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Leya [2.2K]
3 years ago
10

If JKLM is a rhombus, MK = 30, NL = 13, and mZMKL = 41°, find each measure.

Mathematics
1 answer:
oksian1 [2.3K]3 years ago
5 0

Answer:

NK = 15

JL = 26

KL = 19.85

\angle JKM =49

\angle JML =41

\angle MLK = 90

\angle MNL =90

\angle KJL =41

Step-by-step explanation:

Given

MK = 30

NL = 13

\angle MKL = 41

Solving (a): NK

MK is a diagonal and NK is half of the diagonal. So:

NK = \frac{1}{2} * MK

NK = \frac{1}{2} * 30

NK = 15

Solving (b): JL

JL is a diagonal, and it is twice of NL.

JL = 2 * NL

JL = 2 * 13

JL = 26

Solving (c): KL

To solve for KL, we consider triangle KNL where:

\angle KNL = 90

and

KL^2 = NL^2 + NK^2

KL^2 = 13^2 + 15^2

KL^2 = 394

KL = \sqrt{394

KL = 19.85

Solving (d - h):

To do this, we consider triangle JKN

\angle KNL = \angle LNM = \angle MNJ = \angle JNK = 90 -- diagonals bisect one another at right angle

Alternate interior angles are equal. So:

\angle MKL = \angle KMJ = \angle KJL = \angle JLM = 41

Similarly:

\angle MKJ = \angle KML = \angle MJL = \angle JLK = 90 - 41

\angle MKJ = \angle KML = \angle MJL = \angle JLK = 49

So:

\angle JKM =49

\angle JML =41

\angle MLK = \angle MLJ + \angle JLK

\angle MLK = 49 + 41

\angle MLK = 90

\angle MNL =90

\angle KJL =41

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Step-by-step explanation:

Given;

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x² - 2x = 1

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x^2 +  (-1)^2 = 1 + (-1)^2

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⇒ take the square root of both sides;

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3 0
3 years ago
The wind speed s (in miles per hour) is related to the distance (in miles) the tornado travels by the equation s = 93log d + 65.
Vesnalui [34]

Answer:

The distance the tornado traveled was approximately 205 miles.

Step-by-step explanation:

The equation representing the relationship between the wind speed (in miles per hour) and the distance the tornado travels (in miles) is:

s=93\log d+65

Compute the value of <em>d</em> for <em>s</em> = 280 as follows:

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Serggg [28]
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6 0
3 years ago
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Katena32 [7]

Answer:

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The area of a circle (A), measured in square inches, is directly proportional to the square of its diameter (d), measured in inches. That is:

A \propto d^{2}

A = k\cdot d^{2}

Where k is the constant of proportionality, dimensionless.

In consequence, the following relationship between circles A and B is obtained:

\frac{A_{B}}{A_{A}} = \frac{d_{B}^{2}}{d_{A}^{2}}

The area of the circle B is now cleared:

A_{B} =\left(\frac{d_{B}}{d_{A}} \right)^{2}\cdot A_{A}

Given that d_{A} = 20\,in, d_{B} = 60\,in and A_{A} = 300\,in^{2}, then:

A_{B} = \left(\frac{60\,in}{20\,in} \right)^{2}\cdot (300\,in^{2})

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Answer:

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8 0
3 years ago
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