Points E, F, and D are on circle C, and angle G
measures 60°. The measure of arc EF equals the
measure of arc FD.
Which statements about the arcs and angles are
true? Select three options,
O ZEFD - ZEGD
E
O ZEGD ZECD
ED FD
С
G60°
mEF = 60
OmFD = 120
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Answers
Answer:
The correct statements are:
1: mEFD = mEGD
3: mED = mFD
5: mFD = 120°
Step-by-step explanation:
Let's analyse each statement:
1: mEFD = mEGD
Let's find the value of the angle ECD, using the sum of the internal angles of a quadrilateral:
[tex]60 + 90 + 90 + mECD = 360[/tex]
[tex]mECD = 120\°[/tex]
The angle ECD is a central angle, related to the arc ED, so the arc ED also has 120°.
The angle EFD inscribes the arc ED, so we have:
[tex]mEFD = mED/2[/tex]
[tex]mEFD = 120/2 = 60\°[/tex]
So the angles mEFD and mEGD are equal. The statement is TRUE.
2. mEGD = mECD
This statement is FALSE, because mEGD = 60° and mECD = 120°
3. mED = mFD
If mED is 120° and mEF = mFD, we have:
[tex]mED + mEF + mFD = 360[/tex]
[tex]2*mFD = 360 - 120[/tex]
[tex]mFD = 120\°[/tex]
So the statement is TRUE, both arcs have 120°.
4. mEF = 60°
This statement is FALSE, because we calculated before that mEF = mFD = 120°
5. mFD = 120°
This statemente is TRUE, because we calculated before that mFD = 120°.
So the correct statements are 1, 3 and 5
The true statements are: [tex]\angle EFD =\angle EGD[/tex], [tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex]
Start by calculating the measure of angle ECD.
We have:
[tex]\angle ECD = 2 * \angle EGD[/tex]
So, we have:
[tex]\angle ECD = 2 * 60[/tex]
[tex]\angle ECD = 120[/tex]
The above means that:
[tex]\overset{\huge\frown}{ED} = 120[/tex]
So, the measure of angle EFD is:
[tex]\angle EFD = 0.5 * \overset{\huge\frown}{ED}[/tex]
[tex]\angle EFD = 0.5 * 120[/tex]
[tex]\angle EFD = 60[/tex]
From the question, we have:
[tex]\angle EGD = 60[/tex]
So, it is true that:
[tex]\angle EFD =\angle EGD[/tex]
To calculate the measure of arc FD, we have:
[tex]\overset{\huge\frown}{FD} + \overset{\huge\frown}{DE} + \overset{\huge\frown}{EF} =360[/tex]
Lengths EF and DE are congruent.
So, we have:
[tex]2\overset{\huge\frown}{FD} + \overset{\huge\frown}{DE} =360[/tex]
[tex]\overset{\huge\frown}{DE} = \overset{\huge\frown}{ED} = 120[/tex]
So, we have:
[tex]2\overset{\huge\frown}{FD} + 120 =360[/tex]
Divide through by 2
[tex]\overset{\huge\frown}{FD} + 60 =180[/tex]
Subtract 60 from both sides
[tex]\overset{\huge\frown}{FD} =120[/tex]
This means that:
[tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex] are true
Hence, the true statements are: [tex]\angle EFD =\angle EGD[/tex], [tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex]
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Related Questions
Please help me out i need it ASAP
Answers
Answer: C
Step-by-step explanation:
5 squareroot 2 = 7.07 which if you look up a 45 45 90 triangle calculator it is also eqivelant :)
What is this expression in simplified form?
(8/10)(8/5)
OA 64/50
OB. 16/50
OC. 80/2
OD. 320/2
Answers
Answer:
A.64/50
Step-by-step explanation:
8/10*8/5
64/50
The least simplified form of the equation is 32/25
The simplified form of expression is option (D) 64/50 is the correct answer.
What is simplification of an expression?Simplification of an expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression. It involves, multiply out the brackets and then simplify the resulting expression by collecting the like terms.
For the given situation,
The expression is (8/10)(8/5)
The simplified form of expression is
⇒ [tex](\frac{8}{10} )(\frac{8}{5} )[/tex]
⇒ [tex]\frac{64}{50}[/tex]
Hence we can conclude that the simplified form of expression is option (D) 64/50 is the correct answer.
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in which number does the digit 5 have a value that is 10 times as great as the digit 5 in the number 4.59?
