If P is the incenter of triangle JKL, find PJ

If P Is The Incenter Of Triangle JKL, Find PJ

Answers

Answer 1
If P is the incenter of ΔJKL, then we have,
PN = PM = PO


To find PJ first we need to calculate the value of x
Since,

PN = 22
So,
PM = 22

Now, in ΔPJM we have,

PJ^2 = PM^2 + MJ^2
PJ^2= (22)^2 +(2x+3)^2...(1)

Also, In ΔPJO we have,

PJ^2 = PO^2 + OJ^2
PJ^2 = (22)^2 (5x - 45)^2...(2)

From equation (1) and (2) we obtain,

(5x - 45)^2+(22)^2=(2x+3)^2 +(22)^2
25x^2 — 450x + 2025 = 4x^2 + 12x + 9
25x^2 — 4x^2— 450x — 12x + 2025 — 9 = 0
21x^2 — 462x + 2016 = 0
x^2 - 22x+96 = 0
x^2 — 16x — 6x + 96 = 0
x(x - 16) -6(x - 16) = 0
(x - 6)(x - 16) = 0
Either x=6 or x=16

At x = 6
JO = 5 x 6 - 45
= 30 - 45
= -15

Which cannot be possible because edge length cannot be negative
So the value of x = 16

Hence, the length of PJ is

PJ^2 = 484 + (80 - 45)^2
PJ^2 = 484 + 1225
PJ^2 = 1709
PJ = √1709
PJ = 41.33

Therefore, the length of PJ is 41.3 units




Related Questions

Raise 10 to the 3rd power then multiply the result by a

Answers

Answer:

1000a

Step-by-step explanation:

[tex] 10^3 \times a = 10 \times 10 \times 10 \times a = 1000 \times a = 1000a [/tex]


Find all solutions to the equation
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[tex]\bold{FULL ANSWERS:}[/tex]

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Step-by-step explanation:

The formula for slope-intercept form is y = mx + b. Keep y and x as the variables. Replace m with the slope, which can be found by doing rise/run, and replace b with the y-intercept. The y-intercept is the spot where the line intersects the y-axis.

Hope this helps! Have a great day! :)


A cylinder has a height of 5 centimeters. Its volume is 62.8 cubic centimeters. What is the
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Answer: 2

Step-by-step explanation: It would have been 1.99949 but rounded to the nearest hundreth is 2 :)

what is the radius of D

6 cm
12 cm
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24 cm​

Answers

Answer:

3 Is the Radius

Step-by-step explanation:

Diameter is always 2R (R for radius), as they have given us the diameter of 6 we can conclude the answer by forming a simple equations

D=2R

6=2R

3=R

Option 3 is the answer

A long-distance runner finished a race in 2.75 hours. How is the runner's time expressed
as a mixed number?

Answers

yes,

because 2.75 = 11/4

In mixed number it will be 2 3/4

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Hopefully that makes sen to u

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Answers

Answer:

  C and D

Step-by-step explanation:

Population density is the ratio of population to area. Its units are persons per square mile. Here, you're being asked to compare the population densities of several countries to the average population density in several US states.

__

average

The idea of "average population density of the 10 states listed" is somewhat ambiguous. It could mean either of (a) the ratio of the total of the states' population to the total of their land area, or (b) the average of the population densities of the states. (In the attached, we computed both, but the answer remains the same using either number.)

When there are numerous identical calculations to be performed, it is convenient to let a spreadsheet do them. The attached spreadsheet shows the population densities for the 10 states and 5 countries listed.

Depending on how you define it, the average population density of the 10 states is about 10.5 or about 15.7 people per square mile. (15.7 is the average of the density numbers, found using the spreadsheet AVERAGE function.)

__

countries

The 5 countries have population densities ranging from about 7.7 to 236 people per square mile. Two of the countries have density below 10.5, so are the answers to the question asked.

  Canada (C) and Iceland (D) have population density below the US state average.

A display case of hat pins are marked 5 for $3. If Patty has $21, how many hat pins can Patty get? (assume no other taxes and fees)

Answers

Answer: 35

Explanation: If patty has $21, and $3 is the price for 5 hat pins, then: 21/3=7, so she can buy 7 packages which cost $3 and contain 5 pins, and because the question asked the number of pins, we will multiply 7 • 5 and that equals 35

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

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Answer:

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Step-by-step explanation:

Since angle a is 1/2 the size of angle b, a=1/2b and b=2a. In order to get a numeral answer, you need the number of one of the angles.

which is bigger 2m or 275cm

Answers

Answer:

275.

Step-by-step explanation:

If you convert 2m into CM you get 200.
If you convert 275 cm into M you get 2.75. So 275cm is bigger.

275 centimeters is bigger than 2 meters

IMPORTANT: every " a, b, c and + , -" are meant to be exponents

Answers

The expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is an algebraic expression, and the result of simplifying the expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is 1

How to simplify the expression?

