The function p(x) is obtained by subtracting g(x) from f(x)
The rule of p(x) is p(x) = 5.5 x - 50
Step-by-step explanation:
A drill team is raising money by holding a car wash
- The team earns $6.00 for each car washed
- The team's expenses include $50.00 for advertising plus $0.50 in materials for each car washed
- f(x) represent the team's total earning for washing x cars
- g(x) represent the team's total expenses for washing x cars
- p(x) that gives the team's profit for washing x cars
We need to describe how can you use f(x) and g(x) to obtain a function p(x) that gives the team's profit for washing x cars, and then write a rule for p(x)
∵ The team earns $6.00 for each car washed
∵ f(x) represent the team's total earning for washing x cars
- Equate f(x) by the product of x and 6
∴ f(x) = 6 x
∵ The team's expenses include $50.00 for advertising plus $0.50
in materials for each car washed
∵ g(x) represent the team's total expenses for washing x cars
- Equate g(x) by the sum of 50 and the product of 0.5 and x
∴ g(x) = 50 + 0.5 x
The profit = total earning - total expenses
∵ f(x) is the total earning for washing x cars
∵ g(x) is the total expenses for washing x cars
∵ p(x) represents the team's profit for washing x cars
- Subtract g(x) from f(x) and equate the difference by p(x)
∴ p(x) = f(x) - g(x)
The function p(x) is obtained by subtracting g(x) from f(x)
∵ f(x) = 6 x
∵ g(x) = 50 + 0.5 x
∴ p(x) = 6 x - (50 + 0.5 x)
- Simplify the right hand side
∴ p(x) = 6 x - 50 - 0.5 x
- Add the like term
∴ p(x) = 5.5 x - 50
The rule of p(x) is p(x) = 5.5 x - 50
Learn more:
You can learn more about the linear function in brainly.com/question/12363217
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