Which equation has exactly ONE solution? A)
3 + 4x
= 2x + 1
2
B)
6 - 2x
= 15 + 2x
12x - 10
= 3x + 4
4
D)
4x - 20
-= x-5
4

its A

Step-by-step explanation:

Let's solve your equation step-by-step.

3+4x=2x+12

Step 1: Simplify both sides of the equation.

4x+3=2x+12

Step 2: Subtract 2x from both sides.

4x+3−2x=2x+12−2x

2x+3=12

Step 3: Subtract 3 from both sides.

2x+3−3=12−3

2x=9

Step 4: Divide both sides by 2.

2x

2

=

9

2

x=

9

2

x=

9

2

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.

1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.