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# Recent problems solved by 'nerdybill'

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 test/642218: My niece came home with this problem and I have no idea how they came up with the multiple choice answers.... Here's the problem.... 3(12+5 (to the second power))1 solutions Answer 403988 by nerdybill(6957)   on 2012-08-28 07:46:56 (Show Source): You can put this solution on YOUR website!you said: 3(12+5 (to the second power)) . is this what you meant? . if so, we then apply the "order of operations" (PEMDAS):
 Average/642219: -x^2=-5x+20?? give the values of a,b,and c for each equation (rewrite each equation in the form ax^2+bx+c=0 if necessary thanks so much for the help!!!1 solutions Answer 403985 by nerdybill(6957)   on 2012-08-28 07:42:41 (Show Source): You can put this solution on YOUR website!-x^2=-5x+20 adding x^2 to both sides: 0 = x^2-5x+20 or x^2-5x+20 = 0 . it is now in the form of: ax^2+bx+c=0 . From inspection then, a is 1 b is -5 c is 20
 Length-and-distance/642221: A map of a town is drawn on a coordinate grid. The high school is found at point (3,1) and the town hall is found at (-5,7). if the high school is at midpoint between the town hall and the town library, at which ordered pair should you find the library?1 solutions Answer 403984 by nerdybill(6957)   on 2012-08-28 07:39:21 (Show Source): You can put this solution on YOUR website!A map of a town is drawn on a coordinate grid. The high school is found at point (3,1) and the town hall is found at (-5,7). if the high school is at midpoint between the town hall and the town library, at which ordered pair should you find the library? midpoint formula given two points (x1,y1) AND (x2,y2) ((x1+x2)/2 , (y1+y2)/2)) . (3,1) = ((x-5)/2 , (y+7)/2) . solving for x: 3 = (x-5)/2 6 = (x-5) 11 = x . 1 = (y+7)/2 2 = (y+7) -5 = y . answer:(11,-5)
 logarithm/641637: How do you evaluate this function at the indicated value of x without using a calculator? 1 solutions Answer 403747 by nerdybill(6957)   on 2012-08-27 00:49:53 (Show Source):
 Equations/641238: I am having a hard time trying to simplify this equation: (4x+4)/(x^2-1) I know the answer is 4/x-1, but I wonder why. I tried to split the equation into smaller parts: (2*2*x+2*2)/(x*x-1) But as you see, the 4 parts does not contain common factors, therefore I wonder how you can simplify it even further. 1 solutions Answer 403587 by nerdybill(6957)   on 2012-08-26 07:56:49 (Show Source): You can put this solution on YOUR website!(4x+4)/(x^2-1) factoring the numerator: 4(x+1)/(x^2-1) notice, for the denominator, we can rewrite as: 4(x+1)/(x^2-1^2) it is a "difference of squares"-- special factoring case: 4(x+1)/[(x-1)(x+1)] canceling like-terms: 4/[(x-1)] 4/(x-1)
 Polynomials-and-rational-expressions/640941: Factor the trinomial by group. 6x^3-14x^2-12x1 solutions Answer 403487 by nerdybill(6957)   on 2012-08-25 00:58:04 (Show Source): You can put this solution on YOUR website!6x^3-14x^2-12x 2x(3x^2-7x-6) rewrite the middle term as: 2x(3x^2-9x+2x-6) group: 2x((3x^2-9x)+(2x-6)) 2x(3x(x-3)+2(x-3)) 2x(x-3)(3x+2)
 Linear-equations/640950: what is a if the lines with equations y=ax+5 and 2y=(a+4)x-1 are parallel?1 solutions Answer 403486 by nerdybill(6957)   on 2012-08-25 00:53:47 (Show Source): You can put this solution on YOUR website! what is a if the lines with equations y=ax+5 and 2y=(a+4)x-1 are parallel? . If two lines are parallel, they have the same slope. slope of: y=ax+5 is 'a' . slope of: 2y=(a+4)x-1 y=((a+4)/2)x-1/2 is (a+4)/2 . equation is: a = (a+4)/2 2a = a+4 a = 4
 logarithm/640804: How do you solve for "x" in the equation ln(6-5x)= -31 solutions Answer 403410 by nerdybill(6957)   on 2012-08-24 13:32:40 (Show Source): You can put this solution on YOUR website!How do you solve for "x" in the equation ln(6-5x)= -3 . Starting with: ln(6-5x)= -3 6-5x = e^(-3) -5x = e^(-3) - 6 5x = 6 - e^(-3) x = [6 - e^(-3)]/5 x = [5.95]/5 x = 1.19
 Average/640806: on three test I scored 84 65 76 what grade must I obtain on the fourth test to equal 80 for all for test1 solutions Answer 403409 by nerdybill(6957)   on 2012-08-24 13:29:56 (Show Source): You can put this solution on YOUR website! on three test I scored 84 65 76 what grade must I obtain on the fourth test to equal 80 for all for test . Assuming all four tests are equally weighted... . Let x = score on fourth test then (84 + 65 + 76 + x)/4 = 80 (225 + x)/4 = 80 225 + x = 320 x = 320-225 x = 95
 logarithm/640810: 64=2^3n+1 the 3n+1 is all part of the exponent1 solutions Answer 403408 by nerdybill(6957)   on 2012-08-24 13:26:36 (Show Source): You can put this solution on YOUR website! . take log base 2 of both sides: .
