What is the relationship between mod and long division. the length of the cycle of powers of 10 in mod n and how to find it through long division

Find the length of the following tangent segments to the circles centered at o and o' whose radii are 5 and 3 respectively and the distance between o and o' is 12. what is the tangent segment of cd?

If f(x) = 3x2 - 2x+4 and g(x) = 5x + 6x - 8, find (f-g)(x).

Which number is located at point a on the number line? a number line is shown from negative 10 to 10 with each interval mark on the number line representing one unit. point a is labeled one interval mark to the right of negative 5.