We can determine whether the point (-3,5) lies inside, outside, or on the circle with the equation (x+2)^2+(y-4)^2=9 by plugging in the values of x and y into the equation and seeing if the equation is true.
(x+2)^2+(y-4)^2=9
(-3+2)^2+(5-4)^2=9
(-1)^2+(1)^2=9
1+1=9
2 does not equal 9, so the point (-3,5) does not lie on the circle with the equation (x+2)^2+(y-4)^2=9.
To determine whether the point lies inside or outside the circle, we can plot the circle and the point on a graph.
After plotting the circle and the point, we can see that the point (-3,5) lies outside the circle.
Therefore, the point (-3,5) lies outside the circle with the equation (x+2)^2+(y-4)^2=9.