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.

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2