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3 years ago

Which of the following describes the function x3 − 8? (10 points)

Mathematics

1 answer:

ivolga24 [154]3 years ago

7 0

Answer:

a. The degree of the function is odd, so the ends of the graph continue in opposite directions. Because the leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.

Step-by-step explanation:

The given cubic polynomial function is

$f(x) = {x}^{3} - 8$

The degree of this function is odd because 3 is an odd number.

Therefore the ends of the graph, continue in opposite direction.

As x-values gets bigger and bigger negatively, the graph continues down on the Left.

As x-values gets bigger and bigger positively, the graph continues up on the right.

Therefore the correct option is A.

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Help pls im being timed

Nitella [24]

The trigonometric ratios show that the angle FHE is 48.59°.

<h3>RIGHT TRIANGLE</h3>

A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: $(hypothenuse)^2=(leg_1)^2+(leg_2)^2$ . And the main trigonometric ratios are:

$sin(\alpha) =\frac{opposite \;leg }{hypotenuse} \\ \\ cos(\alpha) =\frac{adjacent\;leg }{hypotenuse} \\ \\ tan(\alpha) =\frac{sin(\alpha )}{cos(\alpha )}= \frac{opposite \;leg }{adjacent\;leg } \\ \\$

It is important to remember that the sum of internal angles for any triangle is 180°.

From the question, it is possible to see 2 right triangles (HGF and FHE).

You can find the hypotenuse of the triangle HGF from the trigonometric ratio: sen Θ

$sin45=\frac{opposite\; leg }{hypotenuse} =\frac{\sqrt8}{hypotenuse}\\ \\ \frac{\sqrt{2} }{2} =\frac{\sqrt{8} }{hypotenuse} \\ \\ \sqrt{2}*hypotenuse=2\sqrt{8} \\ \\ hypotenuse=\frac{2\sqrt{8} }{\sqrt{2}} =2\sqrt{4} =2*2=4$

The hypotenuse of triangle HGF is one of legs for the triangle FHE. The, you can find the angle FHE from the trigonometric ratio: tan β. Thus,

$sin \beta =\frac{opposite\; leg }{adjacent\; leg} =\frac{3}{4}\\ \\ sin \beta=\frac{3}{4}=0.84806\\ \\ arcsin\beta =48.59^{\circ \:}$

Learn more about trigonometric ratios here:

brainly.com/question/11967894

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</span><span>2m^2 - 2m - 60 can be reduced to 2(m^2 - m - 30), which in turn can be factored as 2(m+5)(m-6). The trick here is to notice how easily "2" can be factored out of the given equation.
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