He distance from tonopah to round mountain is equal to the distance from tonopah to warm springs. the distance from tonopah to hawthorne is the same as the distance from tonopah to beatty. determine which distance is greater. 5_7 select one: a. warm springs to beatty b. round mountain to hawthorne

The picture in the attached figure

we know that
Since we have two pairs of congruent distances, as described in the given information,
and
we know that 95° >80°
we can use the Hinge Theorem to prove that the distance from Warm Springs to Beatty is greater than the distance from Round Mountain to Hawthorne. 

The Hinge Theorem states that "If two sides of one triangle are congruent, respectively, to two sides of a second triangle, and the included angle of the first triangle is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second"

therefore

the answer is the option 
a.) Warm Springs to Beatty

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.