Find the area of the regular 18-gon with radius 11 mm

What is the following product? <br>(4x square root 5x^2 + 2^2 square root 6)^2

tangare [24]

The product is $104 x^{4}+16 \sqrt{30} x^{4}$

Explanation:

The given expression is $\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}$

We need to determine the product of the given expression.

First, we shall simplify the given expression.

Thus, we have,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x \sqrt{5} x+2 x^{2} \sqrt{6}\right)^2$

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)^2$

Expanding the expression, we have,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)\left(4 x^{2} \sqrt{5}+2 x^{2} \sqrt{6}\right)$

Now, we shall apply FOIL, we get,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=\left(4 x^{2} \sqrt{5}\right)^{2}+2 ( 2 x^{2} \sqrt{6})(4 x^{2} \sqrt{5})+\left(2 x^{2} \sqrt{6}\right)^{2}$

Simplifying the terms, we have,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=16 \cdot 5 x^{4}+16 \sqrt{30} x^{4}+4 \cdot 6 x^{4}$

Multiplying, we get,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=80 x^{4}+16 \sqrt{30} x^{4}+24 x^{4}$

Adding the like terms, we get,

$\left(4 x \sqrt{5 x^{2}}+2 x^{2} \sqrt{6}\right)^{2}=104 x^{4}+16 \sqrt{30} x^{4}$

Thus, the product of the given expression is $104 x^{4}+16 \sqrt{30} x^{4}$

7 0

3 years ago

A rectangular sign must have an arae of 43 square yards. its lenght must be 2 yards more than its width. find the dimensions of

inna [77]

We know A=L•W so set 43 equal to A. Equation should look like this thus far: 43=L•W. Now when the question says more than we know that means adding. Since we don’t know the width let w=width. So know your equation should look like this: 43=2+w•(w). Knowing this equation you should be able to solve for the dimensions of the sign. If you need help on that let me know.

8 0

3 years ago

In 2002 there was estimated to be 6Billon people on earth. 20 percent of people lived on less than a 1$ a day. How many people l

kykrilka [37]

Hiya!

So, 6 billion is 100%. 50% is 3 billion. 25% is 1.5 billion. 20% must be 1.2 billion because 1.2 × 5 is 6. I know that 20% is 1/5 of 100%, and that's how I got my answer.

If you found this especially helpful, I'd appreciate if you'd vote me Brainliest for your answer, if other people did not provide a helpful answer (but, I'm sure they did!). I want to be able to assist more users one-on-one! :)

3 0

3 years ago

Please explain in detail how you solved.

Alex17521 [72]

Step-by-step explanation:

Since this is a right triangle and we are given an angle measure that measure 45, the other angle measure also measure 45.

So this means we are dealing with a 45-45-90 triangle.

A 45-45-90 triangle legs are equal to each other and the hypotenuse measures sqr root of 2 times more than the legs.

The hypotenuse measure 2 times sqr root of 14 so divide by sqr root of 2 to find x and y.

$\frac{2 \sqrt{14} }{1} \times \frac{1}{ \sqrt{2 } } = \frac{ \sqrt{56} }{ \sqrt{2} } = \sqrt{28} = 2 \sqrt{7}$

Since x and y are equal, they both measure

$2 \sqrt{7}$

5 0

3 years ago

how many pieces of string that are 2/7 of an inch long can be cut from a piece of string that is 7/8 of an inch long

Katena32 [7]

It is 3.0625 becuase to combine them in any way they have to have the same denominator.

8 0

3 years ago