A. The US made the Gadsden Purchase.
The US never sold Texas. US won the war. Mexican cession was the US taking land.
One of the main ways in which changes to the railroad helped American industries to grow is that the expansion of the rail system led to increased migration to the west, which led to more farming and agricultural output. Another would be that it led to settlements that ultimately led to business that were able to conduct business over state lines with great ease.
Theodore Roosevelt inherited an empire-in-the-making when he assumed office in 1901. After the Spanish-American War.
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