An adult cat may swat a dog to set limits. Allow your animals to accept one another in their own time and don't leave them alone together until this is accomplished. Never push them toward each other or force interaction. Many cats and dogs become companions and playmates while others simply tolerate each other. Be sure to give your dog lots of extra attention to avoid jealous reactions.
Adult cats are generally more accepting of kittens than of other adults.
Two altered adult cats often become friends in the same home. Let your original cat sniff the cat carrier while your new cat is still confined. Then temporarily confine the established cat to one room while the new cat becomes familiar with his surroundings, including the other cat's scent. Do not force or rush their meeting. Grooming and acceptance of food are signs that your new cat is settling in and may be ready to meet his house mate.