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 Graphs/571119: What is the slope and y-intercept of 30x+5y=20 Thanks1 solutions Answer 367956 by mananth(12270)   on 2012-02-10 22:11:20 (Show Source): You can put this solution on YOUR website!30x+5y =20 5y= 20-30x /5 y=4-6x y=-6x+4 compare with y = mx+b m=-6 the slope b= 4 = y intercept
 Money_Word_Problems/571100: Suppose you invest money in two accounts. One of the accounts pays 8% annual interest, whereas the other pays 9% annual interest. If you have \$2000 more invested at 9% than you have invested at 8%, how much do you have invested in each account if the total amount of interest you earn in a year is \$860?1 solutions Answer 367955 by mananth(12270)   on 2012-02-10 22:08:16 (Show Source): You can put this solution on YOUR website!8%---------------x 9%= x+2000 sum of idividual interests = total interest 0.08x+0.09*(x+2000)=860 0.08x+0.09x+180=860 0.17x=860-180 0.17x=680 /0.17 x= 680/0.17 x= 4000 Amount invested @8% = \$4000 Amount invested @ 9% = \$4000+2000 = \$6000 m.ananth@hotmail.ca
 Linear-equations/571112: Find the line containing P(3,0) and perpendicular to the x-axis. Find the line containing P(-4,5) and parallel to x-axis.1 solutions Answer 367954 by mananth(12270)   on 2012-02-10 21:58:26 (Show Source): You can put this solution on YOUR website!Find the line containing P(3,0) and perpendicular to the x-axis. x=3 Find the line containing P(-4,5) and parallel to x-axis. y=5
 Linear-equations/571113: write an equation in slope intercept form of the line that passes through the point and is perpendicular to the graph and given equation . Through (-2,-4) perpendicular to x-2y=41 solutions Answer 367953 by mananth(12270)   on 2012-02-10 21:55:32 (Show Source): You can put this solution on YOUR website!x-2y = 4 Find the slope of this line -2y=-x+ 4 Divide by -2 y = 1/ 2 x-2 Compare this equation with y=mx+b slope m = 1/ 2 The slope of a line perpendicular to the above line will be the negative reciprocal -2 m1*m2=-1 m= -2 ,point ( -2 , -4 ) Find b by plugging the values of m & the point in y=mx+b -4=4+b b= -8 m= -2 The required equation is y=-2x-8 m.ananth@hotmail.ca
 Rectangles/571067: The length of a rectangular garden is 4 yd greater than the width. The area of the garden is 96 〖yd〗^2.Find the length and the width.1 solutions Answer 367939 by mananth(12270)   on 2012-02-10 19:48:55 (Show Source): You can put this solution on YOUR website!width of garden = x yards Length of garden = x+ 4 yards Area = L*W Area= 96 sq. yards Area = x(x+ 4 ) x(x+ 4 )= 96 x^2 + 4 x = 96 x^2 + 4 x -96 = 0 x^2+ 12 x -8 x - -96 = 0 x(x+ 12 ) -8 (x+ 12 )= 0 (x+ 12 )(x -8 )= 0 x= -12 OR 8 Ignore negative. so x= 8 Width 8 yards Length 12 yards (width + 4 ) m.ananth@hotmail.ca
 Travel_Word_Problems/571009: 1. which speed is greater? 35 km/h or 50 mi/h? 2. what is the difference between speed and velocity?1 solutions Answer 367938 by mananth(12270)   on 2012-02-10 19:27:30 (Show Source): You can put this solution on YOUR website!1 mile = 1.6 km so 50 miles / hour > 35km/h Speed is a scalar quantity. It has magnitude but no direction Velocity is a vector. It has magnitude and direction.
 Points-lines-and-rays/571072: determine the slope of a line through points(4,-8)and(3,-6)1 solutions Answer 367937 by mananth(12270)   on 2012-02-10 19:22:04 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 4 -8 3 -6 slope m = (y2-y1)/(x2-x1) (-6-(-8))/(3- 4 ) ( 2 / -1 ) m= -2
 Travel_Word_Problems/571015: Here is the problem I'm stuck on... A commercial jet travels 1,620 miles in the same amount of time that a corporate jet travels 1,260 miles. The rate of the commercial jet is 120 miles per hour faster than the rate of the corporate jet. Find the rate of each jet. 1 solutions Answer 367936 by mananth(12270)   on 2012-02-10 19:19:30 (Show Source): You can put this solution on YOUR website!Corporate jet B x mph Commercial jet A 120 faster Corporate jet 1260 miles Commercial jet 1620 miles Corporate jet time = Commercial jet time 1260 / x = 1620 /( x + 120 cross multiply 1260 ( x + 120 ) = 1620 x 1260 x + 151200 = 1620 x 1620 x - 1260 x = 151200 360 x = 151200 / 360 x = 420 mph 420 mph Corporate jet 540 mph Commercial jet
 Polynomials-and-rational-expressions/571062: a^2-12a+32=0 The solutions are?1 solutions Answer 367934 by mananth(12270)   on 2012-02-10 19:11:17 (Show Source): You can put this solution on YOUR website!solution (8,4)
 Travel_Word_Problems/571071: A pharmaceutical salesperon's monthly income depends on the amount of his sales. His monthly income is a salary of \$750 plus 11% of his monthlyh sales. Write a linear equation for his monthlyhincome for sales of x dollars. (I=mx+b).1 solutions Answer 367933 by mananth(12270)   on 2012-02-10 19:09:45 (Show Source): You can put this solution on YOUR website!I=0.11x +750
 Triangles/570878: if you have a isosceles triangle with the legs being 9 and the base is 10 find the altitude. how do you solve it. we learn a equation leg squared = half part and base but if you solve it you wouldn't get the base to be 10.1 solutions Answer 367829 by mananth(12270)   on 2012-02-10 10:11:24 (Show Source): You can put this solution on YOUR website!height of isoscles triangle = sqrt(a^2-(b/2)^2) where a is the length of the leg and b the base h=8.64
 Linear-equations/570844: find the equation that passes through the point (2,1) and perpendicular to the line y=5x-3 1 solutions Answer 367802 by mananth(12270)   on 2012-02-10 08:25:36 (Show Source): You can put this solution on YOUR website!1 y = 5 x -3 Divide by 1 y = 5 x -3 Compare this equation with y=mx+b slope m = 5 The slope of a line perpendicular to the above line will be the negative reciprocal - 1/5 m1*m2=-1 m= - 1/5 ,point ( 2 , 1 ) Find b by plugging the values of m & the point in y=mx+b 1 = -2/5 + b b= 7/5 m= - 1/5 The required equation is y = - 1/ 5 x + 7/ 5 m.ananth@hotmail.ca
 Systems-of-equations/570846: Which of these images represents the following system of equations being solved graphically? 6x – 6y = -48 -10x + 4y = 92 1 solutions Answer 367801 by mananth(12270)   on 2012-02-10 08:20:10 (Show Source): You can put this solution on YOUR website!6 x -6 y = -48 .............1 -10 x + 4 y = 92 .............2 equation1 when x= 0 y= 8 ( 0 , 8 ) when y = 0 x= -8 ( -8 , 0 ) Equation 2 when x= 0 y= 23 ( 0 , 23 ) when y = 0 x= -9.2 ( -9.2 , 0 )
 Numbers_Word_Problems/570849: Three times a number is 36 more than twice the number. How do I write this. Im confused. I tried 3x+36=2x1 solutions Answer 367798 by mananth(12270)   on 2012-02-10 08:12:35 (Show Source): You can put this solution on YOUR website!3x=2x+36
 Systems-of-equations/570847: Which of these images represents the following system of equations being solved graphically? 6x – 6y = -48 1 solutions Answer 367797 by mananth(12270)   on 2012-02-10 08:11:24 (Show Source): You can put this solution on YOUR website!Where is the image 6x – 6y = -48 /6 x-y =8 y=x-8
 Quadratic_Equations/570835: I am having a hard time solving this equation quadratic in form: 9x(to the 4th power)=85x(squared)-196. I know it then becomes 9x(to the 4th power)-85x(squared)+196=0. Then u = x squared. So then it becomes 9u squared-85u+196=0 Now I'm stuck on how to solve the equation from here because I don't think I factor here???1 solutions Answer 367796 by mananth(12270)   on 2012-02-10 08:08:23 (Show Source): You can put this solution on YOUR website! u=x^2 In such problems you can solve by quadratic formula or completing the squares Take the square root on both sides 3u-85/6 = -/-(13/6) 3u=85/6 + 13/6 3u=98/6 u=98/18 OR 3u= 85/6 -13/6 3u=72/6 u=72/18 u=4 when u = 4 , x=+/-2 when u=98/18 =====> 49/9===>x=sqrt(49/9)====>+/- 7/3 m.ananth@hotmail.ca
