Question

in which of the tables below are \\(x\\) and \\(y\\) inversely proportional?

\\(\

$$\begin{array}{|c|c|c|c|c|} \\hline x & 0.1 & 0.3 & 25 & 100 \\\\ \\hline y & 200 & 40 & 0.8 & 0.2 \\\\ \\hline \\end{array}$$

\\)

answer

\\(x\\) and \\(y\\) dropdown inversely proportional

Explanation:

Define inverse proportionality

Two variables \(x\) and \(y\) are inversely proportional if their product is a constant value \(k\).

$$ x \cdot y = k $$

Calculate the product for each pair

We will multiply each \(x\) value by its corresponding \(y\) value from the table.
Using the Proportions knowledge point:

• First pair: \(0.1 \cdot 200 = 20\)
• Second pair: \(0.3 \cdot 40 = 12\)
• Third pair: \(25 \cdot 0.8 = 20\)
• Fourth pair: \(100 \cdot 0.2 = 20\)

Determine if they are inversely proportional

Since the product \(x \cdot y\) is not constant for all pairs (the second pair gives \(12\) while the others give \(20\)), the variables in this table are not inversely proportional.

Answer:

\(x\) and \(y\) <blank>are not</blank> inversely proportional