Answer:
[tex](3x+5)+\frac{28}{2x-4}[/tex]
Step-by-step explanation:
Since,
The volume of a rectangular prism = Base area × Height,
Given,
Volume of the rectangular prism = [tex]6x^2-2x+8[/tex]
Base area = 2x - 4
Let h be the height,
[tex]\implies 6x^2-2x+8=(2x-4)h[/tex]
[tex]\implies h = \frac{6x^2-2x+8}{2x-4}[/tex]
By long division ( shown below ),
[tex]h=(3x+5)+\frac{28}{2x-4}[/tex]
Which is the required expression that represents the height.
Answer:
[tex](3x+5) + \frac{14}{x-2}[/tex]
Step-by-step explanation:
We are given the following information in the question:
Volume of rectangular prism =
[tex]6x^2 - 2x + 8[/tex]
Area of base of prism =
[tex]2x -4[/tex]
Formula:
[tex]\text{Volume of Prism} = \text{Area of base}\times \text{Height of prism}\\\\\text{Height of prism} = \displaystyle\frac{\text{Volume of Prism} }{\text{Area of base}}[/tex]
Putting the values we, get,
[tex]\text{Height of prism} = \displaystyle\frac{6x^2 - 2x +8}{2x-4} = \frac{2(3x^2-x+4)}{2(x-2)}= (3x+5) + \frac{14}{x-2}[/tex]
Hence, the height of the prism is given by the expression [tex](3x+5) + \frac{14}{x-2}[/tex]
