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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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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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
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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.
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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
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c)C) 134.591
here 5 is tenth place after decimal
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d)31.757
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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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Answers
Answer:
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Answers
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Answer:
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Step-by-step explanation:
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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
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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:
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Answers
Answer:
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Step-by-step explanation:
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5 square cm
5 cm
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Answers
The answer is A) 5 cm³
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Answers
Answer: 3 notebooks
Step-by-step explanation:
First take the three mechanical pencils out of the equation by doing
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Answer:
3 notebooks
Step-by-step explanation:
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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
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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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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: