1. x+2x-6
2+2(2)-6
2+4-6
0
2. 6x-5-x+8y
6(2)-5-2+8(-1)
12-5-2-8
-27
<h3>Answer:</h3>
(x, y) ⇒ (-y, x)
<h3>Explanation:</h3>
A point at y=1 on the y-axis will rotate to the point x = -1 on the x-axis when it is rotated 90° CCW about the origin. Hence the value of x for the image point is the opposite of the y-value of the original point.
A point at x=1 on the x-axis will rotate to the point y=1 on the y-axis when it is rotated 90° CCW about the origin. Hence the value of y for the image point is the x-value of the original point.
In summary, ...
... (x, y) ⇒ (-y, x)
_____
<em>Comment on rotation matrices</em>
The rotation matrix for rotatation through the angle θ CCW about the origin is ...
![\left[\begin{array}{cc}\cos{(\theta)}&-\sin{(\theta)}\\\sin{(\theta)}&\cos{(\theta)}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Ccos%7B%28%5Ctheta%29%7D%26-%5Csin%7B%28%5Ctheta%29%7D%5C%5C%5Csin%7B%28%5Ctheta%29%7D%26%5Ccos%7B%28%5Ctheta%29%7D%5Cend%7Barray%7D%5Cright%5D)
When θ = 90°, this matrix becomes ...
![\left[\begin{array}{cc}0&-1\\1&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%26-1%5C%5C1%260%5Cend%7Barray%7D%5Cright%5D)
and multiplication by coordinates (x, y) gives ...
![\left[\begin{array}{cc}0&-1\\1&0\end{array}\right]\times\left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}-y\\x\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%26-1%5C%5C1%260%5Cend%7Barray%7D%5Cright%5D%5Ctimes%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-y%5C%5Cx%5Cend%7Barray%7D%5Cright%5D)
Answer:
No false
Step-by-step explanation:
Theres the fibonacci sequance 1,1,2,3,5,8...
Answer:
g(x) is not the inverse of f(x)
Step-by-step explanation:
If f(x)=5x-25 and g(x) = 5x+5, which expression could be used to verify g(x) is the inverse of fx)
We need to show that f(g(x)) = g(f(x))
f(g(x)) = f(5x+5)
f(5x+5) = 5(5x+5) - 25
f(5x+5) =25x+25 - 25
f(5x+5) = 25x
f(g(x)) = 25x
Similarly;
g(f(x)) = g(5x-25)
g(5x-25) = 5(5x-25) + 5
g(5x-25) = 25x - 125 + 5
g(5x-25) = 25x - 120
This shows that g(x) is not the inverse of f(x)
Your answer would be 61 one
I added 31+55+68+70+70+72=366 But then you you count how many numbers you added... there was 6. So now you divide 366 and 6 and you should get 61.
Hope this helps :D