question #3 use determinants to find the value of the variable. $\begin{vmatrix}3&x\\5&2end{vmatrix}=11$ -10…

Explanation:

Step1: Recall determinant formula

For a 2x2 matrix $\begin{vmatrix}a&b\c&d\end{vmatrix}=ad - bc$. Here $a = 3$, $b=x$, $c = 5$, $d = 2$. So $\begin{vmatrix}3&x\5&2\end{vmatrix}=3\times2-5x$.

Step2: Set up equation

Since $\begin{vmatrix}3&x\5&2\end{vmatrix}=11$, we have the equation $3\times2 - 5x=11$.

Step3: Simplify left - hand side

$6-5x = 11$.

Step4: Solve for x

Subtract 6 from both sides: $-5x=11 - 6$, so $-5x=5$. Then divide both sides by - 5, we get $x=-1$.

Answer:

D. -1