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3 years ago

Y=-3+1/2x graph the system of equations and write the solution

Mathematics

1 answer:

Rudik [331]3 years ago

5 0

Answer:

$(x,y) = (2.-2)$

Step-by-step explanation:

Given

$y = -3 + \frac{1}{2}x$

$-2x + y = -6$

Solving (a): Graph the equations

See attachment for graph

Solving (b): The solution

This is the point of intersection between both lines

From the attached graph, the point of intersection is:

$(x,y) = (2.-2)$

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Sinx + siny=a cosx + cosy=b Find cos(x+y/2)

romanna [79]

Using the addition rule of the Sine function and the Cosine function, we obtain $\cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}$ .

<h3>What are the formulas for (sin x + sin y) and (cos x + cos y)?</h3>

The formula for the addition of two Sine functions ( $\sin x+\sin y$ ) is $\sin x + \sin y = 2\sin\frac{x+y}{2}\cos\frac{x-y}{2}$ .
The formula for the addition of two Cosine functions ( $\cos x+\cos y$ ) is $\cos x + \cos y = 2\cos\frac{x+y}{2}\cos\frac{x-y}{2}$ .

Given that

$\sin x + \sin y = a\\\cos x + \cos y = b$

Then using the above formulas, we get:

$2\sin\frac{x+y}{2}\cos\frac{x-y}{2}=a$ (1)

$2\cos\frac{x+y}{2}\cos\frac{x-y}{2}=b$ (2)

Dividing the equation (1) by (2), we get:

$\dfrac{\sin\dfrac{x+y}{2}}{\cos\frac{x-y}{2}}=\dfrac{a}{b}\\\Longrightarrow \tan\dfrac{x+y}{2}=\dfrac{a}{b}$ (3)

Now, we know that $\cos\theta=\dfrac{1}{\sqrt{1+\tan^2\theta}}$ .

Thus, using the above formula, we get from (3):

$\cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\tan^2\dfrac{x+y}{2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\dfrac{a^2}{b^2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}$

Therefore, using the addition rule of the Sine function and the Cosine function, we obtain $\cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}$ .

To know more about Sine and Cosine functions, refer: brainly.com/question/27728553

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How would one convert 125 lb to kilograms (1 oz = 28 g)?

Salsk061 [2.6K]

You would convert 125 lb to 56.699 kg

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Evaluate -2/3 + 5/6

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Answer: .16 Well, we can just call this a simple negative two divided by three plus 5 divided by 6. Using the *cough order of *cough *cough operations, or GEMA, we can see that we can separate this expression into two.

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4 years ago

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