What is the shortest distance, in units, between the circles $(x-9)^2 + (y-5)^2 = 6.25$ and $(x+6)^2 + (y+3)^2 = 49$? Express your answer as a decimal to the nearest tenth.
The center of the first circle is $(9,5)$ and its radius is $\sqrt{6.25} = 2.5$. The center of the second circle is $(-6,-3)$ and its radius is $\sqrt{49} = 7$. To find the shortest distance between the circles, I need to find the distance between their centers and subtract their radii. The distance between the centers is given by the distance formula: $\sqrt{(9-(-6))^2 + (5-(-3))^2} = \sqrt{225 + 64} = \sqrt{289} = 17$. The shortest distance between the circles is then $17 - 2.5 - 7 = 7.5$. 