Celia and Ryan are starting a nutrition program. Celia currently consumes 1200 calories a day and will increase that number by 100 calories each day. Ryan currently consumes 3230 calories a day and will decrease that number by 190 each day. They will continue this pattern until they are both consuming the same number of calories per day. In how many days will that be?

Aroulette wheel has 38 slots in which the ball can land. two of the slots are green, 18 are red, and 18 are black. the ball is equally likely to land in any slot. the roulette wheel is going to be spun twice, and the outcomes of the two spins are independent. the probability that it lands one time on red and another time on black in any order is(a) 0.5 (b) 0.25 (c) 0.4488 (d) 0.2244

Which geometric principle is used to justify the construction below?

Line u passes through points (-52, -18) and (-29, 53). line v passes through points (90, 33) and (19, 56). are line u and line v parallel or perpendicular?