Consider the line \( y=-\frac{5}{6} x+7 \). Find the equation of the line that is perpendicular to this line and passes through the point \( (-5,-2) \). Find the equation of the line that is parallel to this line and passes through the point \( (-5,-2) \). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of perpendicular line: Equation of parallel line:

Solve. \[ 7|x-1|+9 \geq 37 \] If all real numbers are solutions, click on "All reals". If there is no solution, click on "No solution".

Match the following conjugate factors to the appropriate quadratic factor created when multiplying the factors together. \[ \begin{array}{l}(x+7-2 i)(x+7+2 i) \\ \qquad \begin{array}{l}\text { a. } x^{2}+14 x+53 \\ (x+4-2 \sqrt{2})(x+4+2 \sqrt{2}) \\ (x-6 i)(x+6 i)\end{array} \\ \begin{array}{l}\text { b. } x^{2}+8 x+8\end{array}\end{array} . \]

Solve the equation. \[ 2^{2 x+1}=8 \] The solution set is \( \{\square\} \). (Type an integer or a simplified fraction. Use a comma to separate answers as ne

Solve the equation. \[ \left(\frac{2}{5}\right)^{x}=\left(\frac{8}{125}\right) \] The solution set is \( \{\underbrace{3} \). (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

Solve the equation. \[ 32^{-x+52}=256^{x} \] The solution set is (Type an integer or a simplified fraction. Use a comma to separate answers as