What is x? -8=-(x+4)

const2013 [10]

Answer:

$\rm\displaystyle 0,\pm\pi$

Step-by-step explanation:

please note that to find but α+β+γ in other words the sum of α,β and γ not α,β and γ individually so it's not an equation

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we want to find all possible values of α+β+γ when tanα+tanβ+tanγ = tanαtanβtanγ to do so we can use algebra and trigonometric skills first

cancel tanγ from both sides which yields:

$\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \alpha ) \tan( \beta ) \tan( \gamma ) - \tan( \gamma )$

factor out tanγ:

$\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \gamma ) (\tan( \alpha ) \tan( \beta ) - 1)$

divide both sides by tanαtanβ-1 and that yields:

$\rm\displaystyle \tan( \gamma ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \tan( \alpha ) \tan( \beta ) - 1}$

multiply both numerator and denominator by-1 which yields:

$\rm\displaystyle \tan( \gamma ) = - \bigg(\frac{ \tan( \alpha ) + \tan( \beta ) }{ 1 - \tan( \alpha ) \tan( \beta ) } \bigg)$

recall angle sum indentity of tan:

$\rm\displaystyle \tan( \gamma ) = - \tan( \alpha + \beta )$

let α+β be t and transform:

$\rm\displaystyle \tan( \gamma ) = - \tan( t)$

remember that tan(t)=tan(t±kπ) so

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm k\pi )$

therefore when k is 1 we obtain:

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm \pi )$

remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus

$\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm \pi )$

recall that if we have common trigonometric function in both sides then the angle must equal which yields:

$\rm\displaystyle \gamma = - \alpha - \beta \pm \pi$

isolate -α-β to left hand side and change its sign:

$\rm\displaystyle \alpha + \beta + \gamma = \boxed{ \pm \pi }$

when is 0:

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta \pm 0 )$

likewise by Opposite Angle Identity we obtain:

$\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm 0 )$

recall that if we have common trigonometric function in both sides then the angle must equal therefore:

$\rm\displaystyle \gamma = - \alpha - \beta \pm 0$

isolate -α-β to left hand side and change its sign:

$\rm\displaystyle \alpha + \beta + \gamma = \boxed{ 0 }$

and we're done!

8 0

3 years ago

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A bulletin board has a perimeter of 200 inches. Which expression expresses the area A(w) of the bulletin board as a function of

mr Goodwill [35]

Answer:

area A(w) of the bulletin board as a function of its width, w =[100-w]*w= 100w- $w^{2}$

Step-by-step explanation:

let, the shape of the bulletin board is a rectangle,

then the perimeter of it = sum of all sides

= 2[length+width] = 2[l+w]

(let l: length, w : width )

so, 200 = 2[l+w]

100= l+w ( dividing both the sides by 2)

so, l= 100-w

area = length*width=l*w=[100-w]*w

therefore,area A(w) of the bulletin board as a function of its width, w =[100-w]*w= 100w- $w^{2}$

6 0

2 years ago

382,706 in expanded form

tamaranim1 [39]

300,000 + 80,000+2,000+700+0+6 , is your answer.

8 0

3 years ago

Fill in the missing number to complete the pattern 145, 148, 151, _ _ _ I REALLY NEED THIS PLZ

Savatey [412]

Answer:

154 157 160

Step-by-step explanation:

Add 3 each time

3 0

2 years ago

The asymptote of the function f(x) = 3x + 1 – 2 is . Its y-intercept is .

julsineya [31]

There is no asymptote
The Y-int is (0,-1)

6 0

3 years ago

Read 2 more answers