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1 year ago

Help picture below problem 16

Mathematics

1 answer:

weeeeeb [17]1 year ago

5 0

The Pythagorean theorem is the idea that the sum of the two legs which are both squared is equal to the hypotenuse's length squared.

*look at the image I attached for a better explanation

By looking at the picture, we are missing the leg's length, and by using the Pythagorean theorem, we get the equation

$?^2+9^2 = 16^2\\?^2 + 81=256\\?^2 = 175\\? = 13.2$

Thus the missing side length is 13.2 cm

Hope that helps!

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The solutions of the system of equations are the points

$(\frac{1-\sqrt{33}} {2},\frac{5-\sqrt{33}} {2})$

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Step-by-step explanation:

we have

$y=-x^{2} +2x+10$ ----> equation A

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The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

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in this problem we have

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substitute in the formula

$x=\frac{-1\pm\sqrt{1^{2}-4(-1)(8)}} {2(-1)}$

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$x=\frac{-1+\sqrt{33}} {-2}$ -----> $x=\frac{1-\sqrt{33}} {2}$

$x=\frac{-1-\sqrt{33}} {-2}$ -----> $x=\frac{1+\sqrt{33}} {2}$

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For $x=\frac{1-\sqrt{33}} {2}$

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For $x=\frac{1+\sqrt{33}} {2}$

$y=x+2$

$y=\frac{1+\sqrt{33}} {2}+2$ ----> $y=\frac{5+\sqrt{33}} {2}$

therefore

The solutions of the system of equations are the points

$(\frac{1-\sqrt{33}} {2},\frac{5-\sqrt{33}} {2})$

$(\frac{1+\sqrt{33}} {2},\frac{5+\sqrt{33}} {2})$

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