Question

Geometry. Show work and explain.

23. A rectangular pyramid has a base area of
x^2 + 3x - 10 over 2x square centimeters and a height of
x^2 - 3x over x^2 - 5x + 6 centimeters. Write a rational expression to describe the volume of the rectangular pyramid.

Answer 1

\[A=\frac{1}{2}bh\]
\[x^2-4=\frac{1}{2}(2x+4)h\]
\[x^2-4=(x+2)h\] and since
\[x^2-4=(x+2)(x-2)=(x+2)h\] you know \(h=x-2\)

Answer 2

The volume of a pyramid is 1/3 Bh were B is the area of the base.

Answer 3

\[V=\frac{1}{3}\times \frac{x^2+3x-10}{2x} \times \frac{x^2-3x}{x^2-5x+6}\]

Answer 4

I'm assuming that you would factor and simplify that.

Answer 5

I factored, what would I do with the 1/3

Answer 6

Just make 3 a factor of the denominator.

Answer 7

for my answer could I keep the 1 at top and 3 on bottom

Answer 8

\[\frac{(x+5)(x-2)}{3(2x)} \times\frac{x(x-3)}{(x-3)(x-2)}=\frac{x+5}{6}\]

Answer 9

You got a medal thanks! :DDDDDD @Mertsj

Answer 10

yw