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Sauron [17]
2 years ago
5

2x + 5y = 8 x - 2y = -5 Simultaneously pleasee

Mathematics
2 answers:
vodka [1.7K]2 years ago
7 0

Answer:

3

Step-by-step explanation:

mario62 [17]2 years ago
3 0

Answer:

(- 1, 2 )

Step-by-step explanation:

2x + 5y = 8 → (1)

x - 2y = - 5 → (2)

multiplying (2) by - 2 and adding to (1) will eliminate x

- 2x + 4y = 10 → (3)

add (1) and (3) term by term to eliminate x

0 + 9y = 18

9y = 18 ( divide both sides by 9 )

y = 2

substitute y = 2 into either of the 2 equations and solve for x

substituting into (1)

2x + 5(2) = 8

2x + 10 = 8 ( subtract 10 from both sides )

2x = - 2 ( divide both sides by 2 )

x = - 1

solution is (- 1, 2 )

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Step-by-step explanation:

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Given: cosθ= -4/5 , sin x = -12/13 , θ is in the third quadrant, and x is in the fourth quadrant; evaluate tan 1/2 θ
mrs_skeptik [129]

Answer:

Step-by-step explanation:

If you're looking for what the half angle of the tangent of theta is, I'm a bit confused as to why you think the angle in the 4th quadrant, x, is relevant.  But maybe you don't know it isn't and it's a "trick" to throw you off.  Hmm...

Anyways, the half angle identity for tangent is

tan(\frac{\theta}{2})=\frac{sin\theta}{1+cos\theta}

There are actually 3 identities for the tangent of a half angle, but this one works just as well as either of the others do, so I'm going with this one.  

If theta is in QIII, the value of -4 goes along the x axis and the hypotenuse is 5.  That makes the missing side, by Pythagorean's Theorem, -3.  Filling in our formula:

tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{1+(-\frac{4}{5}) } which simplifies a bit to

tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{\frac{5}{5} -\frac{4}{5} }  and a bit more to

tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{\frac{1}{5} }

Bring up the lower fraction and flip it to divide to get

tan(\frac{\theta}{2})=-\frac{3}{5}*\frac{5}{1} which of course simplifies to

-3.  Choice A.

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