Identify the relationship between the two columns in the table, and determine R(1+2).
Understand the Problem
The question presents a table and asks to identify the relationship between the two columns. It also asks a question about R(1+2).
Answer
$R(x) = 4x + 2$ $R(1+2) = 14$
Answer for screen readers
$R(x) = 4x + 2$ $R(1+2) = 14$
Steps to Solve
- Find the pattern
Let's analyze the numbers in the table to find the relationship between $R$ and the corresponding values. We can observe that the difference between consecutive values in the second column is constant: $10 - 6 = 4$ $14 - 10 = 4$ $18 - 14 = 4$ This suggests a linear relationship of the form $y = ax + b$, where $y$ is the value in the second column and $x$ is the value of $R$.
- Determine the equation
Since the difference is 4, the coefficient $a$ is 4. So, $y = 4x + b$. Now, we can use one of the points from the table to find $b$. Let's use the point $(1, 6)$: $6 = 4(1) + b$ $6 = 4 + b$ $b = 2$ Therefore, the equation is $y = 4x + 2$. We can write this as $R(x) = 4x + 2$.
- Calculate $R(1+2)$
We now need to find $R(1+2)$, which simplifies to $R(3)$. Using the equation we found: $R(3) = 4(3) + 2$ $R(3) = 12 + 2$ $R(3) = 14$
$R(x) = 4x + 2$ $R(1+2) = 14$
More Information
The relationship between the column R, and the question mark column is found to be $R(x) = 4x + 2$. Therefore $R(1+2) = 14$.
Tips
A common mistake is to not correctly identify the pattern and assume some other relationship between $R$ and the other column. Another common mistake could be in the substitution when solving for $b$.
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