Question

MODELING WITH MATHEMATICS A farmer plants a garden that contains corn and pumpkins. The total area (in square
feet) of the garden is modeled by the expression 2x2 + 5x + 4. The area of the corn is modeled by the expression
x2 – 3x + 2. Write an equation in standard form that models the area A of the pumpkins.

Answer 1

Answer:

The equation in standard form that models area of pumpkins is:

$A_p = A_G - A_c$

and the area is: $x^2+8x+2$

Step-by-step explanation:

Given that the garden has corn and pumpkins

The expressions are:

Total area of garden: $A_G = 2x^2+5x+4$

Area of Corn: $A_c = x^2-3x+2$

Area of Pumpkins: $A_p = ?$

The sum of areas of corn and pumpkins is the total area of the garden.

It can be expressed mathematically as:

$A_G = A_c+A_p$

If we have to find the area of pumpkins,

$A_p = A_G - A_c$

Putting the values

$A_p = (2x^2+5x+4) - (x^2-3x+2)\\A_p = 2x^2+5x+4-x^2+3x-2\\A_p = 2x^2-x^2+5x+3x+4-2\\A_p = x^2+8x+2$

The equation in standard form that models area of pumpkins is:

$A_p = A_G - A_c$

and the area is: $x^2+8x+2$

Answer 2

The equation in standard form that models the area A of the pumpkins is x² + 8x + 2

From the question, we are given the following parameters

Area of the garden = 2x² + 5x + 4

Area of the corn = x² – 3x + 2

To get the area A of the pumpkin, we will take the difference in the areas as shown:

A = Area of garden - Area of corn

A = (2x² + 5x + 4) - (x² – 3x + 2)

A = 2x² - x² + 5x + 3x + 4 - 2

A = x² + 8x + 2

Hence the equation in standard form that models the area A of the pumpkins is x² + 8x + 2

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