I am so sorry for giving you the wrong answer at first.
Here's the processs
1x=-0.5555
Move the decimal point in the repeating decimal one space forward
10x=-5.55555
Then subtract
10x=5.5555
x=-0.5555= 9x=-5
Divide both sides by 9
9x=-5
9x/9=-5/9
-5/9 is your final answer!
Hope this helps!
Answer:
(#14 - supplementary) x = 10.5
(#15 - supplementary) x = 10
Explanation:
For these problems, we must know that a supplementary angle can be viewed as a sum of angles that add to 180 degrees. With this known, we can write our equations to find x.
(#14)
15x - 12 + 5x - 18 = 180
20x - 30 = 180
20x = 210
x = 10.5
(#15)
6x + 13 + 14x - 33 = 180
20x - 20 = 180
20x = 200
x = 10
Hope this helps.
Cheers.
By definition of tangent,
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
Recall the double angle identities:
sin(2<em>θ</em>) = 2 sin(<em>θ</em>) cos(<em>θ</em>)
cos(2<em>θ</em>) = cos²(<em>θ</em>) - sin²(<em>θ</em>) = 2 cos²(<em>θ</em>) - 1
where the latter equality follows from the Pythagorean identity, cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1. From this identity we can solve for the unknown value of sin(<em>θ</em>):
sin(<em>θ</em>) = ± √(1 - cos²(<em>θ</em>))
and the sign of sin(<em>θ</em>) is determined by the quadrant in which the angle terminates.
<em />
We're given that <em>θ</em> belongs to the third quadrant, for which both sin(<em>θ</em>) and cos(<em>θ</em>) are negative. So if cos(<em>θ</em>) = -4/5, we get
sin(<em>θ</em>) = - √(1 - (-4/5)²) = -3/5
Then
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
tan(2<em>θ</em>) = (2 sin(<em>θ</em>) cos(<em>θ</em>)) / (2 cos²(<em>θ</em>) - 1)
tan(2<em>θ</em>) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)
tan(2<em>θ</em>) = 24/7
169 miles * 5280 ft/ mile = 892320 ft
3 hours * 60 minutes/1 hr = 180 minutes
3 hrs 30 minutes = 180 minutes + 30 minutes = 210 minutes
169 miles/ 3 hrs 30 minutes = 892320 ft/ 210 minutes = 4249.1 ft/ minutes
