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Quadratic_Equations/327900: i am doing completing the square and i want to make sure i have it right
solve: x squared + 2x = 8 by completing the square
1 solutions
Answer 234808 by Earlsdon(6287)   on 2010-08-01 22:37:41 (Show Source):
You can put this solution on YOUR website!Solve:  by completing the square.
 Add the square of half the x-coefficient. 
to both sides.
 Factor the left side.
 Take the square root of both sides.
 or  Subtract 1 from both sides in each solution.
 or 
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Quadratic_Equations/327388: Please help solve the following equation using Quadratic Form (NOT formula):
1 solutions
Answer 234518 by Earlsdon(6287) on 2010-07-31 10:24:48 (Show Source):
You can put this solution on YOUR website!Temporarily substitute  so now you have:
 Add 8 to both sides.
 So now you have a quadratic equation in y. Factor a 2.
 so...
 This will factor nicely into...
 and from the zero product rule you get...
 or  therefore...
 or  Re-substtute
 or  Taking the square root of both of these, we get...
 or  or  or 
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Linear-equations/325419: My Dad has helped me and we still can't get this last few question, please help me. I dont understand all the question. I want to get all right, not just pass
1) 5x-4y=-18 I would like to know to solve not just answer
2) -x-2y=-10 I think got 2 (-2,-4) (-1,-5)
3) -y=x+1 I just don't get this
4) 2y=3x+11 again I just not get it,
1 solutions
Answer 233030 by Earlsdon(6287) on 2010-07-25 14:39:52 (Show Source):
You can put this solution on YOUR website!Notice that all of the given equations have two variables (x and y).
You can't "solve" these equations unless you place some constraints on the variables, such as..."x and y must be integers"
The given equations will have many answers, not just one.
Here's one way to think about these:
Suppose we were to graph the first equation:  by first solving it in terms of y.
Subtract 5x from both sides.
 Now divide both sides by -4.
 Now we'll graph this:
You can immediately see that the value of y depends upon which value of x you choose, so you see that there are numerous solutions to such an equation, one for every value of x you choose.
Sometimes, when you are asked to solve equations with two variables, what is really meant is to put the given equation in terms of one of the variables as we did here:
Sometimes you are asked to find the x- and y-intercepts of equations like this.
You can do this by either inspecting the graph to see at which points the line intersects the axes. In this case, the x-intercept is  and the y-intercept is  or by using algebra.
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Exponents/325111: Please help with this problem; I don't get how to work through it and show work.
9*10^-4/3*10^-6
Thank you SO much...
1 solutions
Answer 232820 by Earlsdon(6287) on 2010-07-23 22:16:36 (Show Source):
You can put this solution on YOUR website!
Do the integers first:  so...
 Now, to divide quantities with exponents, subtract the exponents, so...
 Simplify the exponent.
 or...
 or...
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Linear-equations/324946: 2y + 3x = 12
-4y + 5x = -2
How do I solve the above linear equations using the elimination method? I don't understand
1 solutions
Answer 232675 by Earlsdon(6287) on 2010-07-23 11:26:26 (Show Source):
You can put this solution on YOUR website!Solve by eliminiation:
Here you have two equations in two unknowns. The idea behind the "elimination" method is to eliminate one of the variables (either x or y) then solve for the remaining variable. Once you know the value of one of the variables, you can find the value of the other one by substitution.
Let's start:
1) Multiply this equation by 2.
2)
--------------------
1a) 
2a) Add these two equations to eliminate the y-variable.
----------------------
3)  Divide both sides by 11.
3a) Now substitute this value of x into either one of the two original equations to solve for y. Let's use equation 1).
1) Substitute x = 2.
1a) 
1b)  Subtract 6 from both sides.
1c)  Divide both sides by 2.
1d) 
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Geometry_Word_Problems/322887: If possible, give the name of the convex polygon in which the sum of the interior angles equals 1260°
1 solutions
Answer 231145 by Earlsdon(6287) on 2010-07-16 00:33:06 (Show Source):
You can put this solution on YOUR website!The sum (S) of the interior angles of a polygon with n sides is given by:
 and this is given as 1260 degrees, so...
