The area of a tiled kitchen floor is represented by the expression 4x2 + 24x + 27, where x represents the length of a single tile. the length, l, of the floor is 9 feet more than twice the length of a tile, x. which expression represents the width of the kitchen in terms of x?

Let
x> represents the length of a single tile
L> the length of the floor
W> the width of the floor
A> area of a tiled kitchen floor

we know that
A=W*L
A=4x² + 24x + 27
so
W*L=4x² + 24x + 27> equation 1
L=2x+9> equation 2

substitute equation 2 in equation 1
W*[2x+9]=4x² + 24x + 27
W=[4x² + 24x + 27]/[2x+9]

therefore

the answer is
the expression that represents the width of the kitchen in terms of x is
W=[4x² + 24x + 27]/[2x+9]

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.