The expression is given as:

[tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex]

Apply the power rule of indices

[tex](x^{a-b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex]

Expand the exponents of the expression

[tex]x^{a^2-b^2} \cdot x^{b^2 - c^2} \cdot x^{c^2 - a^2[/tex]

Apply the product rule of indices

[tex]x^{a^2-b^2+b^2 - c^2+c^2 - a^2[/tex]

Collect like terms

[tex]x^{a^2- a^2-b^2+b^2 - c^2+c^2[/tex]

Evaluate the differences

[tex]x^{0-0 - 0[/tex]

This gives

[tex]x^{0[/tex]

Evaluate the exponent

1

Hence, the result of simplifying the expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is 1

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3(p-6)

Which of the expressions is equivalent to the given expression?
Part A
a) (3 * p)-6
b) (3* p)-(3 *6)
c) (3 +p) - (3 *6)
d) (3 * p)* (3-6)

Part B
Which expression is also equivalent to the given expression?
a) p-18
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c)3p-6
d)3p-18

Answers

Part A is c part B is d

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Answers

Step-by-step explanation:

Where do you want to go from here?

What do you want to accomplish?

What obstacles will you have to overcome?

What problems will you have to solve?

What additional knowledge, skills, or resources will you require to achieve your strategic objectives?

The required Strategic planning answers the question "Where do we want to go and how do we get there?"

What is Strategic planning?

Strategic planning is the process of defining an organization's vision, mission, values, goals, and objectives, and developing a roadmap to achieve them.

Here,

"Where do we want to go and how do we get there?"

Strategic planning is the process of defining an organization's vision, mission, values, goals, and objectives, and developing a roadmap to achieve them. It involves assessing an organization's current situation, identifying strengths, weaknesses, opportunities, and threats, and developing strategies to leverage strengths, address weaknesses, seize opportunities, and mitigate threats.

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Identify any transformations that are used in each image below.

Reflections - how many lines of symmetry and what specific type: vertical (y-axis), horizontal (x-axis), diagonal (y=x or y=-x)
Rotations - of which order or how many degrees/angle of rotation

Answers

a. Reflectional symmetry only. The mirror line is vertical along the center of the sunglasses. The left half mirrors over this line to get the right half, and vice versa. There isn't any rotational symmetry because we can't rotate the glasses (some angle between 0 and 360 exclusive of both endpoints) to have the image be the same as the preimage.

---------------------

b. Rotational symmetry only. The puzzle can be rotated 90 degrees and the before and after image will be the exact same. There isn't any reflectional symmetry here.

----------------------

c. Reflectional symmetry and rotational symmetry. Effectively a combination of parts a) and b). We have a horizontal line of symmetry to go with a vertical one. The angle of rotation is 180 degrees.

----------------------

d. Reflectional symmetry and rotational symmetry. Similar to part c). This time the angle of rotation is 360/3 = 120 degrees. There are 3 lines of symmetry and they all pass through a vertex of the triangle, and the symmetry lines are perpendicular to the opposite side.

----------------------

e. Reflectional symmetry and rotational symmetry. We can rotate 180 degrees and not change the image. There are two lines of symmetry which pass through the center, one line is horizontal and the other vertical.

-----------------------

f. Rotational symmetry only. We don't have reflectional symmetry due to the smaller petals not matching up when reflections happen. But we can rotate the figure 120 degrees the same way we can with figure d.

Your answer is incorrect
In the past year, Charmaine watched 28 movies that she thought were very good. She watched 80 movies over the whole year of the movies she watched,
what percentage did she think were very good?
0
?

Answers

V = number of very good movies
T = total number of movies
P = percentage rated as very good

P = (100 V/T)% = (100 x 24/40)% = 60%

subtract x-3 from 3-x + 4​

Answers

Answer:

-2x + 10

Step-by-step explanation:

3 - x + 4 - (x - 3)

1. Combine like terms:

-x + 7 - (x - 3)

2. Apply the distributive law - (a - b) = -a + b :

-x + 7 -x + 3

3. Combine like terms:

-2x + 10

hope this helps!

Edgar and June ate 75% of a pizza. If the pizza had 12 slices, how many slices did they eat

Answers

Answer:

9

Step-by-step explanation:

100% = 12

12/4= 3
25%=3

3+3+3=25%+25%=25%= 75%

To find the time it will take for a train
to travel from Springfield to Franklin,
d
where d
use the expression s,
represents distance and s represents
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Find the time if the train travels
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hour.

Answers

I don’t see how this is solvable
The expression would be 79d, but how would you find the distance if it doesn’t tell you what to put for d.
Are the options to pick from?
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i-Ready
»Evaluate (8+t)³ - 6 when t = 2.
The value of the expression is
Practice: Numeric and Algebra

Answers

Answer:

994

Step-by-step explanation:

8+t(3) - 6 = 1000-6= 994

Vector Vector C D. has an initial point of (–7, 2, 8) and a terminal point of (0, 7, 3). Vector Vector E F. has an initial point of (4, 1, –2) and a terminal point of (6, –2, –3). What is the component form of vector Vector C D minus vector E F.?

LeftAngleBracket negative 5, negative 8, 4 RightAngleBracket.
LeftAngleBracket 5, 8, negative 4 RightAngleBracket.
LeftAngleBracket 9, 2, negative 6 RightAngleBracket.
LeftAngleBracket negative 9, negative 2, 6 RightAngleBracket.