 Divide both sides by 180.
 Add 2 to both sides.
The polygon has 9 sides and this is called a nonagon.
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Quadratic_Equations/322848: Can somebody Please help me solve this problem? I have been working on it a long time and I still do not understand it.
Simplify as much as possible
x sqrt 6t^3-tsqrt24tx^2
Assume that all variables represent positive real numbers
1 solutions
Answer 231121 by Earlsdon(6287) on 2010-07-15 20:37:16 (Show Source):
You can put this solution on YOUR website!Simplify:
 Rewrite this as:
 Now take the square root of the perfect squares that are under the radical and move them outside.
 Factor the common factor of  .
 Perform the indicated subtraction.
 or 
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Miscellaneous_Word_Problems/322376: An object in free fall travels a distance s that is directly proportional to the square of the time t. If an object falls 1,024 feet in 8 seconds, how far will it fall in 12 seconds?
1 solutions
Answer 230819 by Earlsdon(6287) on 2010-07-14 13:49:59 (Show Source):
You can put this solution on YOUR website!Write the equation of proportionality:
 where k is the constant of proportionality.
First find the value of k by substituting the given values of s=1,024 feet and t=8 seconds.
 Substitute this into the given function then you can solve the problem:
 Substitute t = 12.
 Evaluate.
 feet.
The objct will fall 2304 feet in 12 seconds.
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Functions/322392: Imagine you are at a gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation C(g)=3.50(g) please help don't understand.......
find c(7)
1 solutions
Answer 230818 by Earlsdon(6287) on 2010-07-14 13:34:51 (Show Source):
You can put this solution on YOUR website!In the function  , the C stands for the cost of the gas you put into your gas tank. The g stands for the number of gallons of gas you buy, and the 3.50 is the cost, per gallon, of the gas.
If you want to find out how much 7 gallons of gas wiil cost, you replace the g in the function with 7 and solve for C, thus:
 You will interpret this to mean that the cost (C) of 7 gallons of gas (C(7)) is $24.50
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Linear-systems/322205: y= -2/3x + 4
I have to figure out what x and y are and show my work. I don't know how to do this with fractions.
1 solutions
Answer 230650 by Earlsdon(6287) on 2010-07-13 19:11:25 (Show Source):
You can put this solution on YOUR website!Knowing how to do it with fractions won't help you here.
To solve for x, you first must know the value of y.
For example, if had written:
 you could solve for x thus:
 Multiply both sides by  .
 Simplify.
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Rational-functions/321871: Can someone please help me to solve this one, I have tried several times, but I am doing something wrong. Please show me what to do. I tried using the quadratic formular, perhaps that is what I am doing incorrectly.
2sqrt(3x^(2)-2)=10
1 solutions
Answer 230427 by Earlsdon(6287) on 2010-07-12 20:43:10 (Show Source):
You can put this solution on YOUR website!Solve for x:
 Divide both sides by 2 to simplify a bit.
 Square both sides.
 Add 2 to both sides.
 Divide both sides by 3.
 Take the square root of both sides.
 or 
Check the solutions:
Substitute x = 3.
You can try x = -3 yourself!
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Quadratic_Equations/321287: what is the y intercept of y= -2(x-3)^2 +4
when I calculated: y= -2(0-3)^2 +4
y= -2(-3)^2 +4
y= -2(9) +4
y= -18+4
y= -14
but when i use my graphing calculator i get y=-5
1 solutions
Answer 230111 by Earlsdon(6287) on 2010-07-10 20:50:30 (Show Source):
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Quadratic_Equations/321273: Find and label the vertex (ordered pair) and the line of symmetry.
f(x) = 1/5 x^2
1 solutions
Answer 230083 by Earlsdon(6287) on 2010-07-10 18:07:28 (Show Source):
You can put this solution on YOUR website!The equation of the axis of symmetry of  can be found by:
 and in your equation,  and  so...
 This is the equation of the line of symmetry.
The vertex can be found by substituting  into the given equation.
