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?

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

Answer 1

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

Explanation:

He knows its height, h, is one inch less than twice the width, w, that is,

h = 2w – 1

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

l = h + 7

Substitute h into the second equation:

l = (2w – 1) + 7

Solve the right side

l = 2w – 1 + 7

l = 2w + 6

Calculate the volume of the fish tank:

V = h x l x w =

V = (2w – 1) x (2w + 6) x w

V = (4w^2 + 12w – 2w – 6) x w

V = (4w^2 + 10w – 6) x w

V = 4w^3 + 10w^2 – 6w

The trinomial expression 4w3 - 10w2 + 6w represents the volume of the fish tank.

False: V = 4w^3 + 10w^2 – 6w

The binomial expression 4w3 + 10w2 represents the volume of the fish tank.

False: V = 4w^3 + 10w^2 – 6w

The monomial expression 2w represents the height of the fish tank.

False: h = 2w – 1

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

True: l = 2w + 6

Answer 2

The height is
.. h = 2w -1
The length is
.. l = h +7 = 2w -1 +7 = 2w +6
The volume is
.. h*l*w = (2w -1)*(2w +6)*w = 4w^3 +10w^2 -6w

Only the 4th selection is consistent with the above.