Mathematics High School

B, D, E and F are points on a circle, centre O. ABC is a tangent to the circle. ODC is a straight line. BOE is a diameter of the circle. Angle BCD = 48° Find the size of angle DFE. ​

B, D, E And F Are Points On A Circle, Centre O. ABC Is A Tangent To The Circle. ODC Is A Straight Line.

Answers

Answer 1

Answer:

m∠DFE = 69°

Step-by-step explanation:

The tangent of a circle is always perpendicular to the radius.

Therefore, as ABC is the tangent to the circle, and OB is the radius of the circle:

⇒ m∠CBO = 90°

Interior angles of a triangle sum to 180°.  Therefore:

⇒ m∠COB + m∠CBO + m∠BCO = 180°

⇒ m∠COB = 180° - m∠CBO - m∠BCO

⇒ m∠COB = 180° - 90° - 48°

⇒ m∠COB = 42°

Angles on a straight line sum to 180°.  Therefore:

⇒ m∠DOE + m∠COB = 180°

⇒ m∠DOE = 180° - m∠COB

⇒ m∠DOE = 180° - 42°

⇒ m∠DOE = 138°

The angle at the center is twice the angle at the circumference.

Therefore:

⇒ m∠DOE = 2 × m∠DFE

⇒ m∠DFE = m∠DOE ÷ 2

⇒ m∠DFE = 138° ÷ 2

⇒ m∠DFE = 69°

Related Questions

please can someone help me it’s urgent i need it done by 8:00‼️

Answers

Answer: need to clam and not worry to much and study a lot to be come great and great at math

Step-by-step explanation: i try and i give it all i can and not give up

Find n(A) for the set.
1) A = 200, 201,
202, ..., 2000)
A) n(A)= 1801
B) n(A)= 4
C) n(A)=2000

Answers

A=200,201,202.........,2000

Here, it forms an AP with common difference 1

Let the number of terms in the set be n

[tex] T_{n} = a+(n-1)d \\\\ 2000= 200+(n-1) \\\\ 200+n-1= 2000 \\\\ => n=2000-199= 1801[/tex]

Hence,n(A)=1801

Divide x^4+3x^3-8x^2+5x-9 by x+5

Answers

Answer:

x^3−2x^2+2x−5+ 16/x+5

Step-by-step explanation:

Hope this helped

You purchase a bond with a coupon rate of 8.5% and par value of $2,000. The value of the bond rose to $2,500. What is the bond?

Answers

Answer:

The bond yield is 6.80%.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

You purchase a bond with a coupon rate of 8.5% and par value of $2,000. The value of the bond rose to $2,500. What is the bond yield?

The bond can now be calculated as follows:

Coupon payment = Coupon rate * Bond per value = 8.5% * $2,000 = $170

Bond yield = Coupon payment / Current value of the bond = $170 / $2,500 = 0.068, or 6.80%

Therefore, the bond yield is 6.80%.

Amy buy 6 tickets for a match, 3 adult and 3 children tickets. Each ticket costs £7.27. She gets £2.75 off on each children's ticket. How much does Amy finally pay for 6 tickets?

Answers

Answer:

$35.37

Step-by-step explanation:

Answer:

Amy pays £35.37 for 6 tickets

Step-by-step explanation:

since each ticket costs the same amount, we can do 6(£7.27) to find out how much she originally had to pay before she gets £2.75 off on each children's ticket

6(£7.27)=£43.62

now, since she gets £2.75 off on each children's ticket, and there are three children, to find out how much money she got off total:

3(£2.75)=£8.25

finally, we have to subtract £43.62-£8.25 to find the total amount Amy finally pays for 6 tickets

£43.62-£8.25=£35.37

so, Amy pays £35.37 for 6 tickets

What is the total surface area of a regular heptagonal pyramid with a base side length of 7 inches and a slant height of 16 inches.

Answers

Answer: Right Regular Pyramid Surface Area = (½ * Perimeter of Base * Slant Height)

Perimeter of Base = 16 inches

Right Regular Pyramid Surface Area = (½ * 16 * 7)

= 56 square inches

Step-by-step explanation: hope this helped

A botanist wishes to estimate the typical number of seeds for a certain fruit. She samples 41 specimens and counts the number of seeds in each. Use her sample results (mean = 54.7, standard deviation = 5.3) to find the 90% confidence interval for the number of seeds for the species. Enter your answer as an open-interval (i.e., parentheses) accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

Answers

Answer:

(53.3; 56.1)

Step-by-step explanation:

Given that:

Sample size, n = 41

Mean, xbar = 54.7

Standard deviation, s = 5.3

Confidence level, Zcritical at 90% = 1.645

Confidence interval :

Xbar ± Margin of error

Margin of Error = Zcritical * s/sqrt(n)

Margin of Error = 1.645 * 5.3/sqrt(41)

Margin of Error = 1.362

Lower boundary = 54.7 - 1.362 = 53.338

Upper boundary = 54.7 + 1.362 = 56.062

(53.3 ; 56.1)

Miss Johnson bought a roast that weighed 6lb. 4oz. What was the total cost of the roast if the cost per pound was $4.48.

