Final answer:
A city with most power resting with the mayor operates under a mayor-council system, where the mayor has significant executive authority.
Step-by-step explanation:
If most of the power rests with the mayor in a city's government, that city is said to have a mayor-council system of government. Under this system, the voters elect both a mayor and members of the city council. The city council performs legislative functions, while the mayor performs the executive functions. When the mayor is given a great deal of authority, this can be referred to as a strong mayor system. This is in contrast to a council-manager system, where the city council appoints a city manager to handle administrative functions, and a commission government, which combines legislative and executive functions in a single group. Moreover, a federal government is a system of dividing the powers between national and state governments and is not applicable to municipal governance.