preceding second. how far will it slide in 7th second? how far will it slide in 7 seconds? how long will it take to slide 128 feet?1 solutions Answer 447574 by mananth(12270)   on 2013-03-31 05:07:51 (Show Source): You can put this solution on YOUR website!a particle sliding down an inclined plane travels 2 feet the first second. In any second after the first it slides 4 feet farther than it did in the preceding second. how far will it slide in 7th second? how far will it slide in 7 seconds? how long will it take to slide 128 feet? t1=2 =a t2=2+4=6 t3=6+4=10 a=2 d=4 tn= a+(n-1)d t7=2+(7-1)4 t7= 26, 26 feet in the 7th. second Sn=n/2[2a+(n-1)d] S7=7/2[2*2+(7-1)4] S7=7/2[28] S7=98, 98 feet in 7 seconds 128=n/2[4+(n-1)2] 256=4n 256=4n +2n^2 -2n 2n^2+2n-256=0 /2 n^2+n-128=0 solve the quadratic for x you will get n=10.82 In 10.82 sec it will go 128 feet
 Age_Word_Problems/732019: 1. If ram is 10 years younger the his brother shyam and after 7 years ram's age will be half of shaym's age. find actual age of ram and shyam. 2. mat and prateek started a business with initial contribution of 1000 and 12500 respectively, after a year profit earned is is Rs.100/-. what is the profit of mat and prateek. 3. If worker finishes a wall construction in 10 days and 2nd worker in 7 days, how many days it will take to finish if both of them work together.1 solutions Answer 447565 by mananth(12270)   on 2013-03-31 01:01:47 (Show Source): You can put this solution on YOUR website!1. If ram is 10 years younger the his brother shyam and after 7 years ram's age will be half of shaym's age. find actual age of ram and shyam. shyam age =x Ram = x-10 After 7 years Ram age = x-10+7 = x-3 shyam age = x+7 1/2(x+7)= (x-3) x+7 = 2(x-3) x+7=2x-6 x=13 you find out Ram's age 2. mat and prateek started a business with initial contribution of 1000 and 1250 respectively, after a year profit earned is is Rs.100/-. what is the profit of mat and prateek. The ratio of their investment = 1000/1250 = 4/5 so profit is shared in that ratio 3. If worker finishes a wall construction in 10 days and 2nd worker in 7 days, how many days it will take to finish if both of them work together. they will do 1/10 + 1/7 = 17/70 of the job in 1 day so they will take 70 /17 days together.
 Travel_Word_Problems/732123: John and Mary leave their house at the same time and drive in opposite directions. John drives at 90 mi/h and travels 35 mi farther than Mary, who drives at 40 mi/h. Mary's trip takes 15 min longer than John's. For what length of time does each of them drive?1 solutions Answer 447564 by mananth(12270)   on 2013-03-31 00:50:14 (Show Source): You can put this solution on YOUR website!john and Mary leave their house at the same time and drive in opposite directions. John drives at 90 mi/h and travels 35 mi farther than Mary, who drives at 40 mi/h. Mary's trip takes 15 min longer than John's. For what length of time does each of them drive? let mary travel x miles john travels x+35 miles John speed = 90 mph Mary 40 mph Time Mary = x/40 Time john = (x+35)/90 Time Mary -1/4 = Time John x/40 - 1/4 = (x+35)/90 x/40-(x+35)/90 = 1/4 90x-40(x+35)= 900 90x-40x-1400=900 90x-40x-1400=900 50x=2300 x=46 miles John time = (46+35)/90 = 0.9 hours Mary time = 46/40=1.15 hours
 Travel_Word_Problems/732118: a boat travels 2 miles upstream and 2 miles downstream in 5 hours. in still water, the boat travels 2 miles/hour. 1. what is speed of river's current? 2. how fast does it travel upstream? 3. how fast does it travel downstream? 4. how long does it take to travel downstream? 5. how long does it take to travel upstream? Thank you. Gwen1 solutions Answer 447563 by mananth(12270)   on 2013-03-31 00:29:36 (Show Source): You can put this solution on YOUR website!let current speed = x boat speed =2 mph against current 2-x with current x+2 2/(x+2)+2/(2-x) = 5 2(2-x)+2(x+2)=5(4-x^2) 4-2x+2x+4 = 20-5x^2 5x^2=12 x^2= 12/5 x= sqrt(12/5) upstream speed = 2- 1.55= 0.45 mph downstream speed = 2+sqrt(12/5)= 3.55 mph downstream time = 2/3.55= 0.56 hours upstream time = 2/0.45=4.44 Total time = 5 hours
 Travel_Word_Problems/732013: A plane is flying the 2553mile trip from los Angeles to Holohulu into a 60 mph headwind.if the speed of the plane in still air is 310mph.How far from Los Angeles is the plane's point of no retutn1 solutions Answer 447548 by mananth(12270)   on 2013-03-30 21:15:40 (Show Source): You can put this solution on YOUR website!given information 310 + 60 = 370 mph speed with the wind 310 - 60 - 250 mph speed against the wind : Let d = dist to LA from point of no return Then (2553-d) = dist to Honolulu from point of no return : : Time = dist/speed : Return to LA= Continue to Honolulu time d/360 = 2553-d/250 Cross multiply: 250d = 360(2553-d) : 250d = 919080 - 360d : 610d = 919080 d = 1506.69 Check solution by finding the distance to LA and calculating the time to both: 2553-1506.69= = 1046.31 mi Honolulu : Time to L A: 1506.69/360 = 4.19 hrs Time to Honolulu: 1046.31/250 = 4.19 hrs
