Use inductive reasoning to predict the next line in this sequence of computations. Then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct. \( 76 \cdot 9+4=67 \) \( 765 \cdot 9+2=6887 \) \( 7654 \cdot 9+1=68887 \) Make a conjecture by predicting the correct numbers in the line below. \( _{\square \cdot 9+0=\square}^{\text {is the conjecture correct? }} \) A. Yes \( \quad \) B. No

To use inductive reasoning to predict the next line in the sequence of computations, we need to identify the pattern in the given sequence. The given sequence is: 1. \( 76 \cdot 9 + 4 = 67 \) 2. \( 765 \cdot 9 + 2 = 6887 \) 3. \( 7654 \cdot 9 + 1 = 68887 \) From the sequence, we can observe that the first number in each line is increasing by 1, and the second number is 9. The third number is the result of multiplying the first number by 9 and adding the second number. Using this pattern, we can predict the next line in the sequence: 4. \( 76543 \cdot 9 + 0 = 688880 \) Now, let's calculate the result of \( 76543 \cdot 9 + 0 \) to determine if our conjecture is correct. Calculate the value by following steps: - step0: Calculate: \(76543\times 9+0\) - step1: Multiply the numbers: \(688887+0\) - step2: Remove 0: \(688887\) The result of \( 76543 \cdot 9 + 0 \) is 688887. Therefore, our conjecture is correct, and the next line in the sequence should be: 4. \( 76543 \cdot 9 + 0 = 688887 \) So, the answer is A. Yes.