Triangle XYZ is a right triangle with ZQ¯¯¯¯¯⊥XY¯¯¯¯¯¯ . Use the drop-down menus to complete the proof of the Pythagorean theorem. By the angle-angle similarity postulate, △YXZ∼△YZQ and △YXZ∼△ZXQ. Since similar triangles have sides, ac=fa and bc=eb . Solving the equation for a² and b² gives a2=cf and b2= . Adding these together gives a2+b2=cf+ce. Factoring out the common segment gives a2+b2=c(f+e). Using gives a2+b2=c(c), which simplifies to a2+b2=c2 .

Find the total area for the regular pyramid ( follow the answer set up in the picture)

Inez has a phone card. the graph shows the number of minutes that remain on her phone card a certain number of days.

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)