Questions: x y ------ 2 8 5 20 40 12 k=

Transcript text: \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 2 & 8 \\ \hline 5 & 20 \\ \hline & 40 \\ \hline 12 & \\ \hline \end{tabular} $k=$

Solution

Solution Steps

To solve this problem, we need to determine the relationship between $ x $ and $ y $. By examining the given pairs, we can identify a pattern or a function that relates $ x $ to $ y $. Once we have the function, we can use it to find the missing values.

Solution Approach

Identify the relationship between $ x $ and $ y $ using the given pairs.
Use the identified relationship to calculate the missing values for $ y $ when $ x = 12 $ and for $ x $ when $ y = 40 $.

Step 1: Identify the Relationship Between $ x $ and $ y $

Given the data points $(2, 8)$ and $(5, 20)$, we observe that: \[ y = 4x \]

Step 2: Calculate the Missing Value of $ y $ When $ x = 12 $

Using the relationship $ y = 4x $: \[ y = 4 \times 12 = 48 \]

Step 3: Calculate the Missing Value of $ x $ When $ y = 40 $

Using the relationship $ y = 4x $: \[ x = \frac{y}{4} = \frac{40}{4} = 10.0 \]