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Masja [62]
1 year ago
10

Show all work to write the expression in simplified rational exponent form:

Mathematics
1 answer:
tatyana61 [14]1 year ago
7 0

Answer:

x^{\frac{1}{2} } + 48

Step-by-step explanation:

This is hard to explain, but basically you use exponent rules to switch it to an exponent

(\sqrt[4]{x^{2} +4} )^{3}

It's easiest if you calculate 4^{3} first

4³ = 4 x 4 x 4 = 48

Then convert the root to a fraction exponent

\sqrt[4]{x^{2}} = x^{\frac{2}{4}} = x^{\frac{1}{2} }

Combine them using addition, since addition was in the problem

x^{\frac{1}{2} } + 48

I hope this helps!

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Answer:

Option A)   Inside the circle

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The radius is equal to the distance from the center to any point on the circle

the formula to calculate the distance between two points is equal to

d\sqrt{(y2-y1)^2+(x2-x1)^2 }

we have

A(-5,-8),M(-1,-3)

substitute the values

r=\sqrt{(-3+8)^{2}+(-1+5)^{2}}

r=\sqrt{(5)^{2}+(4)^{2}}

r=\sqrt{41}\ units

step 2

Find the distance from the center to point V

we know that

If the distance from the center to point V is equal to the radius, then the point V lie on the circle

If the distance from the center to point V is less than the radius, then the point V lie inside the circle

If the distance from the center to point V is greater than the radius, then the point V lie outside the circle

we have

A(-5,-8),V(-11,-6)

substitute in the formula

d=\sqrt{(-6+8)^{2}+(-11+5)^{2}}

d=\sqrt{(2)^{2}+(-6)^{2}}

d=\sqrt{40}\ units

so

\sqrt{40}\ units< \sqrt{41}\ units

The distance from the center to point V is less than the radius

therefore

The point V lie inside the circle

Hope that helped :)

8 0
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