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 Numeric_Fractions/7020: How do you change .78 repeating and .66 repeating into a fraction?1 solutions Answer 3836 by Earlsdon(6294)   on 2005-08-10 23:48:42 (Show Source): You can put this solution on YOUR website!Change 0.7878... to a fraction. Let n = 0.7878... Multiply both sides by 100 (by 100 when there are two repeating decimal digits) 100n = 78.7878... Subtract n from 100n. 99n = 78 Divide both sides by 99 n = 78/99 but n is 0.7878..., so 0.7878... = 78/99 Similarly with 0.66... Let n = 0.66... Multiply both sides by 10 (by 10 when there is only one repeating digit) 10n = 6.66... Subtract n from 10n. 9n = 6 Divide both sides by 9. n = 6/9 but n is 0.66..., so 0.66... = 6/9 Check using your calculator. 78/99 = 0.787878... and 6/9 = 0.6666...
 Radicals/7007: Please help me find the (sqrt of 3/2) 1 solutions Answer 3830 by Earlsdon(6294)   on 2005-08-10 18:49:53 (Show Source): You can put this solution on YOUR website!Unfortunately, you cannot find the exact value of because it is an irrational number that results in a non-repeating, non-terminating decimal. Your calculator can give you an approximate value: approximately.
 Numbers_Word_Problems/7006: A man died and left the following instructions for his fortune Half went to his wife 1/7 of what was left went to his son 2/3 of what was left went to his butler the man's pet pig got the remaning \$2000 How much money did the man leave behind altogether?1 solutions Answer 3829 by Earlsdon(6294)   on 2005-08-10 18:43:05 (Show Source): You can put this solution on YOUR website!Let x = the deceased man's fortune. To his wife, he leaves (1/2)x To his son, he leaves (1/7) of (1/2)x To his butler, he leaves (2/3) of ((1/7) of (1/2)x) To his pig, he leaves the remaining \$2,000.00 All these amounts should add up to \$x, the deceased man's fortune. (1/2)x + (1/7)(1/2)x + (2/3)(1/7)(1/2)x + \$2,000.00 = \$x Simplify and solve for x. Factor an x from the first three terms. x(1/2 + 1/14 + 2/42) + \$2,000.00 = \$x Add up the fractions. The common denominator is 42. x(21/42 + 3/42 + 2/42) + \$2,000.00 = \$x x(26/42) + \$2,000.00 = \$x Simplify the fraction. x(13/21) + \$2,000.00 = \$x Subtract x(13/21) from both sides. \$2,000.00 = \$x - x(13/21) \$2,000.00 = \$x(8/21) Multiply both sides by the multiplicative inverse of 8/21 \$2,000.00(21/8) = \$x \$x = \$5,250.00 The deceased man's fortune.
 Radicals/6999: what is and how i solve it please with a cherry on top!!!! 2x-3 _____ =4/7 4x-5 Rachel1 solutions Answer 3827 by Earlsdon(6294)   on 2005-08-10 18:22:21 (Show Source): You can put this solution on YOUR website!Well...I have never solved an equation with a cherry on top, but there's always a first time. Cross-multiply; Simplify and solve for x. Subtract 14x from both sides. Add 20 to both sides. Divide both sides by 2. Check: = = =
 Square-cubic-other-roots/6931: directions: write the polynomial function having given the roots. (i don't know what this means.) -1/2,2/3 (its shown as fractions) thank you.1 solutions Answer 3805 by Earlsdon(6294)   on 2005-08-10 00:52:19 (Show Source): You can put this solution on YOUR website! This means: If you had a polynomial (say, in x) and you solved it to find its roots and they turned out to be: x = -1/2 and x = 2/3, what would that polynomial look like? Well, first, since there are two roots, the polynomial must be a quadratic function like: f(x) = ax^2 + bx + c Now, if you have the roots to a quadratic function, you can form the factors of that function by recalling how you get the roots to a quadratic function in the first place. If the roots are x = -1/2 and x = 2/3 then the factors would be: (2x + 1) and (3x - 2) Why is this? Because to get the roots of the quadratic, you had to set each of the factors equal to zero, as in: (2x + 1) = 0, so x = -1/2 and (3x - 2) = 0, so x = 2/3 Now you have the factors of the quadratic function, you can find the function itself by multiplying these factors, (x + 1/2)(x - 2/3). If you do this, you will get: Check, using FOIL:
