The function f(x, y) accepts an ordered pair as input and gives another ordered pair as output. It is defined according to the following rules: If x > 4, f(x, y) = (x - 4,y). If x less equal 4 but y > 4, f(x, y) = (x, y - 4). Otherwise, f(x, y) = (x + 5, y + 6). A robot starts by moving to the point (1,1). Every time it arrives at a point (x, y), it applies f to that point and then moves to f(x, y). If the robot runs forever, how many different points will it visit?​

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  15

Step-by-step explanation:

In order, the points visited are ...

  {1,1}, {6,7}, {2,7}, {2,3}, {7,9}, {3,9}, {3,5}, {3,1}, {8,7}, {4,7}, {4,3}, {9,9}, {5,9}, {1,9}, {1,5}, and {1,1}, which starts the sequence over again.

A total of 15 different points are visited.

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.