as the roman empire declined, leaving imperial order nonexistent, what negative effects did this have on western europe?

answer: this problem has only trivial solutions, with all points on the same line. x=5 or x=7/5.

step-by-step explanation:

there are three triangles, and three unknowns: x, y=length of middle segment, and z=cos(angles marked with red arc).

we need

and law of cosines,

the three equations are

see attached image for solution.

yes

explanation:

the fighting words doctrine, in united states constitutional law, is a limitation to freedom of speech as protected by the first amendment to the united states constitution. in 1942, the u.s. supreme court established the doctrine by a 9–0 decision in chaplinsky v. new hampshire.