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Aneli [31]
3 years ago
8

Find X. Please break down the steps if possible

Mathematics
1 answer:
labwork [276]3 years ago
5 0

Answer: x = 17.5


Step-by-step explanation:

All expressions for the angles as a whole must equal 180 because it is on a line.

so we need to set all the expressions equal to 180 then solve.

4x+2x+30+2x+10=180

combine like terms

(4x+2x+2x) + (30+10) =180

8x + 40 = 180

now subtract 40 from each side

8x=140

isolate the x by dividing each side by 8

x = 17.5



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Step-by-step explanation:

(-5, - 12) lies on the terminal side of angle \theta

\therefore \: ( - 5 \:  - 12) = (x \: y) \\ r =  \sqrt{ {x}^{2}  +  {y}^{2} } \\  =  \sqrt{ {( - 5)}^{2}  +  {( - 12)}^{2} } \\  =  \sqrt{25 + 144}  \\  =  \sqrt{169}  \\  r= 13 \\  \\  \sin \theta =  \frac{y}{r}  =  -  \frac{12}{13}  \\  \\  \cos \theta =  \frac{x}{r}  =  -  \frac{5}{13}  \\  \\  \tan \theta =  \frac{y}{x}  =   \frac{ - 12}{ - 5}  =  \frac{12}{5}  \\  \\  \csc \theta =  \frac{r}{y}  =  -  \frac{13}{12}  \\  \\  \sec \theta =  \frac{r}{x}  =  -  \frac{13}{5}  \\  \\  \cot \theta =  \frac{x}{y}  =   \frac{ - 5}{ - 12}  =  \frac{5}{12}

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