Y=x+3
y=3x+1

A. (1,3)
B. (0,1)
O C. (0,3)
D. (1.4)

D: (1, 4)

Step-by-step explanation:

You can either solve by substitution or elimination. If you are timed, the fastest way is to guess and check (plug-in the answer choices)

I will be using substitution to solve this:

Step 1: Since you have y already, you can set them equal to each other

x+3 = 3x+1

3 = 2x +1

2 = 2x

x = 1

Step 2: Now you have x, plug x into one of the original equations. In this case, I will use the first one

y = 1 + 3

y = 4

Step 3: Now write your answer as a coordinate plane point

x = 1, y = 4

(1, 4)

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.

i believe the correct answer is b.