Answers

Answer:

26.88$

Hope this helps :))

HELP DUE IN 1 Hour!


m∠MYX =?? degrees


° m∠ZMW =?? degrees

Answers

Answer:

<ZMW =90

<MYX = 29

Step-by-step explanation:

Remark

A Rhombus has a lot of peculiar properties. One of them is that the diagonals intersect at right angles. That means <ZMW =90 degrees.

Since the angle XMY = 90 degrees, it follows that <MXY + <MYX = 90 degrees because the third angle of the triangle = 90.

<MXY = 61 is given

So 61 + <MYX = 90                Subtract 61 from both sides.

<MYX = 90 - 61

<MYX = 29

m<MYX=29°

m<ZMW=90 diagonal bisect each other perpendicularly

Step-by-step explanation:

m<MYX+m<MXY+m<XMY=180 sum of interior angle of the triangle

here

m<XMY=90° diagonal bisect each other perpendicularly

m<MYX+61°+90°=180

m<MYX=180-151=29°

+
Find the surface area of this cube. Be sure to include the correct unit in your answer.
3 m
3 m
3 m

Answers

answer is b.Step-by-step explanation:

Answer:

9m

Step-by-step explanation:

yw

The face of a fair sided cube are numbered 1-6 based on rhetorical probability if a number cube is rolled 60 times how many times should a 2 be rolled

Answers

Answer:

10

Step-by-step explanation:

P(2) = 1/6

1/6  = x/60

x = 10

Find the equation of the line shown.
(Please help me)

Answers

Answer:

2y=x

Step-by-step explanation:

8 divided 2 + (3 x 3 - 2)

Answers

Answer:

Step 1.

Step-by-step explanation:

Since You need to do 3 x 3 first, BEFORE 3 - 2, it is incorrect.

Hope that helps!

Answer:

Step 1

Step-by-step explanation:

They are supposed to do 3*3 not 3*1.

What is the measure of angle C?
45°
с
35
B
A 10°
B
80°
C 100°
D
180°

Answers

Answer:

100°

since being sum of angles of triangle

Alan rented a truck for one day. There was a base fee of $20.99, and there was an additional charge of 84 cents for each mile driven. Alan had to pay $267.11 when he returned the truck. For how many miles did he drive the truck?

Answers

Answer:

293 miles

Step-by-step explanation:

(267.11 - 20.99)/0.84 = 293 miles

Answer: my mistake, the answer rightt!!

adding a negative is the same as ______ a positive

A.dividing
B.adding
C.subtracting
D.multiplying

Answers

Answer is Subtracting the 3rd one

C subtracting a positive

Find the volume of the sphere r=3

Answers

Answer:

113.1 Units

Step-by-step explanation:

4 /3πr^3

Answer:

If u consider Pi as 3.14 the answer would be 113.04 .

Step-by-step explanation:

Hope it was helpful , Good luck .

10xy-15x-2y+3 factor the polynomial

Answers

Answer:

(5x - 1)(2y - 3)

Step-by-step explanation:

10xy - 15x - 2y + 3 = 5x (2y - 3) - (2y - 3) = (5x - 1) (2y - 3)

WILL GIVE BRAINLIEST
The diagonals of a quadrilateral are 12 and 10. Is
this a parallelogram rectangle? Explain your answer

Answers

Answer:

the answer is no.a parallelogram is not a rectangular but the opposite is true. the reason is a cause of parallelogram's diagonals.they might not be equal in parallelogram but in rectangular they must be equal.

Step-by-step explanation:

Answer:

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. So yes it is a parallelogram.

Step-by-step explanation:

Diagonals of parallelogram are not necessarily equal. This is a known property of a parallelogram. If all angles are equal, then it means its opposite angles are also equal which is a condition for a quadrilateral to be called parallelogram. If all sides are equal then, opposite sides are also equal.

which is a solutiom (x-3)(x + 9)=-27?​

Answers

The solution is x= 0,-6

Answer:

x = 0, -6

Step-by-step explanation:

(0 - 3)(0 + 9) = (-3)(9) = -27

(-6 - 3)(-6 + 9) = (-9)(3) = -27

at the school book fair, Henry brings $10.00. He purchases a book for $8.50, plus a 6% sales tax. How much money in change will henry receive ?

