The edges of three squares are joined together to form a right triangle with legs of lengths r and s and a hypotenuse of length t. What must be true?

The area of square T is equal to the sum of the areas of square R and square S.

Explanation:

Recall that the pythagorean theorem says

a^2+b^2 = c^2

Visually this means if we had a square with side length 'a', then its area is a^2. The same goes for a square with side length b. Its area is b^2

So a^2+b^2 is the sum of those square areas. It being equal to c^2 tells us that adding the smaller square areas lead to the largest square area.

So that's why the areas of squares R and S add up to the area of square T.

An example:

Let's say...

note how 3^2+4^2 = 9+16 = 25 and how 5^2 = 25. This shows 3^2+4^2 = 5^2

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

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step-by-step explanation: