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3 years ago

1.) A triangle has two interior angle measures of 82º and 19º. Find the measure of

Mathematics

1 answer:

daser333 [38]3 years ago

4 0

Answer:

79°

Step-by-step explanation:

A triangle has 180° in it so 180 - 82 =98- 19=79

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What is the slope of a line perpendicular to the line whose equation is 2x – 2y = 20.

Simora [160]

Answer:

-1

Step-by-step explanation:

Solve for y into y=mx+b

2x-2y=20

-2y=-2x+20

y=(-2x+20)/-2

y=x-10

the slope is m, so it’s 1

A line perpendicular to that would be -1

7 0

2 years ago

A box contains

Usimov [2.4K]

the probability that a pen from the first box is selected
= total number of pens in 1st box/total number of objects in box 1
= 5/12

the probability that a crayon from the second box is selected
= total number of crayons in 2nd box/total number of objects in box 2
= 6/8 = 3/4

7 0

2 years ago

What are the constants in this expression? -10.6+9\10+2\5m-2.4n+3m

Annette [7]

-10.6, and 9/10, are the constants

8 0

3 years ago

Find all possible values of α+

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

===========================

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

2 years ago

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Cottontail rabbits are found in California. Recently, the cottontail's predator, the coyote, has been disappearing due to human

azamat

Answer:

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2 years ago