Question

Dylan has a fish tank at home. He knows its height, h, is one inch less than twice the width, w, and the length, l, of the fish tank is seven inches longer than the height. Which of the following statements is true? A. The trinomial expression 4w3 - 10w2 + 6w represents the volume of the fish tank. B. The binomial expression 2w + 6 represents the length of the fish tank. C. The monomial expression 2w represents the height of the fish tank. D. The binomial expression 4w3 + 10w2 represents the volume of the fish tank.

Answer 1

option (B) is correct.

The binomial expression 2w + 6 represents the length of the fish tank.

Explanation:

Dylan has a fish tank which is in the shape of a cuboid In this way, the volume of the tank is given by this expression:

`V = w* h * l`

Where: h is the height of tank

w is the width of tank and

l is the length of the tank.

Given : height of tank , h, is one inch less than twice the width, w.

Mathematically,
`h=2w-1`

also, The length of the tank l is seven inches longer than the height.

Mathematically,
`7+h \Rightarrow 7+(2w-1)=2w+6`

Thus, volume of tank is
`V = w* h * l`

`V=w(2w-1)(2w+6)`

`V=w(4w^2-2w+12w-6)`

`V=4w^3+10w^2-6w`

Thus, the volume of tank is
`4w^3+10w^2-6w`

Hence, from the given option only option (B) is correct.

The binomial expression 2w + 6 represents the length of the fish tank.