For your first question regarding political trends during the Gilded Age, the correct answer is:
D. The rise of political machines, marked by corruption and community aid.
This reflects the significant role that political machines, like Tammany Hall in New York City, played during the Gilded Age, often characterized by corruption but also providing jobs and social services to immigrants and the urban poor.
For Part B, regarding the cartoon and its implications about New York City and Boss Tweed, the most fitting answer is:
B. That Tweed controlled the city and its politics and no one could change that.
This suggests that Boss Tweed had immense power and influence over the politics of New York City, depicting a scenario where he was untouchable in his control.