Given the functions f(x) = x2 - 2x - 4 and g(x) = 2x - 4, at what values of x do f(x) and g(x) intersect?

x = 0 and x = 4

To find intersection equate them.

x² - 2x - 4 = 2x - 4

subtract 2x - 4 from both sides

x² - 4x = 0 → (take out common factor x)

x(x - 4 ) = 0 ⇒ x = 0 , x = 4

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Step-by-step explanation:

We have been given two functions. and . We are asked to find the point, where both functions intersect.

To find the intersection point of both graphs, we will equate both equations as:

Combine like terms:

Now, we will factor out x as:

Using zero product property, we will get:

Therefore, the both graphs intersect at .

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.