To determine the variable expression that matches the phrase "the speed in miles per hour, 45, times the number of hours," we will break down the phrase and translate it into a mathematical expression step by step.
1. Understand the Phrase:
- "the speed in miles per hour, 45": This tells us that the constant value of the speed is 45 miles per hour.
- "times the number of hours": The word "times" indicates multiplication. The number of hours is variable and often represented by [tex]\( h \)[/tex].
2. Construct the Expression:
- The speed (45 miles/hour) is being multiplied by the number of hours ([tex]\( h \)[/tex]). Therefore, the mathematical representation is:
[tex]\[
45 \times h
\][/tex]
3. Identify the Correct Option:
- Option A: [tex]\( 45h \)[/tex]: This represents 45 times the number of hours, which is exactly what we want.
- Option B: [tex]\( 45 - h \)[/tex]: This represents 45 minus the number of hours, which is not what the phrase is describing.
- Option C: [tex]\( 45 + h \)[/tex]: This represents 45 plus the number of hours, which also does not match the phrase.
- Option D: [tex]\( 45 \div h \)[/tex]: This represents 45 divided by the number of hours, which is again not what we are looking for.
After analyzing the phrase and the options, it is clear that the correct variable expression that matches the phrase is:
[tex]\[
\boxed{A \; 45h}
\][/tex]
