Consider the matrices \( X=\left[\begin{array}{rr}x+y-1 & 0 \\ 0 & 3\end{array}\right] \) and \( Y=\left[\begin{array}{rr}5 & 0 \\ 0 & 2 x-3 y-7\end{array}\right] \) The value(s) of \( x \) for which the matrices \( X \) has no inverse and \( Y=-5 I_{2} \) is/are given bv:

Solve the equation. \( \ln (8 \mathrm{x}+15)-\ln \mathrm{x}=\ln 9 \) Select the correct choice below and, if necessary, fill in th A. The solution set is \( \{ \) B. The solution is the empty set. (Simplify your answer. Use a comma to separate a

Consider the line \( y=\frac{5}{2} x-3 \). Find the equation of the line that is perpendicular to this line and passes through the point \( (2,-5) \). Find the equation of the line that is parallel to this line and passes through the point (2, -5). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of perpendicular line:

Use the properties of logarithms to rewrite the expression. Simplify the res \( \log _{3} \frac{\sqrt{x} \sqrt[3]{y}}{w} \sqrt{z} \) Choose the correct answer. A. \( -\frac{1}{2} \log _{3} x-\frac{1}{3} \log _{3} y+5 \log _{3} w+\frac{1}{2} \log _{3} z \) B. \( \frac{1}{2} \log _{3} x+\frac{1}{3} \log _{3} y-5 \log _{3} w-\frac{1}{2} \log _{3} z \) C. \( { }^{2} \log _{3} x+3 \log _{3} y-5 \log _{3} w-2 \log _{3} z \) D. This cannot be simplified.

b. \( -0.5 p+\frac{1}{2} p-2.75+\frac{2}{3} \)

1 Graph \( y-2=\frac{2}{3}(x-3) \)