Carolinas HealthCare System, already the second largest public hospital system in the country, is expanding again. Officials announced Tuesday that they've signed a 10-year management services agreement with Greensboro-based Cone Health, which has five hospitals and more than $1 billion in annual revenue. When the agreement takes effect Oct. 1, Carolinas HealthCare will own or manage nearly 40 hospitals and have $8 billion in annual revenue. Financial terms of the agreement were not disclosed. It's the first time Carolinas HealthCare has affiliated with a healthcare institution in the Triad area that includes Greensboro, Winston-Salem and High Point.