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3 years ago

B 15 C А. Find the length of "a"using the Pythagorean Theorem.

Mathematics

1 answer:

Sav [38]3 years ago

7 0

Answer:

a = 12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

a is a leg
b is another leg
c is the hypotenuse

Step-by-step explanation:

Step 1: Identify

We are given a right triangle. We can use PT to solve for the missing length a.

Step 2: Define

hypotenuse c = 15

leg b = 9

leg a = ?

Step 3: Find missing length a

Substitute in variables: a² + 9² = 15²
Isolate a term: a² = 15² - 9²
Exponents: a² = 225 - 81
Subtract: a² = 144
Isolate a: a = ±12

Since we are not dealing with a quadrant triangle, we can disregard the negative root of the quadratic.

∴ a = 12 is our final answer.

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Given that $f(x) = \sqrt{7-x}$ and $g(x) = \sqrt{x + 2}$ , we can say the following:

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Thus, let's set what is under both square roots to be greater than 0:

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Since both of the square roots are in the same function, we want to take the union of the domains of the individual square roots to find the domain of the overall function.

$x \leq 7 \,\,\cup x \geq -2 = \boxed{-2 \leq x \leq 7}$

Now, let's look back at the function entirely, which is:

$\Bigg( \dfrac{f}{g} \Bigg)(x) = \dfrac{\sqrt{7 - x}}{\sqrt{x+2}}$

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Thus, our answer is Choice C, or $\boxed{ \{ x | -2 < x \leq 7 \}}$ .

If you are wondering why the choices begin with the $x |$ symbol, it is because this is a way of representing that $x$ lies within a particular set.

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