 logarithm/640818: log(3)64-log(3)8/3+log(3)2=log(3)4r How do i even start problems like this.Do i suppose to get rid of the log(3) or what?1 solutions Answer 403407 by nerdybill(6957)   on 2012-08-24 13:21:43 (Show Source): You can put this solution on YOUR website!log(3)64-log(3)8/3+log(3)2=log(3)4r .
 Mixture_Word_Problems/640703: Kayla wants to make 16 fl. oz. of a 60% acid solution by mixing together a 80% acid solution and pure water. How much of each solution must she use?1 solutions Answer 403380 by nerdybill(6957)   on 2012-08-24 00:53:05 (Show Source): You can put this solution on YOUR website!Kayla wants to make 16 fl. oz. of a 60% acid solution by mixing together a 80% acid solution and pure water. How much of each solution must she use? . Let x = amount (oz) of 80% acid then 16-x = amount (oz) of water . .80x = .60(16) .80x = 9.6 x = 9.6/.80 x = 12 oz of 80% acid solution . amount of water: 16-x = 16-12 = 4 oz
 Rate-of-work-word-problems/640690: Jack can paint a housw twice as fast as Jill. Jill starts at 8 AM, Jacj joins in at 10 AM. They finished at 2 PM. How long does it take each of them to paint the house by themself? PLEASE HELP ME :(1 solutions Answer 403366 by nerdybill(6957)   on 2012-08-23 23:07:42 (Show Source): You can put this solution on YOUR website!Jack can paint a house twice as fast as Jill. Jill starts at 8 AM, Jacj joins in at 10 AM. They finished at 2 PM. How long does it take each of them to paint the house by themself? . Let x = time (hours) it takes for Jack to paint house then 2x = time (hours) it takes for Jill to paint house . Jill has a 2 hour head start then, they both paint for an additional 4 hours . 2(1/(2x)) + 4(1/x + 1/(2x)) = 1 multiplying both sides by 2x: 2(1) + 4(2 + 1) = 2x 2 + 4(3) = 2x 2 + 12 = 2x 14 = 2x 7 hours = x (time it takes for Jack to paint the house alone) . Jill: 2x = 2(7) = 14 hours
 Geometry_Word_Problems/640648: Can you help me solve this word problem? The third angle in an isosceles triangle is half as large as each of the two base angles.Find the measure of each angle.1 solutions Answer 403351 by nerdybill(6957)   on 2012-08-23 21:37:14 (Show Source): You can put this solution on YOUR website!The third angle in an isosceles triangle is half as large as each of the two base angles.Find the measure of each angle. . In an "isosceles triangle" the two base angles are the same. Let x = measure of one of the base angles then x/2 = measure of third angle . x + x + x/2 = 180 multiplying both sides by 2: 2x + 2x + x = 360 5x = 360 x = 72 degrees . third angle: x/2 = 72/2 = 36 degrees . solution: each of the base angle is 72 degrees third angle is 36 degrees
 �t�e�s�t/639887: the width of a rectangle is twice the length. the perimeter is 104 feet. find the dimensions.1 solutions Answer 402917 by nerdybill(6957)   on 2012-08-22 06:57:49 (Show Source): You can put this solution on YOUR website! the width of a rectangle is twice the length. the perimeter is 104 feet. find the dimensions. . Let x = length then 2x = width . 2(x + 2x) = 104 (x + 2x) = 52 3x = 52 x = 14 feet (length) . width: 2x = 2(14) = 28 feet
 Linear_Equations_And_Systems_Word_Problems/639877: george can do a job in 6 hours and john can do the same job in 4 hours. how long will it take to finish the job, if both of them work together? 1 solutions Answer 402916 by nerdybill(6957)   on 2012-08-22 06:55:34 (Show Source): You can put this solution on YOUR website!george can do a job in 6 hours and john can do the same job in 4 hours. how long will it take to finish the job, if both of them work together? . Let x = time (hours) it takes for both then x(1/6 + 1/4) = 1 multiplying both sides by 12: x(2 + 3) = 12 x(5) = 12 x = 12/5 x = 2.4 hours or x = 2 hours and 24 minutes
 test/639888: If 2x+y=8 and x-y=1,then y=1 solutions Answer 402915 by nerdybill(6957)   on 2012-08-22 06:52:05 (Show Source): You can put this solution on YOUR website!If 2x+y=8 and x-y=1,then y= . 2x+y=8 (equation 1) x-y=1 (equation 2) . Solve equation 2 for x: x-y=1 x=y+1 . Substitute above into equation 1 and solve for y: 2x+y=8 2(y+1)+y=8 2y+2+y=8 3y+2=8 3y=6 y = 2
 test/639884: in(1/e^5)=1 solutions Answer 402914 by nerdybill(6957)   on 2012-08-22 06:48:44 (Show Source): You can put this solution on YOUR website!ln(1/e^5) ln(e^(-5)) -5
 Numeric_Fractions/639004: 6/2(2+1) 1 solutions Answer 402530 by nerdybill(6957)   on 2012-08-20 04:46:20 (Show Source): You can put this solution on YOUR website!apply the "order of operations" 6/2(2+1) parenthesis first: 6/2(3) division next: 3(3) 9
 Functions/638700: please help me solve this equation this is factor completely1 solutions Answer 402356 by nerdybill(6957)   on 2012-08-19 10:22:23 (Show Source): You can put this solution on YOUR website! group:
 �t�e�s�t/638492: Find the equation of the line that goes through the point (2,1) and has a slope of 4. Leave equation in point-slope form. Please help me with this, it would be much appreciated! :)1 solutions Answer 402264 by nerdybill(6957)   on 2012-08-18 14:16:22 (Show Source): You can put this solution on YOUR website!Find the equation of the line that goes through the point (2,1) and has a slope of 4. Leave equation in point-slope form. . "point-slope" form of a line is y - y1 = m(x - x1) plugging in our values: y - 1 = 4(x - 2) (this is what they're asking for)
Expressions-with-variables/638540: I need to know how to start to solve this equation.
1/(x-1) + 1/2 = 2/(x^2-1)
1 solutions

Answer 402263 by nerdybill(6957)   on 2012-08-18 14:13:51 (Show Source):
You can put this solution on YOUR website!
Notice that:
(x^2-1)
is a "difference of squares"
(x^2-1^2)
we can factor as:
(x-1)(x+1)
.
So, we can rewrite your original equation:
1/(x-1) + 1/2 = 2/(x^2-1)
as:
1/(x-1) + 1/2 = 2/[(x-1)(x+1)]
multiply both sides by 2:
2/(x-1) + 1 = 4/[(x-1)(x+1)]
Now, we multiply both sides by (x-1)(x+1) to get:
2(x+1) + (x-1)(x+1) = 4
2x+2 + x^2-1 = 4
x^2+2x-1 = 4
x^2+2x-5 = 0
x = {1.45, -3.45}
.
