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Rasek [7]
3 years ago
5

Jeffrey has an aquarium in the shape of a rectangular prism. He is going to place a layer of sand over the base for his iguana.

The area of the base of the aquarium can be represented by the expression (42x3−14x2+21x) feet3. If the width of the aquarium is represented by the expression (7x) feet, what is the length of the aquarium?
Mathematics
1 answer:
nikitadnepr [17]3 years ago
8 0

Answer:

Length = 6x^2 - 2x + 3

Step-by-step explanation:

Given

Area = 42x^3 - 14x^2 + 21x

Width = 7x

Required

Determine the length of the aquarium

The area of a rectangular base is calculated as:

Area = Length * Width

Substitute values for Area and Width

42x^3 - 14x^2 + 21x = Length * 7x

Make Length the subject

Length = \frac{42x^3 - 14x^2 + 21x}{7x}

Factorize the numerator

Length = \frac{7x(6x^2 - 2x + 3)}{7x}

Length = 6x^2 - 2x + 3

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