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nadya68 [22]
2 years ago
7

The volume of a rectangular prism is given by the expression10x3 + 46x2 – 21x – 27. The area of the base of the prism is given b

y the expression 2x2 + 8x – 9. Which of the following expressions represents the height of the prism? (V = Bh)
a. 8x - 3

b. 3x - 5

c. 5x + 3

d. 42x + 3
Mathematics
2 answers:
kondor19780726 [428]2 years ago
8 0
H = V / B
<span>= 10x3 + 46x2 – 21x – 27 /  2x^2 + 8x - 9
</span>= 5x + 3
azamat2 years ago
6 0

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

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