Answer: The correct combination for the first sentence is:
Blake desperately wanted to buy a new car, but he didn't have the money.
The correct combination for the second sentence is:
Richard didn't have the nerve to ask for help with the lab assignment, thus he sat at home that night worried about the next test.
Explanation: The combination "Blake desperately wanted to buy a new car, but he didn't have the money" is correct because it effectively combines two independent clauses (Blake's desire to buy a car and his lack of funds) into a single sentence, using the conjunction "but" to indicate a contrast between the two. The conjunction "but" serves as a linking word that connects the two clauses, creating a clear relationship between them.
The combination "Richard didn't have the nerve to ask for help with the lab assignment, thus he sat at home that night worried about the next test" is correct for similar reasons. The conjunction "thus" serves as a linking word that connects the two independent clauses, indicating a logical relationship between them. The sentence effectively conveys the idea that Richard's inability to ask for help led to his worrying at home.