Final answer:
To write the digits 5, 10, 15, 20, 25, 30, 35, and 40 so that the numbers in the hexagon are equal to the two numbers in the files added together on either side, we can use the rule xPx9 = x(p+q).
Step-by-step explanation:
To write the digits 5, 10, 15, 20, 25, 30, 35, and 40 so that the numbers in the hexagon are equal to the two numbers in the files added together on either side, we can use the rule xPx9 = x(p+q). Let's apply this rule to each number:
- 5P9 = 5(5+4) = 5(9) = 45
- 10P9 = 10(10+4) = 10(14) = 140
- 15P12 = 15(15+4) = 15(19) = 285
- 20P15 = 20(20+4) = 20(24) = 480
- 25P18 = 25(25+4) = 25(29) = 725
- 30P21 = 30(30+4) = 30(34) = 1020
- 35P24 = 35(35+4) = 35(39) = 1365
- 40P27 = 40(40+4) = 40(44) = 1760