SOLUTION: The demand and supply equations for a certain item are given by D = –5p + 40 S = –p2 + 30p – 8 Find the equilibrium price. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Algebra ->  Test -> SOLUTION: The demand and supply equations for a certain item are given by D = –5p + 40 S = –p2 + 30p – 8 Find the equilibrium price. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~      Log On


   

Question 102451: The demand and supply equations for a certain item are given by
D = –5p + 40 S = –p2 + 30p – 8
Find the equilibrium price.

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Can you double check my work for me? I think it is right.
A rectangular garden is to be surrounded by a walkway of constant width.
The garden's dimensions are 30 ft by 40 ft. The total area, garden plus walkway, is to be 1800 ft2. What must be the width of the walkway to nearest thousandth?
Answer: x=3.860
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Is the following trinomial a perfect square? x2 – 18x + 81
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Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry). y = –x2 + 1
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Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
A.
-5p+40=-p^2+30p-8
p^2-35p+48=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-35x%2B48+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-35%29%5E2-4%2A1%2A48=1033.

Discriminant d=1033 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--35%2B-sqrt%28+1033+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-35%29%2Bsqrt%28+1033+%29%29%2F2%5C1+=+33.5701586799882
x%5B2%5D+=+%28-%28-35%29-sqrt%28+1033+%29%29%2F2%5C1+=+1.4298413200118

Quadratic expression 1x%5E2%2B-35x%2B48 can be factored:
1x%5E2%2B-35x%2B48+=+%28x-33.5701586799882%29%2A%28x-1.4298413200118%29
Again, the answer is: 33.5701586799882, 1.4298413200118. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-35%2Ax%2B48+%29

B.
(30+x)(40+x)=1800
1200+70x+x^2=1800
x^2+70x-600=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B70x%2B-600+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2870%29%5E2-4%2A1%2A-600=7300.

Discriminant d=7300 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-70%2B-sqrt%28+7300+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2870%29%2Bsqrt%28+7300+%29%29%2F2%5C1+=+7.72001872658765
x%5B2%5D+=+%28-%2870%29-sqrt%28+7300+%29%29%2F2%5C1+=+-77.7200187265877

Quadratic expression 1x%5E2%2B70x%2B-600 can be factored:
1x%5E2%2B70x%2B-600+=+%28x-7.72001872658765%29%2A%28x--77.7200187265877%29
Again, the answer is: 7.72001872658765, -77.7200187265877. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B70%2Ax%2B-600+%29

C.
Yes.
D.
y = –x2 + 1
axis of symetry=0
Ed
graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C-x%5E2%2B1%29