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# Recent problems solved by 'mananth'

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 Triangles/564079: I'm given a right triangle, i know the three side lengths and need to find the degree of the other two angles. How would i find the degree of those two angles using sin, cos, and tan?1 solutions Answer 365210 by mananth(12270)   on 2012-01-28 20:15:23 (Show Source): You can put this solution on YOUR website!Let ABC be right triangle with angle C as right angle. BC is the base of the triangle. AB is perpendicular to BC Sine angle C =AB/AC Sine angle A = BC/AC angle B = 90deg
 Linear-systems/564073: 5x - 15y + z = 22 -10x + 12y – 2z = -8 4x – 2y – 3z = 9 Help me solve this problem1 solutions Answer 365206 by mananth(12270)   on 2012-01-28 20:02:09 (Show Source): You can put this solution on YOUR website!5x-15y+ z=22 -------------- 1 -10x+12y-2z=-8 -------------- 2 4x-2y-3z=9 -------------- 3 consider equation 1 &2 Eliminate y Multiply 1 by 4 Multiply 2 by 5 we get 20x-60y +4z = 88 -50x + 60y-10z = -40 Add the two -30x-6z = 48 -------------4 consider equation 2 & 3 Eliminate y Multiply 2 by 1 Multiply 3 by 6 we get -10x+12y-2z = -8 24x-12y -18z = 0 Add the two 14x -20z = -8 -------------5 5 Consider (4) & (5) Eliminate x Multiply 4 by 14 Multiply (5) by 30 we get -420x -84z = 672 420x-600z=-240 Add the two -684z = 432 / -684 z = -0.63 OR - 12/19 Plug the value of z in 5 14x + 12.63 = -8 14x = -20.63 x = -1.47 OR -1 9/19 plug value of x & z in 1 -7.37 + -15y + -0.63 = 22 -15y = 7.37 + 0.63 + 22 y= -2 OR -2 CHECK Equation 1 5 -1.47 -15 -2 1 -0.63 -7.37 30 -0.63 22
 Length-and-distance/564036: two cars leave a crossroads at the same time. one heads north at 50 km/h and the other heads east at 70 km/h. how far apart are the cars after 2.0 hours?1 solutions Answer 365203 by mananth(12270)   on 2012-01-28 19:42:20 (Show Source): You can put this solution on YOUR website!they are travelling at right angles to each other. At any given instant they form a right triangle with their starting point after 2 hours one car is 100 km away from starting point and another car 140 km leg1 = 100 km Leg2 = 140 km Hypotenuse^2 100 ^2 + 140 ^2 Hypotenuse^2 10000 + 19600 Hypotenuse^2 29600 take the square root Hypotenuse^2 172.05 km
 Money_Word_Problems/563840: Suppose that Annette invests \$7000 at 7%. How much must she invest at 11% so that the total yearly interest from the two investments exceeds \$974?1 solutions Answer 365200 by mananth(12270)   on 2012-01-28 19:26:26 (Show Source): You can put this solution on YOUR website!let her invest \$x @ 11% 7000 @ 7% Interest =974 0.11x+0.07*7000=974 multiply by 100 11x+49000=974*100 11x= 97400-49000 11x=48400 x=4400 @ 11%
 expressions/563893: i have this question 3a5 x(multiply) 5a3 --------------------- 10A4 I HAVE TO WRITE IT IN SINGLE TERM IN INDEX FROM 1 solutions Answer 365132 by mananth(12270)   on 2012-01-28 09:06:46 (Show Source): You can put this solution on YOUR website! In the numerator since it is a product multiply the co-rfficients and add up the exponents we get OR
