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 Volume/704300: How do i measure the thickness of aluminum foil with the mass of 1.47 grams, area of 305 cm and density of 2.6989 grams?1 solutions Answer 434013 by mananth(12270)   on 2013-01-20 22:32:12 (Show Source): You can put this solution on YOUR website!Density = mass/ volume density = mass/ (area * tk.) 2.6989= 1.47/(305*tk) (305*tk)= 1.47/2.6989 tk = 1.47/(2.6989*305) thickness = 0.001785 cm
 Graphs/703515: Find the slope of a line perpendicular to the line that has x−intercept −3 and has y−intercept of 41 solutions Answer 433531 by mananth(12270)   on 2013-01-17 20:20:11 (Show Source): You can put this solution on YOUR website!The equation of line with in intercept form is multiply equation by LCD -12 so 4x-3y=-12 3y=4x-12 y = 4/3 x -4 slope = m= 4/3 Perpendicular line will have slope which is negative reciprocal of 4/3 = -3/4 The line is passing through (-3,0) equation of line will be (y-y1) = m(x-x1) y-(-3)=-3/4(x-0) y+3= -3/4 x y= -3/4 x -3
 Travel_Word_Problems/703514: a plane can fly 4800km in 4h with the wind. the return trip against the same wind takes 5h. find the rate of the plane in the still air and the rate of the wind. please shows steps thank you1 solutions Answer 433529 by mananth(12270)   on 2013-01-17 20:14:09 (Show Source): You can put this solution on YOUR website!Plane speed =x mph wind speed =y mph against wind 5 hours with wind 4 hours Distance with wind 4800 miles distance against wind 4800 t=d/r against wind (x-y) 4800.00 / ( x - y )= 5.00 5.00 x - -5.00 y = 4800.00 ....................1 with wind (x+y) 4800.00 / ( x + y )= 4.00 4.00 ( x + y ) = 4800.00 4.00 x + 4.00 y = 4800.00 ...............2 Multiply (1) by 4.00 Multiply (2) by 5.00 we get 2.00 20.00 x + -20.00 y = 19200.00 20.00 x + 20.00 y = 24000.00 40.00 x = 43200.00 / 40.00 x = 1080 mph plug value of x in (1) y 5 x -5 y = 4800 5400 -5 -5400 = 4800 -5 y = 4800 -5 y = -600 mph y = 120 Plane 1080 mph wind 120 mph CHECK x+y= 1200 X-y= 960 + 4800.00 / ( 1200.00 )= 4 4800 / ( 960 ) = 5
 Linear-systems/703512: -5x -2y =10 y =(4x-11)1 solutions Answer 433528 by mananth(12270)   on 2013-01-17 20:10:22 (Show Source): You can put this solution on YOUR website!We solve by substitution method -4 x + 1 y = -11 .............1 1 y = -11 + 4 x / 1 = y = -11 + 4 x -5 x + -2 y = 10 .....................2 Substitute y in (2) -5 x + -2 ( -11 + 4 x ) = 10 -5 x + 22 + -8 x = 10 -5 x -8 x = -12 -13 x = -12 / -13 x= 12/13 Plug the value of x in (1) -4 x + 1 y = -11 -4 * 12/13 + 1 y = -11 -48/13 + 1 y = -11 1 y = -95/13 y= -95/13 m.ananth@hotmail.ca
 Linear-equations/703508: Algebra 1 Write an equation of the line that passes through each pair of points. (5/12,-1) (-3/4,1/6) Please show step so I can understand how you do it. :] M=? Y=?1 solutions Answer 433526 by mananth(12270)   on 2013-01-17 20:04:44 (Show Source): You can put this solution on YOUR website!The equation of a line passing through the points (x1,y1) & (x2,y2) is (x1,y1) -(5/12,-1), (x2,y2)- (-3/4,1/6) plug the values in the equation 7/ 6 y-7/ 6 = -7/ 6 x - 35/72 7/ 6 y= -7/ 6 x+49/72 / 7/ 6 y=-1x+ 7/12 m=-1
