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3 years ago

The ratio of the measures of the angles of a triangle is 4:6:8. Find the measure of the largest angle.

Mathematics

1 answer:

garri49 [273]3 years ago

3 0

Answer:

80°

Step-by-step explanation:

The angles can be written as 4x, 6x, and 8x. Since the sum of angles in a triangle is 180 degrees we can write:

4x + 6x + 8x = 180

18x = 180

x = 10 which means the largest angle (8x) = 8 * 10 = 80°

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Show your work (19−7)^( (2) ) −8*3+4*3−5

ArbitrLikvidat [17]

Answer:

Step-by-step explanation:

1 Simplify 19-7 to 12.

12^2−8×3+4×3−5

2 Simplify 12^2 to 144

144−8×3+4×3−5

3 Simplify 8×3 to 24.

144−24+4×3−5

4 Simplify 4×3 to 12.

144−24+12−5

5 Simplify 144-24 to 120.

120+12-5

6 Simplify 120+12 to 132.

132-5

7 Simplify.

127

3 0

2 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

3 years ago

Read 2 more answers

The price, P, of a sweater was discounted by 10% in

aalyn [17]

Answer:

In terms of P, the price of the sweater after the discount is 0.72P.

Step-by-step explanation:

Since the price P would represent 100% and the price was discounted by 10%, you can calculate 10% of 100% and subtract that amount, which would be:

100*10%=10

100-10=90%

This means that the price paid would be 90% of P. Then, the statement says that the price was discounted by another 20%. So, you have to calculate 20% of the price and subtract that amount from the price:

90*20%=18

90-18=72%

According to this, this means that in terms of P, the price of the sweater after the discount is 0.72P.

6 0

3 years ago

Please help I really need it

masha68 [24]

Answer:

There's 2: I've attached an image.

Step-by-step explanation:

Lines of symmetry are found when you fold it, and it's exactly the same on both sides of the line that you folded it.

If your teachers ask, no, it cannot be diagonal. The triangles would not match up.

6 0

2 years ago

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Write the decimal as a fraction in simplest form. 0.25 (with 25 repeating)

zlopas [31]

1/4, because you disregard the repeating 25s and round, and 25 x 4 is one hundred, so simplified it's 1/4.

8 0

3 years ago

Read 2 more answers