In the statement below, the two blanks can be filled by positive single-digit numbers in such a way that the statement is always true:

$$\text{If }2x\equiv y+5\ (\bmod\ 9)\text{, then }x\equiv \underline{\ \ \ }\,y+\underline{\ \ \ }\ (\bmod\ 9).$$What is the product of the two digits that go in the blanks?

35

Explanation:

2x == y+5 (mod 9)

2x * 5 = 10 * x = 1 * x = (y+5) * 5 (mod 9)

(5 is the inverse of 2 (mod 9))

x = 5y + 25 (mod 9)

x= 5y + 7 (mod 9)

5 * 7 = 35

one of the major compromises in the constitutional convention was between the small states and big states. the small states wanted each state to have the same number of representatives in congress. the big states wanted representation based on population.

a. factors that are used to make goods and services