Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the following inequality:
y > 1/2 x + 2
the origin is not included in the shaded region and the shaded area is above the line.
the origin is not included in the shaded region and the shaded area is below the line.
the origin is included in the shaded region and the shaded area is above the line. the origin is included in the shaded region and the shaded area is below the line.

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)

From the top of a tree a bird looks down on a field mouse at an angle of depression of 50°. if the field mouse is 40 meters from the base of the tree, find the vertical distance from the ground to the bird's eyes.

Can someone plz me understand how to do these. plz, show work. in exercises 1-4, rewrite the expression in rational exponent form.[tex]\sqrt[4]{625} \sqrt[3]{512} (\sqrt[5]{4} )³ (\sqrt[4]{15} )^{7}\\ (\sqrt[3]{27} )^{2}[/tex]