Решебник по алгебре 8 класс Мерзляк ФГОС Задание 700

 

\[\boxed{\mathbf{700\ (700).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[5\% = 0,05;\ \ \ \ 45\% = 0,45;\ \ \ \ \]

\[30\% = 0,3\]

\[Пусть\ x_{1} - количество\ лома\ \]

\[первого\ сорта;\]

\[тогда\ x_{2} - количество\ лома\ \]

\[второго\ сорта,\ \]

\[а\ \ \left( x_{1} + x_{2} = 120 \right) - количество\ \]

\[сплава.\]

\[Составим\ уравнение:\]

\[\left\{ \begin{matrix} x_{1} + x_{2} = 120\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 0,05x_{1} + 0,45x_{2} = 0,3 \cdot 120 \\ \end{matrix} \right.\ \]

\[x_{1} = 120 - x_{2}\]

\[0,05 \cdot \left( 120 - x_{2} \right) + 0,45x_{2} = 36\]

\[6 - 0,05x_{2} + + 0,45x_{2} = 36\]

\[0,4x_{2} = 30\]

\[x_{2} = 75\ (тонн) - лома\ \]

\[второго\ сорта.\]

\[x_{1} = 120 - 75 = 45\ (тонн) -\]

\[лома\ первого\ сорта.\]

\[Ответ:45\ т,\ 75\ т.\]

\[\boxed{\mathbf{700.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ (2x - 5)(x + 2) = 18\]

\[2x^{2} + 4x - 5x - 10 - 18 = 0\]

\[2x^{2} - x - 28 = 0\]

\[D = 1 + 4 \cdot 2 \cdot 28 = 225\]

\[x = \frac{1 \pm \sqrt{225}}{4} = \frac{1 \pm 15}{4}\]

\[x_{1} = 4,\ \ x_{2} = - \frac{7}{2} = - 3,5\]

\[Ответ:\ x = - 3,5;x = 4.\]

\[16x^{2} - 24x + 9 + 9x^{2} - 1 - 9 =\]

\[= 0\]

\[25x^{2} - 24x - 1 = 0\]

\[D = 576 + 100 = 676\]

\[x = \frac{24 \pm \sqrt{676}}{50} = \frac{24 \pm 26}{50}\]

\[x_{1} = 1,\ \ x_{2} = - 0,04\]

\[Ответ:\ \ x = - 0,04;x = 1.\]

\[3)\ (x + 3)^{2} - (2x - 1)^{2} = 16\]

\[- 3x^{2} + 10x - 8 = 0\]

\[D = 100 - 4 \cdot 3 \cdot 8 = 100 - 96 =\]

\[= 4\]

\[x = \frac{- 10 \pm \sqrt{4}}{- 6} = \frac{- 10 \pm 2}{- 6}\]

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

\[Ответ:x = 2;\ \ x = 1\frac{1}{3}.\]

\[4)\ (x - 6)^{2} - 2x(x + 3) =\]

\[= 30 - 12x\]

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

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

\[D = 36 + 24 = 60\]

\[x = \frac{- 6 \pm \sqrt{60}}{2} = \frac{- 6 \pm 2\sqrt{15}}{2} =\]

\[= - 3 \pm \sqrt{15}\]

\[Ответ:\ x = - 3 \pm \sqrt{15}.\]