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Complete the two tables below by finding the missing values.

Mathematics

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let's solve these tables.

1. Table 1

  • Rule: The output is obtained by dividing the input by 2 and then adding 2. Output=Input2+2\text{Output} = \frac{\text{Input}}{2} + 2
  • Missing values:
    • For Input = 12: 122+2=6+2=8\frac{12}{2} + 2 = 6 + 2 = 8
    • For Input = 14: 142+2=7+2=9\frac{14}{2} + 2 = 7 + 2 = 9
    • For Input = 16: 162+2=8+2=10\frac{16}{2} + 2 = 8 + 2 = 10
    • For Input = 32: 322+2=16+2=18\frac{32}{2} + 2 = 16 + 2 = 18
    • For Input = 84: 842+2=42+2=44\frac{84}{2} + 2 = 42 + 2 = 44
  • Pattern in output row: The output numbers increase by 1 for every 2-unit increase in the input.
Input2468101214163284
Output3456789101844

2. Table 2

  • Rule: The output is obtained by multiplying the input by 0.5 and then adding 2. Output=0.5×Input+2\text{Output} = 0.5 \times \text{Input} + 2
  • Missing values:
    • For Input = 5: 0.5×5+2=2.5+2=4.50.5 \times 5 + 2 = 2.5 + 2 = 4.5
    • For Input = 6: 0.5×6+2=3+2=50.5 \times 6 + 2 = 3 + 2 = 5
    • For Input = 8: 0.5×8+2=4+2=60.5 \times 8 + 2 = 4 + 2 = 6
    • For Input = 29: 0.5×29+2=14.5+2=16.50.5 \times 29 + 2 = 14.5 + 2 = 16.5
  • Pattern in output row: The output numbers increase by 0.5.
Input123456781729
Output2.533.544.555.5610.516.5

3. Table 3

  • Rule: The output is obtained by multiplying the input by 7 and then subtracting 7. Output=7×Input−7\text{Output} = 7 \times \text{Input} - 7
  • Missing values:
    • For Input = 10: 7×10−7=70−7=637 \times 10 - 7 = 70 - 7 = 63
    • For Input = 14: 7×14−7=98−7=917 \times 14 - 7 = 98 - 7 = 91
    • For Input = 16: 7×16−7=112−7=1057 \times 16 - 7 = 112 - 7 = 105
    • For Input = 44: 7×44−7=308−7=3017 \times 44 - 7 = 308 - 7 = 301
    • For Input = 84: 7×84−7=588−7=5817 \times 84 - 7 = 588 - 7 = 581
  • Pattern in output row: The output numbers increase by 1
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