An angle bisector of a triangle divides the opposite side of the triangle into segments 4 cm and 2 cm long. A second side of the triangle is 4.5 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Draw a picture.

Shortest possible side length is cm.

Longest possible side length is cm.

If f(x)= 3x+6 which of the following is the inverse of f(x)

"curse these trig-loving pirates! " devora mutters as she looks at the map. then, after thinking for a moment, she walks back to the entrance of the secret cave, measuring 48 meters along the way. after performing a calculation, devora walks back to the empty treasure, faces the entrance, and turns a certain number of degrees to her left before walking 89 meters to the treasure. supposing that the angle at the cave entrance is acute and that devora's calculations were correct, how many degrees did she turn?

Three students each examine the system of linear equations shown. 8x + 4y = 16 8x + 2y = 8 caleb says there is exactly one solution. jeremy says there is no solution. kim says there are infinitely many solutions. which student is correct? provide mathematical reasoning to support your answer. answer in complete sentences. : d