I'd like to know if I am right...
A rectangular box is twice as long as it is wide. The height of the box is 3 feet less than the width. If the box is x feet wide, what polynomial represents its volume in cubic feet?
A. 4x - 3
B. 2x^3 + 6x^2
C. 2x^2 - 6x
D. 2x^3 - 6x^2
Am I right?
OOOPSS!SorrY, I picked letter D...Am I right???
you are right.
To find the polynomial that represents the volume of the rectangular box, we need to recall the formula for the volume of a rectangular prism, which is given by length times width times height.
Let's break down the information given in the problem:
- The length of the box is twice as long as it is wide, so the length is 2 times the width.
- The height of the box is 3 feet less than the width, so the height is the width minus 3.
Now we can write the expression for the volume of the rectangular box:
Volume = length * width * height
Given that the width of the box is x, we can substitute the expressions for length and height into the volume formula:
Volume = (2x) * x * (x - 3)
To simplify the expression, we multiply the terms together:
Volume = 2x * x * (x - 3)
Volume = 2x^2 * (x - 3)
Volume = 2x^3 - 6x^2
Therefore, the polynomial that represents the volume of the rectangular box is 2x^3 - 6x^2.
So, your answer D. 2x^3 - 6x^2 is correct.