exercises 11-5

assume that the variables $x$ and $y$ are inversely proportional. determine the missing value in each case.

1. if $x_1 = 7$, $x_2 = 4$, and $y_2 = 21$, determine the value of $y_1$.
2. if $x_1 = 3$, $y_1 = 12$, and $x_2 = 9$, determine the value of $y_2$.
3. if $y_1 = 1.5$, $x_2 = 2.5$, and $y_2 = 3$, determine the value of $x_1$.
4. if $x_1 = 25$, $x_2 = 5$, and $y_2 = 125$, determine the value of $y_1$.
5. if $x_1 = \frac{1}{2}$, $y_1 = 6$, and $y_2 = 9$, determine the value of $x_2$.
6. if $y_1 = 1$, $x_2 = 4$, and $y_2 = 7$, determine the value of $x_1$.

Question

exercises 11-5

assume that the variables $x$ and $y$ are inversely proportional. determine the missing value in each case.

1. if $x_1 = 7$, $x_2 = 4$, and $y_2 = 21$, determine the value of $y_1$.
2. if $x_1 = 3$, $y_1 = 12$, and $x_2 = 9$, determine the value of $y_2$.
3. if $y_1 = 1.5$, $x_2 = 2.5$, and $y_2 = 3$, determine the value of $x_1$.
4. if $x_1 = 25$, $x_2 = 5$, and $y_2 = 125$, determine the value of $y_1$.
5. if $x_1 = \frac{1}{2}$, $y_1 = 6$, and $y_2 = 9$, determine the value of $x_2$.
6. if $y_1 = 1$, $x_2 = 4$, and $y_2 = 7$, determine the value of $x_1$.

Accepted Answer

{ "quality": "clear", "question_count": 6, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inverse Proportion Equations" ], "new_concepts": [], "current_concepts": [ "Inverse Proportion Equations" ] } ## Set up the inverse proportion relation $$ x_1 y_1 = x_2 y_2 = k $$ ## Solve for the missing values $$ \begin{aligned} &\text{1. } 7 \cdot y_1 = 4 \cdot 21 \implies y_1 = \frac{84}{7} = 12\ &\text{2. } 3 \cdot 12 = 9 \cdot y_2 \implies y_2 = \frac{36}{9} = 4\ &\text{3. } x_1 \cdot 1.5 = 2.5 \cdot 3 \implies x_1 = \frac{7.5}{1.5} = 5\ &\text{4. } 25 \cdot y_1 = 5 \cdot 125 \implies y_1 = \frac{625}{25} = 25\ &\text{5. } \frac{1}{2} \cdot 6 = x_2 \cdot 9 \implies x_2 = \frac{3}{9} = \frac{1}{3}\ &\text{6. } x_1 \cdot 1 = 4 \cdot 7 \implies x_1 = 28 \end{aligned} $$ | No. | Answer | |---|---| | 1 | $y_1 = 12$ | | 2 | $y_2 = 4$ | | 3 | $x_1 = 5$ | | 4 | $y_1 = 25$ | | 5 | $x_2 = \frac{1}{3}$ | | 6 | $x_1 = 28$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Inverse Proportion Equations" ] }

No.	Answer
2	\(y_2 = 4\)
3	\(x_1 = 5\)
4	\(y_1 = 25\)
5	\(x_2 = \frac{1}{3}\)
6	\(x_1 = 28\)

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QUESTION IMAGE

Question

Explanation:

Set up the inverse proportion relation

Solve for the missing values

Answer: