If ABCDE is a regular pentagon and diagonals EB and AC intersect at O, then what is the degree measure of angleEOC?
Answers
If ABCDE is a regular pentagon and diagonals EB and AC intersect at O, then the degree measure of angle EOC is 108°.
In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:
Sum of interior angles = 180 × (n - 2)
Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.
Sum of interior angles = 180 × (5 - 2)
Sum of interior angles = 180 × 3
Sum of interior angles = 540°.
Therefore, the measure of each interior angle is given by;
Interior angle of a pentagon = 540°/5
Interior angle of a pentagon = 108°
From triangle EAO, we have:
2m∠EOA = 180° - (54 + 54)°
m∠EOA = 72°/2
m∠EOA = 34°
Now, we can determine the measure of angle EOC;
m∠EOC = 180° - (34 + 34)°
m∠EOC = 108°
Related Questions
1 plus 1/4 equals what??
Answers
The ballpark made a total of $15,000 from ticket sales at Wednesday's game. The ballpark charges $20 for each adult ticket and $10 for each child's ticket. They sold 3 times as many children's tickets as adult tickets. Write a system of equations that can be used to determine the number of adult and child tickets sold.
Answers
To determine the number of adult and child tickets sold, we can set up a system of equations based on the given information. By solving the system of equations, we find that the number of adult tickets sold is 300, and the number of children's tickets sold is 900.
Explanation:Let's assume that the number of adult tickets sold is represented by 'x'.
Since the number of children's tickets sold is three times the number of adult tickets, the number of children's tickets sold can be represented as '3x'.
The total revenue from ticket sales is $15,000, so we can create the following equation:
20x + 10(3x) = 15,000
Simplifying this equation, we get:
20x + 30x = 15,000
Combining like terms, we have:
50x = 15,000
Dividing both sides by 50, we find:
x = 300
So, the number of adult tickets sold is 300, and the number of children's tickets sold is 3 times that, which is 900.
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Angle θ lies in the second quadrant, and sin θ = 3/5
Answers
-3/4 tan
Answer:
sin θ [tex]=\frac{3}{5}[/tex]
It is given that , Angle θ lies in the second quadrant.
In the right triangle, Perpendicular =3 units, and Hypotenuse = 5 Units
As, sinθ is positive in second Quadrant also.That is , sin(π-θ )=sin θ
Also, [tex]sin(\frac{\pi}{2}-\Theta)=cos\Theta[/tex]
[tex]sin (\Theta) = 3/5\\\\ (\Theta) =sin^{-1} \frac{3}{5} {\text{or}} (\Theta) =\pi -sin^{-1} \frac{3}{5}\\\\cos(\frac{\pi}{2}-\Theta)= \frac{3}{5}\\\\ \frac{\pi}{2}-\Theta=cos^{-1}[\frac{3}{5}]\\\\ \Theta= \frac{\pi}{2}-cos^{-1}[\frac{3}{5}][/tex]
So, [tex]\pi-\Theta= \frac{\pi}{2}+cos^{-1}\frac{3}{5}, {\text{or}}\pi -sin^{-1} \frac{3}{5}[/tex]
are values of theta which lies in second quadrant.
Please check answer. Will Upvote.
Evaluate the function rule for the given value.
y = 15 • 3x for x = –3
Is the answer -135?
Answers
Y = 15 • 3(-3)
Y = 15 • (-9)
Y = -135
Answer: Yes
Step-by-step explanation:
Hi, to answer this question we have to substitute x =-3 on the function given, and solve for the variable y.
y = 15 • 3x
Replacing the value of the variable x by -3:
y = 15 • 3(-3)
Multiplying
y = 15 .-9
y = -135
It is correct, the answer is y= -135
Feel free to ask for more if needed or if you did not understand something.
Which digit has the greatest value and why??
Answers
Solve for x: 1 over 4 (2x − 14) = 4
x = 15
x = 15 over 2
x = 9
x = 11
Answers
2x - 14 = 16
2x = 30
x = 15
You invest $5,000 in a savings account that earns 6% interest each year.
A. How much money do you have in your savings account after the first year?
B. How much money do you have in your savings account after the second year?
Answers
B. Multiply the new amount, or $5300 by .06, and add it back to $5300 to get the total after 2 years. This is $5618.
A. $5300
B. $5618
After the first year, with an initial investment of $5,000 and an annual interest rate of 6%, the total amount in the savings account is $5,300. After the second year, the total amount in the account increases to $5,618.
Explanation:You are investing $5,000 in a savings account with an annual interest rate of 6%. The amount of interest you earn each year is calculated using the formula: principal amount *(interest rate/100).
A. After the first year, you would have:
Interest = $5,000 * (6/100) = $300
Therefore, the total amount in the savings account after one year is $5,000 + $300 = $5,300.
B. For the second year, we apply the same formula to the updated balance from the first year:
Interest = $5,300 * (6/100) = $318
Therefore, the total amount in the savings account after two years is $5,300 + $318 = $5,618.
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There are 10 students running a race. The fastest three get a gold, silver, or bronze medal. How many different ways can the students win these medals? ...?
Answers
That's because there are 10 ways for someone to be first, 9 ways for someone to be second after him, and 8 for someone to be third after them, so 10 x 9 x 8 = 720.
Which is an equation in point-slope form for the given point and slope? point: (–2, 4); slope: 5 y – 4 = 5(x – 2) y – 4 = 5(x 2) y 4 = 5x – 10 y 4 = 5(x 2)
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y - 4 = 5( x + 2 )
How do you solve this problem
58=(2/3)w
Answers
Solve.
-7/3n = -42
n =
Answers
Answer:
the real answer is -18 if ur k12
Step-by-step explanation:
In the diagram below, KL = 12 and LM = 8. Which additional facts would guarantee that JKLM is a parallelogram? Check all that apply.
Answers
What is meant by "transposing a term"?
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terms are separated by + and - signs.
Example: solve 2x+3=9 2x+3-3=9-3 (subtract 3 from both sides) 2x=9-3 (the 3 has been TRANSPOSED to the RHS) 2x=6 x=3
what is 234/78 I need help
Answers
Write log3 6 as a logarithm of base 2.
1) (log2)3/(log2)6
2) (log2)6/(log2)3
3) (log3)2/(log6)2
4) (log6)2/ (log3)2 ...?
Answers
Use the change-of-base formula: [tex]log_a(x)= \frac{log_b(x)}{log_b(a)} [/tex]
So, if we want to write log3(6) as a logarithm of base 2, in these example a = 3, x = 6, b = 2:
[tex]log_3(6)= \frac{log_2(6)}{log_2(3)}[/tex]
The correct expression for log3 6 as a logarithm of base 2 is option 1) (log₂ 3) / (log₂ 6).
To express log₃ 6 as a logarithm of base 2, we can use the change of base formula. The change of base formula states that logb x = (logc x) / (logc b), where c is any positive value other than 1.
Applying the change of base formula to log3 6:
log₃ 6 = (log₂ 6) / (log₂ 3)
Therefore, the correct expression for log3 6 as a logarithm of base 2 is option 1) (log₂ 3) / (log₂ 6).
To calculate it properly, we need to find the decimal approximation of this expression:
Using the appropriate logarithmic functions, we have:
(log₂ 3) / (log₂ 6) ≈ 1.58496 / 2.58496 ≈ 0.6124
Thus, log₃ 6 as a logarithm of base 2 is approximately 0.6124.
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Use the three steps to solve the problem.
A "Local" train leaves a station and runs at an average rate of 35 mph. An hour and a half later an "Express" train leaves the station and travels at an average rate of 56 mph on a parallel track. How many hours after it starts will the Express overtake the Local?
Answers
Step 1. Express distances (d1 and d2, d1 = d2 = d) using the formula for the speed v = d/t
Step 2. Make the system of equations.
Step 3. Solve the system of equations and express t2
Step 1.
Local train parameters:
rate: v1 = 35 mph
time: t1
distance: d
v1 = d/t1
d = v1 * t1 = 35*t1
Express train parameters:
rate: v2 = 56 mph
time: t2 = t1 - 1.5 h (because it is leaves hour and a half later then the local)
distance: d
v2 = d/t2
d = v2 * t2 = 56*(t1 - 1.5)
Step 2. Make the system of equations:
d = 35*t
d = 56*(t - 1.5)
Step 3. Solve the system of equations by using substitution method and calculate t2:
35t = 56(t1 - 1.5)
35t = 56t1 - 56*1.5
35t = 56t1 - 84
84 = 56t1 - 35t1
84 = 21t1
t1 = 84/21
t1 = 4
t2 = t1 - 1.5
t2 = 4 - 1.5
t2 = 2.5 h
Is the number ���12/4 rational
Answers
12/4 is 3
If John makes $20 an hour, how long will it take him to make $140?
