To determine which equations represent proportional relationships, we need to check if the ratios of the two quantities are equivalent in each equation.
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43 = 812
- This is not a proportional relationship since 43 does not equal 812.
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4/3 = 8/12
- This equation simplifies to 4/3 = 2/3, which is not a true statement, so it does not represent a proportional relationship.
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11x4 = 16.5x6
- To compare, we can rearrange it:
\( \frac{11}{16.5} = \frac{6}{4} \)
Reducing both fractions gives us:
\( \frac{11}{16.5} = \frac{2}{3} \) and \( \frac{6}{4} = \frac{3}{2} \).
These are not equivalent, so this equation does not represent a proportional relationship.
- To compare, we can rearrange it:
\( \frac{11}{16.5} = \frac{6}{4} \)
Reducing both fractions gives us:
\( \frac{11}{16.5} = \frac{2}{3} \) and \( \frac{6}{4} = \frac{3}{2} \).
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12 = 918
- This is not a proportional relationship since 12 does not equal 918.
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5x6.5 = 4x5.2
- Checking the ratio: \( \frac{5}{4} = \frac{5.2}{6.5} \) simplifies to \( \frac{5}{4} \) and \( \frac{5.2}{6.5} \) can be checked: \( 5/4 = 1.25 \) and \( 5.2/6.5 = 0.8 \), which are not equal. Thus, this equation does not represent a proportional relationship.
After analyzing all the equations, none of them represent proportional relationships.