3 years ago

PLEASE HELP!! 50 points :) Consider functions f and g. Which expressions is equal to f(x)•g(x)?

1 answer:

6 0

Composite functions and Evaluating functions : f(x), g(x ), fog(x), gof(x) Calculator - 1. f(x)=2x+1, g(x)=x+5, Find fog(x) 2. fog(x)=(x+2)/(3x), f(x)=x-2, Find gof(x) 3.

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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC =16 and DC=5 what is the length of BC in the simplest ra

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The length of BC is $4 \sqrt{5}$ .

Solution:

Given ABC is a right triangle.

AC is the hypotenuse and BD is the altitude.

AB and BC are legs of the triangle ABC.

AC = 16 and DC = 5

Leg rule of geometric mean theorem:

$\frac{\text { hypotenuse }}{\text { leg }}=\frac{\text { leg }}{\text { part }}$

$\Rightarrow \frac{AC}{BC}=\frac{BC}{DC}$

$\Rightarrow \frac{16}{x}=\frac{x}{5}$

Do cross multiplication.

$\Rightarrow 16\times 5 = x\times x$

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$\Rightarrow 16\times 5= x^2$

Taking square root on both sides.

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$\Rightarrow \sqrt{4^2\times 5} = \sqrt{x^2}$

square and square roots get canceled, we get

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The length of BC is $4 \sqrt{5}$ .

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