Answer:
is a partition of Z
Step-by-step explanation:
Given
for some integer k![\}](https://tex.z-dn.net/?f=%5C%7D)
for some integer k},
for some integer k},
and
for some integer k}.
Required
Is
a partition of Z
Let
![k = 0](https://tex.z-dn.net/?f=k%20%3D%200)
So:
![$$A _ { 0 } = 4 k \to $$A _ { 0 } = 4 * 0 = 0](https://tex.z-dn.net/?f=%24%24A%20_%20%7B%200%20%7D%20%3D%204%20k%20%5Cto%20%24%24A%20_%20%7B%200%20%7D%20%3D%204%20%2A%200%20%3D%200)
![$$A _ { 1 } = 4 k + 1$$,](https://tex.z-dn.net/?f=%24%24A%20_%20%7B%201%20%7D%20%3D%204%20k%20%2B%201%24%24%2C)
![A _ { 1 } = 4 *0 + 1$$ \to A_1 = 1](https://tex.z-dn.net/?f=A%20_%20%7B%201%20%7D%20%3D%204%20%2A0%20%2B%201%24%24%20%5Cto%20A_1%20%3D%201)
![A _ { 2 } = 4 k + 2](https://tex.z-dn.net/?f=A%20_%20%7B%202%20%7D%20%3D%204%20k%20%2B%202)
![A _ { 2} = 4 *0 + 2$$ \to A_2 = 2](https://tex.z-dn.net/?f=A%20_%20%7B%202%7D%20%3D%204%20%2A0%20%2B%202%24%24%20%5Cto%20A_2%20%3D%202)
![A _ { 3 } = 4 k + 3](https://tex.z-dn.net/?f=A%20_%20%7B%203%20%7D%20%3D%204%20k%20%2B%203)
![A _ { 3 } = 4 *0 + 3$$ \to A_3 = 3](https://tex.z-dn.net/?f=A%20_%20%7B%203%20%7D%20%3D%204%20%2A0%20%2B%203%24%24%20%5Cto%20A_3%20%3D%203)
So, we have:
![\{A_0,A_1,A_2,A_3\} = \{0,1,2,3\}](https://tex.z-dn.net/?f=%5C%7BA_0%2CA_1%2CA_2%2CA_3%5C%7D%20%3D%20%5C%7B0%2C1%2C2%2C3%5C%7D)
Hence:
is a partition of Z
1/4 bc 2/8 (8/32)= .0625
The square root of .0625 is 1/4
C. 68°
we know this because the two sides are congruent (which means it’s an isosceles triangle) so you know that the two angles are congruent