 Numbers_Word_Problems/6924: 1/2 kids have left party 18 kids are standing around 1/3 are dancing how many kids were originally at party1 solutions Answer 3793 by Earlsdon(6294)   on 2005-08-09 21:10:05 (Show Source): You can put this solution on YOUR website!Let x be the number of kids originally at the party. Then: (1/2)x + 18 + (1/3)x = x Simplify and solve for x. (1/2)x + (1/3)x + 18 = x Add the fractions of x, common denominator is 6. (3/6)x + (2/6)x + 18 = x (5/6)x + 18 = x Subtract (5/6)x from both sides. 18 = x - (5/6)x 18 = (1/6)x Multiply both sides by 6. x = 108 The number of kids originally at the party. Check: (1/2)(108) + 18 + (1/3)(108) = 54 + 18 + 36 = 108
 Percentage-and-ratio-word-problems/6770: This is a word problem involving ratios that I have been struggling with for a couple of hours now. Can you please help me. The ratios of teachers to students at Elaine's school is 4 to 52. If there are 27 teachers at this school, then how many students are there? write a complete solution. This what I have been trying: 4/52 = x/27, cross multiplied and 52x = 108, but it is not coming out right.1 solutions Answer 3733 by Earlsdon(6294)   on 2005-08-07 23:38:19 (Show Source): You can put this solution on YOUR website!You have the right idea but the second ratio of your proportion is inverted. Remember to keep like-items in the tops and like-items in the bottoms of the ratios. Teachers/students = 4/52 You had this correctly shown. Let x = # of students, so you want to see the number of teachers on top and the number of students (x) on the bottom. 27/x The proportion looks like: 4/52 = 27/x Solve for x by cross-multiplying. 4x = (52)(27) Divide both sides by 4. x = 1404/4 x = 351 This is the number of students. Check: 4/52 = 27/351 Reduce the fractions. 1/13 = 1/13
 Linear_Equations_And_Systems_Word_Problems/6773: a college student earned \$8800 working as a waiter. the student invested some of the money at 7% and the rest at 6%, if the student recieved a total of \$560 in interest at the end of the year, how much was invested at 7%? This is the formula I used: principal multiplied by rate = interest OR x(.07) = .07x then I added 8800 - x(.06) = 560 which showed as: .07x + 8800 - x(.06) = 560 I tried to solve for x and got 8240. I know I'm doing something wrong. can you help? Sandy1 solutions Answer 3732 by Earlsdon(6294)   on 2005-08-07 23:26:12 (Show Source): You can put this solution on YOUR website!Well, you started out ok but when you got to the line: 8800 - x(.06) = 560, this is where your mistake lies. It should have been: (8800 - x)(.06) This is 6% of the total amount minus that invested at 7% So, you should have: .07x + (8800 - x)(.06) = 560 Solve for x. .07x + (.06)(8800) - .06x = 560 Simplify. .07x - .06x + 528 = 560 0.1x = 32 x = \$3200 The amount invested at 7%
 Coordinate-system/6761: Hi~ I am really having issues with the slope intercept equations and would like your assisance with the below question: The line through (2,-3) that is perpendicular to the line 5x + 3y = 9 Thank you, -Kate1 solutions Answer 3729 by Earlsdon(6294)   on 2005-08-07 18:00:01 (Show Source): You can put this solution on YOUR website!The equation of the line that passes through the point (2, -3) and is perpendicular to the line whose equation is: 5x + 3y = 9 can be found by recalling that perpendicular lines have slopes that are the negative reciprocal of each other. So, you need to determine the slope of the given line and then find the negative reciprocal of it to get the slope of the new line. Put the given equation into the slope-intercept form: y = mx + b 5x + 3y = 9 Subtract 5x from both sides. 3y = -5x + 9 Divide both sides by 3. y = (-5/3) + 3 The slope of the given line is: m = -5/3 The negative reciprocal of -5/3 is 3/5 and this is the slope of the new line. So, for the new line you can write: y = (3/5)x + b Now you need to find b, the y-intercept. This done by substituting the x and y coordinates from the given point (2, -3) into y = (3/5)x + b and solving for b. -3 = (3/5)2 + b Solve for b. -3 = 6/5 + b Subtract 6/5 from both sides. (-15/5)-(6/5) = b -21/5 = b Now you can write the equation of the new line: y = (3/5)x - 21/5 You can check this by seeing that the given point, (2, -3) satisfies this equation and by seeng that the slope of this line is the negative reciprocal of the slope of the given line. This is left as an exercise for the student. If you have any further issues with this, please call again.
