Math Problem Statement
What are the missing values in the table? The table shows two rows labeled x and y with values like (x, y) = (8, 2), (x, y) = (56, ?), (x, y) = (72, ?).
Solution
The image shows a table with two rows labeled and , and various numbers in the columns. The table seems to represent a relationship between and , possibly a proportional or arithmetic one. The incomplete table looks like this:
\hline x & 8 & \_ & 56 & 72 \\ \hline y & 2 & 10 & \_ & \_ \\ \hline \end{array}$$ To solve the missing entries, we need to identify the relationship between $$x$$ and $$y$$. ### Step 1: Analyze the existing pairs. - For $$x = 8$$, $$y = 2$$. - For $$x = 56$$, $$y = \_$$. - For $$x = 72$$, $$y = \_$$. If we assume a direct proportionality (i.e., $$x = k \cdot y$$, where $$k$$ is a constant), we can find $$k$$ using the first pair: $$k = \frac{x}{y} = \frac{8}{2} = 4.$$ ### Step 2: Calculate the missing values using $$k = 4$$. - For $$x = 56$$, $$y = \frac{56}{4} = 14$$. - For $$x = 72$$, $$y = \frac{72}{4} = 18$$. ### Step 3: Find the missing $$x$$ when $$y = 10$$. Since $$x = 4 \cdot y$$, for $$y = 10$$: $$x = 4 \cdot 10 = 40.$$ Thus, the completed table is: $$\begin{array}{|c|c|c|c|c|} \hline x & 8 & 40 & 56 & 72 \\ \hline y & 2 & 10 & 14 & 18 \\ \hline \end{array}$$ Would you like more details on this, or do you have any questions? --- Here are 5 related questions to expand on this: 1. How can you verify whether a relationship between variables is proportional? 2. What happens if the relationship is not proportional but linear instead? 3. How do you find the constant $$k$$ in a directly proportional relationship? 4. Can this table be modeled using a different mathematical function, such as quadratic? 5. What is the significance of the constant ratio in real-world applications? **Tip:** Always check for patterns in known values when dealing with sequences or tables to determine relationships like proportionality or other functions.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Direct Proportion
Algebra
Formulas
x = k * y
k = x / y
Theorems
Proportionality Theorem
Suitable Grade Level
Grades 6-8