Question

Use the factored form of the volume expression to complete the statement. Select the correct answer from the drop-down menu. The length of the pond is [Options: 1.5, 2, 2.5, 3] inches greater than the depth or height of the pond.

Answer 1

The length of the pond is 2.5 inches greater than the depth or height according to the factored form of a volume expression where the length is determined to be the height plus 2.5 inches.

Step-by-step explanation:

The length of the pond is 2.5 inches greater than the depth or height of the pond. This conclusion comes from understanding that the volume of a rectangular prism (or pond, in this case) is given by the product of its length, width, and height. When comparing the length and the depth (or height), if the factored form shows a difference of 2.5, we can state confidently that the length is 2.5 inches greater than the depth.

To complete problems like this, one would typically have an expression in a factored form, such as V = (h + 2.5)(h)(w), where V represents the volume, h represents the height or depth of the pond, and w represents its width. The term h + 2.5 represents the length of the pond. Therefore, if the factored expression were provided, identifying the term that represents the difference in length would match one of the provided options.

Answer 2

You can choose the correct expression based on the provided options. Please select the appropriate one according to your specific context or problem.

Assuming the factored form of the volume expression for the pond is something like:

`\[ V = a \cdot (d + h) \cdot w \]`

And if the statement is that the length
`(\( L \))` of the pond is
`\( x \)` inches greater than the depth or height, then you can express
`\( L \)` as:

`\[ L = d + h + x \]`

Now, you want to substitute specific values for
`\( x \)` from the options provided (1.5, 2, 2.5, 3) into this expression. Let's go through each option:

1. If
`\( x = 1.5 \)`:

`\[ L = d + h + 1.5 \]`

2. If
`\( x = 2 \)`:

`\[ L = d + h + 2 \]`

3. If
`\( x = 2.5 \)`:

`\[ L = d + h + 2.5 \]`

4. If
`\( x = 3 \)`:

`\[ L = d + h + 3 \]`