Angle ABD is 52°. State the size of angle DEB, giving a reason for your answer.
Answers
Answer:
∠ DEB = 52°
Step-by-step explanation:
The angle between a tangent and a chord is equal to the angle in the alternate segment, that is
∠ DEB = ∠ ABD = 52°
The short answer is that you use the tangent-chord theorem. A more lengthy answer is given below.
=================================================
Explanation:
Refer to the diagram below.
I'm going to move point E so that segment EB becomes a diameter of the circle (it goes through the center point F). Points A,B,C,D will stay in place. The red points and red segments show the changes.
In this slightly redrawn diagram, triangle EDB is a right triangle where angle EDB is 90 degrees. This is due to Thales Theorem, which is a special case of the inscribed angle theorem.
Also, the new segment EB is perpendicular to segment AC because the diameter touching the point of tangency is perpendicular to the tangent line. So angle EBA is 90 degrees.
Since points A, D and B didn't move, this means angle ADB is still 52 degrees. This makes the new angle EBD equal to 90-52 = 38 degrees.
Despite the fact that angle E has moved, it has not effected the size of angle DEB. This angle is the same as its original because we're still subtending the same minor arc DB, and that arc hasn't changed size (since segment DB hasn't changed). So that's why it's valid to use the same x for the old angle DEB in black and the new angle DEB in red. They're the same angle.
-------------
Focus on triangle EBD. We have the following interior angles
B = 38D = 90E = xFor any triangle, the three interior angles must add to 180
B+D+E = 180
38+90+x = 180
128+x = 180
x = 180-128
x = 52
Angle DEB is 52 degrees
It's not a coincidence that we end up with the same angle as shown in the original diagram. The tangent-chord theorem says that the angle between a chord and tangent (as shown in the diagram) is exactly equal to the inscribed angle that subtends the arc formed by the chord. Arc DB is formed by chord DB.
In short, the tangent-chord theorem says that inscribed angle DEB and angle ABD are the same measure (both are 52 degrees).
This demonstration I've shown is one way to prove the tangent-chord theorem. Though a more rigorous proof would involve another variable.
Related Questions
Work out the mean.
1, 3, 3. 4. 6, 9, 9
Answers
7 numbers so divide by 7
35/7 = 5
Mean is 5
Kayla bought 8 hot dogs and hamburgers for her and her friends. Hot dogs cost $1.50 and hamburgers cost $1.75. If she spent a total of $13.25, how many hot dogs did she buy?
Answers
Answer:
5 hamburgers and 3 hot dogs
Step-by-step explanation:
D = number of hot dogs
H = number of hamburgers
D + H = 8 then D = 8 - H
1.50D + 1.75H = 13.25
substitute for D
1.50(8-H) + 1.75H = 13.25
12-1.50H + 1.75H = 13.25
subtract 12 from each side
-1.50H + 1.75H = 1.25
0.25H = 1.25
divide both sides by 0.25
H = 5
D = 8-5
D = 3
help , with steps , otherwise I will report !!!
the diameter of rectangular box are in the ratio 2:3:4 and difference between the cost of covering with sheet of paper at the rate of ₹4 and ₹4.50 per m² is 416 . Find the dimension of box .
Answers
Answer:
2x +3x+4x
TSA : 2(lb+bh+hl)
2(6x+12x+8x)
2x26x
=52x²m²
cost of at ₹4=52x²m²×4
=208x²m²
234x²
234x²/26x²
26x²=416
x²=416/26
x²=16
x=4
2x=2×4=8
3x=3×4=12
4x=4×4=16
Step-by-step explanation:
HOPE IT HELPS YOU ......
Answer the following question:
Answers
Answer:
p is goodvjlxhkjdgmdgjmdmthdmyj
A garden table and a bench cost $978 combined. The garden table costs $78 more than the bench. What is the cost of the bench?
Answers
Answer:
$411
Step-by-step explanation:
I divided 978 by 2 and then subtracted 78 to get the bench's price.
