In the diagram, the circle is inscribed in triangle PQR. Find arc EF, FG, and GE.
Answers
Check the picture below.
In essence, the two triangles made by the radii and the twin tangent lines are congruent by SSS or even for right-triangles congruence by LL.
Applying the tangents theorem, the arc measures are:
Arc EG = 140°
Arc EF = 120°
Arc FG = 100°
What is the Tangents Theorem?The tangents theorem states that a tangent to a circle forms a right angle (90 degrees) at the point of tangency, and also, if two tangents meet at point outside a circle, both tangents are equal.
Using the tangent theorem, we would find the central angles opposite arc EF, FG, and GE which are all the same measure as their central angles.
Let the center of the circle be point O.
m∠EOG = 2[180 - m∠PEG + m∠EOP)] (central angle opposite to arc EG)
Substitute
m∠EOG = 2[180 - 90 + 1/2(40)]
m∠EOG = 140°
Arc EG = m∠EOG = 140°
Arc EG = 140°
m∠EOF= 2[180 - m∠QFO + m∠FQO)] (central angle opposite to arc EF)
Substitute
m∠EOF = 2[180 - 90 + 1/2(60)]
m∠EOF = 120°
Arc EF = m∠EOF = 120°
Arc EF = 120°
m∠FOG = 2[180 - m∠RFO + m∠FRO)] (central angle opposite to arc FG)
Substitute
m∠FOG = 2[180 - 90 + 1/2(80)]
m∠FOG = 100°
Arc FG = m∠FOG = 140°
Arc FG = 100°
Therefore, applying the tangents theorem, the arc measures are:
Arc EG = 140°
Arc EF = 120°
Arc FG = 100°
Learn more about tangents theorem on:
https://brainly.com/question/9892082
Related Questions
What fraction of an hour is four minutes
Answers
Answer
1hr/15 mins=60 mins/15 mins=4 minutes.
Step-by-step explanation:
Hi! -2x + y = -11 4x + 4y = 4 System by substitution!!!
Answers
Answer:
Point Form:
(
8
3
,
−
5
3
)
Equation Form:
x
=
8
3
,
y
=
−
5
3
Answer:
x=4, y=-3, or (4,-3)
Step-by-step explanation:
Hi there!
We are given the following system of equations:
-2x+y=-11
4x+4y=4
And the problem wants us to solve it by substitution
In substitution, we will solve one of the equations for one of the variables to equal an expression containing the other variable, then substitute that expression as the variable it equals into the other equation, solve that equation, then use the value of the solved variable to solve for the first equation we made (the one that is a variable equaling an expression containing the other variable)
It's easier to do this when one of the variables already has a coefficient of 1, as we can just move a couple of terms around without having to multiply or divide anything; for example, in the first equation, -2x+y=-11, y already has a coefficient of 1
So we can just add 2x to both sides, in order to solve the equation for y
-2x+y=-11
+2x +2x
______________
y=2x-11
Now substitute this expression into the the second equation as y.
So, 4x+4y=4 would become 4x+4(2x-11)=4
Now we need to solve 4x+4(2x-11)=4
Do the distributive property:
4x+8x-44=4
Combine like terms
12x-44=4
Add 44 to both sides
12x=48
x=4
We found the value of x
Now we need to find the value of y
Substitute 4 as x in y=2x-11
y=2(4)-11
Multiply
y=8-11
subtract
y=-3
The answer is x=4, y=-3, or as a point, (4, -3)
Hope this helps!
See more on solving systems by substitution here:
https://brainly.com/question/24420448
Which polynomials are prime? Check all of the boxes that apply.
x2 + 9
x2 – 9
x2 + 3x + 9
–2x2 + 8
Answers
Answer:
Answer:
The prime polynomials are
x² + 9
x² + 3x + 9
Step-by-step explanation:
Please help mee
A punch recipe requires 2 cups of cranberry juice to make 3 gallons of punch. Using the same recipe, what is the amount of cranberry juice needed for 1 gallon of punch?
Answers
Answer:
0.66 cups of cranberry juice is needed to make 1 gallon of punch
Step-by-step explanation:
2 / 3 = 0.66
i hope this helped! have a wonderful rest of your day :)
( SHOW UR WORK) Find the value of 8.41 + 42.320
Answers
Answer:
See below.
Step-by-step explanation:
42.32
+8.41
50.73
-hope it helps
Answer:
50.73
Step-by-step explanation:
8.41
42.32
+_________
50.73
Hope this helps! Have a great day!!
Can someone help me with this please!
Answers
Answer:
Step-by-step explanation:
How do I solve this?
Answers
the model is using "t" as years after 2003, if we want to know the population in that country using that model at year 2003, then "t" must be 0, when t = 0, that's the initial population for that model.
[tex]A=920.2e^{0.005t}\implies A=920.2e^{0.005(0)}\implies A=920.2(1)\implies A=920.2[/tex]
Given cos 0 = 1/6 and angle 0 is in Quadrant IV, what is the exact value of sin 0 in
simplest form? Simplify all radicals if needed.
Answers
cos 0 = 1/6
1 - cos²0 = sin²0
sin²0 = 35/36
in quadrant IV (4) the cos is positive sin is negative.
sin0 = - √35/6
Write an equation for the line parallel to the given line that contains C.
c(3,8); y= 5/8x + 8
Answers
Answer:
x= - 64/5
Step-by-step explanation:
1- Substitute y = 0
2- Multiply both sides
3- Move the variable to the left
4- Divide both sides
Jimmy's height is 156 cm, Kessie's height is 168 cm, while Lya's height is 132 cm. Define:
Answers
Answer:
132<156<168 or 12×1, 12×2 ...
Step-by-step explanation:
Jimmy's 24cm taller than Lya, and Kessie's 12cm taller than Jimmy
Solve the equation: 30 = 5 + 0.5d
Answers
Answer:
d = 50
Step-by-step explanation:
30 = 5 + 0.5d ( subtract 5 from both sides )
25 = 0.5d ( divide both sides by 0. 5 )
50 = d
(3x-1)•(5x-3)
find area and perimeter in feet
Answers
Answer:
21 is the answers to your question
NEED HELP!! Urgently!
Answers
Add the two sepratw ones and that the answer
The first term of geometric series is -3, the common ratio is 6, and the sum of the series is -4,665. using a table of values, how many terms are in this geometric series
Answers
[tex]\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\stackrel{\textit{first term}}{-3}\\ r=\stackrel{\textit{common ratio}}{6} \end{cases}[/tex]
[tex]\stackrel{S_n}{-4665}~~ = ~~-3\left( \cfrac{1-6^n}{1-6} \right)\implies -4665=-3\left( \cfrac{1-6^n}{-5} \right) \\\\\\ -4665=\cfrac{3}{5}(1-6^n)\implies -4665\cdot \cfrac{5}{3}=1-6^n\implies -7775=1-6^n \\\\\\ -7776=-6^n\implies 7776=6^n\implies 6^5=6^n\implies \boxed{5=n}[/tex]
Answer:
5 terms
Step-by-step explanation:
The attached table shows that the sum of 5 terms is -4665.
__
Additional comment
A table for a problem like this is easily made using a spreadsheet. Each value is 6 times the previous, and each sum is the new value added to the previous sum. The first value and the first sum are -3.
In the attached, we have simply summed the terms, each term being computed using the explicit formula for this geometric sequence.
HELP?!?!
The shaded octagon is transformed to the unshaded octagon in the coordinate plane below.
Which statement about the transformation is true?
The unshaded octagon is a reflection because it is a flip over a diagonal line.
The unshaded octagon is a dilation because it is smaller than the shaded octagon.
The unshaded octagon is a horizontal translation because it is directly to the left of the shaded octagon.
The unshaded octagon is a vertical translation because it is directly under the shaded octagon.
Answers
Answer:
(A) The unshaded octagon is a reflection because it is a flip over a diagonal line.
Step-by-step explanation: Trust, rust, and pixie dust
Answer:
A is correct
The unshaded octagon is a reflection because it is a flip over a diagonal line.
i took the test
What is the ratio in decimal form of 75 people in a 10ft X 10ft square?
Answers
Answer:
(100 ft^2) / (75 people) is a ratio: 1.3333... ft^2/person
Step-by-step explanation:
There are 75 people in a 100 square foot area. The amount of space (floor space) is (100 ft^2) / (75 people) = 1 1/3 square feet.
(100 ft^2) / (75 people) is a ratio: 1.3333... ft^2/person
Is (6,3) a solution to the equation "a"? Yes or No.
Yes
No
Answers
Explanation: When plotted on the graph, equation A's line meets the point. This means it is a possible solution to equation A.
Answer:
Yes
Step-by-step explanation:
15x+3y=27 into slope-intercept form, simplifying all fractions.
Answers
Answer:
y = -5x + 9
Step-by-step explanation:
Slope-intercept form is the form
y = mx + b
So you need to rearrange the terms to get the y all by itself on the left. On the right, the x term goes first and last the constant (a plain number) see image.
Simplify (3x2 − 2) (2x2 − 6x 3). 5x2 − 6x 1 5x2 − 6x − 1 x2 − 6x 1 5x2 − 8x 3.
Answers
Answer:
-566
Alternative form:
-5.66 x [tex]10^{2}[/tex]
Please Help! ASAP. Will give Brainliest
Answers
Answer:
3 Not too sure though
Step-by-step explanation:
don't input my answer, i'm not too sure!
2) Riddington and Greenwick are two small villages.
The population of Riddington has increased from 80 people to 120 people.
The population of Greenwick has decreased from 200 people to 120 people.
Show that Riddington has had the greater percentage change in its population.
You must show all your working.
Answers
Answer:
See belowStep-by-step explanation:
Find the amount of change in both cases and convert the change into percentage, then compare final results.
1. Riddington
Change:
120 - 80 = 40Percent change:
40/80*100% = 50% increase2. Greenwick
Change:
200 - 120 = 80Percent change:
80/200*100% = 40% decreaseAs we see 50% > 40% so this proves the statement.
Help if you understand Thanks
Answers
Answer:
b
Step-by-step explanation:
Repeating domain (x-values) does not represent a function.
Option b does not have any repeating domains.
Hope this helps!
Answer:
The answer is the third one.
Step-by-step explanation:
Hopefully this is helpful :)
17. Alexis has a painting presently valued at $2000. An art dealer told her the painting would
appreciate at a rate of 8% each year. In how many years will the painting be worth $5000?
Round your answer to the nearest tenth.
Show work please
Answers
Answer:
18.8 years
Step-by-step explanation:
8% of $2000 = $160
To be worth $5000, the painting need to rise by $3000
And every year it rise by $160, so it will need 3000 : 160 = 18.75 (round to 18.8) years.
What is the equation of a horizontal line passing through the point (1, 14)?
y=1
y= 14
x=1
x=14
Answers
Answer:
y = 14
Step-by-step explanation:
If the line is horizontal, it will always have the ssame value of y for all values of x. Therefore, y = 14.
1/2 + 2/9 + 27/53 as a fraction
Answers
Answer:
1175/954 there your answer
Evaluate and must show work
But i don’t think there is anything left to be done is there?
Please help
Answers
Answer:
ln(x)/2 -3.810930
Step-by-step explanation:
The relevant rules of logarithms are ...
ln(ab) = ln(a) +ln(b)
ln(a^b) = b·ln(a)
ln(a/b) = ln(a) -ln(b)
ln(e) = 1
__
Your expression expands to ...
[tex]\ln\left(\dfrac{4\sqrt{x}}{9e^3}\right) = \ln(4\sqrt{x})-\ln(9e^3)=\ln(4)+\dfrac{1}{2}\ln(x)-(\ln(9)+3\ln(e))\\\\=\dfrac{1}{2}\ln(x)+\ln(4)-\ln(9)-3\\\\\approx\dfrac{\ln(x)}{2}-3.810930[/tex]
A box is 20 inches long and 21 inches high. What is the diagonal length of the box?
Answers
Answer:
29 inches
Step-by-step explanation:
Answer:
Use Pythagoras' Theorem:
c²=a²+b²
c²=20²+21²
c²=841
c=√841
c=29 inches
Step-by-step explanation:
Ryan and Carlos are getting in shape for football season. Ryan starts at 140 pounds and gains two pounds per week. Carlos starts at 195 pounds but
loses three pounds per week. In how many weeks will they both weigh the same amount, and what will that weight be? (Hint: these are y = equations)
Answers
Answer:
In 11 weeks they will both be 162lbs each
Step-by-step explanation:
Angie packed same-size cubes into a rectangular prism.
Image shows a base of cubes 3 units long, 2 units wide, and with a column of cubes 1 cube wide and 7 cubes tall. PLEASE HELP ME
What is the number of cubes needed to fill this prism?
A.
20 cubes
B.
35 cubes
C.
36 cubes
D.
42 cubes
WILLL GIVE THE BRAINLIEST PLEASE HELP ME IN A RUSH
Answers
Answer:
the answer is 42 can i have brainliest please:)
Step-by-step explanation:
3x7x2=42
Answer:
42
Step-by-step explanation:
The area of a circle is 22.68cm2.
Find the length of the radius rounded to 2 DP.
Answers
Answer: r=2.69. Calculate the radius of circle:Round the number: r=2.69Answer: r=2.69