The height of a rectangular prism is found by dividing volume, v, by the base area, b. if the volume of the rectangular prism is represented by 6x2 – 2x + 8 and the base area is 2x – 4, which expression represents the height? 3x + 5 – 3x – 7 + 3x + 5 + 3x – 7 –

Step-by-step explanation:

Since,

The volume of a rectangular prism = Base area × Height,

Given,

Volume of the rectangular prism =

Base area = 2x - 4

Let h be the height,

By long division ( shown below ),

Which is the required expression that represents the height.

24 units

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4