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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?

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 bas class=
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Answer:

[tex]3x+5 + \frac{28}{2x-4}[/tex]

Step-by-step explanation:

If the volume of the rectangular prism is represented by [tex]6x^2 - 2x + 8[/tex] and the base area is [tex]2x - 4[/tex]

Volume of a prism = base area times height

we replace the volume and the base area

[tex]6x^2-2x+8 = (2x-4) \cdot height[/tex]

Divide both sides by 2x-4

[tex]height= \frac{6x^2-2x+8}{2x-4}[/tex]

we use long division.

                                      3x+5                          

                                ----------------------------------------------

  [tex]2x-4[/tex]                 [tex]6x^2 - 2x + 8[/tex]

                                   [tex]6x^2 - 12x[/tex]

                               -----------------------------------------------(subtract)

                                              [tex]10x+8[/tex]  

                                              [tex]10x-20[/tex]  

                               ------------------------------------------------(subtract)

                                                            28

[tex]3x+5 + \frac{28}{2x-4}[/tex]

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