Question

Сергей вырезал из бумаги несколько шестиугольников и семиугольников. Всего у вырезанных фигурок 44 вершин. Сколько шестиугольников вырезал Сергей?

Answer 1

Ответ:

5

Пошаговое объяснение:

Предположим, что семиугольников только 1, следовательно 44-7=37, этого не может быть потому-что число 33 на 6 не делится.

Если семиугольников 2, то 44-14=30, значит может быть 5 шестиугольников 30/6=5

Answer 2

#### Problem Analysis Sergey has cut out several hexagons and heptagons from paper, and the total number of vertices in the cut-out shapes is 44. We need to determine how many hexagons Sergey cut out. #### Solution Let's assume Sergey cut out 'x' hexagons and 'y' heptagons. Each hexagon has 6 vertices, so the total number of vertices from the hexagons is 6x. Each heptagon has 7 vertices, so the total number of vertices from the heptagons is 7y. According to the problem, the total number of vertices is 44. Therefore, we can write the equation: 6x + 7y = 44 To find the number of hexagons, we need to solve this equation. #### Solving the Equation We can use different methods to solve this equation. One approach is to use trial and error. Let's start by assuming Sergey cut out 1 hexagon (x = 1) and see if we can find a value of y that satisfies the equation. When x = 1, the equation becomes: 6(1) + 7y = 44 6 + 7y = 44 7y = 44 - 6 7y = 38 y = 38/7 Since y is not an integer, this solution does not work. Let's try assuming Sergey cut out 2 hexagons (x = 2) and see if we can find a value of y that satisfies the equation. When x = 2, the equation becomes: 6(2) + 7y = 44 12 + 7y = 44 7y = 44 - 12 7y = 32 y = 32/7 Again, y is not an integer, so this solution does not work. We can continue this process until we find a solution where y is an integer. #### Solution After trying different values of x, we find that when Sergey cut out 4 hexagons (x = 4), the equation becomes: 6(4) + 7y = 44 24 + 7y = 44 7y = 44 - 24 7y = 20 y = 20/7 Since y is not an integer, this solution does not work. Therefore, there is no solution where the number of hexagons Sergey cut out is an integer. #### Conclusion Based on the given information, it is not possible to determine how many hexagons Sergey cut out.