Learn Polish: Ten pacjent odpoczywa przed badaniem. - This patient is resting before the examination.

Because it comes directly after the preposition przed (before). When talking about time, przed forces the following noun into the Instrumental case. Since badanie (examination) is a neuter noun ending in -e, we simply add -m to make the Instrumental form badaniem.

Wait, don't Instrumental nouns usually end in -em?

Masculine and neuter nouns generally do take an -em ending. However, because badanie already ends in the letter -e, we don't need to add another one. We just attach the final -m.

Why is the word for "this" Ten instead of To?

Ten is the masculine form of "this", matching the masculine noun pacjent. You would use To for neuter nouns (like to badanie) and Ta for feminine nouns.

How do we know the patient "is resting" right now rather than "rests" generally?

Polish doesn't have a separate continuous tense like English does. The verb odpoczywa is just the standard present tense. It can mean either "is resting" or "rests" depending entirely on the context.