On the real number line below, with coordinates as labeled, an object moves according to the following set of instructions: From point P the object moves right to , then left to R, then right to S, and finally left until it returns to its original position at P. Which is the closest estimate of the total length, in coordinate units, of the movements this object makes?

In each of the cases that follow, the magnitude of a vector is given along with the counterclockwise angle it makes with the +x axis. use trigonometry to find the x and y components of the vector. also, sketch each vector approximately to scale to see if your calculated answers seem reasonable. (a) 50.0 n at 60.0°, (b) 75 m/ s at 5π/ 6 rad, (c) 254 lb at 325°, (d) 69 km at 1.1π rad.

What is the effect on the graph of the function f(x) = x2 when f(x) is changed to f(x) − 4?

Which shaded region is the solution to the system of inequalities? y y[tex]\geq[/tex]-x+1