 Quadratic_Equations/563890: Average mass of a group of people is 45.2kg. A newcomer to the group weighs 51kg, which increases the average by 0.2kg How many people are now in the group? This is a question which needs a quadratic equation to be set up in the form ax²+bx+c=0 so that it can be solved using the quadratic formula. I just can't figure out how to set it up. Please help me! :-)1 solutions Answer 365124 by mananth(12270)   on 2012-01-28 07:51:29 (Show Source): You can put this solution on YOUR website!let the number in the group be x total mass = x*45.2 =45.2x One person joins so the total mass = 45.2x+ 51 The number of people = x+1 Average of the group = = 45.4(x+1)=45.2x+51 45.4x+45.4=45.2+51 45.4x-45.2x=51-45.4 0.2x=5.6 /0.2 x=28 there are 29 in the group now
 Money_Word_Problems/563888: Hi, the following question could be answered by algebra. However, it is posed to a 7 year old child. How do I answer it in a simple way? Madam five wants to buy some poultry from the market. The seller told her that a chicken and a duck cost \$12, a duck and a turkey cost \$20, a chicken and a turkey cost \$16. How much does each poultry cost?1 solutions Answer 365121 by mananth(12270)   on 2012-01-28 06:48:17 (Show Source): You can put this solution on YOUR website! I am making an attempt to teach a 7 year old Suppose First I buy a chicken and duck . I pay \$12 Then I buy a duck & turkey. I pay \$20 Finally I buy a chicken & turkey . I pay \$16 So Now I have 2 chickens , 2 ducks and 2 turkeys . Total I paid \$48 So 1 chicken ,1duck & 1 turkey will cost half as much = 24 Now all three cost \$24 but chicken & duck cost \$12. So Turkey is \$12 and so on. Was it useful? I am interested m.ananth@hotmail.ca
 Linear-systems/563858: Can you please tell me if when solving the linear equation : 7|5x|+2=6 , if I must divide by 7 after subtracting the 2 from both sides of the ='s sign? Thanks, my email is thissucks2008@live.com1 solutions Answer 365104 by mananth(12270)   on 2012-01-28 01:28:41 (Show Source): You can put this solution on YOUR website!7|5x|+2=6 7|5x|=6-2 7|5x|=4 |5x|=4/7 x=+/- 4/35
 Miscellaneous_Word_Problems/563860: a store mixes kenyan coffee worth \$12 per kilogram and venezuelan coffee worth \$15 per kilogram. The mixture is to sell for \$13 per kilogram. Find out how much of each should be used to make a 360 kilogram mixture.1 solutions Answer 365102 by mananth(12270)   on 2012-01-28 01:13:30 (Show Source): You can put this solution on YOUR website!price-----------uantity Kenyan 12---------x lb Venezuelan15------360-x Mixture 13.00 ---------------- 360 12x+15(360-x)=13*360 12x+5400-15x=4680 12x-15x=4680-5400 -3x=-720 / -3 x=240lb \$12.00 Kenyan 120lb \$15.00 Venezuelan m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/563864: If a rowing team takes 2 hours to travel 16 miles with the current but takes 4 miles to travel the same distance against the current what is their rate of speed in still water? Thank you!1 solutions Answer 365100 by mananth(12270)   on 2012-01-28 01:05:54 (Show Source): You can put this solution on YOUR website!Rowing speed =x mph current speed =y mph against current x-y 2.00 hours withcurrent x+y 2.00 hours Distance = same= 2000 miles t=d/r 4 / ( x - y )= 2.00 2 ( x - y ) = 4.00 2 x -2 y = 4 ....................1 16 / ( x + y )= 2.00 2.00 ( x + y ) = 4 2.00 x + 2.00 y = 16 ...............2 Multiply (1) by 1.00 Multiply (2) by 1.00 we get 2 x + -2 y = 4 2 x + 2 y = 16 4 x = 20 / 4 x = 5 mph speed of rowing plug value of x in (1) 2 x -2 y = 4 10 -2 y = 4 -2 y = 4 -10 -2 y = -6 y = 3 mph current speed
