Решебник по алгебре 9 класс Макарычев Задание 418

 

\[\boxed{\text{418\ (418).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[\left\{ \begin{matrix} x^{2} + y^{2} = 100 \\ y = \frac{1}{2}x^{2} - 10\ \ \\ \end{matrix} \right.\ \]

\[x^{2} + y^{2} = 100\]

\[окружность\ с\ центром\ (0;0)\ и\ \]

\[радиусом\ равным\ 10.\]

\[y = \frac{1}{2}x^{2} - 10\]

\[парабола,\ ветви\ вверх.\]

\[Ответ:(0;\ - 10);\ \ ( - 6;8);(6;8).\]

\[\boxed{\text{418.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[\textbf{а)}\ y = 5x - 7;\ \ y = 3x + 1\]

\[5x - 7 = 3x + 1\]

\[5x - 3x = 1 + 7\]

\[2x = 8\]

\[x = 4.\]

\[y = 3x + 1 = 3 \cdot 4 + 1 = 13.\]

\[Ответ:(4;13).\]

\[\textbf{б)}\ y = - 3x - 2;\ \ y = 8x - 9\]

\[8x - 9 = - 3x - 2\]

\[8x + 3x = - 2 + 9\]

\[11x = 7\]

\[x = \frac{7}{11}.\]

\[y = - 3x - 2 = - 3 \cdot \frac{7}{11} - 2 =\]

\[= - \frac{21}{11} - 2 = - 1\frac{10}{11} - 2 =\]

\[= - 3\frac{10}{11}.\]

\[Ответ:\left( \frac{7}{11};\ - 3\frac{10}{11} \right).\]

\[\textbf{в)}\ y = 0,4x - 5;\ \ y = - 0,1x - 3\]

\[0,4x - 5 = - 0,1x - 3\]

\[0,4x + 0,1x = - 3 + 5\]

\[0,5x = 2\]

\[x = 4.\]

\[y = - 0,1x - 3 = - 0,1 \cdot 4 - 3 =\]

\[= - 0,4 - 3 = - 3,4.\]

\[Ответ:(4; - 3,4).\]

\[\textbf{г)}\ y = 23x - 6;\ \ y = - 2x + 9\]

\[23x - 6 = - 2x + 9\]

\[23x + 2x = 9 + 6\]

\[25x = 15\]

\[x = \frac{15}{25} = \frac{3}{5}\]

\[x = 0,6.\]

\[y = - 2x + 9 = - 2 \cdot 0,6 + 9 =\]

\[= - 1,2 + 9 = 7,8.\]

\[Ответ:(0,6;7,8).\]

\[\textbf{д)}\ y = 98x;\ \ \ y = - 102x - 3\]

\[98x = - 102x - 3\]

\[98x + 102x = - 3\]

\[200x = - 3\]

\[x = - \frac{3}{200} = - \frac{15}{1000}\]

\[x = - 0,015.\]

\[y = 98x = 98 \cdot \left( - \frac{3}{200} \right) =\]

\[= - \frac{49 \cdot 3}{100} = - \frac{147}{100} = - 1,47.\]

\[Ответ:( - 0,015;\ - 1,47).\]

\[\textbf{е)}\ y = - 3;\ \ y = 36x + 1\]

\[36x + 1 = - 3\]

\[36x = - 4\]

\[x = - \frac{4}{36} = - \frac{1}{9}.\]

\[Ответ:\left( - \frac{1}{9};\ - 3 \right).\]