 Money_Word_Problems/732113: an investor invested a total of 2700 dollars in two mutual funds. one funded 5% and the other at 2% profit.if the investors total profit was \$93 how much was invested in each mutual fund1 solutions Answer 447534 by mananth(12270)   on 2013-03-30 20:53:41 (Show Source): You can put this solution on YOUR website!Part I 2.00% per annum ------------- Amount invested =x Part II 5.00% per annum ------------ Amount invested = y 2700 Interest----- 93.00 Part I 2.00% per annum ---x Part II 5.00% per annum ---y Total investment x + 1 y= 2700 -------------1 Interest on both investments 2.00% x + 5.00% y= 93 Multiply by 100 2 x + 5 y= 9300.00 --------2 Multiply (1) by -2 we get -2 x -2 y= -5400.00 Add this to (2) 0 x 3 y= 3900 divide by 3 y = 1300 Part I 2.00% \$ 1400 Part II 5.00% \$ 1300 CHECK 1400 --------- 2.00% ------- 28.00 1300 ------------- 5.00% ------- 65.00 Total -------------------- 93.00 m.ananth@hotmail.ca
 Expressions-with-variables/732114: Y=2/3X-4/5 HOW TO SOLVE THIS PROBLEM STEP BY STEP PLEASE1 solutions Answer 447532 by mananth(12270)   on 2013-03-30 20:51:38 (Show Source): You can put this solution on YOUR website!What do you want to do? with the equation in slope intercept form.
 Linear-equations/731931: graph the system of linear inequalities 4x -2 y < 0 and 2x + 4y <8 1 solutions Answer 447395 by mananth(12270)   on 2013-03-30 03:38:30 (Show Source): You can put this solution on YOUR website!4x -2 y < 0 2y>4x y>2x 2x + 4y <8 4y<8-2x y<2-(1/2)x The equality y=2x Generate points (1,2),(2,4),(-1,-2) y=2-(1/2)x ((2,1), (4,0) , (-2,3) The inequality since y < 2x(something) the region below is the solution and y<2-(1/2)the region below is the solution
 Linear-equations/731936: find the slope-intercept form for the line satisfying the following conditions. passing through (7, -6) and (6, -5) My email is ..... cherrymcknight@att.net 1 solutions Answer 447389 by mananth(12270)   on 2013-03-30 01:50:26 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 7 -6 6 -5 The general equation of the line when co-ordinates of two points are given is 1 y- 6 = - x -7 y= - x -1
 Polynomials-and-rational-expressions/731929: Show me how to do this problem sum of two cubes and show work x^3+271 solutions Answer 447380 by mananth(12270)   on 2013-03-29 23:49:33 (Show Source): You can put this solution on YOUR website!The sum of cubes identity is a^3+b^3= (a+b)(a^2-ab+b^2) x^3 +27 x^3+3^3 here a=x and b=3 (x+3)(x^2-3x+9)
 Polynomials-and-rational-expressions/731928: help with factoring this expression 2x^3+161 solutions Answer 447379 by mananth(12270)   on 2013-03-29 23:46:55 (Show Source): You can put this solution on YOUR website!2x^3+16
 Miscellaneous_Word_Problems/731906: 1. Suppose a refrigerator that sells for \$700 costs \$85 a year for electricity. Write an expression for the cost to buy and run this refrigerator for x years. 2. Suppose another refrigerator costs \$1000 and \$25 a year for electricity. Write an expression for the total cost for the refrigerator over x years. 3. Over 10 years which refrigerator costs the most? By how much? 4. In how many years will the total costs for the two refrigerators be equal?1 solutions Answer 447359 by mananth(12270)   on 2013-03-29 22:05:54 (Show Source): You can put this solution on YOUR website!first refrigerator cost C(x1)=700+85x C(10)= 700+850 C(10)= 1550 refrigerator II C(x2) = 1000+25x C10) =1000+250 C(10)=1250 Now you know it. same cost 700+85x=1000+25x 60x=300 x= 5 years
 Linear-equations/731754: write an equation for (-1,-7) and (-8,-2)1 solutions Answer 447265 by mananth(12270)   on 2013-03-29 10:02:06 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 -1 -7 -8 -2 The general equation of the line when co-ordinates of two points are given is 7 y- 49 = -5 x 5 7 y= -5 x+ 54 / 7 1 y= - 5/ 7 x+ 54/ 7
 Quadratic_Equations/731727: x+3/x-2 - 1-x/x =17/x1 solutions Answer 447253 by mananth(12270)   on 2013-03-29 08:11:39 (Show Source): You can put this solution on YOUR website! Multiply the equation by x(x-2) x=-4 OR x=9/2
 Percentage-and-ratio-word-problems/731729: 40 bicycles were bought for rs 42000. some of them were stolen and the rest of them were sold at rs 1275 each. the gain was 6.25%. find how many bicycles were stolen. A) 20 B) 15 C) 10 D) 51 solutions Answer 447248 by mananth(12270)   on 2013-03-29 06:33:16 (Show Source): You can put this solution on YOUR website!d) 5