(Prove) The angle subtended by an arc at the center is double the angle subtended by it at any
point on the remaining part of the circle.
Answers
Answer:
The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
Step-by-step explanation:
Let us consider the image attached.
Center of circle be O.
Arc AB subtends the angle [tex]\angle APB[/tex] on the circle and [tex]\angle AOB[/tex] on the center of the circle.
To prove:
[tex]\angle AOB = 2 \times \angle APB[/tex]
Proof:
In [tex]\triangle PAO[/tex]: AO and PO are radius of the circles so AO = PO
And angles opposite to equal sides of a triangle are also equal in a triangle.
So, [tex]\angle PAO = \angle OPA[/tex]
Using external angle property, that external angle is equal to sum of two opposite internal angles of a triangle.
[tex]\angle AOQ = \angle PAO + \angle OPA=2 \times \angle APO .... (1)[/tex]
Similarly,
In [tex]\triangle PBO[/tex]: BO and PO are radius of the circles so BO = PO
And angles opposite to equal sides of a triangle are also equal in a triangle.
So, [tex]\angle PBO = \angle OPB[/tex]
Using external angle property, that external angle is equal to sum of two opposite internal angles of a triangle.
[tex]\angle BOQ = \angle PBO + \angle OPB=2 \times \angle BPO .... (2)[/tex]
Now, we can see that:
[tex]\angle AOB = \angle AOQ+\angle BOQ[/tex]
Using equations (1) and (2):
[tex]\angle AOB = 2\angle APO+2\angle BPO\\\angle AOB = 2(\angle APO+\angle BPO)\\\bold{\angle AOB = 2(\angle APB)}[/tex]
Hence, proved.
Hope you could understand.
If you have any query, feel free to ask.
Related Questions
A highway measuring 90 feet x 7 feet requires 1/2 a fluid ounce of cleaning situation per square root how much cleaning situation is required to clean the hallway
Answers
Answer:
1260 ounce of the fluid.
Step-by-step explanation:
Dimension of hallway = 90 feet × 7 feet
Area of the hallway = 90 × 7
= 630 square feet
Given that 1/2 (0.5) of a fluid ounce is required per square foot, the amount of cleaning situation to clean the hallway can be determined as;
= [tex]\frac{area of hallway}{cleaning situation per foot}[/tex]
= [tex]\frac{630}{0.5}[/tex]
= 1260 ounce
The amount of cleaning situation required to clean the hallway is 1260 ounce of the fluid.
The graph shows the equation x2 + y2 = 5. Use the slider for a to move the vertical line on the graph. Based on the vertical
line test, is this equation a function? Why or why not?
Answers
Answer: This equation is not a function.
Step-by-step explanation:
Ok, a function is something like a "machine".
It takes an input value, x, and transforms it into an output value, y.
Such that for every input x, the function can transform it into only one value of y.
for example, if we have a "function" f(x)
such that f(2) = 3 and f(2) = 4
(for the same input, x = 2, we have two different outputs)
Then this is not a function.
Now, the given equation is:
x^2 + y^2 = 5
This is actually the equation for a circle, centered at the point (0, 0) and with a radius equal to √5.
Then, if we want to transform it into y(x), we can see a problem
If x = 0, we have:
0^2 + y^2 = 5
y^2 = 5
then we have two possible values for y:
y = +√5
y = -√5
Then for one value of x, we have two values of y.
This means that this is not a function.
Answer:
No. The vertical line touches the graph at more than one point at once.
Step-by-step explanation:
I just did it
On one day, the stock of Seraj Food Technologies went up by $30\%.$ The next day, the stock fell by $30\%.$ Over the two days, the stock fell overall by $x$ percent. What is $x$?
Answers
Since the stock went up by 30% and fell by 30%, the net increase is 0%. So x = 0.
Given the range (1, 1),(4,2), (2, -1), with a coordinate transformation of f(x, y) = (x+1, y-1), what is the
domain?
Answers
=============================================
Explanation:
The rule f(x,y) = (x+1,y-1) says to add 1 to the x coordinate and subtract 1 from the y coordinate. So let's say the input point is (7,2). This would move it to (8,1).
Now let's say that you accidentally erased the "(7,2)", but you still have the "(8,1)". You'd have to work through the steps backwards to get back to (7,2)
So you'll effectively use this rule g(x,y) = (x-1, y+1) which is the inverse transformation. Whatever f(x,y) does, the g(x,y) function will undo it and go opposite. We'll subtract 1 from the x coordinate and add 1 to the y coordinate.
------------
So that's what we'll do with the set of points { (1,1), (4,2), (2,-1) }
We have (1,1) become (0,2) after applying the g(x,y) rule
(4,2) becomes (3,3) after using g(x,y)
(2,-1) becomes (1,0) after using g(x,y)
Therefore, the domain is { (0,2), (3,3), (1,0) }
-------------
The mapping diagram is shown below.
Is MNO=PQR? If so, name the congruence postulate that applies.
Given:
ME=PQ
NO=QR
MO=PR
A. Congruent - ASA
B. Congruent - SSS
C. Congruent - SAS
D. Might not be congruent
Answers
Answer:
B. Congruent - SSS
Step-by-step explanation:
Since, corresponding sides of both the triangles are congruent. Hence, both the triangles are congruent by SSS Postulate.
ΔMNO ≅ ΔPQR due to Congruent-SSS
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
Given:
In ΔMNO and ΔPQR
Side ME=Side PQ
Side NO=Side QR
Side MO=Side PR
MNO ≅PQR
Since, corresponding sides of both the triangles are congruent.
So, both the triangles are congruent by SSS Postulate.