 Polynomials-and-rational-expressions/703505: Please help me factor this equation: 1 solutions Answer 433523 by mananth(12270)   on 2013-01-17 19:51:40 (Show Source): You can put this solution on YOUR website! 6*12=72 split 72 such that their sum is -14 and product is -72 (r-3)(6r+4)
 Bodies-in-space/701067: the size of a brick is 25 cm by 12 cm by 55 cm and its density is the 1.8 by 10^3 kg/m^3.how many trips must a 3 ton dumper carry out to transport 15000 bricks to a constrution site? 1 solutions Answer 432189 by mananth(12270)   on 2013-01-11 20:16:12 (Show Source): You can put this solution on YOUR website!Volume of brick = 0.25m * 0.12m * 0.55m = 0.0165 cu.m volume of 1 brick = 0.0165 cu.m density = 1.8*10^3 kg/m^3 weight of 1 brick = 0.0165* 1.8*10^3 29.7 kg 15000 bricks will weigh 15000*29.7 =445500 kg = 445.5 tons number of trips = 445.5/3 = 1485 trips
 Trigonometry-basics/701065: The angle a kite string makes with the ground is 24º. If 80 m of string has been let out, how high is the kite above the ground? The angles of elevation from a point A and a point B to the top of a mountain 780m high are shown. Point A is 67 degrees and point B is 48 degrees. How long would a tunnel be through the mountain, connecting A and B?1 solutions Answer 432187 by mananth(12270)   on 2013-01-11 20:07:29 (Show Source): You can put this solution on YOUR website!The kite is vertically above the ground. height ? The length of sting = hypotenuse= 80m The angle of elevation = 24 deg. Sin theta = opposite side/ hypotenuse sin 24 = opposite side/80 height of kite = 80 * sin 24 use calc to find the height ..... Point A elevation is 67 deg point B elevation = 48 deg. height of mountain = 780 m A to mountain foot distance = 780/Tan 67 .............. (1) B to mountain foot distance = 780/tan 48 ..................(2) distance AB = (2)-(1) 780/1.11 -780/2.35 about 370.8 m is the length of the tunnel.
 Equations/700808: Is perpendicular to 4y=3x-8 and passes through (-12,7) Thank you!1 solutions Answer 432024 by mananth(12270)   on 2013-01-10 23:26:14 (Show Source): You can put this solution on YOUR website!-3 x + 4 y = -8 Find the slope of this line 4 y = 3 x -8 Divide by 4 y = 3/ 4 x + -2 Compare this equation with y=mx+b, m= slope & b= y intercept slope m = 3/4 The slope of a line perpendicular to the above line will be the negative reciprocal -4/3 Because m1*m2 =-1 The slope of the required line will be -4/3 m= -4/3 ,point ( -12 , 7 ) Find b by plugging the values of m & the point in y=mx+b 7 = 16 + b b= -9 m= -4/3 The required equation is y = -4/ 3 x -9 m.ananth@hotmail.ca