 Linear-equations/570801: I have several questions like the following that I cannot seem to get the correct answer. Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b. (3,6); x+7y=3. I am missing a step when I try to solve so if I could get a detailed way to solve this that would be great. Thank you.1 solutions Answer 367792 by mananth(12270)   on 2012-02-10 05:27:49 (Show Source): You can put this solution on YOUR website!1 x + 7 y = 3 Find the slope of this line make y the subject 7 y = -1 x + 3 Divide by 7 y = - 1/ 7 x + 3/7 Compare this equation with y=mx+b slope m = - 1/7 The slope of a line parallel to the above line will be the same The slope of the required line will be - 1/7 m= - 1/7 ,point ( 3 , 6 ) Find b by plugging the values of m & the point in y=mx+b 6 = -3/7 + b b= 45/7 m= - 1/7 Plug value of the slope and b in y = mx +b The required equation is y = - 1/7 x + 45/7 m.ananth@hotmail.ca
 Square-cubic-other-roots/570825: find the cube root of 108 x16 without actual muulitipliction1 solutions Answer 367790 by mananth(12270)   on 2012-02-10 05:21:50 (Show Source): You can put this solution on YOUR website!cube root of 108 * 16 find prime factors = cuberoot (2*2*3*3*3*2*2*2*2) =12
 Equations/570823: 1/x-8/21=3/7x1 solutions Answer 367789 by mananth(12270)   on 2012-02-10 05:07:17 (Show Source): You can put this solution on YOUR website! Add 8/21 to both sides of the equation add -(3/7x) to both sides LCD = 7x 7-3=7x*8/21 4=56x/21 multiply by 21 84= 56x /56 x=3/2 m.ananth@hotmail.ca
 Mixture_Word_Problems/570802: How many kilos of tea worth Rs.72 per kg should be mixed with 10kg of tea worth Rs.90 per kg to produce a mixture which will cost Rs.78 per kg1 solutions Answer 367788 by mananth(12270)   on 2012-02-10 05:01:34 (Show Source): You can put this solution on YOUR website!---------------- Price ---------------- quantity Tea type I 90 ----------------10 pounds Tea type II 72 ----------------x pounds Mixture 78 ---------------- 10+x pounds sum of individual components = quantity in mixture 90*10+72x=78(10 +x) 900+72x =780+78 x 72x -78 x=-120 -6x=-120 x= -120 / -6 x= 20 20 pounds of Tea type II costing Rs. 72 has to be added m.ananth@hotmail.ca
 Travel_Word_Problems/570821: A boat can travel on a river 10 miles upstream in the same time it takes to travel 14 miles downstream. Find the speed of the current if the speed of the boat in still water is 18 miles per hour1 solutions Answer 367786 by mananth(12270)   on 2012-02-10 04:48:02 (Show Source): You can put this solution on YOUR website!Boat speed = 18 mph current speed = x mph wind speed speed against current 18 - x 0.07 speed with current 18 + x Distance against wind 10 km Distance with wind 14 km t=d/r time against = time with 10/(18-x)= 14/(18+x) 10(18+x )=14(18 -x) 180+10x =252-14 x 14x+10 x = 72 24 x = 72 / 24 x = 3 mph current speed
 test/570733: 7x+5y=-6 4x+3y=-41 solutions Answer 367779 by mananth(12270)   on 2012-02-10 01:20:52 (Show Source): You can put this solution on YOUR website!7 x + 5 y = -6 .............1 4 x + 3 y = -4 .............2 Eliminate y multiply (1)by -3 Multiply (2) by 5 -21 x -15 y = 18 20 x 15 y = -20 Add the two equations -1 x = -2 / -1 x = 2 plug value of x in (1) 7 x + 5 y = -6 14 + 5 y = -6 5 y = -6 -14 5 y = -20 y = -4
 Equations/570744: Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 147 miles in the same time that Dana travels 129 miles. If Chuck's rate of travel is 6 mph more that Dana's, and they travel the same length of time, at what speed does chuck travel?1 solutions Answer 367778 by mananth(12270)   on 2012-02-10 01:17:03 (Show Source): You can put this solution on YOUR website!Dana x 129 miles Chuck x+ 8 147 miles The time taken by them is the same t=d/r 129 / x = 147 /(x+ 8 ) Cross multiply 129 (x + 8 ) = 147 * x 129 x + 1032 = 147 x 147 x -129 x = 1032 18 x = 1032 / 18 x = 57.33 Dana mph 65.33 Chuck mph
