Which of the following components supports part of the weight of a vehicle and also drives the wheels connected to it?

The choice of a live axle as the correct answer is grounded in its dual function within a vehicle's drivetrain. A live axle not only supports the weight of the vehicle but also transmits power from the engine to the wheels it is connected to. This means that the live axle plays a critical role in both the structural integrity of the vehicle and its ability to move.

In contrast, a dead axle is primarily a non-driving axle that does not provide power to the wheels. It exists to help support the vehicle's weight and provide stability, but it does not engage in the propulsion of the vehicle.

The semi-floating axle, while capable of handling weight and partially driving the wheels, typically relies on additional components to manage its full load and doesn't distribute power in the same manner as a live axle. Finally, a stub axle is simply a shorter axle used for guiding wheels and typically does not support the vehicle’s weight or aid in driving the wheels.

Thus, the live axle distinctly encompasses both supporting vehicle weight and engaging in the vital task of wheel propulsion, making it the correct selection in this context.