Determine the missing information in the paragraph proof. given: lines a and c intersect at point s, creating 4 angles. prove: corresponding angles are congruent. we are given that lines a and c intersect at point s. translate line a down line c until point s reaches point q. call the new line through q line b. because translations preserve orientation, lines a and b are because translations preserve angle measure, ∠rsu ≅ ∠rqu'. for the same reason, ∠rst ≅ ∠rqt', ∠psu ≅ ∠pqu', and ∠pst ≅ ∠pqt'. each of the angle pairs are corresponding angles. therefore, corresponding angles are congruent.

Factor completely. 4p^2 + 36p + 81 express the answer in the form (ap + b)^2

Acar started driving from city a to city b, distance between which is 620 miles, at a rate of 60 mph. two hours later a truck left city b and started moving towards city a at a rate of 40 mph. what distance from city a is the point where the truck and the car will meet?

The school track has eight lanes. each lane is 1.25 meters wide. the arc at each end of the track is 180. the distance of the home straight and the radii for the arcs in the 1st 4 lanes are given. s=85m r1=36.5m r2=37.75m r3=39m r4=40.25m part one: find the radii of lanes 5 through 8 of the track. show your work. part two: if max ran around lane one, how far did he run? show your work and explain your solution. part three: max wants to run a total of three laps around the track, choose two additional lanes (2-8) for him to run and find the distance around those two lanes. show your work and round to the hundredths. part 4: based on your lane choices in part three, what was the total distance max ran in the three laps around the track?