Question

figure cdef is a parallelogram.
which equations are correct? select three options.
n = 10
n = 7
cf = 59
fe = 42
cd = 30

Explanation:

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<reasoning>

Equate opposite sides of the parallelogram

Using the Properties of Parallelograms knowledge point
\[

$$\begin{aligned} &CF = DE\\ &6n - 1 = 5n + 9 \end{aligned}$$

\]

Solve for the variable n

Using the Solving Linear Equations knowledge point
\[

$$\begin{aligned} &(6n - 1) - 5n = (5n + 9) - 5n\\ &n - 1 = 9\\ &n = 10 \end{aligned}$$

\]

Calculate the side lengths

Using the Properties of Parallelograms knowledge point
\[

$$\begin{aligned} &CF = 6(10) - 1 = 59\\ &CD = 4(10) + 2 = 42\\ &FE = CD = 42 \end{aligned}$$

\]

Identify the correct options

Using the Properties of Parallelograms knowledge point
\[

$$\begin{aligned} &n = 10 \quad \text{(Correct)}\\ &CF = 59 \quad \text{(Correct)}\\ &FE = 42 \quad \text{(Correct)} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>n = 10</mcq-correct>
<mcq-option>n = 7</mcq-option>
<mcq-correct>CF = 59</mcq-correct>
<mcq-correct>FE = 42</mcq-correct>
<mcq-option>CD = 30</mcq-option>
</answer>

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Answer:

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<reasoning>

Equate opposite sides of the parallelogram

Using the Properties of Parallelograms knowledge point
\[

$$\begin{aligned} &CF = DE\\ &6n - 1 = 5n + 9 \end{aligned}$$

\]

Solve for the variable n

Using the Solving Linear Equations knowledge point
\[

$$\begin{aligned} &(6n - 1) - 5n = (5n + 9) - 5n\\ &n - 1 = 9\\ &n = 10 \end{aligned}$$

\]

Calculate the side lengths

Using the Properties of Parallelograms knowledge point
\[

$$\begin{aligned} &CF = 6(10) - 1 = 59\\ &CD = 4(10) + 2 = 42\\ &FE = CD = 42 \end{aligned}$$

\]

Identify the correct options

Using the Properties of Parallelograms knowledge point
\[

$$\begin{aligned} &n = 10 \quad \text{(Correct)}\\ &CF = 59 \quad \text{(Correct)}\\ &FE = 42 \quad \text{(Correct)} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>n = 10</mcq-correct>
<mcq-option>n = 7</mcq-option>
<mcq-correct>CF = 59</mcq-correct>
<mcq-correct>FE = 42</mcq-correct>
<mcq-option>CD = 30</mcq-option>
</answer>

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