Answers

Answer:

.99

Step-by-step explanation:

He paid $8.50 + 6% sales tax. So

8.50 x .06 = .51

8.50 + .51 = 9.01 total he paid

$10.00-$9.01=.99

Simplify 6(x-2 + 5(x+12)-12x

Answers

Answer:

48-x

Step-by-step explanation:

6(x-2) + 5(x+12)-12x

6x-12+5x+60-12x

6x+5x-12x-12+60

-x+48

HELP WITH MY MATH AS SOON AS POSSIBLE

Answers

Answer:

67

Step-by-step explanation:

I got it right trust me

What is this (College Math)

Answers

Hi, Which math? Alegbra,calculus, or geometry?) lol

Step-by-step explanation:

Which of the following is true of the values of x and y In the diagram below?

Answers

Answer:

There is no photo sorry

Step-by-step explanation:

Help please! This is worth 50 points it'll mean a lot!

Answers

between 20 and 5000 characters

Help me pleaseeee no links

Answers

I hope it helps its very simple i got the percentage change between the original price and the price after discount ....so the percentage change between the two prices equals the discount

1. Read the price list of different items displayed in a restaurant menu.


veg momo 150.50

chicken momo 210.25
chowmien 170.80
frenchfries 75.25
cold drinks 40.50




Then

solve the following given problems.

a) Calculate the total cost of a plate of Veg. Mo:Mo and a cold drink.

b) Find the total cost of plate of chicken Mo:Mo and a plate of French fries.

c) You and your friend had two plates of Chow Mein and two bottles of cold

drinks. If you have a Rs.500 note to the waiter to clear the bill, how much

change did the waiter return to you?

d) If you have Rs.300 pocket money, what two items do you choose to have in the

restaurant? What is the total cost of those two items? How much money was

left with you after paying the bill?​

Answers

Answer:

a.Rs 191

b.Rs 285.5

c.total amount =Rs 422.6

return amount=500-422.6

=Rs 77.4

d.chicken momo and cold drink=210.25+40.50

=Rs 250.75

left amount=300-250.75

=Rs 49.25

Find the length of the segment indicated.
A) 8.3
C) 9.3
B) 14
D) 10

Answers

Answer:

B

Step-by-step explanation:

radius + equivalent tangents

Mrs. Owens borrowed $50,000 to start a business. In the first two months, expenses amounted to $52,500, and sales came to only $2,500. How much money does Mrs. Owens have going into the third month?

Answers

0
50,000 loan
+2,500 Sales= 52,500. - 52500 expenses
Other Questions
A student is to be selected randomly from a group of students. For each classification of freshman and sophomore, there is a math major, an art major, and a biology major. The probability of each individual being selected is given in the following table:Find the probability that(a) a freshman is selected.(b) an art major is chosen.(c) a freshman math major or a sophomore biology major is chosen. What was the 3rd Agricultural Revolution Green Revolution? Help FAST PLEASE......................!!!!!!!!!!!!!!!11 How do you explain greater than less than equal to? Categorize the compounds below as chiral or achiral. There are 6 compounds. Can married couples join the Peace Corps? you're creating a video ad for a salon and your goal is to drive client bookings through the salon's website. which of the following call-to-actions (ctas) should you use in the ad?Call nowLearn moreCheck us outBook now What is the slope of the line 4y 3x 1? I need help with my math homework Find the value of x and y in the image below! True or false: protons and neutrons are the two particles found in an atoms nucleus ? Which phrase best describes the tone that robert frost uses in his poem "the pasture"?. a small bookshelf is 8/12 yard long. How many books can fit on the shelf if the width of each book is 1/24 yard? Explain What reason best describes why government officials would use the practice of gerrymandering?. Which of the following is not associated with the pons? a. Sensory information from the inferior region of the faceb. Sensory information from the superior region of the face c. Sensory information from the middle region of the face Lateral eye movements What is an example of a discussion sentence? more detailed and context-specific ad targeting is becoming easier to achieve through look-alike audiences artificial intelligence mobile optimization all of the above 1) you believe you will need to have saved 500,000$ by the time you retire in 40 years in order to live comfortably. if the interest rate is 6% per year, how much must you save each year to meet your retirement goal?2) You believe you will spend 40,000$ a year for 20 years once you retire in 40 years. if the interest rate is 6% per year,how much must you save each year until retirement to meet your retirment goal ?3) a couple thinking about retirement decide to put aside 3000$ each year in a savings plan that earns 8% interest. In 5 years they will receivve a gift of 10,000$ that also can be invested.a) how much money will they have accumulated 30 years from now ?b) if their goal is to retire with 800,000$ of savings, how much extra do they to save every year? During the performing stage, team members _____.A)get to know one anotherB)clarify their roles and expectationsC)focus on solving problemsD)resolve differences among them Does the order of addends matter?