3 years ago

Write an expression for the area of the shaded region in its simplest form. Show all of your steps.

1 answer:

3 0

The area of the shaded region will be the area of the rectangle minus the area of the white square inside of it:

((x+10)(2x+5)) - ((x+1)(x+1))

First, FOIL both of the areas separately:

(2x^2 + 5x + 20x + 50) - (x^2 + x + x + 1)

Simplify within the parentheses by adding like terms:

(2x^2 + 25x + 50) - (x^2 + 2x + 1)

Now, subtract one equation from the other:

2x^2 + 25x + 50
-x^2 - 2x - 1
= x^2 + 23x + 49

This will be the equation for the area.

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F(x)=9x^2 g(x)= sqrt 12-x/3 (f o g)(-4)

Slav-nsk [51]

$f(x)=9x^2 \\ g(x)=\frac{\sqrt{12-x}}{3} \\$ So,first step is to write $(fog)(-4)) =f[g(-4)] \\$

Now we start from inner paranthesis ,we need to first find value of $g(-4) =\frac{\sqrt{12-(-4)}}{3}\\ =\frac{\sqrt{12+4}}{3}\\
=\frac{\sqrt{16}}{3}\\
=\frac{4}{3}\\
(fog)(-4)) =f[g(-4)] =f(\frac{4}{3}) =9(4/3)^{2} =9*(16/9) =144/9 =16$