Final answer:
Depressants are drugs that calm the brain and are used to relieve anxiety and induce sleep, with common examples being barbiturates and benzodiazepines.
Step-by-step explanation:
Drugs that relieve anxiety and induce sleep are called depressants. This type of psychoactive drug calms the brain, reduces anxious feelings, and induces sleepiness. Common examples of depressants include barbiturates and benzodiazepines, such as Xanax, which act as agonists of the gamma-Aminobutyric acid (GABA) neurotransmitter system. Due to the quieting effect of GABA on the brain, drugs that serve as GABA agonists likewise have a calming effect on the central nervous system, which can reduce anxiety and promote sleep.
Therefore, the answer to the question, "Drugs that relieve anxiety and induce sleep are called:", is d: depressants.