 Linear-equations/700821: how to write the slope-intercept form of 4x-2y=3 through given points of (2,1)into parallel and perpendicular forms?1 solutions Answer 432023 by mananth(12270)   on 2013-01-10 23:22:13 (Show Source): You can put this solution on YOUR website!PARALLEL 4 x -2 y = 3 Find the slope of this line make y the subject -2 y = -4 x + 3 Divide by -2 y = 2 x -1 1/2 Compare this equation with y=mx+b slope m = 2 The slope of a line parallel to the above line will be the same The slope of the required line will be 2 m= 2 ,point ( 2 , 1 ) Find b by plugging the values of m & the point in y=mx+b 1 = 4 + b b= -3 m= 2 Plug value of the slope and b in y = mx +b The required equation is y = 2 x -3 Perpendicular 4 x + -2 y = 3 Find the slope of this line -2 y = -4 x + 3 Divide by -2 y = 2 x + -1 1/2 Compare this equation with y=mx+b, m= slope & b= y intercept slope m = 2 The slope of a line perpendicular to the above line will be the negative reciprocal - 1/2 Because m1*m2 =-1 The slope of the required line will be - 1/2 m= - 1/2 ,point ( 2 , 1 ) Find b by plugging the values of m & the point in y=mx+b 1 = -1 + b b= 2 m= - 1/2 The required equation is y = - 1/ 2 x 2 m.ananth@hotmail.ca
 Linear-equations/700834: How would i graph the equation y=-2x-1 . Also how would i graph y(greater than or equal to) 3/5x+2 . 1 solutions Answer 432022 by mananth(12270)   on 2013-01-10 23:17:04 (Show Source): You can put this solution on YOUR website!y= -2 x -1 Assume values of x and plug in the equation to get values of y. Plot the points x 0 1 2 -2 y= -1 -3 -5 3 (x,y) (0,-1),(1,-3),( 2,3)
 real-numbers/700844: allison is saving money to buy a video game system. in the first week, her savings were \$8 less then 2/5 of the price of the system. in the second week, she saved 50 cents more than 1/2 the price of the system. she was still \$37 short. whats the price of the system?1 solutions Answer 432021 by mananth(12270)   on 2013-01-10 23:09:24 (Show Source): You can put this solution on YOUR website!allison is saving money to buy a video game system. in the first week, her savings were \$8 less then 2/5 of the price of the system. in the second week, she saved 50 cents more than 1/2 the price of the system. she was still \$37 short. whats the price of the system? Let system cost \$x First week -- (2/5)x -8 II week-------(1/2)x +0.5 She was\$37 short Add up savings + short = price of system (2/5)x-8 + (1/2)x+0.5 +37 =x (2/5)x +(1/2)x -x= -37-0.5+8 (4x+5x-10x)/10 = -29.5 -x = 10*-29.5 -x=-295 x= \$ 295 the price of the system
 Linear_Equations_And_Systems_Word_Problems/700740: \$6000 to invest in two stock funds. Fund A pays 5% while Fund B pays 9%. After a year, \$380 is made in interest, how much money was invested in each account?1 solutions Answer 431980 by mananth(12270)   on 2013-01-10 20:10:41 (Show Source): You can put this solution on YOUR website!Part I 5.00% per annum ------------- Amount invested =x Part II 9.00% per annum ------------ Amount invested = y 6000 Interest----- 380 Part I 5.00% per annum ---x Part II 9.00% per annum ---y Total investment x + 1 y= 6000 -------------1 Interest on both investments 5.00% x + 9.00% y= 380 Multiply by 100 5 x + 9 y= 38000.00 --------2 Multiply (1) by -5 we get -5 x -5 y= -30000.00 Add this to (2) 0 x 4 y= 8000 divide by 4 y = 2000 Part I 5.00% \$ 4000 Part II 9.00% \$ 2000 CHECK 4000 --------- 5.00% ------- 200.00 2000 ------------- 9.00% ------- 180.00 Total -------------------- 380.00 m.ananth@hotmail.ca