120 hours
70 hours
7 hours
160 hours
Answers
For $140, it would be: 140/20 = 7 hours.
So, option C is your final answer.
Hope this helps!
what is a another was to write (3 x 1,000) (3 x 10) (3 x 1/100) (3 x 1/1000)
Answers
how do i simplify -2x - y - 2z ???
Answers
In forming a contract, the “meeting of the minds” is _____. a. an agreement between all parties involved in the contract of the details of the contract. b. a formal meeting of the parties involved in a contract that may or may not result in a signed agreement. c. a phrase used to describe a verbal contract or a contract made without signatures from the parties involved. d. a mental exercise used by a person involved in a contract to try to guess the contract requests of the other parties and offer a compromise
Answers
Answer: (a) an agreement between all parties involved in the contract.
Step-by-step explanation: While forming a contract, we generally use the phrase "meeting of the minds" , which implies that both the parties which are involved in the contract agree to the terms and conditions mentioned in the contract and are aware of the commitments made by each of the parties. Out of the four given options, only option (a) is acceptable, because the other three do not match with our requirement.
Thus, the correct option is (a).
An agreement between all parties involved in the contract. The correct option is A.
What is a “meeting of the minds”?While forming a contract, we generally use the phrase "meeting of the minds", which implies that both the parties which are involved in the contract agree to the terms and conditions mentioned in the contract and are aware of the commitments made by each of the parties. Out of the four given options, only option (a) is acceptable, because the other three do not match with our requirements.
Therefore, an agreement between all parties involved in the contract. The correct option is A.
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Charlene is knitting a baby blanket. She wants its width, w, to be at least half its length, l. She estimates that she has enough yarn to put fringe around the blanket, as long as the perimeter of the blanket is no more than 180 inches. The system of inequalities shown represents the width of the blanket in inches, w, and the length in inches, l.
w ≥ 0.5l
2l + 2w ≤ 180
Answers
Answer:
The length of the blanket should be less than or equal to 60 inches.
The width should be greater than or equal to 30 inches.
Step-by-step explanation:
Let the length of the blanket be = l
Let the width of the blanket be = w
Charlene wants the width, w, to be at least half its length, l. This can be shown as :
[tex]w\geq 0.5l[/tex]
She estimates that she has enough yarn to put fringe around the blanket, as long as the perimeter of the blanket is no more than 180 inches.
This can be shown as :
[tex]2l+2w\leq 180[/tex]
[tex]2l+2(0.5l) \leq 180[/tex]
[tex]2l+1l \leq 180[/tex]
[tex]3l \leq 180[/tex]
[tex]l\leq 30[/tex]
So, we get length of the blanket should be less than or equal to 60 inches.
And the width should be greater than or equal to 30 inches.
The figure below shows a trapezoid, ABCD, having side AB parallel to side DC. The diagonals AC and BD intersect at point O.
If the length of AO is three times the length of CO, the length of BO is
one-third the length of AC
one-third the length of AB
three times the length of DO
three times the length of DC
Answers
Answer:
Length of BO is three times the length of DO.
Step-by-step explanation:
In trapezoid ABCD, [tex]CD\ ||\ AB[/tex]
In ΔCDO and ΔABO,
[tex]m\angle CDO=m\angle ABO[/tex] (Alternate interior angles)[tex]m\angle DCO=m\angle BAO[/tex] (Alternate interior angles)So, [tex]\Delta CDO\sim \Delta ABO[/tex] according to Angle-Angle similarity.
Therefore, the ratio of corresponding sides will be same.
[tex]\Rightarrow \dfrac{OD}{OB}=\dfrac{OC}{OA}[/tex]
[tex]\Rightarrow \dfrac{OD}{OB}=\dfrac{OC}{3\cdot OC}[/tex]
[tex]\Rightarrow \dfrac{OD}{OB}=\dfrac{1}{3}[/tex]
[tex]\Rightarrow OB=3\cdot OD[/tex]
what is x+2+x^2+2
what is x+2+x^2+2
what is x+2+x^2+2
Answers
x + x^2 + 4
If you simplify the expression, your answer would look like this:
x^2 + x + 4
Answer: x^2 + x + 4
Step-by-step explanation:
You factor the expression to x + x^2 +4
Then you simplify to x^2 + x +4
MULTIPLE CHOICE PLEASE HELP FAST!!!!!!!
in one study it was found that the correlation coefficient between two variables is -0.32. which statement is true?
