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

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

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 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

HELP WITH MY MATH AS SOON AS POSSIBLE

Answers

Answer:

67

Step-by-step explanation:

I got it right trust me

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

Answers

Answer:

2y=x

Step-by-step explanation:

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)

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%.

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 :))

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.

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 .

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

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°

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

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

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

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

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

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

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

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

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 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

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

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!!

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

What is this (College Math)

Answers

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

Step-by-step explanation:

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

Answers

between 20 and 5000 characters

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.

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