What are the coordinates of the point on the directed line segment from (-10, -3) to (10, 7) that partitions the segment into a ratio of 3 to 2?

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?

The lengths of nails produced in a factory are normally distributed with a mean of 4.91 centimeters and a standard deviation of 0.05 centimeters. find the two lengths that separate the top 4% and the bottom 4%. these lengths could serve as limits used to identify which nails should be rejected. round your answer to the nearest hundredth, if necessary.

The base of a triangle exceeds the height by 9 inches. if the area is 180 square inches, find the length of the base and the height of the triangle.