Answers

A vector is a quantity in physics that has both magnitude and direction. The component form of Vector CD minus vector EF is <5, 8, -4>.

What is a vector?

A vector is a quantity in physics that has both magnitude and direction. It is often represented by an arrow whose length is proportionate to the magnitude of the quantity and whose direction is the same as that of the quantity.

The value of the Vector CD can be written as,

[tex]|\vec{CD}| = (0+7)\hat i+(7-2)\hat j+(3-8)\hat k = 7\hat i+5\hat j-5\hat k[/tex]

The value of the Vector EF can be written as,

[tex]|\vec{EF}| = (6-4)\hat i+(-2-(-1))\hat j+(-3-(-2))\hat k = 2\hat i-3\hat j-5\hat k[/tex]

Now,  the component form of Vector CD minus vector EF can be written as,

[tex]\vec{CD} - \vec{EF} = < (7-2) , (5-(-3)) , (-5-(-1)) > = < 5,8,-4 >[/tex]

Hence, the component form of Vector CD minus vector EF is <5, 8, -4>.

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76. 30 students at a sports event are
wearing purple. This is 40% of the
students at the event. How many
students are at the event?

Answers

Answer:

75 students

Step-by-step explanation:

So firstly lets make convert these words to alegbra :

30 people are 40%of the total students at the event meaning that the following equation can be made :

30 = 40% of x    (x is the unknown amount of students there)

30 = 40% * x

30 = 0.4x (we can convert the precentage into a decimal by dividing by 100)

Now that we have the equation that 30 = 0.4x we can evalute it and find x :

30=0.4x

30/0.4=0.4x/0.4 (divide by 0.4 on both sides)

75=x

So thats how we get that 75 students were in the event in total.

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Answers

x + 30 = 2x (since angleA = angle D, due to congruency between the two triangles.)

30 = 2x - x

30 = x

hope it helps...!!!

What additional piece of information must be known in order to calculate the volume of the cylinder below?
in.
the diameter of a base
the height of the cylinder
the area of a base
Othe radius of a base

Answers

Answer:

the height of the cylinder

Step-by-step explanation:

This figure represents a platform on a stage. The stage crew needs to paint it black. One gallon of paint will cover 40 square yards.

How many full gallons of paint does the crew need to buy in order to paint the entire platform?

Enter your answer in the box.

gallons

Answers

Answer:

14

Step-by-step explanation:

I took the test.

Answer:

14

Step-by-step explanation: I took the test

Ben spent 1/6 of his money on a burger, fries, and a drink. Then he spent half of the money he had left: $5 on a magazine, $8.25 on a bookmark, and $10.50 on a book. How much money did he have to begin with?

Please answer asap and please explain your answer.

Answers

Answer:

$57

Step-by-step explanation:

I'm not a good person explaining answers, so I will just give the equation.

[2(5+8.25+10.50)+ 23.75) x 4]  ÷ 5

Hope this helps :)

The bigger the payment that you make on your credit card bill, the
А less interest you wil have to pay in total
B more interest you will have to pay in total C higher your APR
D lower your annual fee

Answers

Answer:

A I think

Step-by-step explanation:

Necesito saber cómo lograr el 5 y 6.

Answers

Answer:

5) 12 pieces for $36

6) 12 pieces for $36

They require the same amount of wood pieces.

Step-by-step explanation:

5)

Sandbox A: ? = 2

one side is 6, the other is 4 + ? = 6, so 6-4= ? and 6 - 4 = 2

now we add up the perimeter: 2 + 2 + 4 + 4 + 6 + 6 = 24ft total

we know that each wood piece = 2 ft so:

24 / 2 = 12 pieces of wood

each piece costs $3, so we multiply...

12 * 3 = $36 for all the wood.

____________

Sandbox B: ? = 4

one side is 6, the other is 2 + ? = 6, so 6 - 2= ? and 6 - 2 = 4

now we add up the perimeter: 2 + 2 + 4 + 4 + 6 + 6 = 24ft total

we know that each wood piece = 2 ft so:

24 / 2 = 12 pieces of wood

each piece costs $3, so we multiply...

12 * 3 = $36 for all the wood.

What is the area of the smaller rectangle?

Answers

Answer:

64 mm^2

Step-by-step explanation:

The area of the rectangles is calculated by multiplying width and length:

for the bigger rectangle:

12*48 = 576 mm^2

for the smaller rectangle:

4*16 = 64 mm^2

Solve the equation: (a + 2)^4- 20(a + 2)^2+ 64 = 0

Answers

Answer:

Answer is 7.

Step-by-step explanation:

(a + 2)^4- 20(a + 2)^2+ 64 = 0

2a^4- 20(2a)^2+ 64 = 0

16a-20(4a)+64=0  

-4a    -64  -4a          -64

12a-84=0

    +84 +84

12a=84

84/12=7

The answer is 7
If needed to be solved to show proof text me

What is 125.1 ÷ 6 and if you do how do you do it?

Answers

ans = 20.85

hope it helps...!!!

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