Brooklyn is starting a running plan to train for a race . In the first week of her running plan , Brooklyn will run 8 miles . The plan calls for Brooklyn to increase her weekly mileage by 1.5 miles every week . If Brooklyn sticks to the plan , how many miles would she be expected to run during her 19th week of training plan ?

Mason and christian go to the movie theater and purchase refreshments for their friends. mason spends a total of $45.75 on 3 bags of popcorn and 6 drinks. christian spends a total of $71.50 on 6 bags of popcorn and 4 drinks. write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. using these equations, determine and state the price of a drink, to the nearest cent.

The bottom of ignacio's desktop is 74.5cm from the floor. ignacios sits in his adjustable chair, and the tops of his legs are 49.3cm from the floor. each clockwise rotation of the knob on the chair raises ignacio's legs by 4.8cm. write an inequality to determine the number of clockwise rotations, r, ignacio could make with the knob without his legs touching the desk.

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