 Polynomials-and-rational-expressions/570781: How do I factor a trinomial? I have seen many examples of this problems but i still dont understand, the problem is, -6s2 - s - 5. Can you help me?1 solutions Answer 367777 by mananth(12270)   on 2012-02-10 01:07:56 (Show Source): You can put this solution on YOUR website! -6s2 - s - 5 The coffecient of s^2=-6 The coefficient of third term is -5 Multiply both you get 30 You have to split this number (30)into two parts such that when you add them you get the coefficient of the middle term which is -1 Factorize 30 the prime factors are 2*3*5 From the factors you get, combine the factors. For example 2& 3 , & 5 2*3=6 & 5 5-6=-1 That is the coefficient of the middle term So you can now write -6s^2-6s+5s-5 -6s(s-1)+5(s-1) (s-1)(5-6s) m.ananth@hotmail.ca
 test/570792: Perpendicular to y= 1/3x + 2; (3,3)1 solutions Answer 367776 by mananth(12270)   on 2012-02-10 00:55:57 (Show Source): You can put this solution on YOUR website!1 y = 1/3 x + 2 Divide by 1 y = 1/ 3 x + 2 Compare this equation with y=mx+b slope m = 1/ 3 The slope of a line perpendicular to the above line will be the negative reciprocal -3 m1*m2=-1 m= -3 ,point ( 3 , 3 ) Find b by plugging the values of m & the point in y=mx+b 3 = -9 + b b= 12 m= -3 The required equation isy =-3x + 12 m.ananth@hotmail.ca
 decimal-numbers/570785: the end of a ladder is sitting on the ground 6 feet from a wall and as it leans against a wall the top of the ladder hits a spot 8 feet up the wall. how long is the ladder?1 solutions Answer 367771 by mananth(12270)   on 2012-02-10 00:46:38 (Show Source): You can put this solution on YOUR website!The ladder the ground and the wall form a right triangle The ladder is the hypotenuse of the triangle the height at which it touches the wall is leg1 The distance from the wall to the base of the ladder is leg2 Pythagoras theorem Hypotenuse ^2 = leg1^2+leg2^2 leg1= 8 ft leg2= 6 ft Hypotenuse^2= 8^2+6^2 Hypotenuse^2= 64 + 36 Hypotenuse^2= 100 Hypotenuse = Hypotenuse = 10 ft The height of ladder = 10 ft m.ananth@hotmail.ca
 Triangles/570758: ?...WHAT IS THE AREA OF AN EQUILATERAL TRIANGLE WHOSE SIDE LENGTH IS 12 CM? IS THE ANSWER 72?1 solutions Answer 367755 by mananth(12270)   on 2012-02-09 23:22:41 (Show Source): You can put this solution on YOUR website!The area of an equilateral triangle = where a is the length of the side length = 12 Area = Area = 62.3 cm^2
 Graphs/570738: Hello, I am having trouble grasping how to match an inequality with its graph. EX.- 5y-2x(less than or equal to) 10 1 solutions Answer 367754 by mananth(12270)   on 2012-02-09 23:12:16 (Show Source): You can put this solution on YOUR website! I am not sure whether it is -5x or 5x /5 First you have to find the boundary of the line y=(2/5)x+2 when x=0, y=2 (0,2) when y=0,x=-5 (0,-5) plot the points and draw the line The boundary Since there is an = sign the line should not be dotted. The inequality Since y is less than or equal to something the shaded portion contains all the values of x & y. It will be below the line
 Linear-equations/570750: 1. Find the slope-intercept equation of the line passing through (-2, -6) which is also a. parallel to 4x-16y=2 b. perpendicular to 4x-16y=21 solutions Answer 367753 by mananth(12270)   on 2012-02-09 23:01:18 (Show Source): You can put this solution on YOUR website!1. 4x-16y=2 16y=4x-2 /16 y=(1/4)x-(1/8) slope of this line is (1/4) The parallel line will have same slope = 1/4 point = (-2,-6) Find b , plug point and slope in the equation y = mx+b -6=(1/4)(-2)+b -6=(-1/2)+b -6+1/2=b b=-5 1/2 b= -11/2 Equation ; y= (1/4)x-11/2 --- 4 x -16 y = 2 Find the slope of this line -16 y = -4 x + 2 Divide by -16 y = 0.250 x + -0.13 Compare this equation with y=mx+b slope m = 1/4 The slope of a line perpendicular to the above line will be the negative reciprocal -4 m1*m2=-1 The slope of the required line will be -4 m= -4 ,point ( -2 , -6 ) Find b by plugging the values of m & the point in y=mx+b -6 = 8 + b b= -14 m= -4 The required equation is y =-4x-14 m.ananth@hotmail.ca
 Travel_Word_Problems/570751: Two trains start from stations that are 900 miles apart and travel toward each other on parallel tracks. One train averages 55 miles per hour, and the other train averages 65 miles per hour. How long will it take for the two trains to be 120 miles apart?1 solutions Answer 367752 by mananth(12270)   on 2012-02-09 22:52:07 (Show Source): You can put this solution on YOUR website!the trains are travelling towards each other so the effective speed = 55+65=120 mph they have to travel together 900-120 miles= 780 miles t= d/r t= 780/120 t= 6.5 hours