Hello,
Let's r the ration
We suppose x ≠0
x=r*(x-2)==>r=x/(x-2)
x+3=r*x==> (x+3)/x=x/(x-2)==>(x+3)(x-2)=x²
==>x²+3x-2x-6=x² ==>x-6=0==>x=6
x-2=6-4=4
x=6
x+3=6+3=9
6=4*3/2
9=6*3/2
Ration 3/2
First term: 4
Answer:
The Center is (-2 , 3)
Radius of the circle is 3
Step-by-step explanation:

∴ the center is ( -2, 3)
radius of thw circle is 3
Answer:
g(x) = - x² - 4 ⇒ A
Step-by-step explanation:
Let us revise the reflection and translation of a function
- If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)
- If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k
f(x) = x² is the blue curve
g(x) is its image is the red curve
∵ g(x) is the image of f(x)
∵ f(x) is opened upward
∵ g(x) is opened downward
→ That means the sign of y-coordinates of all points on the blue
graph are opposite
∴ f(x) is reflected about the x-axis
∴ Its image is - f(x)
∵ The vertex of f(x) is (0, 0)
∵ The vertex of g(x) = (0, -4)
→ That means the function translated 4 units down
∴ - f(x) is translated 4 units down
∴ Its image is - f(x) - 4
∴ g(x) = - f(x) - 4
∵ f(x) = x²
∴ g(x) = - x² - 4