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3 years ago

Find the side of a square whose diagonal measures 15 square root of 2

Mathematics

2 answers:

solmaris [256]3 years ago

8 0

Answer: 15 units .

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In this case, a square, the two sides of the square (forming a right triangle) are equal), and the "diagonal" forming is the hypotenuse of the right triangle.

In these cases, the measurements of the angles of the right triangle are "45, 45, 90" ; and the measurements of the sides are: "a, a, a√2" ; in which "a√2" is the hypotenuse.

We are given: "15√2" is the hypotenuse" ; and we are given that this is a right triangle of a square with a diagonal length (i.e. "hypotenuse" of "15√2" ; so the measure of the side of the "square" (and other two sides of the triangle formed) is: 15 units. (i.e., 15, 15, 15√2 ).

makvit [3.9K]3 years ago

8 0

23 is the correct answer if 79026484483773737373747474

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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

Write the equation of the conic section with the given properties:

timurjin [86]

Answer:

$\frac{x^2}{64} + \frac{y^2}{25} =1$

Step-by-step explanation:

An ellipse with vertices (-8, 0) and (8, 0)

Distance between two vertices = 2a

Distance between (-8,0) and (8,0) = 16

2a= 16

so a= 8

Vertex is (h+a,k)

we know a=8, so vertex is (h+8,k)

Now compare (h+8,k) with vertex (8,0) and find out h and k

h+8 =8, h=0

k =0

a minor axis of length 10.

Length of minor axis = 2b

2b = 10

so b = 5

General formula for the equation of horizontal ellipse is

$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b} =1$

a= 8 , b=5 , h=0,k=0. equation becomes

$\frac{(x-0)^2}{8^2} + \frac{(y-0)^2}{5} =1$

$\frac{x^2}{64} + \frac{y^2}{25} =1$

5 0

3 years ago

I don’t know how to take a picture on this and send it out for a question

Amanda [17]

Answer:

Where it says "add attachment" with the paper clip, select your picture from there. If you don't know how to do that, take a picture of it with your phone, email it to yourself, and download it on your computer. It should then be in a folder called "downloads" or something similar. Feel free to ask further questions if you're still stuck!

Step-by-step explanation:

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List all 6 whole numbers between -3.5 and 5.5

Alenkinab [10]

Answer012345

Step-by-step explanation:

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