Question

A prism's volume is given by the expression

6k2 – 13k + 5. The area of the base of the
prism is 2k – 1.

Which expression represents the height of the prism?

k + 4
3k – 5
3k – 8 +
4k – 7 –

Answer 1

The volume of any prisma no matter wich one side it have got the following formula:

V=Ab*h where Ab is the base area and h is called height.

From our data we know the volume (6k^2-13K+5) and we know the base area (2k-1). Inserting this data in the general formula we got:

6k^2-13K+5=(2k-1)*h, solving for our unknown variable the height h

h=6k^2-13K+5/2k-1

factoring numerator :

h=(3k-5)(2k-1)/2k-1 simplifying

h=3k-5

The answer is 3k-5

Answer 2

Remark

The Volume = B * h

V = 6k^2 - 13k + 5

B = 2k - 1

h = ??

The volume will factor into (2k - 1)(3k - 5)

You can tell that one of the factors is 2k - 1 because that is the given amount for the base. You need only find the other factor. 3k is needed to multiply 2k to 6k^2.

- 1 needs - 5 to get the answer to 5

So the other factor is 3k - 5

Solution

V/b = h

(6k^2 - 13k + 5)/(2k - 1)

(3k - 5)(2k - 1) / (2k - 1) The (2k - 1)s Cancel out

Answer

B = 3k - 5 Second one down.