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

The correct answer is:

The volume of the triangular prism is equal to the volume of the cylinder

Step-by-step explanation:

Given that there are two figures

1. A right triangular prism and

2. Right cylinder

Area of cross section of prism is equal to Area of cross section of cylinder.

Let this value be A.

Also given that Height of prism = Height of cylinder = 6

Volume of a prism is given as:

Cross section of cylinder is a circle.

Area of circle is given as:

Area of cross section, A =

Volume of cylinder is given as:

From equations (1) and (2) we can see that

Hence, the correct answer is:

Volume of prism is equal to the volume of cylinder.

14

step-by-step explanation:

14 x 3 = 42

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1