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Math
Posted 3 months ago

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Answer from Sia
Posted 3 months ago
Pattern Sequences
Pattern 1
In Triangle A, the sum of the numbers in the smaller triangles (8, 3, 18) is 8+3+18=298 + 3 + 18 = 29. The number at the top vertex is 55
Pattern 2
In Triangle B, the sum of the numbers in the smaller triangles (9, 4, 24) is 9+4+24=379 + 4 + 24 = 37. The number at the top vertex is 44
Pattern Rule
The sum of the numbers in the smaller triangles is equal to the top vertex number multiplied by a constant factor.
Answer
In Triangle C, the top vertex number is 99. To find the missing number in the top center triangle, we use the pattern rule to determine the constant factor. For Triangle A, 29=5×k29 = 5 \times k and for Triangle B, 37=4×k37 = 4 \times k. Solving for kk gives us k=29/5=5.8k = 29/5 = 5.8 and k=37/4=9.25k = 37/4 = 9.25. Since these factors are not consistent, we need to re-evaluate the pattern. Upon closer inspection, we notice that the sum of the numbers in the smaller triangles is actually 7 more than the top vertex number multiplied by 4. For Triangle A, 29=5×4+729 = 5 \times 4 + 7 and for Triangle B, 37=4×4+737 = 4 \times 4 + 7. Applying this to Triangle C, we have 9×4+7=36+7=439 \times 4 + 7 = 36 + 7 = 43. Therefore, the missing number in the top center triangle of Triangle C is 43(5+5)=3343 - (5 + 5) = 33.
Key Concept
Pattern Recognition and Arithmetic Operations
Explanation
The key to solving the pattern is recognizing the relationship between the sum of the numbers in the smaller triangles and the top vertex number, then applying arithmetic operations to find the missing number.

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