Question
Use inductive reasoning to predict the next line in the pattern. \( \begin{array}{l}11 \times 41=451 \\ 11 \times 42=462 \\ 11 \times 43=473\end{array} \) The next line is \( \square \times \square=\square \).
Ask by Paul Gibbs. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The next line is \( 11 \times 44 = 484 \).
Solution
To predict the next line in the pattern, let's analyze the given equations step by step.
1. **Identify the pattern:**
- The first line is \( 11 \times 41 = 451 \).
- The second line is \( 11 \times 42 = 462 \).
- The third line is \( 11 \times 43 = 473 \).
2. **Observe the multipliers:**
- The multipliers are increasing by 1 each time: 41, 42, 43.
3. **Observe the products:**
- The products are 451, 462, and 473.
- Notice that each product increases by 11:
- \( 462 - 451 = 11 \)
- \( 473 - 462 = 11 \)
4. **Predict the next line:**
- Following the pattern, the next multiplier should be \( 43 + 1 = 44 \).
- The next product should be \( 473 + 11 = 484 \).
Thus, the next line in the pattern is:
\[
11 \times 44 = 484
\]
So, the complete next line is \( 11 \times 44 = 484 \).
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Simplify this solution Beyond the Answer
The pattern you've provided shows that as the multiplier increases by 1, the product increases by 11. Following this trend, the next line in the pattern will be \( 11 \times 44=484 \). So, the next line is \( 11 \times 44=484 \).
