Final answer:
The nucleus controls the cell's activities by directing gene expression, and the mitochondria generate energy by converting glucose into ATP during cellular respiration.
Step-by-step explanation:
Organelle #1 is the nucleus, which controls the activities of the cell, and organelle #3 is the mitochondrion, which breaks down glucose to create energy for the cell.
The nucleus is often referred to as the control center of eukaryotic cells because it houses the cell's genetic information and directs the synthesis of proteins and other important cellular processes. The mitochondria are known as the "powerhouses" of the cell, where adenosine triphosphate (ATP), the cell's main energy-carrying molecule, is produced.
They convert the energy found in glucose into ATP during the process of cellular respiration, which requires oxygen and produces carbon dioxide as a waste product. Chloroplasts, which are mentioned in the reference but not included in the answer choices, perform the function of converting sunlight into glucose through the process of photosynthesis. Together, these organelles play a crucial role in maintaining the vitality and function of the cell.