Question

(lesson 17.3) find the difference between the two polynomials to evaluate and solve a real-world problem. (1 point each)

1. a companys cost, in dollars, of manufacturing x tablet computers can be represented by $20x + 200$. the companys predicted revenue of selling x tablet computers is $100 + 30x$. write a polynomial expression that represents the profit of selling x tablets. simplify as much as possible (profit = revenue - cost)
2. if the company sells 100 computers, how much profit will the company make?

(lesson 18.1) find each product. (1 point each)

1. $(5a^{3}b)(2ab)$
2. $5y(-y^{2} + 7y - 2)$

Explanation:

Step1: Define profit formula

$\text{Profit} = \text{Revenue} - \text{Cost}$

Step2: Substitute given polynomials

$\text{Profit} = (20x + 200) - (100 + 30x)$

Step3: Distribute the negative sign

$\text{Profit} = 20x + 200 - 100 - 30x$

Step4: Combine like terms

$\text{Profit} = (20x - 30x) + (200 - 100) = -10x + 100$

Step1: Use profit polynomial from Q11

$\text{Profit} = -10x + 100$

Step2: Substitute $x=100$

$\text{Profit} = -10(100) + 100$

Step3: Calculate the value

$\text{Profit} = -1000 + 100 = -900$

Step1: Multiply coefficients and variables

$(5a^3b)(2ab) = 5 \times 2 \times a^3 \times a \times b \times b$

Step2: Simplify using exponent rules

$10a^{3+1}b^{1+1} = 10a^4b^2$

Step1: Distribute $5y$ to each term

$5y(-y^2) + 5y(7y) + 5y(-2)$

Step2: Simplify each product

$-5y^3 + 35y^2 - 10y$

Answer:

$\boldsymbol{-10x + 100}$

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