A. There is a weak positive association between the variables
B. There is a weak negative association between the variable
C. There is a strong positive association between the variable
D. There is a strong negative association between the variable
A study of several cities shows a positive correlation between the percent of people biking to work and that percent of people spending their vacation time at home.
Which statement is most likely true?
A. Bike riding makes people want to vacation at home
B. Vacationing makes people want to rife their bikes
C. The correlation is due to a third variable: cost of milk
D. The correlation is due to a third variable: cost of gas
Answers
Answer:
Just took the test and got an 100% so the answers are in fact,
in one study it was found that the correlation coefficient between two variables is -0.32. which statement is true?
B. There is a weak negative association between the variable
A study of several cities shows a positive correlation between the percent of people biking to work and the percent of people spending their vacation time at home.
Which statement is most likely true?
A. Bike riding makes people want to vacation at home
Have a wonderful day if you need any other questions from this test let me know!!!!!!!
Final answer:
The correct answer for the correlation coefficient of -0.32 is B. There is a weak negative association.
For the correlation between biking and vacationing at home, the likely third variable is cost of gas, choice D: The correlation is due to a third variable: cost of gas
Explanation:
The correlation coefficient measures the strength and direction of the relationship between two variables. In this case, the correlation coefficient is -0.32, which indicates a weak negative association between the variables. A negative correlation means that as one variable increases, the other variable tends to decrease. So, option B - There is a weak negative association between the variables - is true.
For the second question, based on the information given, it is most likely that option D - The correlation is due to a third variable: cost of gas - is true. This means that the positive correlation between the percent of people biking to work and the percent of people spending their vacation time at home is likely influenced by the cost of gas as a third variable.
The difference between 6 thirty-sixes and 4 thirty-sixes?
Answers
Which would be equal to 72.
2•36 = 72
What is the lcm of 6,15?
Answers
Solve for x: 3(x + 1) = −2(x − 1) + 6
A. 1
B. 4
C. 5
D. 25
Answers
3x+3=-2x+8
5x=5
x=1
Thus, A would be the answer.
Answer:
Correct option is:
A. 1
Step-by-step explanation:
3(x + 1) = −2(x − 1) + 6
⇒ 3x+3= -2x+2+6
⇒ 3x+3= -2x+8
⇒ 3x+2x=8-3
⇒ 5x=5
dividing both sides by 5
⇒ x=1
Hence, the correct option is:
A. 1
What is the measure of ∠XYZ
Answers
The measure of angle ∠XYZ is 66°.
Given:
∠W + ∠X = ∠XYZ (Sum of opposite interior angles is equal to the exterior angle)
Let's solve for x:
2x + 12 + 2x + 14 = 5x + 16
4x + 26 = 5x + 16
26 - 16 = 5x - 4x
10 = x
Now substitute the value of x into the equation for ∠XYZ:
∠XYZ = 5x + 16
∠XYZ = 5 * 10 + 16
∠XYZ = 50 + 16
∠XYZ = 66°
Therefore, the measure of ∠XYZ is 66°.
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Which of the following statements are true of a transversal?
It is a line.
It is parallel to other coplanar lines.
It intersects two or more coplanar lines.
It bisects line segments.
It can be perpendicular to other lines.
Answers
Definition: A transversal is a line that crosses at least two other lines.
Main properties:
It is a line (A is true).It is not parallel to other coplanar lines, because it crosses them (B is false).It intersects two or more coplanar lines (C is true).It bisects line segments (D is false).It can be perpendicular to other lines, it can be perpendicular to lines which it crosses (E is true).Answer: true are options A, C and E.
A transversal in Mathematics is a line that intersects two or more lines at different points, but does not necessarily have to be parallel or bisect these lines. It can, however, be perpendicular to them.
Explanation:In the subject of Mathematics, a transversal refers to a line that intersects two or more coplanar lines at different points. Therefore, the statement 'It is a line' and 'It intersects two or more coplanar lines' are true for a transversal.
The term transversal doesn't necessitate that it be parallel to other coplanar lines, nor does it indicate that it bisects line segments, so these statements are false. However, a transversal can be perpendicular to other lines if it intersects them at 90-degree angles.
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