Randall purchased a plot of land for his business. the figure represents a plan of the land showing the location of the office space, parking lot and open space for a yard so that the employees and visitors can enjoy time outside. the coordinates represent points on a rectangular grid with units in feet. how much bigger is the area of the parking lot in comparison to the area of the yard

2000 sq. ft.

Step-by-step explanation:

The parking lot is rectangle, so the area is base * height.

Looking at lower coordinates, the base is from x=100 to x = 140, so base is 40.

Looking at first coordinate pair where y = 20 and top coordinate pair where y = 100, so height is 80.

Area of parking lot = 40 * 80 = 3200

Now,

The yard is diamond shape. It can be broken down into 2 triangles. Area of triangle is given by 1/2 * base * height.

First triangle (left one):

Height will be from x = 40 to x = 60, so height is 20.

Base would be 40 to 80, so base is 40.

Area = 1/2 * 40 * 20 = 400

Second triangle (right one):

Height will be from x= 60 to x = 100, height is 40.

Base is same as first triangle, which is 40.

Area = 1/2 * 40 * 40 = 800

Area of Yard = 800 + 400 = 1200

Parking lot is bigger by 3200 - 1200 = 2000 square feet

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)