 Mixture_Word_Problems/700759: How many quarts of a 10% solution of basic acid must be added to 2 quarts of a 3% solution of basic acid to obtain a 4% solution? What are the steps to answer this question. Thank you. 1 solutions Answer 431979 by mananth(12270)   on 2013-01-10 20:08:25 (Show Source): You can put this solution on YOUR website!-------------- percent ---------------- Amount Acid I 3 ---------------- 2 quarts Acid II 10 ---------------- x quarts Mixture 4 ---------------- 2 + x quarts 3 * 2 + 10 x = 4 ( 2 + x ) 6 + 10 x = 8 + 4 x 10 x -4 x = -6 + 8 6 x = 2 / 6 x = 0.33 quarts Acid II m.ananth@hotmail.ca
 Quadratic_Equations/700763: instructions: solve the quadratic equation. 1.2x^2-3x-11=01 solutions Answer 431977 by mananth(12270)   on 2013-01-10 20:05:58 (Show Source): You can put this solution on YOUR website!Find the roots of the equation by quadratic formula a= 2 b= -3 c= -11 b^2-4ac= 9 - -88 b^2-4ac= 97 = 9.85 x1=( 3 + 9.85 )/ 4 x1= 3.21 x2=( 3 -9.85 ) / 4 x2= -1.71
 Distributive-associative-commutative-properties/700732: 2h+2(2h+4)=26 i have tried so hard to understand algebra using distributive property and my teacher doesn't will not sit and explain it to me and if i could get any help it would be appreciated. Thank you very much Jordan.1 solutions Answer 431975 by mananth(12270)   on 2013-01-10 20:01:45 (Show Source): You can put this solution on YOUR website!a(b + c) = ab + ac you multiply each term in the parenthisis with the term outside it. example 2h+2(2h+4)=26 2h+(2*2h)+(2*4)=26 2h+4h+8=26 6h+8 =26 -8 6h=18 /6 h=3 4 x 53 (4 x 50) + (4 x 3) 200 + 12 212 4 x 27 =4(20 +7) =4(20) + (7) =80 + 28 =108 The Distributive Property a(b + c) = ab + ac 3x(x+6) = 3x(x) + 3x(6) =3x2+18x (x + y)(x + 2y) x(x+2y) + y(x+2y)
 Numbers_Word_Problems/700750: how many liters of a solution that is 37% key ingredient should be added to 143 liters of a 73% solution to yield a 51% solution?1 solutions Answer 431969 by mananth(12270)   on 2013-01-10 19:40:06 (Show Source): You can put this solution on YOUR website!-------------- percent ---------------- Amount solution I 73 ---------------- 143 liters solution II 37 ---------------- x liters Mixture 51 ---------------- 143 + x liters 73 * 143 + 37 x = 51 ( 143 + x ) 10439 + 37 x = 7293 + 51 x 37 x -51 x = -10439 + 7293 -14 x = -3146 / -14 x = 224.71 liters solution II m.ananth@hotmail.ca
 Money_Word_Problems/700253: Suppose Gus invested a total of 8000\$ part of it at 4% the remainder at 6% his yearly income from the two invest,nets was 380\$ how much did he invest at each rate1 solutions Answer 431771 by mananth(12270)   on 2013-01-09 20:11:50 (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 8000 Interest----- 380 Part I 4.00% per annum ---x Part II 6.00% per annum ---y Total investment x + 1 y= 8000 -------------1 Interest on both investments 4.00% x + 6.00% y= 380 Multiply by 100 4 x + 6 y= 38000.00 --------2 Multiply (1) by -4 we get -4 x -4 y= -32000.00 Add this to (2) 0 x 2 y= 6000 divide by 2 y = 3000 Part I 4.00% \$ 5000 Part II 6.00% \$ 3000 CHECK 5000 --------- 4.00% ------- 200.00 3000 ------------- 6.00% ------- 180.00 Total -------------------- 380.00 m.ananth@hotmail.ca
 Money_Word_Problems/700285: The owner of a movie theater was counting the money from one day's ticket sales. He knew that a total of 150 tickets were sold. Adult tickets cost \$7.50 each and children's tickets cost \$4.75 each. If the total receipts for the day were \$891.25, how many of each kind of ticket were sold?1 solutions Answer 431769 by mananth(12270)   on 2013-01-09 20:08:50 (Show Source): You can put this solution on YOUR website!x= number of child tickets y= number of adult tickets Total sold 1.00 x + 1.00 y = 150.00 .............1 Total value 4.75 x + 7.50 y = 891.25 .............2 Eliminate y multiply (1)by -7.50 Multiply (2) by 1.00 -7.50 x -7.50 y = -1125.00 4.75 x + 7.50 y = 891.25 Add the two equations -2.75 x = -233.75 / -2.75 x = 85.00 plug value of x in (1) 1.00 x + 1.00 y = 150.00 85.00 + y = 150.00 y = 150.00 -85.00 y = 65.00 y = 65.00 x= 85 number of child tickets y= 65 number of adult tickets m.ananth@hotmail.ca
 Graphs/700254: 20x+3y=20 and -20x+5y=60 using elimination 20x+3y=20 -20x+5(10)=60 -20x+5y=60 -20x+50= 60 ----------- -50 -50 0+8y=80 --- --- -- -- -20x-110 8 8 ---- --- y=10 x=5.5 My question is, did I get the right answer, if not how did I mess up? 1 solutions Answer 431766 by mananth(12270)   on 2013-01-09 20:05:34 (Show Source): You can put this solution on YOUR website!20x+3y=20 and -20x+5y=60 using elimination 20x+3y=20 -20x+5(10)=60 -20x+5y=60 -20x+50= 60 ----------- -20x= -50 +60 0+8y=80 --- --- -- -- -20x= 10 8 8 ---- --- y=10 x=-0.5
 Money_Word_Problems/700279: what is the total value of 3,700 at 6% compounded annually for 5 years? 1 solutions Answer 431756 by mananth(12270)   on 2013-01-09 19:56:50 (Show Source): You can put this solution on YOUR website!Find Amount Principal P = 3700 Amount= A years=n 5.00 compounded 1 times a year t Rate = 6.00 0.06 Amount = P*((n+r)/n)^n*t Amount = = 3700 *( 1 + 0.06 /t)^ 5 * 1 Amount = 3700 *( 1 + 0.06 )^ 5 3700 *( 1.06 )^ 5 Amount = 4951.43
 Equations/700262: I am doing a practice apptitude test and have a question which is 3*=81 what is the value of * , they say the answer is 4 .I am having trouble understanding this. Could you please explain this to me? Thankyou, Its been a long time since school for me.1 solutions Answer 431754 by mananth(12270)   on 2013-01-09 19:52:08 (Show Source): You can put this solution on YOUR website!prime factors of 81 are 3*3*3*3 3*3*3*3=81 so 3^4= 81 3^*=4=3^4 *=4
 Linear-equations/700272: Is there a relationship between the sign (positive or negative) of the slope of a line and the angle the line makes with the x-axis? For example, if you graph y = 3x + 5, versus the graph of y = -3x + 5.1 solutions Answer 431752 by mananth(12270)   on 2013-01-09 19:49:36 (Show Source): You can put this solution on YOUR website!take the equation y=mx+b if m is positive the line will rise from the third quadrant to the first quadrant. if m is negative the line will rise from the fourth quadrant to the second quadrant. When the value of | b | the y intercept increases the angle made by the line with X axis increase.
