To determine the term that represents the cost of the shoes after the discount, let's carefully examine and break down the given expression: [tex]\( c + (1-0.15) s + 0.09[c + (1-0.15) s] \)[/tex].
Here's the meaning of each part of the expression:
- [tex]\( c \)[/tex]: This term represents the cost of the clothes.
- [tex]\( (1-0.15) s \)[/tex]: This term represents the cost of the shoes after applying the 15% discount.
- [tex]\( 0.09[c + (1-0.15) s] \)[/tex]: This term represents the 9% tax applied to the total cost of clothes and the discounted cost of the shoes.
We need to find the term that solely represents the cost of the shoes after the discount.
Step-by-step, let's evaluate the pertinent term:
1. The shoes originally cost [tex]\( s \)[/tex].
2. The store offers a [tex]\( 15\% \)[/tex] discount on the shoes.
3. To find the discount, we calculate:
[tex]\[
15\% \text{ of } s = 0.15s
\][/tex]
4. To find the price after the discount, we subtract the discount from the original price:
[tex]\[
s - 0.15s = s(1 - 0.15) = 0.85s
\][/tex]
Thus, the term representing the cost of the shoes after the discount is:
[tex]\[ (1-0.15)s \][/tex]
This corresponds to choice C.
Therefore, the correct answer is:
[tex]\[ \boxed{(1-0.15)s} \][/tex]
