Rocky has 7 bottles of water. He will buy more bottles of water from the store. The store has 8 cases in stock and each case contains 24 bottles of water. The store will not sell partial cases. The function that models the number of bottles of water Rocky will have after his purchase is f(c)=24c+7, where c is the number of cases of water he buys. What is the practical domain of the function?

(b) {1, 2, 3, 4, 5, 6, 7, 8}

Explanation:

In this problem, we use the variable c to represent the independent quantity.  This means that the domain is all possible values for c.

Since the store only has 8 cases of water, the domain cannot be any number larger than 8.

Since the store only sells complete cases, not partial cases, of water, the domain cannot be a fraction or decimal number.

This means that the practical domain, or domain that makes sense for the problem situation, is {1, 2, 3, 4, 5, 6, 7, 8}.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)