What properties were used to write the numeric statement (18 - 5) + (432 x 15) = (15 x 432) + (18 - 5)

The properties that have been used are the;

commutative property of addition

commutative property of multiplication

Step-by-step explanation:

The commutative property of addition can be stated algebraically as follows;

a + b = b + a

where a and b are any real numbers

On the other hand, the commutative property of multiplication can be stated algebraically as follows;

a * b = b * a

where a and b are any real numbers

If we let 18 - 5 = a, 432 = m and 15 = n, then we have;

a + (m * n)

Using the commutative property of addition, the expression can be written as;

(m * n) + a

Using the commutative property of multiplication, the term in brackets can be written as;

(m * n) = (n * m)

Combining the two properties we find that;

a + (m * n) = (m * n) + a = (n * m) + a

Therefore, (18 - 5) + (432 x 15) = (15 x 432) + (18 - 5)

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.

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step-by-step explanation: