Exercice 1 : suite de l'exercice 7 du td précédent... Un consommateur dépense la totalité de son revenu R à l'achat de deux biens X et Y en quantités x et y aux prix Px et Py. Ses préférences sont stables et peuvent être exprimées par la fonction d'utilité : \( U(X, Y)=(X+2)(Y+2) \)

Solve the following system of equations by graphing. Determine If the system is consistent or inconsistent, if consiatens give the coordinate. Last, determme if the equation is dependent or independent. \[ y=3 x+2 \] \[ 6 x-2 y=9 \] braph the equations into two slope- intercept fums. \[ y=\square x+\square \] \[ y=\square \]

\( \left. \begin{array} { l } { ( 9 ) = x ^ { 2 } - 6 x + 9 } \\ { F ( x ) = 8 } \end{array} \right. \)

A point on the terminal side of an angle \( \theta \) in standard position is \( \left(\frac{\sqrt{77}}{9}, \frac{2}{9}\right) \). Find the exact value of each of the six trigonometric functions of \( \theta \).

\( \left\{\begin{array}{l}\frac{x^{2}+a}{2 x+4} \quad \text { si } x<0 \\ 10 x^{2}+x+b \quad \text { si } x \geq 0\end{array}\right. \)

2. Themes: The underlying themes have been provided for you. Identify where in the story each theme can be found/proven. Tell how it is shown and explain. Theme \( 1: \).The reluctance of people to reject outdated traditions, ideas, rules, laws, and practices. Theme \( 2: \) Society wrongfully designates scapegoats to bear the sins of the community. Theme \( 3: \).The wickedness of ordinary people can be just as horrifying as the heinous crime of a serial killer or a sadistic head of state.