Question

Val has a gift box with dimensions, in inches, as algebraic expressions. Select the expression that represents the gift box’s capacity to occupy items inside.

A. (7x small3) inches small 3
B. (4x small 3- 25) inches small 3
C. (12x small 3 - 75x) inches small 3
D. (12x small 3 - 30x small 3 + 75x) inches small 3

Answer 1

To find the expression that represents the capacity of the gift box, we should look for an expression that is a cubic polynomial in terms of volume (since volume is usually calculated in cubic inches).

Each of the options you provided seems to use "small3" to represent cubic inches (or inches cubed). Let's analyze the options:

A. \( (7x \text{ small} 3) \) - This indicates a simple cubic term, suggesting a volume of 7 times some variable \( x \) in cubic inches.

B. \( (4x \text{ small} 3 - 25) \) - This has both a cubic term and a constant, which is unusual for a volume since it would typically be non-negative.

C. \( (12x \text{ small} 3 - 75x) \) - This has a cubic term and a linear term. It could represent a volume, but typically volume expressions do not contain linear terms like \(-75x\) which could suggest negative volume.

D. \( (12x \text{ small} 3 - 30x \text{ small} 3 + 75x) \) - Simplifying this, \( 12x \text{ small} 3 - 30x \text{ small} 3\) would give \(-18x \text{ small} 3 + 75x\), which is again not a standard representation of volume because of the linear term.

Among these options, the simplest and most straightforward expression for cubic volume, without any constant subtractions or negative terms, is:

**A. \( (7x \text{ small} 3) \)**

This expression represents a capacity that can occupy items inside the gift box.