Lisa is going to make a sculpture from a rectangular block of clay the volume of the block is (2x-1)(x-3)(x+4) which statement about the volume of the block is true

Question:

Lisa is going to make a sculpture from a rectangular block of clay. the volume of the block is (2·x – 1)(x – 3)(x + 4). which statement about the volume of the block of clay is true?

a. the volume is the product of the length, 2·x – 1, and the width, x – 3.

b. the volume does not depend on the length, 2·x – 1.

c. the volume is the product of the area of the base, (2·x – 1)(x – 3), and the height, x + 4.

d. the volume is the sum of the length, 2·x – 1, the width, x – 3, and the height, x + 4.

The correct option is;

c. the volume is the product of the area of the base, (2·x – 1)(x – 3), and the height, x + 4.

Step-by-step explanation:

Here we have the formula for the volume of rectangular block is given as;

Volume = Length × Width × Height

And the formula for the area of the base is

Area of Base =  Length × Width

If the length of the rectangular block is

Length = 2·x-1 and

The width = x - 3

Therefore, the area of the base = Length × Width

= (2·x - 1) × (x -3)

From which the volume of the rectangular block can be given as

Area of base × Height

Volume =  (2·x - 1) × (x -3) × (x + 4).

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: