In un rettangolo l'altezza è di 10 cm più corta della base. Il perimetro è \( 2,6 \mathrm{~m} \). Calcola l'area del rettangolo.

\( 1 \leftarrow \quad \begin{array}{l}\text { A company finds it can produce } 25 \text { heaters for } \$ 6550 \text {, while producing } 30 \text { heaters costs } \$ 7800 \text {. Express the cost, } \\ \text { as a linear function of the number of heaters, } x \text {. Determine the cost to produce } 40 \text { heaters. } \\ \text { Express the cost, } y \text {, as a linear function of the number of heaters, } x \text {. } \\ y=\square \\ \text { (Simplify your answer.) } \\ \text { The cost to produce } 40 \text { heaters is } \$ \square\end{array} \).

Solve for \( x \) in the logarithmic equation \( 10^{\log \left(10^{24}\right)}=10^{x} \). (1 point) \( \begin{array}{l}x=10^{24} \\ x=24^{10} \\ x=24 \\ x=10\end{array} \)

If \( 10^{\log x}=10^{18} \), what is the value of \( x ? \) (1 point) 18 \( 10^{18} \) -18 \( 10^{-18} \)

Use the rule \( \log _{b}(x y)=\log _{b} x+\log _{b} y \) to find \( \log _{2}(16 \cdot 64) \). (1 point)

Find all x -intercepts of the following function. Write your answer or answers as coordinate points. Be sure to select the appropriate number of \( x \)-intercepts. \[ f(x)=\frac{3 x^{2}-x}{x^{2}-3 x-54} \]