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PIT_PIT [208]
3 years ago
8

To factor the quadratic expression x^2−8x−10 by completing the square, what value would be added? A. 64 B. 8 C. 16 D.-16

Mathematics
2 answers:
Elan Coil [88]3 years ago
4 0

Answer:

C

Step-by-step explanation:

When completing the square, we essentially want to create a perfect square trinomial by adding a constant.

If we have the following expression:

x^2+bx

And we want to complete the square, we will need to divide the b-coefficient by half and then square it.

Thus, the added term should be:

(b/2)^2

In the given equation, we have:

(x^2-8x)-10

The b term here is 8. Therefore:

(8/2)^2\\=(4)^2\\=16

The value we would add would be 16.

The answer is C.

Further notes:

To complete the square, add 16 like mentioned earlier. However, we also need to subtract 16 to balance things out:

(x^2-8x)-10\\=(x^2-8x+16)-10-16\\

The expression inside the parentheses is now a perfect square trinomial. Factor it:

=((x)^2-2(4)(x)+(4)^2)-26\\=(x-4)^2-26

And we are done!

levacccp [35]3 years ago
3 0

A quadratic function equation is as follows:

ax^{2}   +  bx + c

To complete the square, move the constant (c) to the other side of the equation and take half of the b value, square it, and add and subtract the same number.

In this problem, you will add 16.

\frac{ - 8}{2}  =  - 4

- 4^{2}  = 16

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The sum of the measures of the interior angles of a polygon is 2880°. How many sides does the polygon have?
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Let

S------> The sum of the measures of the interior angles of a polygon

n-------> number of sides of a polygon

we know that

The formula to find the sum of the measures of the interior angles of a polygon is equal to

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in this problem

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Solve for n

S=(n-2)*180\\ \\ n=\frac{S}{180}+2\\ \\ n=\frac{2880}{180}+2\\ \\ n=16+2\\ \\ n=18\ sides

therefore

the answer is

18\ sides


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