Решебник по алгебре 7 класс Мерзляк ФГОС Задание 874

 

\[\boxed{\text{874\ (874).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ y = 3,7x + 10\ \ и\ \]

\[\ y = 1,4x - 13\]

\[3,7x + 10 = 1,4x - 13\]

\[2,3x = - 23\]

\[x = - 10\]

\[y = 3,7 \cdot ( - 10) + 10 =\]

\[= - 37 + 10 = - 27\]

\[Ответ:( - 10;\ - 27).\]

\[2)\ y = 4 - \frac{2}{7}\text{x\ \ }и\ \ y = \frac{9}{7}x + 26\]

\[4 - \frac{2}{7}x = \frac{9}{7}x + 26\]

\[- \frac{11}{7}x = 22\]

\[x = \frac{- 22 \cdot 7}{11} = - 14\]

\[y = 4 - \frac{2}{7} \cdot ( - 14) = 4 + 4 = 8\]

\[Ответ:( - 14;8).\]

\[\boxed{\text{874.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ x² - 4x + 3 =\]

\[= \left( x^{2} - 4x + 4 \right) - 1 =\]

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

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

\[= (x - 3)(x - 1)\]

\[2)\ a² + 2a - 24 =\]

\[= \left( a^{2} + 2a + 1 \right) - 25 =\]

\[= (a + 1)^{2} - 25 =\]

\[= (a + 1 - 5)(a + 1 + 5) =\]

\[= (a - 4)(a + 6)\]

\[3)\ y² + 12y + 35 =\]

\[= \left( y^{2} + 12y + 36 \right) - 1 =\]

\[= (y + 6)^{2} - 1 =\]

\[= (y + 6 - 1)(y + 6 + 1) =\]

\[= (y + 5)(y + 7)\]

\[4)\ x² + x - 6 =\]

\[= \left( x^{2} + x + \frac{1}{4} \right) - 6,25 =\]

\[= (x + 0,5)^{2} - 2,5² =\]

\[= (x + 0,5 + 2,5)(x + 0,5 - 2,5) =\]

\[= (x + 3)(x - 2)\]

\[5)\ c² + 8cd + 15d² =\]

\[= \left( c^{2} + 8cd + 16d^{2} \right) - d^{2} =\]

\[= (c + 4d)^{2} - d^{2} =\]

\[= (c + 4d - d)(c + 4d + d) =\]

\[= (c + 3d)(c + 5d)\]

\[6)\ 9x² - 30xy + 16y^{2} =\]

\[= \left( 9x^{2} - 30xy + 25y^{2} \right) - 9y^{2} =\]

\[= (3x - 5y)^{2} - 9y^{2} =\]

\[= (3x - 5y + 3y)(3x - 5y - 3y) =\]

\[= (3x - 2y)(3x - 8y)\]