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3 years ago

Analyze the diagram below and answer the question that follows.

Mathematics

1 answer:

Basile [38]3 years ago

3 0

Answer:

Length KL is 128 units

Step-by-step explanation:

The question is incomplete, as the required statements are not given.

From the image of the attached triangle, we can see hat the triangle is right-angled.

So, we have:

$219^2 = 178^2 + KL^2$

Rewrite as:

$KL^2 = 219^2 - 178^2$

$KL^2 = 16277$

Take square roots

$KL = 128$ -- approximated

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A point of the form 25 +bi is 37 units from 13 – 31i. What is the value of b

Svetach [21]

If we consider the positive value of b, then the value of b is 4.

<h3>What is the coordinate plane of a complex number?</h3>

A complex number in the form z = x + iy takes a coordinate plane in terms of (x,y). From the given information, we are given a distance between two points:

25 + bi = (25,b)
13-31i = (13, -31)

Now, the distance between two points can be represented by using the relation:

$\mathbf{D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}$

$\mathbf{37 = \sqrt{(13-25)^2+(-31-b)^2}}$

$\mathbf{37 = \sqrt{(-12)^2+(31+b)^2}}$

$\mathbf{37 = \sqrt{144+(31+b)^2}}$

Taking the square of both sides

1369 = 144 + (31 + b)²

1369 - 144 = (31 + b)²

1225 = (31 + b)²

(31 + b)² = (35)²

(31 + b) = ±35

b = 35 - 31 or -35 -31

b = 4 or -66

Learn more about solving complex numbers here:

brainly.com/question/23729437

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8 0

2 years ago

If the owner of a sole proprietorship is sued by a customer who slipped and fell in her store,

Setler [38]

Answer:

the sole proprietor is personally liable for damages the injured woman is awarded by the courts.

Step-by-step explanation:

6 0

4 years ago

Please help me! This is is rational function and I don’t know how to/ don’t remember how do this! How would I find and write the

ivanzaharov [21]

An answer is

$\displaystyle f\left(x\right)=\frac{\left(x+1\right)^3}{\left(x+2\right)^2\left(x-1\right)}$

Explanation:

Template:

$\displaystyle f(x) = a \cdot \frac{(\cdots) \cdots (\cdots)}{( \cdots )\cdots( \cdots )}$

There is a nonzero horizontal asymptote which is the line y = 1. This means two things: (1) the numerator and degree of the rational function have the same degree, and (2) the ratio of the leading coefficients for the numerator and denominator is 1.

The only x-intercept is at x = -1, and around that x-intercept it looks like a cubic graph, a transformed graph of $y = x^3$ ; that is, the zero looks like it has a multiplicty of 3. So we should probably put $(x+1)^3$ in the numerator.

We want the constant to be a = 1 because the ratio of the leading coefficients for the numerator and denominator is 1. If a was different than 1, then the horizontal asymptote would not be y = 1.

So right now, the function should look something like

$\displaystyle f(x) = \frac{(x+1)^3}{( \cdots )\cdots( \cdots )}.$

Observe that there are vertical asymptotes at x = -2 and x = 1. So we need the factors $(x+2)(x-1)$ in the denominator. But clearly those two alone is just a degree-2 polynomial.

We want the numerator and denominator to have the same degree. Our numerator already has degree 3; we would therefore want to put an exponent of 2 on one of those factors so that the degree of the denominator is also 3.

A look at how the function behaves near the vertical asympotes gives us a clue.

Observe for x = -2,

as x approaches x = -2 from the left, the function rises up in the positive y-direction, and
as x approaches x = -2 from the right, the function rises up.

Observe for x = 1,

as x approaches x = 1 from the left, the function goes down into the negative y-direction, and
as x approaches x = 1 from the right, the function rises up into the positive y-direction.

We should probably put the exponent of 2 on the $(x+2)$ factor. This should help preserve the function's sign to the left and right of x = -2 since squaring any real number always results in a positive result.

So now the function looks something like

$\displaystyle f(x) = \frac{(x+1)^3}{(x+2 )^2(x-1)}.$

If you look at the graph, we see that $f(-3) = 2$ . Sure enough

$\displaystyle f(-3) = \frac{(-3+1)^3}{(-3+2 )^2(-3-1)} = \frac{-8}{(1)(-4)} = 2.$

And checking the y-intercept, f(0),

$\displaystyle f(0) = \frac{(0+1)^3}{(0+2 )^2(0-1)} = \frac{1}{4(-1)} = -1/4 = -0.25.$

and checking one more point, f(2),

$\displaystyle f(2) = \frac{(2+1)^3}{(2+2 )^2(2-1)} = \frac{27}{(16)(1)} \approx 1.7$

So this function does seem to match up with the graph. You could try more test points to verify.

======

If you're extra paranoid, you can test the general sign of the graph. That is, evaluate f at one point inside each of the key intervals; it should match up with where the graph is. The intervals are divided up by the factors:

x < -2. Pick a point in here and see if the value is positive, because the graph shows f is positive for all x in this interval. We've already tested this: f(-3) = 2 is positive.
-2 < x < -1. Pick a point in here and see if the value is positive, because the graph shows f is positive for all x in this interval.
-1 < x < 1. Pick a point here and see if the value is negative, because the graph shows f is negative for all x in this interval. Already tested since f(0) = -0.25 is negative.
x > 1. See if f is positive in this interval. Already tested since f(2) = 27/16 is positive.

So we need to see if -2 < x < -1 matches up with the graph. We can pick -1.5 as the test point, then

$\displaystyle f(-1.5) = \frac{\left(-1.5+1\right)^3}{\left(-1.5+2\right)^2\left(-1.5-1\right)} = \frac{(-0.5)^3}{(0.5)^2(-2.5)} \\= (-0.5)^3 \cdot \frac{1}{(0.5)^2} \cdot \frac{1}{-2.5}$

We don't care about the exact value, just the sign of the result.

Since $(-0.5)^3$ is negative, $(0.5)^2$ is positive, and $(-2.5)$ is negative, we really have a negative times a positive times a negative. Doing the first two multiplications first, (-) * (+) = (-) so we are left with a negative times a negative, which is positive. Therefore, f(-1.5) is positive.