Final answer:
New Jersey is the state that lies with the Delaware River to its west, bordering Pennsylvania and Delaware, and includes the Hudson and Toms Rivers. Significant historical explorations by Henry Hudson under the Dutch East India Company contributed to the founding of early settlements in the region.
Step-by-step explanation:
The state that has the Delaware River between it and Pennsylvania, and Delaware to the west, and includes the Hudson and Toms River, is New Jersey. The explorer Henry Hudson is credited with exploring the Delaware and Hudson Rivers in his search for the Northwest Passage under the commission of the Dutch East India Company in 1609. His explorations led to the establishment of trading relationships and later Dutch settlements, like Fort Nassau near present-day Albany. The founding of Delaware occurred when the English took control of New Netherland and the region west of the Delaware Bay was ceded to William Penn, eventually leading to the formation of the so-called "Lower Counties," which is now known as Delaware, incorporated with Pennsylvania.