Final answer:
The nucleus is responsible for carrying genes in a cell, containing the cell's genetic material, including DNA, which holds the information for the cell's structure and function.
Step-by-step explanation:
The structure within a cell that is responsible for carrying genes is the nucleus. The nucleus is sometimes referred to as the "command center" of the cell. It houses most of the cell's genetic material, which includes DNA. DNA is organized into chromosomes, and this genetic material contains the information necessary for the cell's structure and function, in the form of genes. These genes regulate the activities of the cell by dictating gene expression, which is the process by which genes are used to synthesize proteins. Although mitochondria also contain DNA, their DNA makes up just a small percentage of the cell's overall genetic content and is primarily focused on mitochondrial function.