Mai has $36 to spend on movie tickets. each movie ticket costs $4.50.how many tickets can she buy?

a. write a multiplication equation and a division equation to represent this situation.

b. find the answer. draw a diagram, if needed.

c use the multiplication equation to check your answer.

see explaination

Step-by-step explanation:

a) $4.50 × ? = $36 $36 ÷ $4.50 = ?

b) 8 (divide)

c) replace question marks with x and solve algebraically still equals 8

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.

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225