We have the following information
[tex]\begin{gathered} x_1=-10 \\ x_2=-3 \end{gathered}[/tex]and the function
[tex]f(x)=\sqrt[]{-9x+5}[/tex]In order to find the average rate, we need to find y1 and y2. Then, by substituting x1 into the function, we have
[tex]\begin{gathered} f(-10)=\sqrt[]{-9(-10)+5} \\ f(-10)=\sqrt[]{90+5} \\ f(-10)=\sqrt[]{95} \end{gathered}[/tex]Similarly, by substituting x2, we get
[tex]\begin{gathered} f(-3)=\sqrt[]{-9(-3)+5} \\ f(-3)=\sqrt[]{27+5} \\ f(-3)=\sqrt[]{32} \end{gathered}[/tex]Therefore, the average rate is given by
[tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{\sqrt[]{32}-\sqrt[]{95}}{-3-(-10)}[/tex]which gives
[tex]\begin{gathered} \frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{\sqrt[]{32}-\sqrt[]{95}}{7} \\ \frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{5.6568-9.7467}{7} \\ \frac{f(x_2)-f(x_1)}{x_2-x_1}=-\frac{4.0899}{7} \end{gathered}[/tex]Therefore, the average rate is
[tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}=-0.58[/tex]