Total Profit Equation Simplification

The video tutorial explains how to model a company's profit for two items using equations. The profit for the first item is given by the equation f(x) = 2x^2 + 3x - 1, and for the second item by g(x) = x - 7. The total profit is defined as the sum of these two equations, resulting in t(x) = 2x^2 + 4x - 8 after combining like terms. The tutorial guides through the process of adding the equations and simplifying the result.

What is the profit function for the first item?

• F(x) = 2x^2 + 3x + 1

• F(x) = 2x^2 + x - 1

• F(x) = x^2 + 3x - 1

• F(x) = 2x^2 + 3x - 1

How is the profit for the second item represented?

• G(x) = x - 1

• G(x) = x - 7

• G(x) = 2x - 7

• G(x) = x + 7

What is the expression for the total profit T(x) before simplification?

• T(x) = 2x^2 + 4x - 8

• T(x) = 2x^2 + 3x - 1 + x - 7

• T(x) = 2x^2 + 3x - 1 - 7

• T(x) = 2x^2 + 3x + x - 7

What is the first step in simplifying the total profit equation?

• Multiply the equations

• Combine the constant terms

• Combine the x terms

• Divide the equations

What is the simplified form of the total profit equation T(x)?

• T(x) = 2x^2 + 3x - 7

• T(x) = 2x^2 + 4x - 7

• T(x) = 2x^2 + 3x - 8

• T(x) = 2x^2 + 4x - 8

Which terms are combined to simplify the total profit equation?

• 3x and x, -1 and -7

• 2x^2 and x, -1 and -7

• 3x and x, 2x^2 and -7

• 2x^2 and 3x, -1 and x