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Ber [7]
2 years ago
6

If P is the incenter of JKL, find m Please show the work, that would be really helpful, thank you!

Mathematics
1 answer:
mezya [45]2 years ago
7 0

Answer:

34^{\circ}

Step-by-step explanation:

The incenter of a triangle can be defined as the intersection of three angle bisectors that bisect all angles of the triangle.

By definition, an angle bisector divides an angle into two equal smaller angles.

Therefore:

\angle KJN=\angle LJN,\\\angle KLM=\angle JLM, \\\angle JKP=\angke LKP

What we're given:

  • \angle KJN=\angle LJN=30^{\circ}
  • \angle KLM=\angle JLM=26^{\circ}

The sum of the interior angles of a triangle always add up to be 180 degrees. Since these six angles make up the total sum of the interior angles, we have the following equation:

\angle KJN+\angle LJN+\angle KLM +\angle KLM +\angle JKP+ \angle LKP=180^{\circ}

Substituting given values:

30+30+26+26+\angle JKP+\angle LKP=180

Since \angle JKP=\angle LKP,

30+30+26+26+2(\angle JKP)=180,\\112+2(\angle JKP)=180,\\2(\angle JKP)=180-112,\\2(\angle JKP)=68,\\\angle JKP=\frac{68}{2}=\boxed{34^{\circ}}

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Drag the tiles to the correct boxes to complete the pairs.
Mashcka [7]

Answer:

Part 1) -17\frac{8}{9} -----> -6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}

Part 2) -15.11 ------> -12.48-(-2.99)-5.62

Part 3) -19\frac{8}{9} -----> -19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})

Part 4) -201.65 -----> -353.92-(-283.56)-131.29

Part 5) 74 ------> 83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})

Step-by-step explanation:

Part 1) we have

-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}

To calculate the subtraction convert the mixed numbers to an improper fractions

6\frac{4}{9}=\frac{6*9+4}{9}=\frac{58}{9}

3\frac{2}{9}=\frac{3*9+2}{9}=\frac{29}{9}

8\frac{2}{9}=\frac{8*9+2}{9}=\frac{74}{9}

substitute

-\frac{58}{9}-\frac{29}{9}-\frac{74}{9}=-\frac{(58+29+74)}{9}=-\frac{161}{9}

Convert to mixed number

-\frac{161}{9}=-(\frac{153}{9}+\frac{8}{9})=-17\frac{8}{9}

Part 2) we have

-12.48-(-2.99)-5.62

To calculate the subtraction eliminate the parenthesis first

-12.48-(-2.99)-5.62=-12.48+2.99-5.62=-15.11

Part 3) we have

-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})

To calculate the subtraction convert the mixed numbers to an improper fractions

19\frac{2}{9}=\frac{19*9+2}{9}=\frac{173}{9}

4\frac{1}{9}=\frac{4*9+1}{9}=\frac{37}{9}

3\frac{4}{9}=\frac{3*9+4}{9}=\frac{31}{9}

substitute

-\frac{173}{9}-\frac{37}{9}-(-\frac{31}{9})

Eliminate the parenthesis

-\frac{173}{9}-\frac{37}{9}+\frac{31}{9}=\frac{(-173-37+31)}{9}=-\frac{179}{9}

Convert to mixed number

-\frac{179}{9}=-(\frac{171}{9}+\frac{8}{9})=-19\frac{8}{9}

Part 4) we have

-353.92-(-283.56)-131.29

To calculate the subtraction eliminate the parenthesis first

-353.92+283.56-131.29=-201.65

Part 5) we have

83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})

To calculate the subtraction convert the mixed numbers to an improper fractions

83\frac{1}{5}=\frac{83*5+1}{5}=\frac{416}{5}

108\frac{2}{5}=\frac{108*5+2}{5}=\frac{542}{5}

99\frac{1}{5}=\frac{99*5+1}{5}=\frac{496}{5}

substitute

\frac{416}{5}-\frac{542}{5}-(-\frac{496}{5})

Eliminate the parenthesis

\frac{416}{5}-\frac{542}{5}+\frac{496}{5}=\frac{(416-542+496)}{5}=\frac{370}{5}=74

3 0
3 years ago
Rectangle R has varying length l and width w but a constant perimeter of 4 ft. A. Express the area A as a function of l. What do
ivanzaharov [21]
Given:
l = length of the rectangle
w = width of the rectangle
P = 4 ft, constant perimeter

Because the given perimeter is constant,
2(w + l) = 4
w + l = 2
w = 2 - l            (1)

Part A.
The area is
A = w*l 
   = (2 - l)*l
 A  = 2l - l²
This is a quadratic function or a parabola.

Part B.
Write the parabola in standard form.
A = -[l² - 2l]
   = -[ (l -1)² - 1]
   = -(l -1)² + 1
This is a parabola with vertex at (1, 1). Because the leading coefficient is negative the curve is downward, as shown below.

The maximum value occurs at the vertex, so the maximum value of A = 1.
From equation (1), obtain
w = 2 - l = 2 - 1 = 1.
The maximum value of the area occurs when w=1 and l=1 (a square).

Answer:
The area is maximum when l=1 and w=1.
The geometric argument is based on the vertex of the parabola denoting maximum area.

4 0
3 years ago
Find the 2nd term of (2x+3y)^3
puteri [66]

Answer:

The 2nd term is 3y

Step-by-step explanation:

2x +       3y

__          __

1            2

term     term

5 0
2 years ago
Read 2 more answers
Z+w−3=k<br> 6z−10w=8<br><br> ​ <br><br><br> ​
ludmilkaskok [199]

Answer:

if your looking for z it is 5/8k+2.375

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
how many legs do 10 people have? if two people dont have legs. one person has 3 legs and one person has one leg. and mary has a
Ganezh [65]
So here is the answer. Normally, 10 people have 20 legs since each person has 2 legs each. But given the scenario that two people don't have legs, this would mean 20 minus 4, is 16 legs. Then one person has 3 legs, 16 plus 3 and it is 19. And then, another person has one leg, 19 plus 1 is 20. Therefore, the total legs would still be 20. Hope this helps. The dog does not count.
5 0
2 years ago
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