Answers
Answer:
2775.9
Step-by-step explanation:
options are
A) 578
B) 2775.9
C) 134.591
D) 31.757
Value of digit 5 in 4.59 is 0.5 as is is at tenth place after decimal
0.5 = 5/10
ten times of this value = 5/10*10 = 5
Thus, 5 is the value, and hence the number which we require should be at unit place of the required number.
In the given question
A) 578
here 5 is at hundredth place
other way to represent is is 500+70+8
B) 2775.9
here 5 is unit place and is correct option
it can be represented as
2000+ 700+ 70+ 7 + 9/10
c)C) 134.591
here 5 is tenth place after decimal
it can be represented as
100+ 30+ 5 + 5/10+9/100 + 1/1000
d)31.757
here 5 is hundredth place after decimal
it can be represented as
30+ 1 + 7/10+5/100 + 7/1000\
Hence, 2775.9 is correct choice.
Trying to find the missing segment to the triangle in the attached image.
Answers
Answer:
44 units length
Step-by-step explanation:
The side splitter theorem states that if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally. Therefore:
20/10 = x/22
20/10*22 = x
44 = x
The degree of the polynomial function f(x) is 4. The roots of the equation f(x)=0 are −2, −1, 1 and 3.
Answers
Answer:
f(x) = x^4 - x^3 - 7x^2 + x + 6
Step-by-step explanation:
Please, always share the instructions with every question you post. I am assuming that you are to write out the factors corresponding to the given roots, thus constructing a 4th degree polynomial, and then performng the multiplication necesssary to produce that polynomial with terms in descending order by power of x. Note that there must be 5 such terms.
f(x) = (x + 2)(x + 1)(x - 1)(x - 3)
Multiplying this out, we get:
f(x) = (x + 2)(x^2 - 1)(x - 3), or
f(x) = (x^3 - x + 2x^2 - 2)(x - 3), or:
f(x) = (x^3 + 2x^2 - x - 2)(x - 3), or:
f(x) = x^4 + 2x^3 - x^2 - 2x - 3x^3 - 6x^2 + 3x + 6
Combining like terms, we get:
f(x) = x^4 - x^3 - 7x^2 + x + 6
Note that because this is a 4th degree polynomial, the end behavior resembles that of the graph of y = x^4. As x increases, y initially decreases in Quadrant II, passes through the y-intercept (0, 6), and then increases without bound in Quadrant I.
Which statement is true regarding the graphed functions?
Answers
Answer:
C
Step-by-step explanation:
You can look them up in the graphs.
f(2) means "where is the blue graph when x=2?", and you can see it is at y=0.
PLEASE HURRY! ILL GIVE BRAINLEIST!
The school baseball team has 3 pitchers. How many different 3-player pitching schedules can the coach choose from?
A. 3 schedules B. 5 schedules C. 6 schedules D. 9 schedules
Answers
Answer:
b
Step-by-step explanation:
What is the value of a?
Answers
Answer:
6sqrt(2)
Step-by-step explanation:
Use the right angle altitude theorem.
4/a = a/18
a^2 = 4 * 18
a^2 = 2 * 36
a = 6sqrt(2)
When 10 b = 5 (StartRoot c EndRoot + 2) is solved for c, one equation is c = (2b minus 2) squared Which of the following is an equivalent equation to find c? c = 10 b minus 10 minus 5 c = (10 b minus 10 minus 5) squared c = StartFraction (10 b minus 2) squared Over 25 EndFraction c = StartFraction (10b minus 10) squared Over 25 EndFraction
Answers
Answer:
Option D.
Step-by-step explanation:
The given equation is
[tex]10b=5(\sqrt{c}+2)[/tex]
We need to find an equation which is equivalent to the given equation.
Using distributive property, we get
[tex]10b=5(\sqrt{c})+5(2)[/tex]
[tex]10b=5\sqrt{c}+10[/tex]
Subtract both sides by 10.
[tex]10b-10=5\sqrt{c}[/tex]
Divide both sides by 5.
[tex]\dfrac{10b-10}{5}=\sqrt{c}[/tex]
Taking square on both sides.
[tex]\left(\dfrac{10b-10}{5}\right)=(\sqrt{c})^2[/tex]
[tex]\dfrac{(10b-10)^2}{25}=c[/tex]
[tex]c=\dfrac{(10b-10)^2}{25}[/tex]
This equation is equivalent to the given equation.
Therefore, the correct option is D.
Answer:
d on edgenuity
Step-by-step explanation:
Does the graph represent a function?
Answers
Answer:
yes
Step-by-step explanation:
In the proportionm 1/Z 4/5/8 which number is equal to Z in the proportion?
