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.

Solve. \( d=n z x \), for \( x \)

Audrey has \( \$ 440 \) to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. - She buys a new bicycle for \( \$ 259.52 \). - She buys 2 bicycle reflectors for \( \$ 3.07 \) each and a pair of bike gloves for \( \$ 29.12 \). - She plans to spend some or all of the money she has left to buy new biking outfits for \( \$ 72.61 \) each. Write and solve an inequality which can be used to determine \( o \), the number of outfits Audrey can purchase while staying within her budget.

Resuelve los siguientes problemas y determina si la solución de la ecuación es pertinente al contexto. Justifica tu respuesta e indica si es posible darla a partir de la solución de la ecuación. a. Al preguntarle la edad a lsabel, ella contesta que, si se le restan 9 años al doble de su edad, se obtiene el triple de su edad. ¿Cuántos años tiene Isabel? ¿Es posible que ocurra lo que ella señala)

Tentukan kecerunan dan pintasan-y bagi garis lurus berikut (a) \( \quad y=4 x+6 \)

Solve for \( z:-6 z \leq 54 \) \( \begin{array}{l}z=-9 \\ 0 z \leq-9 \\ 0 z \geq 9 \\ 0 z \geq-9\end{array} \)