40 POINTS

What is the length of side s of the square shown below? ​

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 The correct option is (C)  

Step-by-step explanation:  We are given to find the length of side 's' of the square shown in the figure.

We know that

all the four sides of a square are equal in length and all the four angles are right angles.

So, each of the two equal parts of the square form a right-angled triangle with hypotenuse as the diagonal.

Therefore, using Pythagoras theorem in one of the right-triangles, we get

s² + s² = 8²

⇒ 2s² = 64

⇒ s² = 32

⇒ s = ± √32

⇒ s = ± 4√2.

Since the length of a side of a square cannot be negative, so we get,

s = 4√2 units.

Option (C) is CORRECT.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

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step-by-step explanation:

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