 Rational-functions/700270: x^4=1 how do you solve this 1 solutions Answer 431749 by mananth(12270)   on 2013-01-09 19:43:17 (Show Source): You can put this solution on YOUR website!x^4=1 x^4-1=0 (x^2+1)(x^2-1)=0 (x^2+1)(x+1)(x-1)=0 If (x^2+1)=0 x^2=-1 x= sqrt(-1)=i OR x= -1 OR +1
 Trigonometry-basics/699813: The directions say "Solve each Equation for Principal values of x. Express solutions in degrees" the problem says sinx=1+cos^2x. I changed cos^2x to 1-sin^2x so I have sinx=1+1-sin^2x but I'm not sure what to do next. My Teacher has done a lot of factoring with problems like these and then solves for the two solutions, but I don't get how he factors them. 1 solutions Answer 431565 by mananth(12270)   on 2013-01-08 20:03:48 (Show Source): You can put this solution on YOUR website!sinx = 1+cos^2x sinx = 1+1-sin^2x sin x= 2-sin^2x Rearrage sin^2x+sinx-2 =0 factor the quadratic equation sin^2x+2sinx-sinx-2=0 sinx(sinx+1)-1(sinx+2)=0 (sinx+1)(sinx-1)=0 sin x= -1 OR xinx =1
 Polynomials-and-rational-expressions/699814: 9x^2-6x-8/3x-41 solutions Answer 431563 by mananth(12270)   on 2013-01-08 19:57:27 (Show Source): You can put this solution on YOUR website! =(3x+2)
 Money_Word_Problems/699803: You want to put \$8,000 in a simple interest account. It has a 2% annual interest rate. How long must you invest that money to earn \$400 in interest? Use I=prt 1 solutions Answer 431562 by mananth(12270)   on 2013-01-08 19:53:29 (Show Source): You can put this solution on YOUR website!I = P * r * t P= 8000 r=2% = 0.02 t=? I = 400 400=8000*0.02*t 400/(8000*0.02) =t 400/160=t 2.5 = t 2 1/2 years
 test/699769: Solve by elimination: 10x+2y=46 3x-3y=211 solutions Answer 431559 by mananth(12270)   on 2013-01-08 19:45:37 (Show Source): You can put this solution on YOUR website!10 x + 2 y = 46 .............1 3 x -3 y = 21 .............2 Eliminate y multiply (1)by 3 Multiply (2) by 2 30 x 6 y = 138 6 x -6 y = 42 Add the two equations 36 x = 180 / 36 x = 5 plug value of x in (1) 10 x + 2 y = 46 50 + 2 y = 46 2 y = 46 -50 2 y = -4 y = -2 x= 5, y= -2 m.ananth@hotmail.ca
 Linear-equations/699796: Write the slope-intercept form of the equation of the line perpendicular to the graph of y = − 3 x − 7 that passes through 2 (3, –2). ￼1 solutions Answer 431556 by mananth(12270)   on 2013-01-08 19:41:26 (Show Source): You can put this solution on YOUR website!1 y = -3 x -7 Divide by 1 y = -3 x + -7 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 1/3 Because m1*m2 =-1 The slope of the required line will be 1/3 m= 1/3 ,point ( 3 , -2 ) Find b by plugging the values of m & the point in y=mx+b -2 = 1 + b b= -3 m= 1/3 The required equation is y = 1/ 3 x -3 m.ananth@hotmail.ca
 test/699745: Solve by substitution: 4x+y=10 14x-y=-11 solutions Answer 431553 by mananth(12270)   on 2013-01-08 19:35:55 (Show Source): You can put this solution on YOUR website!4 x + 1 y = 10 .............1 1 y = 10 + -4 x / 1 = y = 10 + -4 x 14 x + -1 y = -1 .....................2 Substitute y in (2) 14 x + -1 ( 10 + -4 x ) = 14 x + -10 + 4 x = -1 14 x 4 x = 9 18 x = 9 / 18 x= 1/ 2 Plug the value of x in (1) 4 x + 1 y = 10 4 * 1/ 2 + 1 y = 10 2 + 1 y = 10 1 y = 8 / 1 y= 8 m.ananth@hotmail.ca
 Numbers_Word_Problems/699756: the sum of the reciprocal of a number and the reciprocal of 3 less than the number is 8 times the reciprocal of the original number. find the original number. choices (in case this helps) a) 7/2 b) -2 c) 8/5 d) 21/81 solutions Answer 431548 by mananth(12270)   on 2013-01-08 19:32:33 (Show Source): You can put this solution on YOUR website!let number be x reciprocal = 1/x reciprocal of 3 =1/3 (1/3)-x (1/x) + (1/(x-3) = (8/x) multiply equation by x(x-3) (x-3) +x=8(x-3) x-3+x=8x-24 6x=21 x=7/2