Factor the numerator and denominator and then reduce the fraction:

Mathematics

1 answer:

Kazeer [188]3 years ago

5 0

$\boxed{\frac{2xy-3y}{x}}$

<h2>Explanation:</h2>

Here we have the following expression:

$\frac{16xyz-24zy}{8xz} \\ \\ \\ Prime \ factorization: \\ \\ 16=2^4 \\ \\ 24=2^3\cdot 3 \\ \\ 8=2^3$

So we can rewrite this as follows:

$\frac{2^4xyz-2^3\cdot 3zy}{2^3xz} \\ \\ \\ Common \ factor \ 2^3z \ in \ the \ numerator: \frac{2^3z(2xy-3y)}{2^3xz} \\ \\ \\ Commutative \ property \ in \ the \ denominator: \\ \\ \frac{2^3z(2xy-3y)}{2^3zx} \\ \\ \\ Simplyfing: \\ \\ \boxed{\frac{2xy-3y}{x}}$

<h2>Learn more:</h2>

Simplify: brainly.com/question/10644722

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Schach [20]

9. You need an exact answer. So I will give you it but I'll also give you an approximation because it might help you understand it more.

Because we know the cosine fo theta, we can evaluate the inverse cosine of -2/3 first to find theta.

$sin^{-1}(-2/3)$ = 131.81° approx.

Because 131.81° is in the second quadrant its third quadrant partner is 228.19°. Which would make the sine 0.75 approximately.

But we need an exact answer I suppose so which is this disgusting mess... $sin(2\pi -cos^{-1}(\frac{-2}{3}))$ . I know it looks scary but it is basically all the steps we just did but without evaluating anything.