Answer :
To understand what the constant term in the expression represents, let's break down the problem:
The expression given 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. The expression models the average amount a cab driver collects on a particular day.
Now, let's focus on the constant term, [tex]\(250\)[/tex], in this expression:
1. The constant [tex]\(250\)[/tex] is added to the term [tex]\(\frac{180x}{x+4}\)[/tex]. This addition is independent of the number of senior citizens [tex]\(x\)[/tex].
2. To understand its meaning, consider the scenario where no senior citizens travel. In this case, set [tex]\(x = 0\)[/tex]:
[tex]\[
\frac{180 \times 0}{0 + 4} = 0
\][/tex]
3. Thus, when no senior citizens travel, the expression simplifies to just [tex]\(250\)[/tex].
This tells us that the constant [tex]\(250\)[/tex] represents the amount the cab driver collects on a day when there are no senior citizens traveling. Therefore, 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 given 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. The expression models the average amount a cab driver collects on a particular day.
Now, let's focus on the constant term, [tex]\(250\)[/tex], in this expression:
1. The constant [tex]\(250\)[/tex] is added to the term [tex]\(\frac{180x}{x+4}\)[/tex]. This addition is independent of the number of senior citizens [tex]\(x\)[/tex].
2. To understand its meaning, consider the scenario where no senior citizens travel. In this case, set [tex]\(x = 0\)[/tex]:
[tex]\[
\frac{180 \times 0}{0 + 4} = 0
\][/tex]
3. Thus, when no senior citizens travel, the expression simplifies to just [tex]\(250\)[/tex].
This tells us that the constant [tex]\(250\)[/tex] represents the amount the cab driver collects on a day when there are no senior citizens traveling. Therefore, 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.
