explain 3 modeling with polynomials
read the section below and complete the following activity.
you can model many situations using polynomials. sometimes you can model a new situation by adding two or more polynomials.
examples solve by adding the polynomials. the models needed in each situation are provided.
a. a box - company owns two factories in different parts of the country. the profit for each factory is modeled by a polynomial with x representing the number of boxes each produces. the first factory makes - 0.03x² + 20x - 500, and the second makes - 0.04x² + 25x - 1000. what is the polynomial that represents the box companys total profit if both its factories make the same number of boxes?
(-0.03x² + 20x - 500)+(-0.04x² + 25x - 1000) use a plus (+) sign to add the polynomials.
-0.03x² + 20x - 500+-0.04x² + 25x - 1000 remove the parenthesis.
(-0.03x² - 0.04x²)+(20x + 25x)+(-500 - 1000) group like terms together.
-0.07x² + 45x - 1500 combine like terms. write in standard form.
the total profit from the two factories is modeled by the polynomial - 0.07x² + 45x - 1500
b. find the polynomial for the sum of the areas of the rectangles to the right.
(4x + 4)+(5x + 5)+x²+10 use a plus (+) sign to add the polynomials.
4x + 4+5x + 5+x²+10 remove the parenthesis.
(4x + 5x)+(4 + 5 + 10)+x² group like terms together.
x²+9x + 19 combine like terms. write in standard form.
the sum of the areas of the rectangles is modeled by the polynomial x² + 9x + 19
solve by adding the polynomials. the models needed for the situation are provided.
1. a farmer must add the areas of two plots of land to determine the amount of seed to plant. the area of plot a can be represented by 3x² + 7x - 5, and the area of plot b can be represented by 5x² - 4x + 11. write a polynomial that represents the total area of both plots of land.

Question

explain 3 modeling with polynomials
read the section below and complete the following activity.
you can model many situations using polynomials. sometimes you can model a new situation by adding two or more polynomials.
examples solve by adding the polynomials. the models needed in each situation are provided.
a. a box - company owns two factories in different parts of the country. the profit for each factory is modeled by a polynomial with x representing the number of boxes each produces. the first factory makes - 0.03x² + 20x - 500, and the second makes - 0.04x² + 25x - 1000. what is the polynomial that represents the box companys total profit if both its factories make the same number of boxes?
(-0.03x² + 20x - 500)+(-0.04x² + 25x - 1000) use a plus (+) sign to add the polynomials.
-0.03x² + 20x - 500+-0.04x² + 25x - 1000 remove the parenthesis.
(-0.03x² - 0.04x²)+(20x + 25x)+(-500 - 1000) group like terms together.
-0.07x² + 45x - 1500 combine like terms. write in standard form.
the total profit from the two factories is modeled by the polynomial - 0.07x² + 45x - 1500
b. find the polynomial for the sum of the areas of the rectangles to the right.
(4x + 4)+(5x + 5)+x²+10 use a plus (+) sign to add the polynomials.
4x + 4+5x + 5+x²+10 remove the parenthesis.
(4x + 5x)+(4 + 5 + 10)+x² group like terms together.
 x²+9x + 19 combine like terms. write in standard form.
the sum of the areas of the rectangles is modeled by the polynomial x² + 9x + 19
solve by adding the polynomials. the models needed for the situation are provided.
1. a farmer must add the areas of two plots of land to determine the amount of seed to plant. the area of plot a can be represented by 3x² + 7x - 5, and the area of plot b can be represented by 5x² - 4x + 11. write a polynomial that represents the total area of both plots of land.

Accepted Answer

# Explanation:
## Step1: Write the sum of polynomials
$(3x^{2}+7x - 5)+(5x^{2}-4x + 11)$
## Step2: Remove the parentheses
$3x^{2}+7x - 5+5x^{2}-4x + 11$
## Step3: Group like terms together
$(3x^{2}+5x^{2})+(7x-4x)+(-5 + 11)$
## Step4: Combine like terms and write in standard form
$8x^{2}+3x + 6$
# Answer:
$8x^{2}+3x + 6$

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QUESTION IMAGE

Question

Explanation:

Step1: Write the sum of polynomials

Step2: Remove the parentheses

Step3: Group like terms together

Step4: Combine like terms and write in standard form

Answer: