Ted is building a square-shaped deck around a tree in his backyard. The empty area which holds the tree is in the shape of a square with a side length of 5 feet, and the deck has a side length that is x ft longer.Which of the following inequalities could be used to solve for x if Ted wants the area of the deck to be at least 96 square feet? A. x2 + 10x + 96 > 0 B. x2 + 10x - 96 < 0 C. x2 + 10x - 96 > 0

A rectangular deck is made up of four wooden beams. The length of the rectangular deck is given by x feet, and the width is 4 feet less than the length, as shown by the diagram below.The total area of the deck, in square feet, is a function of the distance x, in feet.What is the function, A(x), that represents the total area of the deck, in square feet?

Simone is designing a deck to add to a house. Her plans have the rectangular deck graphed with corners at (−3,1) , (3,1) , (3,6) , and (−3,6) . What is the area of the deck?(1 point) Responses 15 sq. ft. 15 sq. ft. 36 sq. ft. 36 sq. ft. 30 sq. ft. 30 sq. ft. 22 sq. ft

Sam decides to build a square garden. If the area of the garden is 9x2 − 24x + 16 square feet, what is the length of one side of the garden? (3x + 4) feet (3x − 4) feet (4x − 3) feet (4x + 3) feet

A school is planning to construct two rectangular play areas in the playground.The length of play area A must be 1 foot longer than four times its width. The width of play area B must be 2 feet longer than the width of play area A, and the length must be 2 feet longer than three times its own width. In addition, the areas of the two play areas must be equal.Write a system of equations to represent this situation, where y is the area of the play areas and x is the width of play area A. Which statement describes the number and viability of the system’s solutions? A. The system has two solutions, but only one is viable because the other results in a negative width. B. The system has only one solution, but it is not viable because it results in a negative width. C. The system has only one solution, and it is viable because it results in a positive width. D. The system has two solutions, and both are viable because they result in positive widths.

The length of a rectangle is 20 units more than its width. The area of the rectangle is x4 - 100.Which statement about the width of the rectangle is true?x2 – 10 because the area expression can be rewritten as (x2 – 10)( x2 + 10) which equals (x2 – 10)((x2 – 10) + 20).x2 + 10 because the area expression can be rewritten as (x2 + 10)( x2 – 10) which equals (x2 + 10)((x2 + 10) – 20).x2 – 30 because the area expression can be rewritten as (x2 + 10)( x2 – 10) which equals (x2 + 10)((x2 – 30) + 20).x2 + 30 because the area expression can be rewritten as (x2 – 10)( x2 + 10) which equals (x2 – 10)((x2 + 30) – 20).