Jessica is voting for dancers in a contest. she votes for the first contestant 5 times, the second contestant 9 times, and the third contestant 13 times. if she continues this pattern, how many total votes will jessica cast for the first four contestants? explain.

  44 votes

Step-by-step explanation:

The fourth contestant will get 17 votes (4 more than the 3rd contenstant). The total votes cast are then ...

  5 + 9 + 13 + 17 = 44

"This pattern" seems to be that each contestant gets 4 more votes than the one before.

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.

you answer is a

step-by-step explanation: