100 Points! A box without a top is to be made to hold copious bags of coffee. It is made from a rectangular piece of cardboard, with dimensions 4.5 ft by 3 ft, by cutting out square corners with side length x and folding up the sides.a) Write an equation for the volume V of the box in terms of x.
(b) Use Desmos to graph and estimate the value of x, to the nearest tenth, that gives the greatest volume. Explain your process. Post a snapshot of your graph with your work.
(c) Explain what the x- and y-coordinates represent in your equation.

Let the length of the side of the square being cut out equal x

The length of the box would be 4.5 - 2x

The width of the box would be 3 -2x

Volume = (4.5 -2x) * (3-2x) * x

Simplify to:

V = 4x^3 - 15x^2 + 13.5x

B See picture: The greatest volume would be the point of the highest curve.

x = 0.589 y = 3.565, Rounded to the nearest tenth x = 0.6

Process: entered the equation from A into Desmos. The Y value would be the volume, so found where the volume was the highest and then found the related x value.

C) X is the side length of the corner squares being cut out, which would also be the height of the box. The Y value is the volume of the box.

Let the length of the side of the square being cut out equal x

The length of the box would be 4.5 - 2x

The width of the box would be 3 -2x

Volume = (4.5 -2x) * (3-2x) * x

Simplify to:

V = 4x^3 - 15x^2 + 13.5x

B See picture: The greatest volume would be the point of the highest curve.

x = 0.589 y = 3.565, Rounded to the nearest tenth x = 0.6

Process: entered the equation from A into Desmos. The Y value would be the volume, so found where the volume was the highest and then found the related x value.

C) X is the side length of the corner squares being cut out, which would also be the height of the box. The Y value is the volume of the box.

6, 10

9, -13

12, -21

18, -23

step-by-step explanation:

you just add 6 to the x-coordinate and subtract 10 from the y-coordinate.

5x + 5

step-by-step explanation:

you should always add the diagrams and graphs we cannot see. this particular question is kind of borderline because we can make a graph for you.

(f + g)x = -x^2 +3x + 5 + x^2 + 2x

(f + g)x = 5x + 5

the graph of z = 5x + 5 is shown below. always use desmos when in doubt.