Solve the system algebraically. Check your work. 5x + 3y = 18 2x + 3y = 9 Make sure there are NO SPACES in your answer. Be sure to include a comma between the x and y values. ANSWER: {( a0 )}

(3,1)

Step-by-step explanation:

5x + 3y = 18

2x + 3y = 9

So we can use elimination here to solve this system of equations by multiplying the second equation by -1

Now we have:

5x + 3y = 18

-2x - 3y = -9

Now we add straight down and combine like terms

The y terms cancel and we are left with 3x = 9, dividing both side by 3 we get x = 3

Now we can plug this x value into one of the original equations to solve for our y value

I will use the first equation: 5(3) + 3y = 18 → condensing the terms we get  15 + 3y = 18 → subtracting the 15 from both sides we get 3y = 3 → dividing both sides by 3 we get y = 1

The solution to this system of equations is (3, 1)

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.

25

step-by-step explanation: