Solve the following equation. Write the answer in terms of the natural logarithm. \( e^{7 x}=2 \)

Which expression is equivalent to \(( x^ { \frac { 3} { 7} } ) ^ { 2} \) ?A. \(x^ { \frac { 6} { 14} } \)B. \(x^ { \frac { 17} { 7} } \)C. \(x^ { \frac { 6} { 7} } \)D. \(x^ { \frac { 5} { 7} } \)

Solve the system of quadratic inequalities: \[ \begin{array}{c}\mathrm{y}>\mathrm{x}^{2}-1 \\ \mathrm{y} \leq-\frac{1}{3} \mathrm{x}^{2}+5\end{array} \]

Find the points of intersection for the system \[ \begin{array}{l}\mathrm{y} \geq 2 \mathrm{x}^{2}+3 \mathrm{x}-20 \\ \mathrm{y} \leq \mathrm{x}^{2}+\mathrm{x}-5\end{array} \]

Which graph represents the solution to the system of quadratic inequalities? \( y \geq \mathrm{x}^{2}+3 \mathrm{x}-7 \) \( \mathrm{y} \leq-\mathrm{x}^{2}+5 \mathrm{x}+2 \)

Solve the system of quadratic inequalities: \[ \begin{array}{l}y<x^{2}-4 \\ y>-x^{2}+2\end{array} \]