The length of a rectangular prism is 1 more than three times the width w. The volume of the prism is 3 w cubed plus 19 w squared plus 6 w. What is a simplified expression for the height of the prism?

Let w represent width of the rectangle.

We have been given that the length of a rectangular prism is 1 more than three times the width w. So length of the rectangle would be .

We have been given that the volume of the prism is .

We know that volume of rectangular prism is width times length times height.

So we can set an equation as:

Let us factor out w from numerator.

Now we will cancel out from numerator and denominator.

Therefore, the height of the prism is units.

answer: the equation matches the regression

step-by-step explanation: