Write the English phrase as an algebraic expression. Then simplify the expression. Let x represent the numbe A number decreased by the sum of the number and six. What is the algebraic expression? (Do not simplify.)

Find the following matrices where \( A=\left[\begin{array}{rrr}-13 & 11 & 5 \\ 7 & -13 & -1 \\ 1 & -14 & -7\end{array}\right] \) and \( B=\left[\begin{array}{rrr}5 & 0 & 8 \\ 0 & 11 & 3 \\ 6 & 6 & -13\end{array}\right] \) a. \( A+B \quad \) b. \( A-B \quad \) d. \( 5 A-5 B \) a. Select the correct choice below and if necessary, fal in the answer box to complete your oh A. \( A+B= \) (Simplity your answer) B. This matrix operation is not possible

\( \left(\frac{a}{b}\right)^{3} \) \( \left(\frac{a}{b}\right)^{3}=\left(\frac{a}{b}\right) \) (Simplify your answers.)

Dxercice 2: (1) Montrer les implications suivantes: a \( (\forall x, y \in \mathbb{R}) ; \quad \mathrm{Si} \quad(|\mathrm{x}| \leq 1 \) et \( |y| \leq 1) \quad \) alors \( \sqrt{1-\mathrm{x}^{2}}+\sqrt{1-\mathrm{y}^{2}} \leq 2 \sqrt{1-\left(\frac{\mathrm{x}+\mathrm{y}}{2}\right)^{2}} \) b \( \left(\forall \mathrm{x}, \mathrm{y} \in \mathbb{R}^{*}\right) ; \quad 2 \mathrm{x}+4 \mathrm{y}=1 \Rightarrow \frac{1}{\mathrm{x}^{2}+\mathrm{y}^{2}} \leq 20 \) (2) En utilisant "Le raisonnement par les équivalences successives", montrer que: a \( \left(\forall \mathrm{x}, \mathrm{y} \in \mathbb{R}^{+}\right) ; \quad \mathrm{x} \sqrt{\mathrm{x}^{2}+1}=y \sqrt{\mathrm{y}^{2}+1} \Longleftrightarrow x=y \) \( \mathrm{~b}\left(\forall \mathrm{x}, \mathrm{y} \in \mathbb{R}_{+}^{*}\right) ; \quad \mathrm{x} \prec \mathrm{y} \Longleftrightarrow \frac{\mathrm{x}}{\mathrm{y}} \prec \frac{2 \mathrm{x}+5 \mathrm{y}}{5 \mathrm{x}+2 \mathrm{y}} \prec \frac{\mathrm{y}}{\mathrm{x}} \)

9 protons, 10 electrons Express your answer as an ion.

Si la raíz cuadrada de 10 se divide por 4 , se obtiene