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.

an altitude of 15,000 feet

step-by-step explanation:

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18