Answer :
To understand what the constant term in the given expression represents, let's break down the expression:
[tex]\[
\frac{150}{x+4} + 250
\][/tex]
Here, [tex]\( x \)[/tex] represents the number of senior citizens who travel by the company's cabs.
1. Identifying the Constant Term:
- In the expression, [tex]\( 250 \)[/tex] is the constant term. It does not change with different values of [tex]\( x \)[/tex], meaning it remains the same regardless of how many senior citizens are traveling.
2. Analyzing the Role of the Constant Term:
- To understand what this constant represents, we consider a scenario where no senior citizens travel by the cabs. This means [tex]\( x = 0 \)[/tex].
3. Evaluating the Expression for [tex]\( x = 0 \)[/tex]:
- Substitute [tex]\( x = 0 \)[/tex] into the expression:
[tex]\[
\frac{150}{0+4} + 250 = \frac{150}{4} + 250
\][/tex]
- The calculation of [tex]\(\frac{150}{4}\)[/tex] is a specific value, but crucially, the expression still includes the number [tex]\( 250 \)[/tex].
4. Understanding the Context:
- If no senior citizens are traveling ([tex]\( x = 0 \)[/tex]), the expression [tex]\(\frac{150}{4}\)[/tex] will give an additional part that reflects other factors affecting daily earnings, but the [tex]\( 250 \)[/tex] remains unchanged in the total.
- This indicates that the [tex]\( 250 \)[/tex] must be a baseline amount collected every day regardless of how many senior citizens are traveling.
5. Conclusion:
- Therefore, the constant [tex]\( 250 \)[/tex] represents the average amount a cab driver collects on a particular day when no senior citizens travel by the company's cabs, which aligns with option A.
Thus, the correct interpretation of the constant term is:
A. The constant 250 represents the average amount a cab driver collects on a particular day when no senior citizens travel by the company's cabs.
[tex]\[
\frac{150}{x+4} + 250
\][/tex]
Here, [tex]\( x \)[/tex] represents the number of senior citizens who travel by the company's cabs.
1. Identifying the Constant Term:
- In the expression, [tex]\( 250 \)[/tex] is the constant term. It does not change with different values of [tex]\( x \)[/tex], meaning it remains the same regardless of how many senior citizens are traveling.
2. Analyzing the Role of the Constant Term:
- To understand what this constant represents, we consider a scenario where no senior citizens travel by the cabs. This means [tex]\( x = 0 \)[/tex].
3. Evaluating the Expression for [tex]\( x = 0 \)[/tex]:
- Substitute [tex]\( x = 0 \)[/tex] into the expression:
[tex]\[
\frac{150}{0+4} + 250 = \frac{150}{4} + 250
\][/tex]
- The calculation of [tex]\(\frac{150}{4}\)[/tex] is a specific value, but crucially, the expression still includes the number [tex]\( 250 \)[/tex].
4. Understanding the Context:
- If no senior citizens are traveling ([tex]\( x = 0 \)[/tex]), the expression [tex]\(\frac{150}{4}\)[/tex] will give an additional part that reflects other factors affecting daily earnings, but the [tex]\( 250 \)[/tex] remains unchanged in the total.
- This indicates that the [tex]\( 250 \)[/tex] must be a baseline amount collected every day regardless of how many senior citizens are traveling.
5. Conclusion:
- Therefore, the constant [tex]\( 250 \)[/tex] represents the average amount a cab driver collects on a particular day when no senior citizens travel by the company's cabs, which aligns with option A.
Thus, the correct interpretation of the constant term is:
A. The constant 250 represents the average amount a cab driver collects on a particular day when no senior citizens travel by the company's cabs.
