In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding $\displaystyle y$ value for $\displaystyle x=9$. We can plug $\displaystyle 9$ into the $\displaystyle x$ in our equation to solve for $\displaystyle y$.

$\displaystyle y=11(9)+7$

$\displaystyle y=99+7$

$\displaystyle y=106$

In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding $\displaystyle y$ value for $\displaystyle x=11$. We can plug $\displaystyle 11$ into the $\displaystyle x$ in our equation to solve for $\displaystyle y$.

$\displaystyle y=12(11)+5$

$\displaystyle y=132+5$

$\displaystyle y=137$

In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding $\displaystyle y$ value for $\displaystyle x=3$. We can plug $\displaystyle 3$ into the $\displaystyle x$ in our equation to solve for $\displaystyle y$.

$\displaystyle y=13(3)+3$

$\displaystyle y=39+3$

$\displaystyle y=42$

In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding $\displaystyle y$ value for $\displaystyle x=6$. We can plug $\displaystyle 6$ into the $\displaystyle x$ in our equation to solve for $\displaystyle y$.

$\displaystyle y=14(6)+6$

$\displaystyle y=84+6$

$\displaystyle y=90$

The question asks that you first determine the pattern, then use said pattern to find A and B, which can then be substituted into the equation $\displaystyle 2A*B$. The pattern is to add 5 to the previous number to achieve the next number, which results in

$\displaystyle A=11$ and $\displaystyle B=26$

Putting A and B into the equation gives:

$\displaystyle (2*(11))*26=572$

The other answers are wrong for the following reasons:

286 is $\displaystyle A*B$, not $\displaystyle 2A*B$

48 is $\displaystyle 2A +B$

63 is $\displaystyle 2B+A$

624 is a result of having $\displaystyle A=12$, a pattern addition mistake

To answer this question, the pattern must first be found. There is no common interval between the numbers, however it can be seen that the next number is the sum of the number plus the number before. A good way to address a tricky pattern is to write the difference of the two numbers above the number, as seen below where the bold numbers are the orginal numbers and the nonbolded numbers are the differences.

    0     1      1     2     3

1     1     2     3      5     8

Using this pattern the value of A will be $\displaystyle 8+13=21$

The first stop to determining what the $\displaystyle 57th$ tile will be is to determine how many repeats of the pattern will occur before hand. There are $\displaystyle 5$ colors in the pattern, so divide $\displaystyle 57$ by $\displaystyle 5$. This results in $\displaystyle 11$ with a remainder of $\displaystyle 2$. This means that there will be $\displaystyle 11$ repeats of the pattern and at the $\displaystyle 57th$ tile, it will be at the second spot in the pattern, which is Blue. So, the $\displaystyle 57th$ tile is Blue. 

In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding $\displaystyle y$ value for $\displaystyle x=6$. We can plug $\displaystyle 6$ into the $\displaystyle x$  in our equation to solve for $\displaystyle y$.

$\displaystyle y=7(6)+3$

$\displaystyle y=42+3$

$\displaystyle y=45$

The pattern for the set is all even numbers up until $\displaystyle 20$.  The missing even number between $\displaystyle 10$ and $\displaystyle 14$ would be $\displaystyle 12$ and the missing number between $\displaystyle 14$ and $\displaystyle 18$ would be $\displaystyle 16$.

Add 23 to the first element to get the second element. The increment decreases by two with each successive entry. The pattern can be seen below:

$\displaystyle 8 \bold {+23} = 31$

$\displaystyle 31 \bold {+21} = 52$

$\displaystyle 52 \mathbf{+ 19} = 71$

$\displaystyle 71 \mathbf{+ 17} = 88$

To get the element in the circle, add 15:

$\displaystyle 88\mathbf{ + 15}= 103$, the correct response.

This is confirmed by adding 13;

$\displaystyle 103 \mathbf{+ 1 3 } = 116$, the next number in the sequence.