Use your knowledge of polynomials to help the company design the box for one of its products. I selected the football: It is twice as long as it is wide, so its box will have a rectangular base. SportsBounceCo makes volleyballs with three different diameters: 8 inches, 10 inches, and 12 inches. You will use what you know about polynomials to find out how much material you will need to make the boxes.
2. Here is some more information about making the boxes:
SportsBounceCo uses flat sheets of cardboard to make boxes.
The company uses square sheets for volleyball boxes and rectangular sheets for football boxes.
The boxes have no top, so that customers can see and touch the product.
The height of the box is always 1 inch greater than the width of the ball.
To assemble the box, corners are cut out of each sheet and the edges are taped together.
Use x for the width and x + 1 for the height.
3. Now use your drawing to write an equation for the area of the entire sheet of cardboard. First write the equation as the product of two binomials, and then as a simplified trinomial.
4. Next write an equation for the surface area of the box (after the sheet has been folded).
6. SportsBounceCo makes only boxes that have sides that are measured in whole inches, like the boxes you have been describing so far. Is it possible for them to produce a box that has a surface area that is not a whole number? How do you know?

(a) The area of the sheet is (9x² - 12x + 4).

(b) The total surface area of the box is x (5x - 4) inches².

Step-by-step explanation:

It is provided that the width and the length of the box are x inches and the height of the box is (x - 1) inches

Then the width of the sheet is:

Width of sheet = (x - 1) + x + (x - 1)

                         = x - 1 + x + x - 1

                         = 3x - 2

(1)

The area of the sheet is:

Area of sheet = (3x - 2)² =

                       = (3x)² - 2 · 3x · 2 + (2)²

                       = 9x² - 12x + 4

Thus, the area of the sheet is (9x² - 12x + 4).

(2)

The central area, i.e. the base of the box = x²

Each arm folded up = x by (x - 1)

Then the areas of the 4 arms = 4 · x · (x - 1) = 4x² - 4x

Then the total surface area is:

Total Surface Area = Central Area + Areas of the 4 arms

                                = (x²) + (4x² - 4x )

                                 = 5x² - 4x

                                = x (5x - 4) inches²

Thus, the total surface area of the box is x (5x - 4) inches².

10.416 m/s

step-by-step explantion:

distance=100m

time= 9.6s

average speed=100/9.6

=10.416 m/s

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.