SOLUTION: use the Pythagorean theorem to find the value of y, ti the nearest hundredth. side a is y+2, side b is y and side c is 17. can u plz help me out thnx

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: use the Pythagorean theorem to find the value of y, ti the nearest hundredth. side a is y+2, side b is y and side c is 17. can u plz help me out thnx      Log On


   

Question 391244: use the Pythagorean theorem to find the value of y, ti the nearest hundredth. side a is y+2, side b is y and side c is 17. can u plz help me out thnx
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
use the Pythagorean theorem to find the value of y, ti the nearest hundredth. side a is y+2, side b is y and side c is 17.
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Assuming 17 is the long side:
y%5E2+%2B+%28y%2B2%29%5E2+=+17%5E2
2y%5E2+%2B+4y+-+285+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B4x%2B-285+=+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=%284%29%5E2-4%2A2%2A-285=2296.

Discriminant d=2296 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+2296+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+2296+%29%29%2F2%5C2+=+10.9791485507109
x%5B2%5D+=+%28-%284%29-sqrt%28+2296+%29%29%2F2%5C2+=+-12.9791485507109

Quadratic expression 2x%5E2%2B4x%2B-285 can be factored:
2x%5E2%2B4x%2B-285+=+%28x-10.9791485507109%29%2A%28x--12.9791485507109%29
Again, the answer is: 10.9791485507109, -12.9791485507109. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B-285+%29

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Ignore the negative solution
y = 10.98
side b = 10.98
side a = 12.98

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
use the Pythagorean theorem to find the value of y, to the nearest hundredth. side a is y+2, side b is y and side c is 17.
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If I assume that c is the hypotenuse I get:
17^2 = y^2 + (y+2)^2
289 = y^2 + y^2+4y+4
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Rearrange:
2y^2 + 4y -285 = 0
y = [-4 +- sqrt(16-4*2*-285)]/4
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y = [-4 +- sqrt(2296)]/4
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y = [-4 +- 47.92]/4
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y = [43.92]/4
---
y = 10.98
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Cheers,
Stan H.
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