 Geometry_Word_Problems/6765: An angle's measure is 24 degrees less than that of its supplement. how would I measure find the measure of the triangle1 solutions Answer 3728 by Earlsdon(6294)   on 2005-08-07 17:23:56 (Show Source): You can put this solution on YOUR website!Well, let the angle be A. The supplement of angle A is (180 - A) degrees. The problem says that the measure of angle A is 24 degrees less than (180-A). So we have: A = (180-A) - 24. Solve for A A = 180 - A - 24 Add A to both sides. 2A = 180 - 24 2A = 156 Divide both sides by 2. A = 78 degrees. A = (180-78)-24 A = (102)-24 A = 78 degrees. Check: A = (180-A)-24 A = (180-78)-24 A = (102)-24 A = 78
 Equations/6766: Please provide solution and explanation for the flwg: X/180-x = 1/8 Don't understand how to eliminate fractions. Thank you 1 solutions Answer 3727 by Earlsdon(6294)   on 2005-08-07 17:08:29 (Show Source): You can put this solution on YOUR website!flwg??? Solve: x/(180 - x) = 1/8 or (x/180) - x = 1/8? It's probably x/(180-x) = 1/8 x/(180-x) = 1/8 Multiply both sides by (180-x) x = (180-x)/8 Multiply both sides by 8. 8x = 180-x Add x to both sides. 9x = 180. Divide both sides by 9. x = 20 Check: 20/(180-20) = 20/160 = 1/8
 test/6763: I need help solving this word problem: The sum of two numbers is 10. Their product is -24. Find the numbers. Write a complete solution1 solutions Answer 3726 by Earlsdon(6294)   on 2005-08-07 16:57:00 (Show Source): You can put this solution on YOUR website!Try this! Let the two numbers be x and y. Then: x + y = 10 Rewrite as: x = 10 - y and substitute into equation below. xy = -24. (10 - y)Y = -24 Solve for y. 10y - y^2 = -24 Add 24 to both sides and put into standard form. y^2 - 10y - 24 = 0 Solve the quadratic by factoring. (y + 2)(y - 12) = 0 Apply the zero product principle. y + 2 = 0, y = -2 y - 12 = 0, y = 12 Now substitute these values of y into the original equations: x = 10 - y x = 10 - (-2) x = 12 And: x = 10 -y x = 10 - 12 x = -2 The two numbers are: -2 and 12 Check: 12 + (-2) = 10, and 12(-2) = -24
 Radicals/6739: sqrt(5x+6)-sqrt(3x-2)=2 solve for x. please show all the steps involved. thanks!1 solutions Answer 3719 by Earlsdon(6294)   on 2005-08-06 22:17:38 (Show Source): You can put this solution on YOUR website!Solve: Add to both sides. Square both sides. Simplify. Subtract 3x from both sides. Subtract 2 from both sides. Square both sides. Simplify. Subtract 48x from both sides. Add 32 to both sides. Divide both sides by 4. Solve by factoring. Apply the zero product principle. x - 2 = 0, x = 2 or x - 6 = 0, x = 6
 logarithm/6738: I am having trouble finding the y intercept on this problem. I have come up with an answer but not sure if its correct. Heres the problem... 2x - 5y = -10 Thank you for any help you can provide.1 solutions Answer 3718 by Earlsdon(6294)   on 2005-08-06 21:50:01 (Show Source): You can put this solution on YOUR website!The simplest way to find the y-intercept is to let x = 0 and solve for y. Let x = 0 Recall that the y-axis crosses the x-axis at x = 0. Divide both sides by -5. The y-intercept is at (0, 2)
 Quadratic_Equations/6736: Can somebody show me how to find the coordinates of the vertex of the graph of ? Thank you!1 solutions Answer 3716 by Earlsdon(6294)   on 2005-08-06 21:39:23 (Show Source): You can put this solution on YOUR website!There are several ways to find the coordinates of the vertex of a parabola. I'm assuming that there is a typographical error in your question. You probably meant to type: If not, your question is meaningless. If this is the equation you intended, then read on. 1) You could graph the equation and find the location of the vertex of the parabola, or 2) You could put the equation into the form: and read the coordinates of the vertex from: (h, k) This method requires that you perform an operation known as "completing the square". 3) You could put your equation into standard form . Then find the x-coordinate of the vertex which is located at -b/2a. Then you could get the y-coordinate by substituting the x-value into the equation and solve for y. Here's method 2. Set you equation equal to zero. Subtract 2 from both sides. Add the square of half the x-coefficient (-3)^2 = 9 to both sides. Factor the left side. Add 7 to both sides. You now have the equation in the a(x-h)^2 + k form h = 3 and k = -7 The coordinates of the vertex are: (h, k) or (3, -7)
 Linear_Algebra/6688: HI, I have the following vertices of a rectangle: (-2,1), (1,4), (3,2), and (0,-1). How do I find the length of the diagonal of the rectangle?1 solutions Answer 3671 by Earlsdon(6294)   on 2005-08-05 21:32:21 (Show Source): You can put this solution on YOUR website!First, you'll need to find the coordinates of opposite corners of the rectangle. This is best done by sketching the rectangle on graph paper using the coordinates of the given vertices. According to my sketch, the coordinates of the opposite corners are: (-2, 1) & (3, 2) (0, -1) & (1, 4) Use the distance formula to find the distance between one pair of opposite corners: Take either pair of coordinates and substitute the appropriate x, y values into the distance formula and solve for the distance, d. Let's take the second pair of points, (0, -1) & (1, 4)
 Linear-systems/6670: How do you factor: x^3 - 8 (x cubed minus 8)1 solutions Answer 3669 by Earlsdon(6294)   on 2005-08-05 21:12:52 (Show Source): You can put this solution on YOUR website!You'll notice that the given expression is the difference of two cubes: x^3 and 2^3 The difference of two cubes is factored as follows: In the given expression: A = x and B = 2