The value of r represents the directed distance when plotting a point in polar coordinates. a. true b. false

The given statement is a TRUE statement.

Step-by-step explanation:

In polar coordinates i.e. (r,θ); r represents the polar distance and θ represents the polar angle.

A point in the plane is at a distance 'r' from the origin and the angle 'θ' is the distance between the line drawn from origin to a point at a distance r and the x-axis.

Hence, The value of r represents the directed distance when plotting a point in polar coordinates.

17 1/3

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4