Bench price: $411
Garden table price: $567
Rewrite the radical expression as an expression with rational exponents.
cube root of x to the power of 8
Answers
Answer: [tex](\sqrt[3]{x} )^8[/tex]
Step-by-step explanation:
Radical expression :
Cube root of any expression 'a' = [tex]\sqrt[3]{a}[/tex]
Radical exponent:
'a' to the power n = [tex]a^n[/tex]
Similarly cube root of x = [tex]\sqrt[3]{x}[/tex]
cube root of x to the power of 8 = [tex](\sqrt[3]{x} )^8[/tex]
Now , the required radical expression with rational exponents for "cube root of x to the power of 8" = [tex](\sqrt[3]{x} )^8[/tex]
Hence, the required expression =[tex](\sqrt[3]{x} )^8[/tex]
PLEASE HELP ME 9(6j + 7 + 2j)
Answers
Answer:
72j + 63
Step-by-step explanation:
collect the terms
9(8j+7)
Distribute through the parentheses
72j+63
What is the median and mean of 18,15, 11, 3, 8, 4, 13, 12, 3, 18
Answers
I need some help with these problems
Answers
Answer:
calculate by yourself
Step-by-step explanation:
use sin theorem
1.
[tex] \frac{s}{ \sin(60) } = \frac{12}{ \sin(30) } [/tex]
2.
[tex] \frac{s}{ \sin(90) } = \frac{4}{ \sin(30) } [/tex]
3.
[tex] \frac{s}{ \sin(60) } = \frac{10}{ \sin(90) } [/tex]
istanbuldaki marmaray hattında tren maksimum 100km/sa'tir Trenin saniyedeki hızı kaç m/sn'dir
Answers
Answer:
27,77
1 saatte 3600 saniye var
100 km de 100.000 metre yapar o halde
100.000/3600 = 27,77 m/sn yapar
alıntıdır (◍•ᴗ•◍)
Use the diagram and the information given to find the indicated measure:
1. ZX is the perpendicular axis of WY, yYZ = 13.75. Find the value of WZ.
2. ZX is the perpendicular axis of WY,
WZ = 4n − 13, and YZ = n + 17. Find the value of
AND Z.
3. Find the value of WX when
W Z = 20.5, W Y = 14.8, and Y Z = 20.5
Answers
which of the following is a phytogrean triples
Answers
Answer:
Of these, only 16 are primitive triplets with hypotenuse less than 100: (3, 4,5), (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41), (28, 45, 53), (11, 60, 61), (33, 56, 65), (16, 63, 65), (48, 55, 73), (36, 77, 85), (13, 84, 85), (39, 80, 89), and (65, 72, 97) (OEIS A046086, A046087, and ...
Step-by-step explanation:
your answer
There are _____ tenths in 2 tenths
Please?
Answers
Answer:
Not sure what you mean, but there are 2 tenths in two tenths?? Just incase you meant "How many hundredths are in two tenths", the answer would be 20 hundredths.
Step-by-step explanation:
Katelin is the pastry chef at the Brown Palace Hotel. She is making scones for their afternoon tea. Her recipe serves 6 people, but she needs to make
enough for 50 servings. The recipe calls for cup of sugar. How many cups of sugar will she need in all?
Answers
Hope it helps
The total number of cups required to make the recipe for 50 people will be equal to 8.3 cups.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the provided instructions in the question,
The recipe is for 6 people in which 1 cup of sugar is required.
Total number of people = 50
Cup of sugar required for the recipe = 50/6 = 8.33 cups.
It means that 8.33 cups of sugar is required to make the recipe for 50 people.
To know more about arithmetic operations:
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can someone help me? Am confused
Select the correct answer.
The city mayor wants to use the reserved section of a rectangular park for gardening lessons conducted by the city public school. The rest of the park will be turned into a lawn. What will the area of the lawn be?
A.
168 square feet
B.
224 square feet
C.
280 square feet
D.
448 square feet
Answers
Anybody good in geometry and know how to do this?
Answers
Answer:
D
Step-by-step explanation:
Answer:
I believe its C
I NEED HELLP PLZZZZZZZZZZZ
Complete the statement. Round to the nearest hundredth if necessary.
45 lb ≈
kg
Answers
(one pound is .454 kilograms)
Answer:
45 lb is about 20.412; rounding it would be 20.4
Step-by-step explanation:
1 kg is about 2 pounds. (Used a conversion thing).
Irina has 6 tubs yogurt. She wants to scoop it all into bowls. Each bowls holds 1/4 tub of yogurt. Which division equation can be used to find b, number of bowls she needs.