 Graphs/563820: Write the slope-intercept equation for the line with slope -5/6 and y-intercept (0,4)1 solutions Answer 365085 by mananth(12270)   on 2012-01-27 22:32:07 (Show Source): You can put this solution on YOUR website!The equation of a straight line in slope intercept form y= mx+b m is the slope b is the y intercept and the point passes through (x,y) when x = 0 the value of y is the y intercept plug b & m in the equation y=(-5/6)x+4
 Graphs/563824: I need help understanding how to graph inequalities need a lot of help I'm so lost I can't get the points on my own..1 solutions Answer 365083 by mananth(12270)   on 2012-01-27 22:29:11 (Show Source): You can put this solution on YOUR website!send me a problem I will explain m.ananth@hotmail.ca
 Numbers_Word_Problems/563846: Four times the difference of a number and 3 is the same as 3 increased by four times the number plus 3 times the number. Find the number1 solutions Answer 365081 by mananth(12270)   on 2012-01-27 22:27:40 (Show Source): You can put this solution on YOUR website!number = x difference of x & 3 = x-3 4 times 4(x-3) .. 4 times the number= 4x 3+4x +3x 3+7x 4(x-3)=3+7x 4x-12=3+7x 3x=-15 /3 x=-5
 Travel_Word_Problems/563819: Two trains are 330 miles apart, and their speeds differ by 200 mph. They travel toward each other and meet in 3 hours. Find the speed of each train. 1 solutions Answer 365079 by mananth(12270)   on 2012-01-27 22:25:03 (Show Source): You can put this solution on YOUR website!Train A x mph Train B = x+20 mph they are moving against each other add up speeds the effective speed = 2x+20 d=330 miles t= d/r 3=330/(x+20) 3(x+20)=330 3x+60=330 3x=270 /3 x= 90 mph Train A speed = 90 mph Train B speed = 90+20 =110 mph
 Graphs/563826: Write the slope intercept equation for the line that passes through (-2,3) and is perpendicular to 2x-9y=-121 solutions Answer 365077 by mananth(12270)   on 2012-01-27 22:21:02 (Show Source): You can put this solution on YOUR website!2 x -9 y = -12 Find the slope of this line -9 y = -2 x -12 Divide by -9 y = 2/ 9 x + 1 1/3 Compare this equation with y=mx+b slope, m=2/9 The slope of a line perpendicular to the above line will be the negative reciprocal -4.5 m1*m2=-1 m= -9/2 ,point (-2,3) Find b by plugging the values of m & the point in y=mx+b 3 = 9.00 +b b=-6 m=-9/2 The required equation is y=-(9/ 2)x-6 m.ananth@hotmail.ca
 Travel_Word_Problems/563831: A plane can fly 362 mph in still air. If it can fly 210 miles downwind in the same amount of time it can fly 152 miles upwind, find the velocity of the wind. 1 solutions Answer 365074 by mananth(12270)   on 2012-01-27 22:16:14 (Show Source): You can put this solution on YOUR website!plane speed = 362 mph wind speed = x mph wind speed speed against wind 362 - x speed with wind 362 + x Distance against wind 152 miles Distance with wind 210 miles t=d/r time against = time with wind 152/(362-x)=210 /(362+x) 152(362 +x)=210 (362-x) 55024+ 152x=76020-210x 210x+152x=20996 362x=20996 / 362 x=58mph wind speed m.ananth@hotmail.ca
 Equations/563804: y=3x-8 y=4-x1 solutions Answer 365045 by mananth(12270)   on 2012-01-27 20:15:51 (Show Source): You can put this solution on YOUR website!-3 x + 1 y = -8 .............1 1 x + 1 y = 4 .............2 Eliminate y multiply (1)by -1 Multiply (2) by 7 3 x -1 y = 8 7 x 7 y = 28 Add the two equations 10 x = 36 / 10 x = 3.60 plug value of x in (1) -3 x + 1 y = -8 -10.8 + 1 y = -8 1 y = -8 + 10.8 1 y = 2.8 y = 2.80
