Final answer:
Bluish mucous membranes in a patient suggest hypoxia, indicating low levels of oxygen in the blood, which is a serious condition requiring immediate medical intervention.
Step-by-step explanation:
When a patient has bluish mucous membranes, this is commonly a sign of hypoxia, which is a lower-than-normal level of oxygen in the blood. This condition means that not enough oxygen is reaching the body's tissues, which can be a serious and possibly life-threatening state requiring prompt medical attention. The other options listed such as hepatitis, compensated shock, and frostbite have other distinct signs. Hepatitis is often indicated by jaundice, not blue mucous membranes. Compensated shock might involve rapid heart rate or low blood pressure rather than cyanosis, and frostbite typically involves damage to the skin from freezing, not blueness of mucous membranes.