The graph appears to begin at \( ( 0,0 ) \) . Is \( ( 0,0 ) \) a valid point in terms of the context of the situation? Why or why not? Select the option that correctly answers both questions.  The point is valid in terms of the context because when Maura buys \( 0 \) feet of fence, the perimeter of the garden is \( 0 \) feet. The point is valid in terms of the context because it represents the smallest garden Maura can have as well as the amount of fence she must buy. The point is valid in terms of the context because it shows that the area and perimeter start at \( 0 \) . The point is not valid in terms of the context because the garden can't have an area of \( 0 \) square feet.  

If \( \sum_{p=0}^{k}\left(\frac{1}{3} p+\frac{1}{6}\right)=20 \frac{1}{6} \), determine the value of \( k \)

\( \mathrm{C}=\frac{\sqrt{3}}{\sqrt{3}+1}-\frac{\sqrt{3}-1}{\sqrt{3}+2}- \) et \( D=\left(\sqrt{5}+\frac{1}{\sqrt{5}}\right)^{2} \) 3) Soient \( x, y \) et \( z \) trois nombres réels strictement positifs. a) Montre que si \( x y+y z+x z=0 \) alors \( \frac{y+z}{x}+\frac{x+z}{y}+\frac{x+y}{z}=-3 \).

if: \( x=\frac{5}{4} y \), what is \( \sqrt{x^{2}-y^{2}} \) \( \begin{array}{llll}\text { 1) } 1 & \text { 2)2 } & \text { 3) } 3 & 4) 4\end{array} \)

Question (2): Solve all the following Problem Marks] a) If \( A=\left[\begin{array}{cc}0 & -1 \\ 2 & 5 \\ 1 & 3\end{array}\right] \) and \( B=\left[\begin{array}{cc}-1 & 0 \\ 5 & -1 \\ 3 & 2\end{array}\right] \), find \( 3 A-B \). b) If \( A=\left[\begin{array}{cc}1 & 2 \\ -1 & 0 \\ 0 & 3\end{array}\right] \), and \( B=\left[\begin{array}{ccc}0 & -1 & 2 \\ -4 & 1 & 0\end{array}\right] \), find \( B A \). c) Find the inverse of the Matrix \( A=\left[\begin{array}{ccc}4 & -2 & 1 \\ 5 & 0 & 3 \\ -1 & 2 & 6\end{array}\right] \) d) Solve the following system of equations using jacobi method. \( x+y+z=9 \) \( \quad 2 x+5 y+7 z=52 \) \( 2 x+y-z=0 \)

PARTIE B 1) Effectuer les opérations suivantes et donner le résultat sous la forme de fraction irréductible : \( A=\left(\frac{1}{2}-\frac{11}{24}\right) \times\left(2-\frac{4}{3}\right) \) et \( B=\left(2-\frac{3-\frac{1}{3}}{3+\frac{1}{3}}\right):\left(1+\frac{1+\frac{3}{4}}{1-\frac{3}{4}}\right) \) 2) Calculer puis écrire sans radical au dénominateur les expressions suivantes : \( \mathrm{C}=\frac{\sqrt{3}}{\sqrt{3}+1}-\frac{\sqrt{3}-1}{\sqrt{3}+2}- \) et \( D=\left(\sqrt{5}+\frac{1}{\sqrt{5}}\right)^{2} \) 3) Soient \( x, y \) et \( z \) trois nombres réels strictement positifs. a) Montre que si \( x y+y z+x z=0 \) alors \( \frac{y+z}{x}+\frac{x+z}{y}+\frac{x+y}{z}=-3 \). b) Montrer que si \( x<y \) alors \( \sqrt{x+y+2 \sqrt{x y}}+\sqrt{x+y-2 \sqrt{x y}}=2 \sqrt{y} \) c) Montrer que si \( x \geq 2 \) alors \( (\sqrt{x+2 \sqrt{x-1}}+\sqrt{x-2 \sqrt{x-1}})^{2}=4(x-1) \) Bonus Démontrer que \( \sqrt{2} \) est irrationnelle \( (0,5 \mathrm{pt}) \)