Mr. Miller is replacing a cylindrical air-conditioning duct. He estimates the radius of the duct by folding a ruler to form two 8-in. tangents to the duct, which makes 2 tangent lines form an angle. Mr. Miller measures the angle bisector from the vertex to the duct to be 4 inches long. What is the radius of the duct?

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y < 4x − 8 y is greater than or equal to negative 5 over 2 times x plus 5 part a: describe the graph of the system, including shading and the types of lines graphed. provide a description of the solution area. (6 points) part b: is the point (5, −8) included in the solution area for the system? justify your answer mathematically. (4 points)

In δabc, m∠acb = 90°, cd ⊥ ab and m∠acd = 45°. find: a find cd, if bc = 3 in

Point r divides in the ratio 1 : 5. if the coordinates of e and f are (4, 8) and (11, 4), respectively, what are the coordinates of r to two decimal places?