Answers
Answer:
Z = 8
Step-by-step explanation:
4 5/8 = 37/8
1/Z = 37/8
So..
Z = 8
Hope this helps! :)
which of the sequence is an arithmetic sequence?
Answers
Answer:
D
Step-by-step explanation:
An arithmetic sequence has to increase or decrease by the same amount each time
-3 ,-10,-17,-24,-31
Decreases by 7 each time so it is an arithmetic sequence
Answer:
i think its D not to sure
Step-by-step explanation:
I need help I don't understand I was on a streak and now this stupid problem is just unsolvable I just want to finish this stupid work and play gtao
Answers
Explanation:
Area of rectangle A: 48
Area of rectangle B: 96
48/96 = 4/8 = 1/2
Ratio of the area of rectangle A and B is 1:2
Answer:
the ratio is 1:3
Step-by-step explanation:
HURRRYYYY FIRST GETS BRAINLLEST Janine wrote the numbers 1-100 and placed them in a bag. If she selects a number without looking, what is the probability that the number is even and greater than 80? Input your answer as a decimal or fraction.
Answers
Answer:
1/10 or ( 0.1 )
Step-by-step explanation:
no. of even no.s greater than 80 = 10
Total no.of numbers = 100
So P(no. of even no.s greater than 80) = 10/100 = 1/10
Answer:
There are 10 even numbers greater than 80.
So Probability of getting an even numbers greater than 80 is 10/100 (1/10)
Hope it helps you. Please mark Brainliest :)
Have a nice day PPLS!!!!!!!
A car travels at 60 miles per hour. If d is the distance traveled and t is the time in hours: Write a function for the distance traveled d in t hours. What is the dependent variable? What is the independent variable? Make a table with at least 5 coordinate pairs. Graph the coordinate pairs and draw the function
Answers
Answer:
Step-by-step explanation:
d= distance
t= time
The independent variable is t, time. The distance the car travels depends on the time in hours spent travelling. The dependent variable is d, distance. Here is a table with 5 coordinate pairs that can be used.
(T) (D)
1 30
2 60
3 90
4 120
5 150
These are the coordinate pairs for the function. When we use division and determine the rate of change, we can determine that the average rate of speed (MPH) is 30 MPH.
a savings account receives 12% simple interest p.a. how long would it take for £30000 to gain £28800 in interest
Answers
Answer:
8 yearsStep-by-step explanation:
Given,
Principal (P) = £ 30000
Simple Interest ( I ) = £ 28800
Rate (R) = 12%
Time (t) = ?
Now,
[tex]t = \frac{i \times 100}{p \: \times \: r} [/tex]
[tex] = \frac{28800 \times 100}{30000 \times 12} [/tex]
[tex] = \frac{2880000}{360000} [/tex]
[tex] = 8 \: years[/tex]
Hence, It would take 8 years.
Hope this helps...
Good luck on your assignment...
PreCalculus Unit 3 Activity 90 POINTS
Answers
Answer:
19900kk
Step-by-step explanation:
i need deez points fr doe
Step-by-step explanation:
convert the angle from radian to degree you will get 225°
To draw it draw first 180° then ad 45° to make it easy
Standing on the roof of her apartment building, the top of Carla’s head is 15 yards above the ground.
She spots a curb 20 yards from the base of the building. What is the height of the flagpole?
Answers
Answer: 9 yards
Step-by-step explanation:
The proportion x/15 = 12 / 20 ||| X * 20 = 20X ||| 12 x 15 = 180 ||| 180 / 20 = 9
Helen drives 195 miles in 3 hours.
a) What is her average speed in mph?
Matthew drives at an average speed of 62 mph for 5 hours.
b) How many miles does Matthew drive?
Answers
Answer:
a) What is her average speed in mph?
= 65 mph
b) How many miles does Matthew drive?
=310 miles
Step-by-step explanation:
The average speed in meters per hour (mph) of Helen is 65 miles per hour
Given:
Total distance = 195 miles
Time taken = 3 hours
Average speed = Total distance ÷ Time taken= 195 miles ÷ 3 hours
= 65 miles per hour
If Matthew drives at an average speed of 62 mph for 5 hours.
Total distance between traveled = Average speed × Time taken
= 62 mph × 5 hours
= 310 Miles
Therefore the total miles Helen traveled in 5 hours at the rate of 62 mph is 310 miles
Read more:
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SOMEONE PLEASE HELP ME ASAP PLEASE!!
Answers
Answer:
1
Step-by-step explanation:
answer is 1 trust me use simple algebra
Rohit visited a pumpkin patch with his family. The table shows the relationship between the weight and price of a pumpkin.