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=24 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.44948974278318, -3.44948974278318. Here's your graph:

 Graphs/638536: Sketch a line with the given slope m and y-intercept b. Write its slope- intercept form m= -1/5 , b=-2 graph the equation using slope and y-intercept1 solutions Answer 402261 by nerdybill(6957)   on 2012-08-18 14:06:25 (Show Source): You can put this solution on YOUR website!Sketch a line with the given slope m and y-intercept b. Write its slope- intercept form m= -1/5 , b=-2 . Slope-intercept form of a line: y = mx + b plug in our values: y = (-1/5)x + (-2) y = (-1/5)x - 2 . graph the equation using slope and y-intercept
 Trigonometry-basics/638506: Find an equation of a straight line that intersects the parabola y=(x^2)+1 only at the poiny (1,2) 1 solutions Answer 402259 by nerdybill(6957)   on 2012-08-18 13:54:50 (Show Source): You can put this solution on YOUR website!Find an equation of a straight line that intersects the parabola y=(x^2)+1 only at the poiny (1,2) . Since the parabola is "vertical", we know that all vertical lines will intersect the parabola only once (vertical line test). Therefore, the equation of a straight line is x = 1
 Graphs/638537: I have no idea how to begin this problem. Thanks for the help. Find the domain f(x)=x/2x-61 solutions Answer 402258 by nerdybill(6957)   on 2012-08-18 13:48:58 (Show Source): You can put this solution on YOUR website!Find the domain f(x)=x/2x-6 . The "domain" merely specifies all values that 'x' can take. The ONLY value x can't take is if it drives the denominator to zero. So, we set the denominator to zero and solve for x: 2x-6 = 0 2x = 6 x = 3 This is the ONLY value can't take. So, the domain is: (-oo, 3) U (3, +oo) where oo is for infinity
 Functions/638400: I am trying to find out what f/g is for f(x)= x^2-2x-24 and g(x)=x^2-x-30. I know that you must divide them and I successfully completed the other parts to this problem which was finding f+g, f-g, and f*g. I just can't remember how to divide equations with variables in them. This is the problem that needs to be solved. x^2-2x-24/x^2-x-30. Also I need to specify the domain. Thank you1 solutions Answer 402199 by nerdybill(6957)   on 2012-08-18 01:32:31 (Show Source): You can put this solution on YOUR website!f/g is for f(x)= x^2-2x-24 and g(x)=x^2-x-30 . f/g: [x^2-2x-24]/[x^2-x-30] factor both: [(x-6)(x+4)]/[(x-6)(x+5)] Note: this is where you can determine domain canceling: (x+4)/(x+5) (this is f/g) . Domain specifies what values x can take (we just have to avoid when the denominator becomes zero). The denominator becomes zero when x=6 OR x=-5 domain is therefore: (-oo, -5) U (-5,6) U (6,+oo) where oo stands for infinity
 Travel_Word_Problems/638440: 1200 miles on 55 gallons of gas how many miles to the gallon did truck get thank you1 solutions Answer 402197 by nerdybill(6957)   on 2012-08-18 01:25:52 (Show Source): You can put this solution on YOUR website!1200 miles on 55 gallons of gas how many miles to the gallon did truck get: . 1200/55 21.8 mpg
 Trigonometry-basics/638438: URGENT PLEASE! :) thank you! rewrite as a logarithmic equation. 8^-2 = 1/641 solutions Answer 402196 by nerdybill(6957)   on 2012-08-18 01:24:19 (Show Source): You can put this solution on YOUR website! rewrite as a logarithmic equation.
 Rate-of-work-word-problems/637699: Nancy can mow a yard in 3 hours and Peter can mow it in 4 hours. Suppose they both work together, how long would it take to finish?1 solutions Answer 401821 by nerdybill(6957)   on 2012-08-15 11:53:48 (Show Source): You can put this solution on YOUR website! Nancy can mow a yard in 3 hours and Peter can mow it in 4 hours. Suppose they both work together, how long would it take to finish? . Let x = time (hours) it takes for both then x(1/3 + 1/4) = 1 multiplying both sides by 12: x(4 + 3) = 12 x(7) = 12 x = 12/7 hours or x = 1 hour and 43 minutes
 Equations/637703: find the number of real number solutions for the equation x^2-13x+42=01 solutions Answer 401820 by nerdybill(6957)   on 2012-08-15 11:51:11 (Show Source): You can put this solution on YOUR website!find the number of real number solutions for the equation x^2-13x+42=0 factoring: (x-6)(x-7) = 0 x = {6, 7}
 logarithm/637690: what is the answer if i mathematically Evaluate 2log10 5 +log 10 36 - log 10 9,Please i need solvings too1 solutions Answer 401819 by nerdybill(6957)   on 2012-08-15 11:45:37 (Show Source): You can put this solution on YOUR website!Starting with: then, applying "log rules":