In 1999, there were 41,275 shopping centers in a certain country. In 2009, there were 48,199.

A) write an equation expressing the number y of shopping centers in terms of the number x of years after 1999.
B) when will the number of shopping centers reach 80,000?

a)

b) The number of shopping centers will reach 80,000 in 2055.

Step-by-step explanation:

The number of shopping centers in the city may be expressed by the following equation

In which y is the number of shopping centers, x is the number of years, a is the slope(average rate of change) and b is the initial number of shopping centers.

In 1999, there were 41,275 shopping centers in a certain country

This means that

In 2009, there were 48,199.

2009 is 10 years after 1999. So

A) write an equation expressing the number y of shopping centers in terms of the number x of years after 1999.

Applying what we have, we can find a.

So

B) when will the number of shopping centers reach 80,000?

This is x years after 1999, when y(x) = 80,000. So

1999 + 56 = 2055

So the number of shopping centers will reach 80,000 in 2055.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: