Question

MODELING WITH MATHEMATICS A farmer plants a garden that contains corn and pumpkins. The total area (in square

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: $x^2+8x+2$