How do conjectures and counterexamples play a role in the process of finding a pattern? ( Please don’t do long answers :) )

If ac = 12 and ab=7 is it possible that bc =10

Two fire-lookout stations are 190 miles apart, with station a directly south of station b. both stations spot a fire. the bearing of the fire from station a is upper n 55 degrees upper e and the bearing of the fire from station b is upper s 60 degrees e. how far, to the nearest tenth of a mile, is the fire from each lookout station?

The data in the table represent the height of an object over time. which model best represents the data? height of an object time (seconds) height (feet) 05 1 50 2 70 3 48 quadratic, because the height of the object increases or decreases with a multiplicative rate of change quadratic, because the height increases and then decreases exponential, because the height of the object increases or decreases with a multiplicative rate of change exponential, because the height increases and then decreases