Use the construction in the proof of the Chinese remainder theorem to find all solutions to the system of congruences x -= 2 (mod 3), x -= 1 (mod 4), and x -= 3 (mod 5).

The value of the operation $[9]+[8]\in$ ${\displaystyle Z_{13}}$ and to write the answer in the form [r] with ${\displaystyle 0\le r<m}$.

Solve the congruence ${\displaystyle x^{20}-1\equiv 0\left(\text{mod}61\right)}$

To find: the name of the corresponding parts in the congruent triangles. And complete the congruence statement.
Given:
The congruence statement is ${\displaystyle \mathrm{△}CAB}$.

To decide: Whether the given information is enough to prove that ${\displaystyle \mathrm{△}WXZ\stackrel{\sim }{=}\mathrm{△}YZX}$ using SAS Congruency Theorem. If so write a proof if not then explain the reason.
Given:
The given figure is as follows.

Justify Conclusions take a conjecture about the sum of th interior angles of a quadrilateral. Justify your reasoning.

Given: K is between H and J, HK= 2x - 5, KJ = 3x + 4, and HJ = 24.
What is the value of x?
A. 9
B. 5
C. 19
D. 3

Solve the following linea congruence: 17x congruence 3(mod 210)