Rainsford asks Zaroff to
excuse him for the night
because he feels sick.

Explanation:

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i believe the answer is d

  this riddles' answer is library.

  the "leaves" are a reference to the books' pages that the library contains; the branches are a network of libraries that connect multiple libraries' collections, resources, and items in a system of a common database, integrating them; the branches' organization are a useful management tool for coordinating the multiple collections many libraries have.