Question

CONNECTING CONCEPTS The volume of the triangular prism is given by V=2r³-5r² - 19x + 42. Find an

expression for the missing dimension.
1
x + 3
?
2x - 4
Expression for the missing dimension:

Answer 1

The expression for the missing dimension (height) is
`\( x \)`.

To find an expression for the missing dimension in the volume formula
`\( V = 2r^3 - 5r^2 - 19x + 42 \)`, we can compare it to the general formula for the volume of a triangular prism.

The volume
`\( V \)` of a triangular prism is given by the formula:

`\[ V = (1)/(2) * \text{base} * \text{height} * \text{length} \]`

In this case, it seems like the variable
`\( x \)` represents the height of the triangular prism. Therefore, we can set
`\( x \)` equal to the height:

`\[ x = \text{height} \]`

So, the expression for the missing dimension (height) is
`\( x \)`.