The cross-sectional areas of a right triangular prism and a right cylinder are congruent. The right triangular prism has a height of 2 units, and the right cylinder has a height of 6 units. Which conclusion can be made from the given information? A.) The volume of the triangular prism is half the volume of the cylinder. B.)The volume of the triangular prism is not equal to the volume of the cylinder.
C.)The volume of the triangular prism is twice the volume of the cylinder.
D.) The volume of the triangular prism is equal to the volume of the cylinder.

B.)The volume of the triangular prism is not equal to the volume of the cylinder.

Step-by-step explanation:

Let A be the cross-sectional area of both congruent right triangular prism and right cylinder.

Since the prism has height 2 units, its volume V₁ = 2A.

Since the cylinder has height 6 units, its volume is V₂ = 6A

Dividing V₁/V₂ = 2A/6A =1/3

V₁ = V₂/3.

The volume of the prism is one-third the volume of the cylinder.

So, since the volume of the prism is neither double nor half of the volume of the cylinder nor is it equal to the volume of the cylinder, B is the correct answer.

So, the volume of the triangular prism is not equal to the volume of the cylinder.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this