Alocal business was looking to hire a landscaper to work on their property. they narrowed their choices to two companies. flourish landscaping company charges a flat rate of $120 per hour. green thumb landscapers charge $70 per hour plus a $1600 equipment fee. write a system of equations representing how much each company chargers. determine and state the number of hours that must be worked for the cost of each company to be the same. if it is estimated to take at least 35 hours to complete the job, which company will be less expensive? justify your answer

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?