Ralph wants to build a rectangular deck with a predefined area of 66 feet squared. One side of the deck will be 5 feet longer than the other. To find the side lengths, he first writes the equation (x)(x+5)=66 and later simplifies (x-6)(x+11)=0 it to , where x is the length of the shorter side. Which of these are the side lengths, in feet, of the rectangular deck? Select all that apply

Step-by-step explanation:

The options are not given, but we could solve and arrive at an answer

say the shorter side is x

and the longer side is x+5

we know that the area of a rectangle is given as

x*(x+5)=66

open the bracket

x^2+5x=66

x^2+5x-66=0

Find two factors of  -66  whose sum equals the coefficient of the middle term, which is   5 .

the factors are 11 and -6

splitting the middle term using the two factors  11  and  -6

x2 +11x - 6x - 66=0

x(x+11)-6(x+11)=0

(x-6)=0

x=6

(x+11)=0

x=-11

The shorter side is 6 ft and the longer side is 11 ft

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!

where is the figure