What events finalized the borders of the western United States

answer: Through the Louisiana Purchase of 1803 and treaties with Spain and Britain, the nation's borders moved west to the Rocky Mountains, north to the 49th parallel, and south to Florida and the Gulf of Mexico

Explanation: Incorporating the Western Territories. Under the Treaty of Paris (1783) which ended the Revolutionary War, Britain relinquished to the United States a large tract of land west of the Appalachian mountains, doubling the size of the new nation.

b) a state law could be declared illegal if it contradicted the constitution.

explanation:

the conflict of this case originated when james w. mcculloch, a cashier of the baltimore branch of the second bank of the united states that the congress had chartered in 1816, refused to pay a tax imposed by the maryland state.

in the case, the state of maryland appealed that the establishment of a second bank was unconstitutional since the constitution didn't say anything about granting that power to congress. however, the case determined that even if such right wasn't specifically stated in the constitution, it was part of the "implied powers" of the government enunciated in article i, section 8.

the case also eliminated maryland's legislation to impose taxes to a national bank, asserting that even though the states retained the power of taxation, the constitution's laws are supreme and can not be controlled by the states, therefore, if a state law contradicts the constitution, it should be declared illegal.

explanation:

it was the first amendment