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3 years ago

What is the measure of angle x?

Mathematics

2 answers:

Kitty [74]3 years ago

8 0

The two horizontal lines are parallel.

This makes the 80 degree angle and the angle ox x and 20 degrees are alternate interior angles and are the same.

This means x + 20 needs to equal 80.

X = 80-20 = 60 degrees.

klasskru [66]3 years ago

5 0

Answer: it measures 60˚

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Step-by-step explanation:

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Step-by-step explanation:

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2 years ago

What are the period and phase shift for f(x) = −4 tan(x − π)?

nadya68 [22]

$\bf ~~~~~~~~~~~~\textit{function transformations}
\\\\\\
% function transformations for trigonometric functions
% templates
f(x)=Asin(Bx+C)+D
\\\\
f(x)=Acos(Bx+C)+D\\\\
f(x)=Atan(Bx+C)+D
\\\\
-------------------$

$\bf \bullet \textit{ stretches or shrinks}\\
~~~~~~\textit{horizontally by amplitude } A\cdot B\\\\
\bullet \textit{ flips it upside-down if }A\textit{ is negative}\\
~~~~~~\textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }B\textit{ is negative}$

$\bf ~~~~~~\textit{reflection over the y-axis}
\\\\
\bullet \textit{ horizontal shift by }\frac{C}{B}\\
~~~~~~if\ \frac{C}{B}\textit{ is negative, to the right}\\\\
~~~~~~if\ \frac{C}{B}\textit{ is positive, to the left}\\\\
\bullet \textit{vertical shift by }D\\
~~~~~~if\ D\textit{ is negative, downwards}\\\\
~~~~~~if\ D\textit{ is positive, upwards}$

$\bf \bullet \textit{function period or frequency}\\
~~~~~~\frac{2\pi }{B}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\
~~~~~~\frac{\pi }{B}\ for\ tan(\theta),\ cot(\theta)$

with that template in mind, let's see this one.

$\bf f(x)=\stackrel{A}{-4}tan(\stackrel{B}{1}x\stackrel{C}{-\pi })+\stackrel{D}{0}
\\\\\\
\stackrel{period}{\cfrac{2\pi }{B}\implies \cfrac{2\pi }{1}\implies 2\pi }
\\\\\\
\stackrel{phase/horizontal~shift}{\cfrac{C}{B}\implies \cfrac{-\pi }{1}}\implies -\pi \qquad \textit{shifted to the right by }\pi \textit{ units}$

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Answer:

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