Answer: x = 38, y = 81, z = 75
Step-by-step explanation:
First, because it's a quadrilateral, we know that (z - 3) + 108 + (y - 9) + (3x - 6) = 360.
Then, we also know that (3x - 6) = 108, because in a parallelogram the two opposite angles are congruent. So, we know that x = 38.
Next, we also know that (z - 3) = (y - 9), because (again) the opposite angles are congruent. But since there are 2 variables and 1 equation, we cannot solve it yet.
But, we also know that (y - 9) + (3x - 6) = 180, because the same side angles are supplementary. We already know that (3x - 6) = 108, so (y - 9) = 180 - 108 = 72. y = 81.
Then, we can also figure out (z - 3) because it's the same as (y - 9), so (z - 3) = 72. z = 75.
So, x = 38 degrees, y = 81 degrees, and z = 75 degrees.
<em>P.S. If this is wrong, please tell me! I'll try my best to fix it. </em>
<span><span>You draw a queen on the first draw and one on the second<span><span><span>4/52 </span>∗ <span>3/51 </span>= <span>12/2652 </span>= <span>1/22 </span></span></span></span><span>
You draw something other than a queen on the first draw and a queen on the second<span><span><span>
48/52 </span>∗ <span>4/51 </span>= <span>192/2652</span>=<span>16/221</span></span></span></span></span>
So in total, the chance is:
<span><span><span>1/221 </span>+ <span>16/221 </span>= <span>17/221</span>=
<span>4/52</span></span></span>
Answer:
The option is D
![(n+4)^{2} - n^{2} = 8(n + 2)](https://tex.z-dn.net/?f=%28n%2B4%29%5E%7B2%7D%20-%20n%5E%7B2%7D%20%3D%208%28n%20%2B%202%29)
Step-by-step explanation:
Given
![(n+4)^{2} - n^{2} = 8(n + 2)](https://tex.z-dn.net/?f=%28n%2B4%29%5E%7B2%7D%20-%20n%5E%7B2%7D%20%3D%208%28n%20%2B%202%29)
put
we get
![(1+4)^{2}- 1^{2}= 8(1+2)\\5^{2}- 1^{2}= 8\times 3 = 24](https://tex.z-dn.net/?f=%281%2B4%29%5E%7B2%7D-%201%5E%7B2%7D%3D%208%281%2B2%29%5C%5C5%5E%7B2%7D-%201%5E%7B2%7D%3D%208%5Ctimes%203%20%3D%2024)
Similarly,
put
we get
![(2+4)^{2}- 2^{2} = 8(2+2)\\6^{2}- 2^{2}= 8\times 4 = 32](https://tex.z-dn.net/?f=%282%2B4%29%5E%7B2%7D-%202%5E%7B2%7D%20%3D%208%282%2B2%29%5C%5C6%5E%7B2%7D-%202%5E%7B2%7D%3D%208%5Ctimes%204%20%3D%2032)
put
we get
![(4+4)^{2}- 4^{2} = 8(4+2)\\8^{2}- 4^{2} = 8\times 6 = 48](https://tex.z-dn.net/?f=%284%2B4%29%5E%7B2%7D-%204%5E%7B2%7D%20%3D%208%284%2B2%29%5C%5C8%5E%7B2%7D-%204%5E%7B2%7D%20%3D%208%5Ctimes%206%20%3D%2048)
8 cans
48/6=8
since each student collected equal amounts then divide the number of cans by the number of students