What are parallel lines

Mathematics

1 answer:

tankabanditka [31]3 years ago

7 0

Answer:

Parallel lines are lines in the same plane that do not intersect, like lines on notebook paper.

The "in the same plane" requirement is important! Take a look at the attached image. Lines AD and DC don't intersect, but they are not in the same plane (face of the rectangular solid). We don't call those parallel, we call them skew lines.

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I need help on 2 questions !

Fudgin [204]

4. Yes, line L is parallel to M because they do not intersect, the angles do not matter.

5.

A. 2 and 3 would be Alt. Int. Angles.

B. 2 and 4 are congruent angles.

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3 years ago

State the vertical asymptote of the rational function. f(x) =((x-9)(x+7))/(x^2-4)

Lubov Fominskaja [6]

$D:x^2-4\not=0\\
D:x^2\not=4\\
D:x\not=-2 \wedge x\not =2\\\\
\displaystyle
\lim_{x\to-2^-}\dfrac{(x-9)(x+7)}{x^2-4}=\\
\dfrac{(-2-9)(-2+7)}{(-2^-)^2-4}=\dfrac{-11\cdot5}{4^+-4}=\dfrac{-55}{0^+}=-55\cdot\infty=-\infty\\
\dfrac{(-2-9)(-2+7)}{(-2^+)^2-4}=\dfrac{-11\cdot5}{4^--4}=\dfrac{-55}{0^-}=-55\cdot(-\infty)=\infty
$

$\displaystyle
\lim_{x\to2^-}\dfrac{(x-9)(x+7)}{x^2-4}=\\
\dfrac{(2-9)(2+7)}{(2^-)^2-4}=\dfrac{-7\cdot9}{4^--4}=\dfrac{-63}{0^-}=-63\cdot(-\infty)=\infty\\
\dfrac{(2-9)(2+7)}{(2^+)^2-4}=\dfrac{-7\cdot9}{4^+-4}=\dfrac{-63}{0^+}=-63\cdot\infty=-\infty\\$

So, the vertical asymptotes are $x=\pm 2$