For the recurrence below, use the tree expansion method to find a guess of what it could solve to. Make your guess as tight as possible (look for the correct bound you can find). T(1) = a, T(n) = 3T(n/3) + bn for n ≥ 2 (where a and b are constants)

Which of the following is the result of expanding the series

(50 ) mrs. julien’s and mrs. castillejo’s classes are selling cookie dough for a school fundraiser. customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. mrs. julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. mrs. castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) write the system of equations that model the problem. be sure to explain which equation represents which situation. (b) find the cost of each type of cookie. show your work. (c) explain which method you used to solve the system and why you chose that method.

Algebraically prove that a clockwise and counterclockwise rotation of 180° about the origin for triangle abc are equivalent rotations.