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Troyanec [42]
3 years ago
9

triangle MNP is similar to triangle HJK, and both triangles are isosceles. If angle P > 90 degrees, name all angles that are

congruent to angle H
Mathematics
1 answer:
puteri [66]3 years ago
4 0

Answer:

∠ H = ∠ J = ∠N = ∠ M

Step-by-step explanation:

Triangle MNP is similar to triangle HJK and both triangles are isosceles triangles.

If the angle P is greater than 90 degrees, then angles M and N are the equal angles of the isosceles triangle MNP.  

Hence, angle M = angle N

Now, as Δ MNP and Δ HJK are similar so, ∠ M = ∠ H, ∠ N = ∠ J, and ∠ P = ∠K

Again ∠ H = ∠ J as Δ HJK is isosceles.

Therefore, ∠ H = ∠ J = ∠N = ∠ M (Answer)

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Step-by-step explanation:

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ABCD is a rectangle. The measure of angle BCE is 4x-23 and the angle measure of angle DCE is 5+5x. Find the measure of angle BEC
Temka [501]
<h2>Explanation:</h2><h2></h2>

The diagram for this problem is shown below. Point E is the intersection of the two diagonals and we know that:

\angle BCE=\beta \\ \\ \angle DCE=\theta

Every internal angle of any rectangle measures 90 degrees, so:

\beta +\alpha=90 \\ \\ (4x-23)+(5+5x)=90 \\ \\ \\ Isolating \ x: \\ \\ (4x+5x)+(5-23)=90 \\ \\ 9x-18=90 \\ \\ 9x=108 \\ \\ x=\frac{108}{9}=12

So:

\beta=4x-23=4(12)-23=25^{\circ}

So the measure of angle BEC can be found as follows:

We know that triangle ΔCEB is an isosceles triangle because the diagonals of any rectangle measure the same. So

\angle EBC=\beta

The sum of internal angles of any triangle add up to 180 degrees, so:

\beta + \beta+\angle BEC=180^{\circ} \\ \\ 2\beta+\angle BEC=180^{\circ} \\ \\ \angle BEC=180^{\circ}-2\beta \\ \\ \angle BEC=180^{\circ}-2(25^{\circ}) \\ \\ \angle BEC=180^{\circ}-50^{\circ} \\ \\ \boxed{\angle BEC=130^{\circ}}}

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Answer:

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Grasshoppers are distributed at random in a large field according to a Poisson process with parameter a 5 2 per square yard. How
HACTEHA [7]

In this question, the Poisson distribution is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given interval.

Parameter of 5.2 per square yard:

This means that \mu = 5.2r, in which r is the radius.

How large should the radius R of a circular sampling region be taken so that the probability of finding at least one in the region equals 0.99?

We want:

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Thus:

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We have that:

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Then

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r = -\frac{\ln{0.01}}{5.2}

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Thus, the radius should be of at least 0.89.

Another example of a Poisson distribution is found at brainly.com/question/24098004

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