Suppose a car dealer receives a profit of $500 for each mid-sized car m sold and $750 for each sport-utility vehicle s sold. the dealer must sell at least two mid-sized cars for each sport-utility vehicle and must earn at least $3500 per week. 13suppose a car dealer sells 2 sport-utility vehicles. how many mid-sized cars must be sold to earn at least $3500?

Step-by-step explanation:

            500m = profit on mid-sized cars

             750s = profit on SUVs

500m + 750s = total profit  

You have two conditions:

(1) 500m + 750s ≥ 3500

(2)                   m ≥ 2s

Let s = 2

Check condition (1)

500m + 750 × 2 ≥ 3500

   500m + 1500 ≥ 3500

               500m ≥ 2000

                      m ≥ 4

Check condition (2)

(2) m ≥ 2 × 2

      m ≥ 4

Check:

500 × 4 + 750 × 2 ≥ 3500          4 ≥ 2 × 2

       2000 + 1500 ≥ 3500          4 ≥ 4

                   3500 ≥ 3500

OK.

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!

answer: the two figures are congruent.

step-by-step explanation: they're congruent because figure efgh is reflected across the x and y axis but it was also rotated.

hope it !