Answer:
arithmetic
Step-by-step explanation:
This is an arithmetic sequence since there is a common difference between each term. In this case, adding 2 to the previous term in the sequence gives the next term. In other words, an=a1+d(n−1) a n = a 1 + d ( n - 1 ) .
Same as last time:
d^2=(x2-x1)^2+(y2-y1)^2
d^2=(6--1)^2+(-2-4)^2
d^2=7^2+(-6)^2
d^2=49+36
d^2=85
d=√85 (85=5*7 and both 5 and 7 are prime so √85 cannot be simplified any further)
The exact distance is √85 units.
Answer:
8.96
Step-by-step explanation:
8×112:100 uh it t 8tc7tct8 it 7rct8 ig e6zw6 og ì ì og
![x=2,\: z=3,\: y=-1](https://tex.z-dn.net/?f=x%3D2%2C%5C%3A%20z%3D3%2C%5C%3A%20y%3D-1)
1) Let's solve this system. We can start by rewriting it this way:
![\mleft\{\begin{matrix}3x-8y+z=17 \\ -x+y-z=-6 \\ x-3y=5\end{matrix}\mright.](https://tex.z-dn.net/?f=%5Cmleft%5C%7B%5Cbegin%7Bmatrix%7D3x-8y%2Bz%3D17%20%5C%5C%20-x%2By-z%3D-6%20%5C%5C%20x-3y%3D5%5Cend%7Bmatrix%7D%5Cmright.)
Let's pick the 3rd equation and isolate x, from it:
![x=5+3y](https://tex.z-dn.net/?f=x%3D5%2B3y)
2) Now, we can plug that into the first and the 2nd equation.
Now let's solve this system to find y
![\begin{gathered} \mleft\{\begin{bmatrix}3\mleft(5+3y\mright)-8y+z=17 \\ -\mleft(5+3y\mright)+y-z=-6\end{bmatrix}\mright? \\ 15+y+z=17 \\ -5-2y-z=-6 \\ ------------- \\ y=-z+2 \\ -5-2(-z+2)-z=-6 \\ -5+2z-4-z=-6 \\ z-9=-6 \\ z=9-6 \\ z=3 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cmleft%5C%7B%5Cbegin%7Bbmatrix%7D3%5Cmleft%285%2B3y%5Cmright%29-8y%2Bz%3D17%20%5C%5C%20-%5Cmleft%285%2B3y%5Cmright%29%2By-z%3D-6%5Cend%7Bbmatrix%7D%5Cmright%3F%20%5C%5C%2015%2By%2Bz%3D17%20%5C%5C%20-5-2y-z%3D-6%20%5C%5C%20-------------%20%5C%5C%20y%3D-z%2B2%20%5C%5C%20-5-2%28-z%2B2%29-z%3D-6%20%5C%5C%20-5%2B2z-4-z%3D-6%20%5C%5C%20z-9%3D-6%20%5C%5C%20z%3D9-6%20%5C%5C%20z%3D3%20%5Cend%7Bgathered%7D)
Now, let's find y based on y=-z+2 plug into that z=3
![\begin{gathered} y=-3+2 \\ y=-1 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D-3%2B2%20%5C%5C%20y%3D-1%20%5Cend%7Bgathered%7D)
2.2) And finally, let's find x
![\begin{gathered} x=5+3y \\ x=5+3(-1) \\ x=5-3 \\ x=2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%3D5%2B3y%20%5C%5C%20x%3D5%2B3%28-1%29%20%5C%5C%20x%3D5-3%20%5C%5C%20x%3D2%20%5Cend%7Bgathered%7D)
Hence, the answer is: