The two technological advances that led to a significant increase in the enslaved population in Georgia from 1830 to 1860 are:
A. Cotton Gin
The cotton gin, invented by Eli Whitney in 1793, greatly increased the efficiency of cotton processing, leading to a boom in cotton cultivation, which in turn increased the demand for enslaved labor.
B. Railroads
Railroads facilitated the transportation of goods, including cotton, and helped to expand the agricultural economy, further increasing the demand for enslaved labor in the region.
So the correct answers are A (Cotton Gin) and B (Railroads).