85.6k views
3 votes
The length in meters of a cardboard box is represented by the expression 5x - 12. The width in meters of the cardboard box is represented by the expression 3x + 7. The height of the cardboard box is 3x meters. What simplified expression represents the capacity that the cardboard box could hold?

User Mbritto
by
7.8k points

1 Answer

6 votes

Final answer:

The simplified expression for the volume of a cardboard box with the given dimensions (5x - 12) for length, (3x + 7) for width, and (3x) for height is 45x^3 - 3x^2 - 252x cubic meters.

Step-by-step explanation:

The student is asking for the simplified expression that represents the volume or capacity of a cardboard box. Given that the length, width, and height of the box are represented by the expressions 5x - 12, 3x + 7, and 3x respectively, the volume can be found by multiplying these expressions together.

The calculation would be as follows:

  • Volume = Length × Width × Height
  • Volume = (5x - 12) × (3x + 7) × 3x

To find the simplified expression, we need to perform the multiplication:

  1. Multiply the expressions for length and width: (5x - 12)(3x + 7).
  2. This gives us a quadratic expression: 15x2 + 35x - 36x - 84.
  3. Simplify the quadratic expression: 15x2 - x - 84.
  4. Multiply the result by the height: (15x2 - x - 84) × 3x.
  5. This yields the simplified expression for volume: 45x3 - 3x2 - 252x.

Therefore, the capacity of the cardboard box, in cubic meters, is represented by the simplified expression 45x3 - 3x2 - 252x.

User Ben Lin
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories