Answer:
Matrix transformation = ![\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D)
Vertices of the new image: P'= (5,-2), Q'= (6,-3), R'= (2,-3)
Step-by-step explanation:
Transformation by reflection will produce a new congruent object in different coordinate. Reflection to y-axis made by multiplying the x coordinate with -1 and keep the y coordinate unchanged. The matrix transformation for reflection across y-axis should be: .
To find the coordinate of the vertices after transformation, you have to multiply the vertices with the matrix. The calculation of the each vertice will be:
P'= ![\left[\begin{array}{ccc}-5\\-2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%5C%5C-2%5Cend%7Barray%7D%5Cright%5D)
= (5,-2)
Q'= ![\left[\begin{array}{ccc}-6\\-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-6%5C%5C-3%5Cend%7Barray%7D%5Cright%5D)
= (6,-3)
R'= ![\left[\begin{array}{ccc}-2\\-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%5C%5C-3%5Cend%7Barray%7D%5Cright%5D)
= (2,-3)
Completed question:
In the game of tic-tac-toe, if all moves are performed randomly the probability that the game will end in a draw is 0.127. Suppose six random games of tic-tac-toe are played. What is the probability that at least one of them will end in a draw?
Answer:
0.557
Step-by-step explanation:
For each game, the probability of not end in a draw is 1 - 0.127 = 0.873. Thus, because each game is independent of each other, the probability of all of them not end in a draw is the multiplication of the probability of each one:
0.873x0.873x0.873x...x0.873 = 0.873⁶ = 0.443
Thus, the probability that at least one of them end in a draw is the total probability (1) less the probability that none of them en in a draw:
1 - 0.443
0.557
You can use substitution and solve y-x=2 for y which is y= x+ 2 and plug it into the y of the other equasion and you get x=5 y=7