Replace f(x) with y.
 Substitute
The vertex is at (0, 0)
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Bodies-in-space/321274: how many times does the volume of a sphere increases if the radius is
1) double 2)half
1 solutions
Answer 230080 by Earlsdon(6287) on 2010-07-10 17:57:19 (Show Source):
You can put this solution on YOUR website!The volume of a sphere is given by:
 Where r = radius.
1) Let's what happens when you double the radius:
 Move the 8 to the front.
 ...and you can see that the volume V is 8 times the original volume.
2) ...and if we divide the radius by 2...
 or...
 ...so the volume is decreased by a factor of 8.
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Radicals/321246: please help with this...
sqrt (x-4)+ sqrt (x+1) = 5
1 solutions
Answer 230075 by Earlsdon(6287) on 2010-07-10 17:39:47 (Show Source):
You can put this solution on YOUR website!Solve for x:
 First, subtract  from both sides.
 Now square both sides.
 Simplify the right side.
 Subtract x from both sides.
 Subtract 26 from both sides.
 Divide both sides by -10.
 Square both sides.
 Subtract 1 from both sides.
 or 
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Quadratic_Equations/320743: (1)What does the Principle of Zero Products state? How is it used to solve a quadratic equation?
(2)Explain how to complete the square on x2 + 14x. Then write the resulting perfect square trinomial as the square of a binomial.
1 solutions
Answer 229721 by Earlsdon(6287) on 2010-07-08 15:42:53 (Show Source):
You can put this solution on YOUR website!1) The Principle of Zero Prducts states:
If A*B = 0, then either A = 0, or B = 0, or both A and B are 0.
In solving quadratic equations by factoring, you typically end up with two binomial factors whose product equals zero; for example...
 and, when factored you get:
 Applying the principle of Zero Products, you can state that...
 or  from which follows...
 or 
2) To complete the square of  you will add the square of half the x-coefficient to both sides of the equation, thus...
 Simplifying this you get...
 Factoring the left side gives you...
 which is readily solved by taking the square root of both sides and solving for x.
 or  so that...
or 
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Quadratic_Equations/320785: Any help with the following word problem would be great. I just really need the help setting up the problem.
A gardener has a rose garden that measures 30 feet by 20 feet. He wants to put a uniform border of pine bark around the outside of the garden. Find how wide the border should be if he has enough pine bark to cover 336 square feet.
1 solutions
Answer 229716 by Earlsdon(6287) on 2010-07-08 15:14:50 (Show Source):
You can put this solution on YOUR website!Let the width of the path be x feet.
The plan is to express the area of the garden with the border in terms of x, then subtract the area of just the garden. This will result in a quadratic equation in x which you solve by any of the appropriate methods available to you.
The area of the garden with border  can be expressed as:
 Simplify this to:
The area of just the garden  is:
 sq.ft.
Now subtract from .
 This is the area of the border of width x ft. which is given as 336 sq.ft., so...
 Subtract 336 from both sides.
 Simplify by factoring out a 4.
 ...and from the zero product rule, you get that:
You can solve this by factoring and you should get:
or
The width cannot be a negative quantity, so the width must be 3 feet.
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Polynomials-and-rational-expressions/320015: I have tried to solve the equations many times, each time I come up with a different answer, Please help me with a step-by-step guide.
(x-3)^2+(x+2)^2=17
1 solutions
Answer 229189 by Earlsdon(6287) on 2010-07-05 23:41:36 (Show Source):
You can put this solution on YOUR website!Solve for x:
 Expand the two terms in parentheses.
 Simplify the left side.
 Subtract 17 from both sides.
 Factor 2 from the left side.
 Apply the zero product rule.
 Factor the left side.
 Apply the zero product rule.
 or  so...
or 
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logarithm/319722: Solve the following equation for the value of the variable x.
log 25 5 = x
the problem should read as x is the logarithm of 5 with base of 25.
Thank you for taking a look at this, it is appreciated.
1 solutions
Answer 228982 by Earlsdon(6287) on 2010-07-04 22:16:57 (Show Source):
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