Answers
Answer:
6 divided by 1/4 = b
Step-by-step explanation:
Answer:
b = 6 ÷ 1/4
i did it before lol
pls help will mark branliest
Answers
Answer:
25 divided by 1/4
Step-by-step explanation:
hi can anyone solve and give a explaination plz? its for a friend
Answers
6.75
-2.25
----------
4.50
-2.25
----------
2.25
-2.25
----------
0.00
you could bowl 3 times (it starts off at 6.75 because I took away the cost of the shoes)
3 games.
Explanation:
$2.50 is a one time cost so we want to subtract that from $9.25 to see how many games we can play. This leaves us with $6.75.
Next, we divide $6.75 / $2.25 = 3.
This means the total amount of games one can play is 3.
Please help! Will mark brainliest!
Answers
Answer:
12) 20
13) 12.5
14)124
Find the next three terms in each geometric sequence.
3. 400,200,100,50, .......
4. 4,-12,36,-108, ........
Answers
Answer:
3) 25, 12.5, 6.25
4) 324, -972, 2916
Step-by-step explanation:
Priyanka drives at 45km/h and reaches Delhi in 5 hours.What time will she take to complete the same journey if she increases her speed by 5km/h ?
Answers
Answer: Increasing her speed by 5km/h, she will take 4.5 hours to complete the journey.
Step-by-step explanation:
Step 1
Speed= Distance / TIme
Given Speed = 45km/h
and Time = 5 hours
Distance covered = Speed x Time
= 45 km/h x 5 hours
=225 kilometres.
Step 2
Increasing her speed by 5km/h makes the new Speed = 45 +5 = 50 km/h
At the same Distance of 225 km
Therefore she will complete the journey in
Time = Distance/ Speed
=225km/ 50km/h
=4.5 hours
Find the number that makes the ratio equivalent to 1:8.
7:__
Answers
Answer:
56
Step-by-step explanation:
1:8= 7:?
1*?=7
/1 /1
1*7=7
8*7=56
1:8 = 7:56
Answer:
7:56
Step-by-step explanation:
1:8
we need to turn the one into seven. Turn the ratio 1:8 into the fraction 1/8.
multiply by 7/7 to turn the one into seven and 8 into 56
7/56 can now be turned into ratio 7:56. You could omit the turning of the ratio into the fraction at the beginning, but I find it makes it simpler.
What is the slope of the line than contains (4, -1) and (3, 3)
Answers
Answer: -4
Step-by-step explanation:
m= y2−y1/ x2−x1
= 3−−1 /3−4
= 4/ −1
=−4
a) Draw the graph of y = 4x - 1
on the grid.
o
b) Use the graph to estimate the
value of x when y = 1
Answers
a) The graph of y = 4x - 1 is shown in attached image.
b) By using the graph at y = 1 the value of x is 1/2.
What is Linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The function is,
y = 4x - 1
Now, The graph of function y = 4x - 1 is shown in image.
And, At y = 1;
By the graph the value of x = 1/2.
And, In mathematically;
At y = 1
The value of x is;
y = 4x - 1
1 = 4x - 1
4x = 2
x = 2/4
x = 1/2
Thus,
a) The graph of y = 4x - 1 is shown in attached image.
b) By using the graph at y = 1 the value of x is 1/2.
Learn more about the linear expression visit:
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help plss it's urgent
Answers
Step-by-step explanation:
step 1. (5/3)^(-5) x (5/3)^11 = (5/3)^(-5+11) = (5/3)^6
step 2. (-2/5)^7 ÷ (-2/5)^5 = (-2/5)^7 x (-2/5)^(-5) =(-2/5)^(7-5) = (-2/5)^2.
What does the symbol 7NS2 represents
Answers
Answer:
7. NS. A. 2 Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers.
Step-by-step explanation:
have a nice day
Can somebody tell me what's 43 divided by 1032 in long division? (Step by step) Or send a picture please
Answers
Answer:
24
Step-by-step explanat
Divide both the numerator and denominator by the GCD
1032 ÷ 43
43 ÷ 43
Reduced fraction:
24
1
Therefore, 1032/43 simplified to lowest terms is 24/1.
A rectangle is 15 cm wide and 18 cm long. If both dimensions are
decreased by the same amount, the area of the new rectangle formed is
116 cm less than the area of the original. Find the dimensions of the
new rectangle
Answers
Answer:
not 100percent sure but found this online 11 cm x 14 cm
Step-by-step explanation:
