Mathematics High School

If P is the incenter of triangle JKL, find PJ.

Answers

Answer 1

Answer:

PJ = 41.34

Step-by-step explanation:

P is incenter, three angles bisector meet

∠MJP ≅ ∠OJP

PM = PN = PO = 22 (radius: property of incenter)

∠JPM = 90 - ∠MJP = 90 - OJP = ∠JPO

ΔJPM ≅ ΔJPO (ASA) or (SAS)

LM = JO

2x + 3 = 5x - 45

3x = 48

x = 16

JM = 35

PJ = √35²+22² = √1709 = 41.34

Answer 2

The value of PJ in triangle KJL is 41.32 units.

What is incenter?

The point formed at the intersection of the three angle bisectors of a triangle; also the centre of the incircle.

Given that, P is incenter of the triangle KJL,

Considering the triangles ΔMJP and ΔOJP

PM = PO (property of incenter)

∠ JMP ≅ ∠ JOP

JP is common segment.

ΔJPM ≅ ΔJPO (by SAS rule)

JM = JO (CPCTC)

2x + 3 = 5x - 45

3x = 48

x = 16

JM = 35

Using the Pythagoras theorem,

PJ² = PM²+JM²

PJ = √35²+22² = √1709 = 41.34

Hence, The value of PJ in triangle KJL is 41.32 units.

For more references on incenter, click;

https://brainly.com/question/29480777

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Related Questions

Solve this system of equations. Show or explain your work.

3x+4y=35

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Answer:

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Step-by-step explanation:

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Answer:

7.5 cm

Step-by-step explanation:

If they are similar, then they are proportionate.

The 4 is proportionate to the 6 and so is the x to the 5.

6/4= 1.5

1.5*5=7.5

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Ryan has $470 in his bank account. His bank
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balance in his account now?

Answers

Answer:

He has 445$ in his account

Step-by-step explanation:

First, if he has 470 in his account and he makes a check for 55, 470 - 55 = 415, then he made a deposit his account now holds 445$, thus your final answer is 445$ is the balance in his bank account.

Hope This Helps!

3.
Mrs. Jones is making 8 sandwiches for lunch She has exactly 2 pounds (lb) of turkey and wants to use the same amount of turkey for each sandwich
0
1 lb
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Answers

Answer:

0.25 lbs for each sandwich.

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Answers

Answer:

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E. 0, the graph could represent no change over time.

assume the point on the graph is the origin, you can graph these

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Step-by-step explanation:

What is the volume of a sphere with a radius of 6.9 ft

Answers

V=4/3 π•r^3
r=6.9 ft
V=4/3 π• (6.9)^3
V=4/3 π • 328.509 ft^3
V= π•438.012 ft^3
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Answers

Answer:

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Step-by-step explanation:

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A pair of dice was rolled many times and the results appear below. Based upon these result what is the experimental probability of rolling a 7
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Answers

The experimental probability of rolling a 7 would be 4/25 (16%). Experimental probably is found by putting the frequency of the event over the total number of trials. In this case that is 16/100, which reduces to 4/25.

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Answers

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Answers

Factor using the perfect square rule.

( 3 y − 4 ) ^2

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Step-by-step explanation:

9x^2 + 24x + 16 =(3x +4) (3x + 4)

lenth of each side 3x+ units

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Answers

Answer:

32,768 ways

Step-by-step explanation:

True/ false questions = 5 ; number of options = 2 (True or false)

Ways of answering = 2^5 = (2 * 2 * 2 * 2 * 2) = 32

Number of Multiple choice questions = 5

Number of options (A - D) = 4 options

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Brooke bought 5 plates for $44. If the price of the plates is always the same, which represents the total cost, y, of buying any number of plates, x?

Answers

Answer:

y = 8.80x

Step-by-step explanation:

Th price of one plate = $44 / 5 = $8.80

the cost of any x plate can be determined by multiplying $8.80 by x

y = $8.80x

For example if x is 10, y = $8.80(10) = $88

If x = 100, y = $8.80(100) = $880

Answer:

y = 8.80x

Step-by-step explanation:

Th price of one plate = $44 / 5 = $8.80

the cost of any x plate can be determined by multiplying $8.80 by x

y = $8.80x

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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(9,12) would become (9,15)

Step-by-step explanation:

the points would change as follows:

(3,4) would become (3,5)

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Answers

Answer:

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Step-by-step explanation:

What distance does the particle travel over the interval 0 ≤ t ≤ 1?

The distance is the integral of the velocity.

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Answers

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Step-by-step explanation:

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Answers

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Answers

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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Answer:

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