Respuesta :
Answer
option (c) is correct .
To proof
Reason
Formula
Volume of the rectangular prism = Base × Height
The expression is in the Question be
10x ³ + 46 x² - 21x -27
And the area of the base of the prism is given by the expression
2x² + 8x - 9 .
Put in the formula
10x ³ + 46 x² - 21x -27 = 2x² + 8x - 9 × Height
The factor of 10x ³ + 46 x² - 21x -27 are (5x +3 )(2x² + 8x - 9) .
put in the formula
(5x +3 )(2x² + 8x - 9) = (2x² + 8x - 9) × Height
Cancelled 2x² + 8x - 9 on both side.
(5x+3)unit = Height
Hence proved
Answer:
The expression for the height of the prism will be [tex]5x+3[/tex] .
Step-by-step explanation:
Given information
The expression for the volume of the prism
[tex]V =10x^3+46x^2-21x-27[/tex]
The expression for the Area of the base of the prism
[tex]A=2x^2+8x-9[/tex]
As given
Volume = base * height
Height = volume / base
[tex]H= \frac{(10x^3+46x^2-21x-27)}{2x^2-8x-9}[/tex]
[tex]H=\frac{(2x^2-8x-9)(5x+3)}{2x^2-8x-9}[/tex]
on solving above equation
[tex]H= 5x+3[/tex]
Hence the expression for the height of the prism will be 5x+3 .
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https://brainly.com/question/22023329?referrer=searchResults
