Question

Алгебра... Нужна помощь!

Answer 1

1) (x + 2y)² - (x - y)(y + x) = x² + 4xy + 4y² - (x² - y²) = x² + 4xy + 4y² - x² + y² = 5y² + 4xy

$5*(\frac{1}{5})^{2}+4*1*\frac{1}{5}=5*\frac{1}{25}+\frac{4}{5}=\frac{1}{5}+\frac{4}{5}=\frac{5}{5}=1\\\\2)\frac{5x+2}{3}*15+\frac{3x-1}{5}*15=5*15\\\\5(5x+2)+3(3x-1)=75\\\\25x+10+9x-3=75\\\\34x=75-7\\\\34x=68\\\\x=2$

$3)\frac{(3^{4})^{2}*2^{11}}{3*36^{4}}=\frac{3^{8}*2^{11}}{3*(2^{2}*3^{2})^{4}}=\frac{3^{8}*2^{11}}{3*2^{8}*3^{8}}=2^{11-8}*3^{8-1-8}=2^{3}*3^{-1}=\frac{8}{3} =2\frac{2}{3}$

$4)A(-8;30),B(22;60)\\\\y=kx+b\\\\\left \{ {{30=-8k+b} \atop {60=22k+b}} \right.\\\\-\left \{ {{22k+b=60} \atop {-8k+b=30}} \right. \\------\\30k=30\\\\k=1\\\\b=30+8k=30+8*1=38\\\\Otvet:\boxed{y=x+38}$