Six friends together with their respective partners all meet up for a meal. To  commemorate the occasion, they arrange for a photograph to be taken of all 12 of them  standing in a line. How many different arrangements are these if each friend is standing next to his or her partner?​

1440 different arrangements are possible.

Step-by-step explanation:

Number of arrangements of n elements:

The number of arrangements of n elements is given by:

In this question:

6 couples, in which each can be positioned in 2 ways(him/her or her/him). So

1440 different arrangements are possible.

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116