Peter says, "if you subtract 14 from my number and multiply the difference by -6, the result is -150." what is peter's number?

(n-14)*(-6)=-150

distribute

-6*n -14*-6 = -150

-6n +84 = -150

subtract 84 from each side

-6n +84-84 = -150-84

-6n = -234

divide by -6

-6n/-6 = -234/-6

n = 39

Peter's number is 39

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.

2,600 divided by 80 = 32.5

step-by-step explanation: