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Answer :
To determine the inequality that represents the volume condition for a wooden board shaped like a rectangular prism, we need to consider the dimensions of the board and the constraint on its volume.
1. Understanding Volume of a Rectangular Prism:
- The volume [tex]\( V \)[/tex] of a rectangular prism is calculated using the formula:
[tex]\[
V = \text{length} \times \text{width} \times \text{height}
\][/tex]
2. Given Information:
- We know the volume of the board is less than 224 cubic inches.
3. Determine the Inequality:
- From the choices provided, some suggest a structure where the dimensions of the board form a product like [tex]\( x(x-24)(x-26) \)[/tex].
- In this scenario, let [tex]\( x \)[/tex] be the length of the board, and let's assume the width and height are expressed as [tex]\( (x-24) \)[/tex] and [tex]\( (x-26) \)[/tex].
4. Setting Up the Volume Inequality:
- The equation for volume based on the assumed dimensions becomes:
[tex]\[
V = x(x-24)(x-26)
\][/tex]
- Since we know the volume is less than 224, we set up the inequality:
[tex]\[
x(x-24)(x-26) < 224
\][/tex]
5. Conclusion:
- Therefore, the correct inequality to represent the condition where the volume of the board is less than 224 cubic inches is:
[tex]\[
x(x-24)(x-26) < 224
\][/tex]
So, the solution to the problem is to use the inequality [tex]\( x(x-24)(x-26) < 224 \)[/tex] to find the length of the board such that the volume is less than 224 cubic inches.
1. Understanding Volume of a Rectangular Prism:
- The volume [tex]\( V \)[/tex] of a rectangular prism is calculated using the formula:
[tex]\[
V = \text{length} \times \text{width} \times \text{height}
\][/tex]
2. Given Information:
- We know the volume of the board is less than 224 cubic inches.
3. Determine the Inequality:
- From the choices provided, some suggest a structure where the dimensions of the board form a product like [tex]\( x(x-24)(x-26) \)[/tex].
- In this scenario, let [tex]\( x \)[/tex] be the length of the board, and let's assume the width and height are expressed as [tex]\( (x-24) \)[/tex] and [tex]\( (x-26) \)[/tex].
4. Setting Up the Volume Inequality:
- The equation for volume based on the assumed dimensions becomes:
[tex]\[
V = x(x-24)(x-26)
\][/tex]
- Since we know the volume is less than 224, we set up the inequality:
[tex]\[
x(x-24)(x-26) < 224
\][/tex]
5. Conclusion:
- Therefore, the correct inequality to represent the condition where the volume of the board is less than 224 cubic inches is:
[tex]\[
x(x-24)(x-26) < 224
\][/tex]
So, the solution to the problem is to use the inequality [tex]\( x(x-24)(x-26) < 224 \)[/tex] to find the length of the board such that the volume is less than 224 cubic inches.
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