The correct answer is; Yes.
Explanation:
This is allowed by Tennessee law. If the Kentucky firm is using a web server that is owned by a Tennessee owned company then it is legal. Since the server is based out of Tennessee, the Kentucky firm can advertise as a Tennessee real estate firm.
If the reality office makes a sale in Kentucky while operating from the same state, they will have to pay Tennessee taxes since they are operating as a Tennessee company. The firm will also have to follow all real estate laws that Tennessee has and comply with all laws, rules, and regulations.
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