A table titled Pumpkin Patch Sales with two columns and six rows. The first column, Weight in pounds, has the entries, 4, 8, 12, 16, 20. The second column, Price in dollars, has the entries, 6, 12, 18, 24, 30.
Which statement describes the slope of a graph of the data?
For each additional pound, the price increases $0.50.
For each additional pound, the price increases $1.50.
For every additional dollar, the pumpkin can increase by 1.5 pounds.
For every additional dollar, the pumpkin can increase by 0.5 pounds.
Answers
Answer:
For each additional pound, the price increases $1.50.
Step-by-step explanation:
Lets find the slope of the graph of othe given data.
Let x be the weight of pumpkin in pounds
Let y be the price of the pumpkin in dollars.
For 4 pound pumpkin the price is 6 dollars, so first point is (4,6)
For 8 pound pumpkin the price is 12 dollars, so first point is (8,12)
Find the slope between these points
m = y₂ - y₁ / x₂ - x₁
m = 12 - 6 / 8 -4
m = 6/4
m = 1.5
Which means that for every pound increase in weight, the price of pumpkin increases by 1.5 dollars
Answer:
B
Step-by-step explanation:
Which represents a measure of volume?
5 cm³
5 square cm
5 cm
5 cm²
Answers
The answer is A) 5 cm³
Volume is represented by cubic units.
Hope it helps <3
Need help finding the missing length to the attached triangle.
Answers
Answer:
1500
Step-by-step explanation:
Let the length of the perpendicular dropped from the right angle to the hypotenuse be h units.
Now by geometric mean property:
[tex]h = \sqrt{1600 \times 900} \\ h = 40 \times 30 \\ h = 1200 \: units \\ Next \: by \: Pythagoras \: Theorem: \\ {x}^{2} = {h}^{2} + {900}^{2} \\ {x}^{2} = {1200}^{2} + {900}^{2} \\ {x}^{2} = 1440000 + 810000 \\ {x}^{2} = 2,250,000 \\ x = \sqrt{2,250,000} \\ \huge \red{ \boxed{x = 1500\: units }}[/tex]
Answer:
1500
Step-by-step explanation:
Use the right triangle altitude theorem.
x/900 = 2500/x
x^2 = 900 * 2500
x = sqrt(900 * 2500)
x = 30 * 50
x = 1500
PROBABILITY. 22 chocolate bars total. 3 Mr.Good bars, 7 Krackel bars, and 12 Hershey’s bars. You are going to grab 7 bars WITHOUT replacement. Express answers in decimal form, round to at least 4 decimal places. 1: P(3 Mr.Good bars and 4 krackel bars)? 2:P( 3 Krackel bars and 4 Hershey’s bars)? 3: P(none of the 7 are Hershey bars)?
Answers
Answer:
.7
Step-by-step explanation:
How many terms are in the following expression 55+ 14n -2m +3p
Answers
Answer:
4 terms
Step-by-step explanation:
There are 4 terms in the given expression:
=> 55
=> 14n
=> -2m
=> 3p
which point is a solution to the solution≤8x-3
Answers
Answer:
-24
Step-by-step explanation:
8×-3=-24
hope you understood
I am interested in the how, not just an answer. Who can show me the correct solution path?
Answers
Grace's mom gave her $15.00 to buy school supplies. Grace needs to buy 3 mechanical pencils and some notebooks. If each mechanical pencil costs $1.75 and each notebook costs $2.99, how many notebooks can Grace buy using only the money her mom gave her? 2 notebooks 3 notebooks 4 notebooks 5 notebooks
Answers
Answer: 3 notebooks
Step-by-step explanation:
First take the three mechanical pencils out of the equation by doing
15 - (3*1.75) = 9.75. Because each notebook costs 3 dollars, she can afford 3 notebooks, with 1 dollar left over.
Hope it helps <3
Answer:
3 notebooks
Step-by-step explanation:
(1,75x3)=5.25 15.00-5.25=9.75
2.99x=9.75
x=3,26
so she can buy 3 notebooks
32. The expression a^x means that a is to be used as a factor x times. Therefore, if a^x is squared, the result is
A) a^x^2
B) a^2^x
C) 2a^2^x
D) 2a^x
Answers
Answer:
B. a^2x
Step-by-step explanation:
squaring a^x gives. (a^x)²
by applying the rules of indices, ^2 multiplies x therefore making it a^2x
what is pi rounded to the nearest 15th
Answers
Answer:
3.1415926535 8979
Step-by-step explanation:
bruh just search it in google