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3 years ago

Need help ASAP

Mathematics

1 answer:

Nastasia [14]3 years ago

4 0

Answer:

$y+ 6 = 2 (x-7)$

Step-by-step explanation:

1) Lines that are perpendicular have slopes that are opposite reciprocals of each other. y = -1/2x - 8 is in y = mx + b form, in which the number in place of m represents the slope. So, the slope of y = -1/2x - 8 is -1/2. The opposite reciprocal of it would be (remember to flip the fraction and reverse the sign) 2. So, 2 is the slope we need for the answer.

2) When you know a point that the line must pass through and its slope, you can use point-slope form ( $y-y_1 = m (x - x_1)$ ) to write an equation. $x_1$ and $y_1$ represents the x and y values of the point the line intersects, and m represents the slope. So, substitute 2 for m, 7 for $x_1$ , and -6 for $y_1$ .

$y-(-6) = 2 (x- 7)\\y + 6 = 2 (x-7)$

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A line joins the point

Harrizon [31]

Intersection of the first two lines:

$\begin{cases}5x - 2y + 3 = 0\\4x - 3y + 1 = 0\end{cases}$

Multiply the first equation by 4 and the second by 5:

$\begin{cases}20x - 8y + 12 = 0\\20x - 15y + 5 = 0\end{cases}$

Subtract the two equations:

$(20x - 8y + 12)-(20x - 15y + 5)=0 \iff 7y+7=0 \iff y=-1$

Plug this value for y in one of the equation, for example the first:

$5x - 2\cdot (-1) + 3 = 0\iff 5x+5=0 \iff x=-1$

So, the first point of intersection is $(-1,-1)$

We can find the intersection of the other two lines in the same way: we start with

$\begin{cases}x=y\\x=3y+4\end{cases}$

Use the fact that x and y are the same to rewrite the second equation as

$x=3x+4 \iff 2x=-4 \iff x=-2$

And since x and y are the same, the second point is $(-2, -2)$

So, we're looking for a line passing through $(-1,-1)$ and $(-2, -2)$ . We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be $y=x$

In the attached figure, line $5x - 2y + 3 = 0$ is light green, line $4x - 3y + 1 = 0$ is dark green, and their intersection is point A.

Simiarly, line $x=y$ is red, line $x = 3y + 4$ is orange, and their intersection is B.

As you can see, the line connecting A and B is the red line itself.

5 0

3 years ago

I need help with linear inequalities one question. the question is -7x-86 less than -93.

Andreyy89

-7x<-93+86
-7x<-7
x>1 is the answer

DO YOU NEED TO GRAPH TOO?

5 0

3 years ago

How do u do #10? Plz show on paper

Studentka2010 [4]

Reflection across the line y=x simply swaps the x and y coordinates.
K'(-2, -5), A'(1, -4), I'(-1, 0), J'(-4, -2)

3 0

3 years ago

If x = a cosθ and y = b sinθ , find second derivative

Olin [163]

I'm guessing the second derivative is for <em>y</em> with respect to <em>x</em>, i.e.

$\dfrac{\mathrm d^2y}{\mathrm dx^2}$

Compute the first derivative. By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

We have

$y=b\sin\theta\implies\dfrac{\mathrm dy}{\mathrm d\theta}=b\cos\theta$

$x=a\cos\theta\implies\dfrac{\mathrm dx}{\mathrm d\theta}=-a\sin\theta$

and so

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{b\cos\theta}{-a\sin\theta}=-\dfrac ba\cot\theta$

Now compute the second derivative. Notice that $\frac{\mathrm dy}{\mathrm dx}$ is a function of $\theta$ ; so denote it by $f(\theta)$ . Then

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm dx}$

By the chain rule,

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm df}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

We have

$f=-\dfrac ba\cot\theta\implies\dfrac{\mathrm df}{\mathrm d\theta}=\dfrac ba\csc^2\theta$

and so the second derivative is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\frac ba\csc^2\theta}{-a\sin\theta}=-\dfrac b{a^2}\csc^3\theta$

4 0

3 years ago

Use complete sentences to describe why it is valid to say that both a function and its inverse describe the same relationship.

Serhud [2]

Answer:

Step-by-step explanation:

A comparison between a function and its inverse would show that the domain and range of the original function swap. The domain of the function becomes the range of the inverse, the range of the function becomes the domain of its inverse.

Looking at ordered pairs of the function and its inverse would look like this:

(2,4) on the original function becomes (4,2) on the inverse.

While the graph of a function and its inverse are noticeably different an important thing to note is that it is merely a reflection across the line y=x.

So even though they appear different you are looking at the same relationship just as y vs. x instead of x vs. y

I hope this helped you because i barley understood this myself.

Read more on Brainly.com - brainly.com/question/2834818#readmore

3 0

3 years ago