Dzr96id
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What type of lines are  4x + 8y = 10 and  4x - 2y = 21 ?

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Lilithid
[tex]4x + 8y = 10\\ 4x - 2y = 21 \\ \\ 8y =-4x+10 \ \ /:8 \\ -2y=-4x+21\ \ / : (-2)\\ \\y =-\frac{4}{8}x+\frac{10}{8}\\y=2x-\frac{21}{2}[/tex]

[tex]y =-\frac{1}{2}x+\frac{5}{4}\\y=2x-10.5\\\\ a_{1}\cdot a_{2}=-1\\m_{1}=-\frac{1}{2}, \ \ m_{2}=2 \\ m _{1}*m _{2} = -1 \ it \ perpendicular \ lines \ we \ have \\\\ m _{1}*m _{2} = -1\\\\-\frac{1}{2}\cdot 2 = -1\\-1=-1 \\ \\L=R [/tex]

Kate200468id
[tex]k:\ \ \ 4x + 8y = 10\ \ \ \Rightarrow\ \ \ 8y=-4x+10\ \ \ \Rightarrow\ \ \ y=- \frac{1}{2}x+1 \frac{1}{4}\\\\ \Rightarrow\ \ \ m_ 1=- \frac{1}{2} \\\\l:\ \ \ 4x - 2y = 21\ \ \ \Rightarrow\ \ \ -2y=-4x+21\ \ \ \Rightarrow\ \ \ y=2x-10 \frac{1}{2} \\\\\Rightarrow\ \ \ m_2=2\\\\m_1\cdot m_2=(- \frac{1}{2} )\cdot2=-1\ \ \ \Rightarrow\ \ \ k\ \perp\ l\\\\Ans.\ The\ lines\ are\ perpendicular.[/tex]

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