Final answer:
The group Z₄₀ has several subgroups corresponding to the divisors of 40, and the elements in Z₄₀ that have order 10 are the multiples of 4 up to 36. Identification of elements of order 10 in ⟩x⟪ requires additional context about the group that x belongs to.
Step-by-step explanation:
The question pertains to finding the number of subgroups of the group Z₄₀, and identifying elements of a given order within those subgroups. In group theory, the structure of the cyclic group Z₄₀ (the integers modulo 40 under addition) can be analysed to determine its subgroups, which correspond to the divisors of the group order (40 in this case). Also, the elements of order 10 in Z₄₀ can be determined by finding integers a such that 10a is congruent to 0 modulo 40, but the smallest positive integer k for which ka=₀ modulo 40 is 10.
Upon analysis, one would find that the only elements of Z₄₀ that have order 10 are 4, 8, 12, ..., 36. If the symbol ⟩x⟪ represents a cyclic subgroup generated by an element x in some group, then finding elements of order 10 in ⟩x⟪ requires knowledge of the group from which x originates.