We consider the system given by the following augmented matrix \( \left[\begin{array}{rrr|r}1 & -2 & 1 & 4 \\ 0 & 1 & -1 & 3 \\ 0 & 0 & \alpha^{2}-\alpha-2 & \alpha+1\end{array}\right] \) Determine the value (s) of \( \alpha \) for which the system has exactly one solution.

5) \( 4(2-x)=x+3 \)

Suppose the linear regression line \( y=3.009 x \) - 77.131 predicts a pizza parlor's profits based on the number of pizzas sold. If \( x \) represents the number of pizzas sold, and \( y \) represents the pizza partor's profits in dollars, about how much can the plizza parlor expect in profits if it sells 275 pizzas? A. \( \$ 750 \) B. \( \$ 900 \) C. \( \$ 825 \) D. \( \$ 675 \)

a) \( \log _{2} x=1-x \);

Which of the following equations has no solution \( \begin{array}{l}x+20-5 x=7(3+x)-3 x \\ \begin{array}{l}5 x+20-7 x=7(3+x)-3 x \\ 5 x+21-x=7(3+x)-3 x \\ 5 x+20-x=7(3+x)-3 x\end{array} \\ \begin{array}{l}5\end{array}\end{array} \$ \begin{array}{l}\text { - }\end{array} \)

a) \( \log _{2} x=1-x \);