I'd love some help with this, and I'll mark brainliest! :))

He will work out for a total of 2,835 min or 47.25 hours

He will not meet his minimum workout time for the18 week period

Step-by-step explanation:

The pattern is tat he adds 15 min each week to his work out regime:  

Wk1: 30min       Wk11:180min

Wk2: 45 min      Wk12: 195in

Wk 3: 60 min      Wk 13:210min

WK4: 75min         Wk 14: 225 min

Wk5 90 min         Wk15: 240min

Wk6: 105 min        Wk16: 255 min

Wk7; 120min         Wk17: 270min

Wk8: 135min         Wk 18: 285min    For a total of 2,835 min and divide by

                                      60 to get the number of hours= 47.25 hours

Wk9: 150min

Wk 10: 165 min

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!

-2 is the right