Answer :
To understand what the constant term in the expression represents, let's analyze the expression:
[tex]\[
\frac{180x}{x+4} + 250
\][/tex]
Here, [tex]\( x \)[/tex] is the number of senior citizens traveling by the company's cabs. We need to determine what the constant term [tex]\( 250 \)[/tex] indicates.
To do this, let's consider the scenario when no senior citizens are traveling, which means [tex]\( x = 0 \)[/tex]:
1. Substitute [tex]\( x = 0 \)[/tex] into the expression:
[tex]\[
\frac{180 \times 0}{0 + 4} + 250 = \frac{0}{4} + 250 = 0 + 250
\][/tex]
This simplifies to 250.
2. When [tex]\( x = 0 \)[/tex], the term [tex]\(\frac{180x}{x+4}\)[/tex] becomes zero because it involves multiplying by zero.
3. Therefore, the expression simplifies entirely to the constant term 250.
This indicates that when no senior citizens are traveling (i.e., [tex]\( x = 0 \)[/tex]), the average amount a cab driver collects is represented by the constant term.
So, the correct interpretation for the constant term, 250, in the context of the expression 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] is the number of senior citizens traveling by the company's cabs. We need to determine what the constant term [tex]\( 250 \)[/tex] indicates.
To do this, let's consider the scenario when no senior citizens are traveling, which means [tex]\( x = 0 \)[/tex]:
1. Substitute [tex]\( x = 0 \)[/tex] into the expression:
[tex]\[
\frac{180 \times 0}{0 + 4} + 250 = \frac{0}{4} + 250 = 0 + 250
\][/tex]
This simplifies to 250.
2. When [tex]\( x = 0 \)[/tex], the term [tex]\(\frac{180x}{x+4}\)[/tex] becomes zero because it involves multiplying by zero.
3. Therefore, the expression simplifies entirely to the constant term 250.
This indicates that when no senior citizens are traveling (i.e., [tex]\( x = 0 \)[/tex]), the average amount a cab driver collects is represented by the constant term.
So, the correct interpretation for the constant term, 250, in the context of the expression 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.
