a rectangle with constant area has possible lengths and widths as shown in the table below.

width vs. length of a rectangle
\begin{tabular}{|c|c|}
\hline
width (w) & length (l) \\
\hline
2 & 37.5 \\
\hline
4 & 18.75 \\
\hline
6 & 12.5 \\
\hline
8 & 9.375 \\
\hline
\end{tabular}

which equation can be used to find any corresponding length and width that fit the pattern in this table?

$l = \frac{k}{w}$, where $l$ is the length, $w$ is the width, and $k$ is a constant $(w \
eq 0)$

$l = mw + b$, where $l$ is the length, $w$ is the width, and $m$ and $b$ are constants

$l = kw^{\frac{1}{2}}$, where $l$ is the length, $w$ is the width, and $k$ is a constant

$l = aw^2$, where $l$ is the length, $w$ is the width, and $a$ is a constant

Question

a rectangle with constant area has possible lengths and widths as shown in the table below.

width vs. length of a rectangle
\begin{tabular}{|c|c|}
\hline
width (w) & length (l) \\
\hline
2 & 37.5 \\
\hline
4 & 18.75 \\
\hline
6 & 12.5 \\
\hline
8 & 9.375 \\
\hline
\end{tabular}

which equation can be used to find any corresponding length and width that fit the pattern in this table?

$l = \frac{k}{w}$, where $l$ is the length, $w$ is the width, and $k$ is a constant $(w \
eq 0)$

$l = mw + b$, where $l$ is the length, $w$ is the width, and $m$ and $b$ are constants

$l = kw^{\frac{1}{2}}$, where $l$ is the length, $w$ is the width, and $k$ is a constant

$l = aw^2$, where $l$ is the length, $w$ is the width, and $a$ is a constant

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inverse Variation" ], "new_concepts": [], "current_concepts": [ "Inverse Variation", "Rational Functions" ] } ## Determine the relationship between variables $$ \begin{aligned} A &= l \cdot w \ k &= l \cdot w \quad (\text{where } k \text{ is the constant area}) \end{aligned} $$ ## Solve for length $$ l = \frac{k}{w}, \quad w eq 0 $$ ## Verify with table values $$ \begin{aligned} 2 \cdot 37.5 &= 75 \ 4 \cdot 18.75 &= 75 \ 6 \cdot 12.5 &= 75 \ 8 \cdot 9.375 &= 75 \ k &= 75 \end{aligned} $$

(A) $l = \frac{k}{w}$, where $l$ is the length, $w$ is the width, and $k$ is a constant $(w eq 0)$

(B) $l = mw + b$, where $l$ is the length, $w$ is the width, and $m$ and $b$ are constants

(C) $l = kw^{\frac{1}{2}}$, where $l$ is the length, $w$ is the width, and $k$ is a constant

(D) $l = aw^2$, where $l$ is the length, $w$ is the width, and $a$ is a constant

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Inverse Variation" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the relationship between variables

Solve for length

Verify with table values

Answer: