we are given the following vector:
[tex]z=<9,-2>[/tex]We are asked to determine its magnitude. To do that we will use the following formula:
[tex]||z||=\sqrt{x^2+y^2}[/tex]Where:
[tex]\begin{gathered} x=\text{ x-component} \\ y=\text{ y-component} \end{gathered}[/tex]Now, we plug in the values:
[tex]||z||=\sqrt{(9)^2+(-2)^2}[/tex]Solving the operations:
[tex]||z||=\sqrt{85}=9.22[/tex]Therefore, the magnitude is 9.22
