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 monomial expression 2w represents the height of the fish tank.
B.
The binomial expression 2w + 6 represents the length of the fish tank.
C.
The trinomial expression 4w3 - 10w2 + 6w represents the volume of the fish tank.
D.
The binomial expression 4w3 + 10w2 represents the volume of the fish tank.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given to us

height, h, is one inch less than twice the width,

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

Let the width of the fish tank be w.

From the given statement, "height, h, is one inch less than twice the width, ".We can write the height of the fish tank as,

h = 2w - 1

Now, the length, l, of the fish tank is seven inches longer than the height. therefore, the length of the fish tank can be written as,

l = 7 + h

we know the value of h, substitute the value of h,

l = 7 + (2w - 1)

l = 7 + 2w - 1

l = 2w + 6

The volume of the first tank can be found by multiplying, length, width, and height together,

[tex]Volume = l \times b \times h[/tex]

[tex]V = w \times (2w -1) \times (2w+6)\\\\V = 4w^4 + 12w^3 -2w^3 -6w^2\\\\V = 4w^4 + 10w^3 -6w^2[/tex]

Hence, the only statement that is true is the binomial expression 2w + 6 represents the length of the fish tank.

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