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2 years ago

Write the equation of the line that passes through (-4, 8) and is parallel to the line that passes through (2, 1) and (-2, -1).

Mathematics

2 answers:

stealth61 [152]2 years ago

6 0

Answer:

Step-by-step explanation:

(2,1), (-2,-1)

slope(m) = (-1-1) / (-2 - 2) = -2/-4 = 1/2

parallel lines will have the same slope

y = mx + b

slope(m) = 1/2

(-4,8)...x = -4 and y = 8

now sub and find b, the y int

8 = 1/2(-4) + b

8 = -2 + b

8 + 2 = b

10 = b

so ur equation is : y = 1/2x + 10 <==

marshall27 [118]2 years ago

3 0

Answer:

$\displaystyle x - 2y = -20\:OR\:y = \frac{1}{2}x + 10$

Step-by-step explanation:

First, find the rate of change [slope]:

$\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-1 - 1}{-2 - 2} = \frac{-2}{-4} = \frac{1}{2}$

Now plug [−4, 8] into the Slope-Intercept Formula instead of the Point-Slope Formula because you get it done much more swiftly:

8 = ½[−4] + b

−2

$\displaystyle 10 = b \\ \\ y = \frac{1}{2}x + 10$

If you want it in Standard Form:

y = ½x + 10

- ½x - ½x

__________

−½x + y = 10 [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]

−2[−½x + y = 10]

$\displaystyle x - 2y = -20$

I am joyous to assist you anytime.

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Lapatulllka [165]

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7 0

2 years ago

Save me the headache

maxonik [38]

$(9\sin2x+9\cos2x)^2=81$

Taking the square root of both sides gives two possible cases,

$9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1$

$9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1$

Recall that

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

If $\alpha=2x$ and $\beta=\dfrac\pi4$ , we have

$\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}$

so in the equations above, we can write

$\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1$

Then in the first case,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi$

(where $n$ is any integer)

$\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi$

$\implies x=n\pi\text{ or }\dfrac\pi4+n\pi$

and in the second,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi$

$\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi$

$\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi$

Then the solutions that fall in the interval $[0,2\pi)$ are

$x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4$

5 0

2 years ago

Read 2 more answers

Can you help me with 1 - 4

miv72 [106K]

Me das mas información porfavor?

5 0

2 years ago

S see Use the graph y=e^x to evaluate these expression e^0

nika2105 [10]

Answer:

$y= e^x$

And we want to evaluate e^0 using the graph

And as we can see in the plot the y intercept is the blue point with y=0 and that correspond with:

$y(0)= e^0 =1$

Step-by-step explanation:

For this problem we know the following function:

$y= e^x$

And we want to evaluate e^0 using the graph

And as we can see in the plot the y intercept is the blue point with y=0 and that correspond with:

$y(0)= e^0 =1$

5 0

2 years ago

Find the angle that the line through the given pair of points makes with the positive direction of the x-axis

alexdok [17]

Answer:

Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.

Step-by-step explanation:

Given:

Let

A(x₁ , y₁) = (1 , 4) and

B( x₂ , y₂ ) = (-1 , 2)

To Find:

θ = ?

Solution:

Slope of a line when two points are given is given bt

$Slope(AB)=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }$

Substituting the values we get

$Slope(AB)=\dfrac{2-4}{-1-1}=\dfrac{-2}{-2}=1\\\\Slope=1$

Also Slope of line when angle ' θ ' is given as

$Slope=\tan \theta$

Substituting Slope = 1 we get

$1=\tan \theta$

$\tan \theta=1\\\theta=\tan^{-1}(1)$

We Know That for angle 45°,

tan 45 = 1

Therefore

$\theta=45\°$

Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.

5 0

2 years ago