Решебник по алгебре 9 класс Макарычев Задание 383

 

\[\boxed{\text{383\ (383).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[x^{2} + 6x - 7 \leq 0\]

\[D_{1} = 3^{2} + 7 = 16\]

\[x_{1,2} = - 3 \pm 4\]

\[x_{1} = - 7;\ \ x_{2} = 1.\]

\[(x + 7)(x - 1) \leq 0\]

\[\Longrightarrow x \in \lbrack - 7;1\rbrack.\]

\[x^{2} - 2x - 15 \leq 0\]

\[D = 1 + 15 = 16\]

\[x_{1,2} = 1 \pm 4\]

\[x_{1} = - 3;\ \ x_{2} = 1.\]

\[(x + 3)(x - 1) \leq 0\]

\[\Longrightarrow x \in \lbrack - 3;1\rbrack.\]

\[Общее\ решение:\ x \in \lbrack - 3;1\rbrack.\]

\[\boxed{\text{383.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[\textbf{а)}\ \left\{ \begin{matrix} 5x + 2y = 30\ | \cdot ( - 2) \\ 3x + 4y = - 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} - 10x - 4y = - 60 \\ 3x + 4y = - 3\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ ( + )\]

\[\left\{ \begin{matrix} - 7x = - 63\ \ \ \ \\ 3x + 4y = - 3 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} x = 9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 27 + 4y = - 3 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 9\ \ \ \ \ \ \ \ \\ y = - 7,5. \\ \end{matrix} \right.\ \]

\[Ответ:(9; - 7,5).\]

\[\textbf{б)}\ \left\{ \begin{matrix} 2x - y = 85\ \ \ \ | \cdot ( - 2) \\ 5x - 2y = 200\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} - 4x + 2y = - 170 \\ 5x - 2y = 200\ \ \ \ \ \ \\ \end{matrix} \right.\ ( + )\]

\[\Longrightarrow \left\{ \begin{matrix} x = 30\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2y = 4x - 170 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow \left\{ \begin{matrix} x = 30\ \ \ \ \ \ \ \ \ \ \\ y = 2x - 85 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 30\ \ \ \ \\ y = - 25. \\ \end{matrix} \right.\ \]

\[Ответ:\ \ (30;\ - 25).\]