Final answer:
The statement that political machines demonstrated corruption in local government best reflects the impact of political machines, as exemplified by Tammany Hall's control over New York City.
Step-by-step explanation:
Based on the information provided about political machines like Tammany Hall, the statement that best reflects the impact of political machines is that political machines demonstrated corruption in New York City's local government. These machines, including the notorious Tammany Hall led by William "Boss" Tweed, were known for their informal yet powerful control over local elections and city affairs, often through corrupt means such as graft and bribery. They provided timely solutions and services to citizens, often immigrants and the working class, in exchange for political support and votes. Despite their corruption, political machines like Tammany Hall were effective in maintaining control over city politics for decades.