Jacob is ordering custom t-shirts for his soccer team. long-sleeved shirts cost $15 each and short-sleeved shirts cost $10 each. jacob can spend at most $250 and he wants to order at least 20 shirts. let x represent the number of long-sleeved shirts. let y represent the number of short-sleeved shirts. which inequalities are among the constraints for this situation? select each correct answer. x+y≤250 15x+10y≥250 x+y≥20 15x+10y≤250 15x+10y≥20 x+y≤20

the least common denominator is 40

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.