Question 5 1 pts
Tina is saving to buy a notebook computer. She has two options. The firskoption is to put $300 away initially and save $20 every month.
The second option is to put $120 away initially and save $50 every month. After how many months would Tina save the same amount
using either option?

 After 6 months

Step-by-step explanation:

We can represent the first option by the equation y = 20x  + 300  where x is the number of months. The second option can also be represent by the equation  y = 50x + 120  .  

Using these equations we can solve for the months the amounts will be the same  using either option .

y = 20x +300

y = 50x + 120     substitute y into one of the equations.

20x +300 = 50x +120  

        -120             -120

20x + 180 = 50x  

-20x               -20x

      180 = 30x

   x= 6  

no, because the sides are not congruent

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!