The area of a square in square feet is
represented by 625z^2 − 150z + 9. find an
expression for the perimeter of the
square. then find the perimeter when
z = 15 ft.

Part 1) The expression for the perimeter is or  

Part 2) The perimeter when  z = 15 ft. is

Step-by-step explanation:

Part 1)

we have

Find the roots of the quadratic equation

Equate the equation to zero

Complete the square

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Factor the leading coefficient  

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

-----> root with multiplicity 2

so

The area is equal to  

The length side of the square is

therefore

The perimeter is equal to

Part 2) Find the perimeter when  z = 15 ft.

we have

substitute the value of z

1) is right

step-by-step explanation:

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.