MATHEMATICS HIGH SCHOOL

Given:- KLMN is a trapezoid
- KL = MN
- LN = √(89)
- LH: altitude
- LM = 3
- KN = 13
Find: m∠LKN
See attached image.

Answers

Answer 1

Answer:

Answer:

45 degrees

Step-by-step explanation:

If KL = MN, and LM =3 and KN = 13, then HN = 13 - (13-3)/2 = 8

LN = sqrt(HN^2 + LH^2) -->

LN = sqrt89 sqrt(8^2 + LH^2) -->

89 = 64 + LH ^2 -->

25 = LH^2 -->

LH = 5

Because HN = 8, HK = 13 - 8 = 5

That makes both legs equal, which makes m∠LKN = 45 degrees

Answer 2

Answer:

The angle m∠LKN is equal to 45 degrees.

To understand more, check below explanation.

Trapezoid :

It is given that,

KL = MN, LM =3 , KN = 13 and LN $=√(89)$

So that, HN = 13 - (13-3)/2 = 13 - 5 = 8

$LN = \sqrt{(HN)^(2)+(LH)^(2) }\n\n√(89) = \sqrt{(8)^(2)+(LH)^(2) }\n\n89=64+(LH)^(2) \n\nLH=√(25)=5$

Since, HN = 8. So that, HK = 13 - 8 = 5

In a triangle, if two sides are equal. Then, opposite angle of both sides are also equal.

In triangle LKH, LH = HK = 5 and $\angle H=90$

So that, m∠LKN = 90/2 = 45 degree.

Hence, the angle m∠LKN is equal to 45 degrees.

Learn more about the trapezoid here:

brainly.com/question/1463152

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Answer:3

Step-by-step explanation:

Answer:

the answer is that 3 pounds of coffee was bought.

Step-by-step explanation:

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=24.72

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How do I do x/3-x/9=6 Pls solve with steps

Answers

Answer:

Step-by-step explanation:

Hello,

do you agree that

$(1)/(3)-(1)/(9)=(3-1)/(9)=(2)/(9)$ ?

Then,

we can simplify as below and multiply by 9 both sides and divide by 2

$(x)/(3)-(x)/(9)=(2x)/(9)=6\n\n<=> 2x = 54\n\n<=> x = 54/2= 27$

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L is the midpoint of MN¯¯¯¯¯¯¯, ML=2x+7 and LN=3x−3. Find ML, LN, and MN.

Answers

Answer:

$ML=27\nLN=27\nMN=54$

Step-by-step explanation:

Since L is the midpoint of MN, by the definition of midpoint:

$ML=LN$

We can picture the following segment:

M----------L----------N

We know that $ML=2x+7$ and $LN=3x-3$ . Since the two segments are equivalent, we can set them equal to each other:

$2x+7=3x-3$

Now, let's solve for x. Subtract -7 from both sides:

$2x=3x-10$

Subtract 3x from both sides:

$-x=-10$

Divide both sides by -1:

$x=10$

So, the value of x is 10.

With this, we can find the remaining lengths.

We know that ML is $2x+7$ .

Substitute 10 for x. So, the length of ML is:

$ML=2(10)+7=20+7=27$

We know that LN is $3x-3$ . So, the length of LN is:

$LN=3(10)-3=30-3=27$

Finally, MN will be the combined lengths of ML and LN. So:

$MN=ML+LN=27+27=54$

And we're done!

The lengths of each segment are:

ML = 27, LN = 27, and MN = 54.

We have,

Let's use the information given to find the values of ML, LN, and MN.

ML = 2x + 7

LN = 3x - 3

L is the midpoint of MN, which means that ML is equal to LN:

2x + 7 = 3x - 3

Now, let's solve for x:

Move the x term to one side of the equation:

2x - 3x = -3 - 7

-x = -10

Now, multiply both sides by -1 to get rid of the negative sign:

x = 10

Now that we have the value of x, we can find the lengths ML, LN, and MN:

ML = 2x + 7

ML = 2(10) + 7

ML = 20 + 7

ML = 27

LN = 3x - 3

LN = 3(10) - 3

LN = 30 - 3

LN = 27

MN = ML + LN

MN = 27 + 27

MN = 54

Thus,

The lengths of each segment are:

ML = 27, LN = 27, and MN = 54.

Learn more about midpoints of linesegments here:

brainly.com/question/13792156

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Which describes all of the values for which the graph is positive and decreasing?A.all real values of x where x < −1
B.all real values of x where x < 1
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The statement that describes all of the values for which the graph is positive and decreasing is:

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Answer:

Step-by-step explanation:

The number 1 ensures that the value of x will remain positive.

Since x is less than 3, then the value of x is decreasing.

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