Answer:
3 and 9
if f(x)=x^2+13 and g(x)=12x-14
Step-by-step explanation:
So when we are looking for the intersection of two functions, we are trying to figure out when they are the same. When you think same, you should think equal (=).
So we want to find when f(x)=g(x) for x.
f(x)=g(x)

Let's get everything to one side.
Subtracting 12x and adding 14 to both sides.

I'm going to reorder the left hand side and also simplify the 13+14 part:

Now since the coefficent of x^2 is just 1 our job is to find two numbers that multiply to be 27 and add up to be -12.
Those numbers are -3 and -9 since -3(-9)=27 and -3+(-9)=-12.
So the factored form of our equation is

Since the product is 0, then at least one of the factors must be 0.
So we want to solve both x-3=0 and x-9=0.
x-3=0 can be solved by adding 3 on both sides. This gives us x=3.
x-9=9 can be solved by adding 9 on both sides. This gives us x=9.
The intersection of f and g happens at x=3 or x=9.
Answer:
12x⁶+24x⁵-180x⁴/ 30x³+240x²+450x
Step-by-step explanation:
(x-3)(x+5)=x²+2x-15
12x⁴(x²+2x-15)= 12x⁶+24x⁵-180x⁴
(x+3)(x+5)=x²+8x+15
30x(x²+8x+15)= 30x³+240x²+450x
The equation that fits is y=3x+1
Answer:

Step-by-step explanation:
The equation of a circle in standard form:

(h, k) - center
r - radius
We have the endpoints of the diameter: (-1, 6) and (5, -4).
Midpoint of diameter is a center of a circle.
The formula of a midpoint:

Substitute:

The center is in (2, 1).
The radius length is equal to the distance between the center of the circle and the endpoint of the diameter.
The formula of a distance between two points:

Substitute the coordinates of the points (2, 1) and (5, -4):

Finally we have:
