D) Considérons les vecteurs \( \vec{u} \) et \( \vec{v} \) tels que \( \|\vec{v}\|=5 \). \( \|\vec{v}\|=2 \) et \( \vec{u} \cdot \vec{v}=10 \). Montrez que la norme du vecteur \( \vec{w} \vec{i}=2 \vec{u}+3 \vec{v} \) est égale à 16 et que celle du \( \vec{w}=2 \vec{u}-3 \vec{v} \) est égale à 4

2. Find the domain and perform each of the following indicated operations. \[ \begin{array}{ll}\text { a. } \frac{x-1}{x+2}+\frac{x+3}{x^{2}+6 x+5} & \text { c. } \frac{x-1}{x+2} \times \frac{x+3}{x^{2}+6 x+5} \\ \text { b. } \frac{x-1}{x+2}-\frac{x+3}{x^{2}+6 x+5} & \text { d. } \frac{x-1}{x+2} \div \frac{x+3}{x^{2}+6 x+5}\end{array} \]

3. Factorize os seguintes polinómios: a) \( 2 x+a x+4 y+2 a y \) b) \( x^{3}-4 x \) \( \begin{array}{l}\text { 4. Sobre a equação do } 2^{\circ} \text { grau, determine a solução da seguinte eq } \\ \left.-2 x^{2}+3 x+5=0-1\right) \\ \text { 5. Encontre a solução do seguinte sistema de } 2 \text { equações: } \\ \qquad\left\{\begin{array}{c}2 x+4 y=11 \\ 5 x-15 y=-20\end{array}\right.\end{array} \)

15. Determine whether the function \( f: \mathbf{Z} \times \mathbf{Z} \rightarrow \mathbf{Z} \) is onto if a) \( f(m, n)=m+n \). b) \( f(m, n)=m^{2}+n^{2} \). c) \( f(m, n)=m \). d) \( f(m, n)=|n| \). e) \( f(m, n)=m-n \).

\( \begin{array}{l}\qquad x=8 \\ \text { So, length of the given rectangle }=(8+9) \mathrm{cm}=17 \mathrm{~cm} \\ \text { And, breadt of the given rectangle }=8 \mathrm{~cm} .\end{array} \) EXERCISE 15 B 1. 17 less than four times a number is 11 . Find the number.

3) The sign of function \( f(X)=7-X \) is not negative in .............. \( \begin{array}{lll}\text { (a) }]-\infty, 7[ & \text { (b) }[0,7[ & \text { (c) }]-\infty, 7]\end{array} \)