Once the switch was flipped, the machine was ______________ and began operating smoothly.

The correct answer is activated.

Explanation:

To choose the word that best completes the sentence, let's analyze the context provided in the sentence: "Once the switch was flipped, the machine was ______________ and began operating smoothly."

The clause "began operating smoothly" indicates that the machine turned on or started functioning after the switch was flipped. Let's look at the definitions of the options:

1. Weltered: Rolled about or wallowed in something (e.g., mud or blood); moved in a turbulent or chaotic way.
2. Invoked: Called upon (a deity, spirit, law, or authority) for assistance, support, or inspiration.
3. Activated: Made active or operative; turned on or set in motion.
4. Captivated: Attracted and held the interest or attention of; charmed.
5. Deactivated: Made inactive or turned off (which contradicts "began operating smoothly").

Therefore, activated is the most logical and contextually appropriate fit for the sentence.