Answer :
To understand what the constant term in the given expression represents, let's break down the expression step-by-step:
The expression is:
[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're interested in understanding the role of the constant term, which is 250, in this expression.
1. Analyze the Expression:
- The expression [tex]\(\frac{180x}{x+4}\)[/tex] indicates the additional amount collected by the cab driver based on the number of senior citizens [tex]\(x\)[/tex].
- The term 250 is added to this fraction, indicating a fixed amount.
2. Understand the Constant Term:
- A constant in such a context usually represents a fixed value that doesn't change with [tex]\(x\)[/tex].
- Thus, [tex]\(250\)[/tex] is the amount the cab driver collects regardless of the number of senior citizens traveling.
3. Consider the Case When No Senior Citizens Travel:
- If [tex]\(x = 0\)[/tex], the fraction becomes [tex]\(\frac{180 \times 0}{0+4} = 0\)[/tex].
- Therefore, when [tex]\(x=0\)[/tex], the expression simplifies to [tex]\(250 + 0 = 250\)[/tex].
From this, we can conclude that 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.
Thus, the correct interpretation of the constant term 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.
The expression is:
[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're interested in understanding the role of the constant term, which is 250, in this expression.
1. Analyze the Expression:
- The expression [tex]\(\frac{180x}{x+4}\)[/tex] indicates the additional amount collected by the cab driver based on the number of senior citizens [tex]\(x\)[/tex].
- The term 250 is added to this fraction, indicating a fixed amount.
2. Understand the Constant Term:
- A constant in such a context usually represents a fixed value that doesn't change with [tex]\(x\)[/tex].
- Thus, [tex]\(250\)[/tex] is the amount the cab driver collects regardless of the number of senior citizens traveling.
3. Consider the Case When No Senior Citizens Travel:
- If [tex]\(x = 0\)[/tex], the fraction becomes [tex]\(\frac{180 \times 0}{0+4} = 0\)[/tex].
- Therefore, when [tex]\(x=0\)[/tex], the expression simplifies to [tex]\(250 + 0 = 250\)[/tex].
From this, we can conclude that 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.
Thus, the correct interpretation of the constant term 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.
