Final answer:
The question is about a mathematics function used to calculate the final cost of an item after applying a discount and sales tax, where x represents the original price in dollars. The function includes both the discount and tax in its calculation.
Step-by-step explanation:
The student is asking about a mathematical function C(x) = 1.06(x - 10) which is used to calculate the final cost of an item after applying a $10 discount in a retail store. This function includes the effect of a sales tax of 6%. To understand how the function works, let us apply it to a real example.
Let us assume an item costs $50. Using the coupon, the price reduces by $10, resulting in a new price of $40. Now, we apply the sales tax by multiplying 1.06 (representing a 6% sales tax) with the new price:
C(x) = 1.06(x - 10) = 1.06(50 - 10) = 1.06(40) = $42.40.
The final cost of the item after applying the coupon and including the sales tax would be $42.40.