Answer :
To solve this question, let's analyze the given expression:
[tex]\[
\frac{180x}{x+4} + 250
\][/tex]
Here, [tex]\(x\)[/tex] represents the number of senior citizens who travel by the company's cabs. We need to identify what the constant term [tex]\(250\)[/tex] represents.
Step-by-Step Explanation:
1. Understand the Expression:
The expression [tex]\(\frac{180x}{x+4} + 250\)[/tex] models the average amount a cab driver collects. The term [tex]\(\frac{180x}{x+4}\)[/tex] depends on the number of senior citizens traveling. The value of this term changes with different values of [tex]\(x\)[/tex].
2. Role of the Constant Term:
The constant term in the expression is [tex]\(250\)[/tex], and it doesn't depend on [tex]\(x\)[/tex]. It remains unchanged regardless of how many senior citizens ([tex]\(x\)[/tex]) are traveling.
3. Interpreting the Constant Term (250):
- When no senior citizens travel, set [tex]\(x = 0\)[/tex]. Substitute [tex]\(x = 0\)[/tex] into the expression:
[tex]\[
\frac{180 \times 0}{0 + 4} + 250 = \frac{0}{4} + 250 = 0 + 250 = 250
\][/tex]
- This shows that when no senior citizens are involved, the average amount the cab driver collects is [tex]\(250\)[/tex].
4. Conclusion:
- The constant term [tex]\(250\)[/tex] specifically represents the average amount a cab driver collects on a day when no senior citizens travel by the company's cabs.
Therefore, the correct answer is C: 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]\[
\frac{180x}{x+4} + 250
\][/tex]
Here, [tex]\(x\)[/tex] represents the number of senior citizens who travel by the company's cabs. We need to identify what the constant term [tex]\(250\)[/tex] represents.
Step-by-Step Explanation:
1. Understand the Expression:
The expression [tex]\(\frac{180x}{x+4} + 250\)[/tex] models the average amount a cab driver collects. The term [tex]\(\frac{180x}{x+4}\)[/tex] depends on the number of senior citizens traveling. The value of this term changes with different values of [tex]\(x\)[/tex].
2. Role of the Constant Term:
The constant term in the expression is [tex]\(250\)[/tex], and it doesn't depend on [tex]\(x\)[/tex]. It remains unchanged regardless of how many senior citizens ([tex]\(x\)[/tex]) are traveling.
3. Interpreting the Constant Term (250):
- When no senior citizens travel, set [tex]\(x = 0\)[/tex]. Substitute [tex]\(x = 0\)[/tex] into the expression:
[tex]\[
\frac{180 \times 0}{0 + 4} + 250 = \frac{0}{4} + 250 = 0 + 250 = 250
\][/tex]
- This shows that when no senior citizens are involved, the average amount the cab driver collects is [tex]\(250\)[/tex].
4. Conclusion:
- The constant term [tex]\(250\)[/tex] specifically represents the average amount a cab driver collects on a day when no senior citizens travel by the company's cabs.
Therefore, the correct answer is C: 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.
