Question

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

Explanation:

Step1: Set equal opposite sides

In parallelogram CDEF, opposite sides are equal: $6n - 1 = 5n + 9$

Step2: Solve for n

Subtract $5n$ from both sides: $n - 1 = 9$
Add 1 to both sides: $n = 10$

Step3: Calculate CF length

Substitute $n=10$ into $CF=6n-1$:
$CF = 6(10) - 1 = 60 - 1 = 59$

Step4: Calculate CD length

Substitute $n=10$ into $CD=4n+2$:
$CD = 4(10) + 2 = 40 + 2 = 42$ (Note: $FE=CD$ in a parallelogram, so $FE=42$)

Answer:

$\boldsymbol{n = 10}$, $\boldsymbol{CF = 59}$, $\boldsymbol{FE = 42}$