 Equations/563806: 2x+7y=3 x=1-4y1 solutions Answer 365044 by mananth(12270)   on 2012-01-27 20:13:47 (Show Source): You can put this solution on YOUR website!2 x + 7 y = 3 .............1 1 x + 4 y = 1 .............2 Eliminate y multiply (1)by -4 Multiply (2) by 7 -8 x -28 y = -12 7 x 28 y = 7 Add the two equations -1 x = -5 / -1 x = 5 plug value of x in (1) 2 x + 7 y = 3 10 + 7 y = 3 7 y = 3 -10 7 y = -7 y = -1
 Quadratic_Equations/563800: (Solve)Air Travel: A turbo-jet flies 50mph faster than a super-prop plane. If a turbo-jet goes 2000mi in 3hr less time than it takes the super-prop to go 2800mi, find the speed of each plane.1 solutions Answer 365043 by mananth(12270)   on 2012-01-27 20:12:05 (Show Source): You can put this solution on YOUR website!prop -x mph turbo ---x+50 mph t=d/r t(prop) - t(turbo) = 3 2800/x - 2000/(x+50) = 3 LCD = x(x+50) 2800(x+50)-2000x=3x(x+50) 2800x+140000-2000x=3x^2+150x 3x^2-650x-140000=0 Find the roots of the equation by quadratic formula a= 3 b= -650 c= -140000 b^2-4ac= 422500 - 1680000 b^2-4ac= 2102500 = 1450 x1=( 650 + 1450 )/ 6 x1= 350 x2=( 650 -1450 ) / 6 x2= -133.33 Ignore negative value x = 350 mph speed of prop speed of turbo = 400 mph
 Linear-equations/563585: write the slope-intercept equation for the line that passes through (5,4) and (7,8) please show all of your work1 solutions Answer 364950 by mananth(12270)   on 2012-01-27 09:43:00 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 5 4 7 8 slope m = (y2-y1)/(x2-x1) (8-4)/(7-5) ( 4 / 2 ) m= 2 Plug value of the slope and point (5,4) in Y = m x + b 4.00 = 10 + b b= 4 - 10 b= -6 So the equation will be Y=2x-6 m.ananth@hotmail.ca
 Functions/563588: I am having a very difficult time with part of function notation problems. f(x)=-2x + 4 find f(-1/5) I need first grade example of how the 4 ends up as 20/5. 1 solutions Answer 364949 by mananth(12270)   on 2012-01-27 09:39:31 (Show Source): You can put this solution on YOUR website!f(x)=-2x + 4 find f(-1/5) f(-1/5) = 2(-1/5)+4 f(-1/5)= (-2/5) +4 the LCD = 5 ((-2*5 + 5*4)/5 =-2/5 +20/5 =18/5
 Linear-equations/563586: write the slope-intercept equation for the line that passes through (-5,-8) and is perendicular to 10x-6y=-11 please show all of your work1 solutions Answer 364948 by mananth(12270)   on 2012-01-27 09:33:17 (Show Source): You can put this solution on YOUR website!10x-6y= -11 Find the slope of this line -6y=-10 x-11 Divide by -6 y = 5/ 3 x + 11/6 Compare this equation with y=mx+b slope m =5/3 The slope of a line perpendicular to the above line will be the negative reciprocal -3/5 m1*m2=-1 m= - 3/5 ,point ( -5 , -8 ) Find b by plugging the values of m & the point in y=mx+b -8 = 3.00 + b b= -11 m= - 3/5 The required equation is y =- ( 3/ 5)x-11 m.ananth@hotmail.ca
 Linear-equations/563579: find the x and y intercepts and graph the equation plotting the intercepts please show all of your work. 6x-7y=421 solutions Answer 364947 by mananth(12270)   on 2012-01-27 09:26:58 (Show Source): You can put this solution on YOUR website!equation 6x-7y=42 7y=6x-42 y=(6/7)x+6 when x= 0 y= 6 ( 0 , 6 ) when y = 0 x= -7 ( -7 , 0 ) y intercept =6 X intercept = -7
 Linear-equations/563578: given the linear equation y=7/5x+2 find the y-coordinates of the points(-5,),(0,), and (5,) plot these points and graph the linear equation. please show all of your work.1 solutions Answer 364946 by mananth(12270)   on 2012-01-27 09:15:25 (Show Source): You can put this solution on YOUR website!y=7/5x+2 find the y-coordinates of the points(-5,),(0,), and (5,) plot these points and graph the linear equation. please show all of your work. y=7/5x+2 x=-5, y=-5 (-5,-5) x=0, y=2(0,2) x=5 , y=9 (5,9)
 Angles/563571: what is complimentary to a 32 degree angle1 solutions Answer 364935 by mananth(12270)   on 2012-01-27 08:11:57 (Show Source): You can put this solution on YOUR website!90-32=58 The sum of complimentary angles = 90 deg
 Linear_Equations_And_Systems_Word_Problems/563567: Kathi and Robert Hawn had a pottery stand at the annual skipcack craft fair. They sold some of their pottery at the original price of \$9.50 for each piece, but later decreased the price by \$2. If they sold all 90 pieces and took in \$713, find how many pieces they sold at the original price and how many pieces they sold at the reduced price?1 solutions Answer 364933 by mananth(12270)   on 2012-01-27 07:57:52 (Show Source): You can put this solution on YOUR website!let them sell x pieces at \$9.50 and y pieces at \$7.50 x+y=90 9.5x+7.5y=713 \$9.50 x numbers \$7.50 y numbers 1 x + 1 y = 90 .............1 9.5 x + 7.5 y = 713 .............2 Eliminate y multiply (1)by -7.5 Multiply (2) by 1 -7.5 x -7.5 y = -675 9.5 x 7.5 y = 713 Add the two equations 2 x = 38 / 2 x = 19 plug value of x in (1) 1 x + 1 y = 90 19 + 1 y = 90 1 y = 90 -19 1 y = 71 y = 71 \$9.50 19 numbers \$7.50 71 numbers m.ananth@hotmail.ca
 Quadratic_Equations/563566: Solve for x: 1 solutions Answer 364932 by mananth(12270)   on 2012-01-27 07:53:47 (Show Source): You can put this solution on YOUR website! take the square root ax+1= 0 ax=-1 x=-1/a
 Distributive-associative-commutative-properties/563560: If the parentesis are missing, how do you solve 3-5*4+2? Is it -17? Thanks1 solutions Answer 364931 by mananth(12270)   on 2012-01-27 07:51:02 (Show Source): You can put this solution on YOUR website!3-5*4+2 3-(5*4)+2 19 The rule for such additions is division then multiplication then addition then subtraction If parenthesis is given then first solve the parenthesis and then the order given
 Linear-equations/563565: Answer? write the equation of the line that is parallel to the given line and passes through the given point. y= -2x-1, (2,6) 1 solutions Answer 364930 by mananth(12270)   on 2012-01-27 07:46:38 (Show Source): You can put this solution on YOUR website!y =-2 x-1 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 (2,6 ) Find b by plugging the values of m & the point in y=mx+b 6 = -4 + b b= 10 m= -2 Plug value of the slope and b in y = mx +b The required equation is y = -2x+ 10 m.ananth@hotmail.ca
 Complex_Numbers/563537: I have a few I am totally stuck on. #1)2/x+3 - 2x+3/x-1 = 6x-5/x^2+2x-3 Okay so I know that the LCD here is going to be (x+3) and (x+1) but I can not figure out how to distribute it. #2.)x^2-10/x^2-x-20 = 1 + 7/x-5 Here I have I think the LCD is (x-5) (x+4) but again am not being able to figure out how to distribute it properly. #3)5y^(negative)2 +1=6y^(negative)1 No clue the negative exponents are really throwing me here....Thanks so much for your help1 solutions Answer 364929 by mananth(12270)   on 2012-01-27 06:10:19 (Show Source): You can put this solution on YOUR website! LCD = (x+3) (x-1) Multiply the equation by LCD = (x+6)(2x+1)=0 x=-6 OR -0.5 m.ananth@hotmail.ca