This is the 2118th most frequent Russian word.
соединенных
"Соединенных" means "united" or "connected" in English.
Here, 'соединенных' is used as part of a proper noun, reflecting 'United States'.
На карте показаны границы Соединенных Штатов Америки.
The map shows the borders of the United States of America.
Here, 'соединенных' functions as a past participle adjective, describing parts that are already united or joined.
Мы работаем над проектом, целью которого является объединение соединенных частей системы.
We are working on a project aimed at uniting the joined parts of the system.
In this context, 'соединенных' characterizes efforts that are united, emphasizing mutual cooperation or integration.