Given the expression for the total number of pizzas sold in an hour:
[tex]\[ \frac{41z}{5x + 2} + 12 \][/tex]
Let's analyze what each part of the expression represents.
- Fractional part [tex]\(\frac{41z}{5x + 2}\)[/tex]: This part represents the variable number of pizzas sold based on the number of discount coupons [tex]\(x\)[/tex] offered and another variable factor represented by [tex]\(z\)[/tex].
- Constant term [tex]\(12\)[/tex]: This is the term we need to interpret.
The constant term in an expression typically provides a fixed value that does not change with the variables. It's helpful to consider what happens when [tex]\(x = 0\)[/tex] to understand the role of the constant term.
When [tex]\(x = 0\)[/tex], the expression simplifies to:
[tex]\[ \frac{41z}{5(0) + 2} + 12 \][/tex]
[tex]\[ \frac{41z}{2} + 12 \][/tex]
Notice that the term [tex]\(12\)[/tex] still remains even when there are no discount coupons offered.
Therefore, the constant term [tex]\(12\)[/tex] represents the number of pizzas sold in an hour if 0 discount coupons are offered. This term accounts for the baseline number of pizzas sold regardless of any discounts being applied.
So, the correct interpretation is:
The constant term [tex]\(12\)[/tex] represents the number of pizzas sold in an hour if 0 discount coupons are offered.
