Question

Consider the relationship 9r + 8t = 18. a. Write the relationship as a function r = f(t). Enter the exact answer. f(t) = 1 b. Evaluate f(-9). f(-9) =c. Solve f(t)=34t=

Answer 1

$\begin{gathered} 9r+8t=18 \\ r=f(t) \end{gathered}$$\begin{gathered} 9r+8t=18 \\ 9r=18-8t \\ r=2-\frac{8}{9}t \\ f(t)=2-\frac{8}{9}t \end{gathered}$$\begin{gathered} f(-9)=2-\frac{8}{9}\times-9 \\ f(-9)=2+8=10 \end{gathered}$$\begin{gathered} f(t)=34 \\ 2-\frac{8}{9}t=34 \\ -\frac{8}{9}t=32 \\ \text{cross multiply} \\ -8t=288 \\ t=\frac{288}{-8} \\ t=-36 \end{gathered}$