Which pair of equations represents two perpendicular lines? answers shown in picture.

Mathematics

1 answer:

kolezko [41]4 years ago

3 0

Answer:

y =1/2x+6

y = -2x+2

Step-by-step explanation:

Perpendicular line have slopes that multiply to -1

The slopes are negative reciprocals

-4*4 = 16 not perpendicular

1/2 * -2 = -1 perpendicular

1/5 *5 = 1 not perpendicular

2/3 * 2/3 = 4/9 not perpendicular

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an oatmeal recipe calls for 1 1/2 cups of oat and 2 1/2 cups of water. A If you have 3 cups of oats,how many cups of oats water

natima [27]

$\bf \stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}}~\hfill \stackrel{mixed}{2\frac{1}{2}}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}}\\\\[-0.35em]\rule{34em}{0.25pt}$

$\bf \begin{array}{ccll}oats&water\\\cline{1-2}\frac{3}{2}&\frac{5}{2}\\[0.8em]3&x\end{array}\implies \cfrac{~~\frac{3}{2}~~}{3}=\cfrac{~~\frac{5}{2}~~}{x}\implies \cfrac{~~\frac{3}{2}~~}{\frac{3}{1}}=\cfrac{~~\frac{5}{2}~~}{\frac{x}{1}}\implies \cfrac{3}{6}=\cfrac{5}{2x}\\\\\\6x=30\implies x=\cfrac{30}{6}\implies \blacktriangleright x=5 \blacktriangleleft$

$\bf \begin{array}{ccll}oats&water\\\cline{1-2}\frac{3}{2}&\frac{5}{2}\\[0.8em]2&x\end{array}\implies \cfrac{~~\frac{3}{2}~~}{2}=\cfrac{~~\frac{5}{2}~~}{x}\implies \cfrac{~~\frac{3}{2}~~}{\frac{2}{1}}=\cfrac{~~\frac{5}{2}~~}{\frac{x}{1}}\implies \cfrac{3}{4}=\cfrac{5}{2x}\\\\\\6x=20\implies x=\cfrac{20}{6}\implies x=\cfrac{10}{3}\implies \blacktriangleright x=3\frac{1}{3} \blacktriangleleft$

$\bf \begin{array}{ccll}oats&water\\\cline{1-2}\frac{3}{2}&\frac{5}{2}\\[0.8em]5&x\end{array}\implies \cfrac{~~\frac{3}{2}~~}{5}=\cfrac{~~\frac{5}{2}~~}{x}\implies \cfrac{~~\frac{3}{2}~~}{\frac{5}{1}}=\cfrac{~~\frac{5}{2}~~}{\frac{x}{1}}\implies \cfrac{3}{10}=\cfrac{5}{2x}\\\\\\6x=50\implies x=\cfrac{50}{6}\implies x=\cfrac{25}{3}\implies \blacktriangleright x=8\frac{1}{3} \blacktriangleleft$

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