Hence , ΔMNO ≅ ΔPQR
learn more about of congruent triangles
brainly.com/question/4364353
#SPJ5
I need the answers for Q10 part b and Q11 ASAP!!!
Answers
Answer:
Q10ii: x axis horizontal, y axis vertical, a straight line through the origin and point (5,20)
Q11i: z = 8y
Q11ii: y axis horizontal, z axis vertical, a straight line through the origin and (6,48)
Step-by-step explanation:
Linear proportions will always produce straight lines when graphed. Also, they will have to go through the origin when there is not some kind of offset.
What is the simplified expression for 22 • 2?
24
O 20
021
O 22
0 23
Answers
2^1 would be the answer.
2^2 x 2^3 is 32
2^4 is 16
32/16 is 2
2^1 is 2 so the answer is 2^1
Answer:
2¹
Step-by-step explanation:
When multiplying exponents of the same base, you can simply add the exponents together so 2² * 2³ = 2⁽²⁺³⁾ = 2⁵. When dividing exponents of the same base, you can simply subtract the exponents so 2⁵ / 2⁴ = 2⁽⁵⁻⁴⁾ = 2¹.
The price of tiling a room varies directly as the size of the room. Sam is laying tile in his kitchen. If the tiling costs $4,224.00 for 264 square feet, what is the size of a kitchen that costs $3,824.00?
Answers
Answer:
239 ft².
Step-by-step explanation:
Let P represent the price for tiling.
Let S represent the size of the room.
From the question,
Price (P) varies directly as the size (S) i.e
P & S
P = KS
Where K is the constant of proportionality.
Next, we shall determine the value of K as follow
Price (P) = $ 4224
Size (S) = 264 ft²
Constant of proportionality (K) =?
P = KS
4224 = K × 264
Divide both side by 264
K = 4224/264
K = 16
Finally, we shall determine the size of the kitchen that will cost $ 3824 for tiling.
This is illustrated below:
Price (P) = $ 3824
Constant of proportionality (K) = 16
Size (S) =?
P = KS
3824 = 16 × S
Divide both side by 16
S = 3824/16
S = 239 ft²
Therefore, the size of the kitchen is 239 ft².
(08.02)How many solutions are there for the system of equations shown on the graph? No solution One solution Two solutions Infinitely many solutions
Answers
Answer: Infinitely many solutions
Step-by-step explanation:
There are many solutions because the lines lies on top of each other.
i dont know the exact answer but its not
One solution
Two solutions
so its most likely
Infinitely many solutions
Suppose that a population begins at a size of 100 and grows continuously at a rate of 200% per year. Give the formula for calculating the size of that population after t years.
Answers
Answer:
y = 100(3)^t
Step-by-step explanation:
Use the formula y = P(1 + r)^t where y is the new amount, P is the starting amount, r is the rate as a decimal, and t is the time.
Plug in the values given:
y = 100(1 + 2)^t
y = 100(3)^t
Answer:
Step-by-step explanation:
y = 100(3)^t
We want to factor the following expression: 16x^4-25
Answers
Answer:
(4x2 +5)⋅(4x2 −5)
Point R is on line segment QS. Given QR=3 and QS=17, determine the length RS.
Answers
Answer:
14
Step-by-step explanation:
RS = QS - QR
RS = 17 - 3
RS = 14
Answer:
[tex]\large \boxed{14}[/tex]
Step-by-step explanation:
Point R is on the line segment QS.
QS = QR + RS
Solve for RS.
RS = QS - QR
RS = 17 - 3
RS = 14
Suppose that F(x) = x? and g(x) = -3x? Which statement best compares the
graph of G(x) with the graph of F(x)?
Answers
Answer:
flipped over the x-axis and stretched verticallyStep-by-step explanation:
Multiplying y by a value greater than 1 results in a vertical stretch. When the sign of it is negative there is a reflection over the x-axis. The appropriate choice is shown below.
__
The second attachment shows how the graph is flipped and stretched.
Calculate YZ if WY = 25, XY = 23, and VZ = 35
Answers
Answer:
WY= 25
XY= 23
VZ=36
so,
WY/XY = YZ/VZ
25/23 = YZ/25 (then do cross multiply)
25×25 = 23 × YZ
625= 23 × YZ
625/23= YZ
27,17= YZ
#i'm indonesian
#hope it helps.
Answer:
[tex]\huge \boxed{13.04}[/tex]
Step-by-step explanation:
The triangles are congruent, we can use ratios to solve.
WY/XY = (WY+YZ)/VZ
Let the length of YZ be x.
25/23 = (25+x)/35
Cross multiply.
23(25+x) = 25 × 35
575 + 23x = 875
Subtract 575 from both sides.
575 + 23x - 575 = 875 - 575
23x = 300
Divide both sides by 23.
(23x)/23 = 300/23
x = 13.0434782609...
4 > - 4404 true or false
Answers
Answer:
True
Step-by-step explanation:
-4404 is always smaller than 4Answer:
true as positive are bigger than negetive
Step-by-step explanation:
What’s the function of the Unit Circle and why is it called the unit Circle?
Answers
Answer:
It is a unit of radius that is radius of 1. Thus, the distant to the middle to any edge is always 1.
Step-by-step explanation:
the length of rectangle is 6/5 of its breath and perimeter is 132 m find area of rectangle
Answers
Answer:
1,080 meters squared.
Step-by-step explanation:
Let's say the breadth of the rectangle is x. That means the length of it is 6/5x.
The perimeter is 132 meters. The formula for the perimeter is 2 times the breadth plus two times the length.
2(x) + 2(6/5x) = 132
2x + 12/5x = 132
10/5x + 12/5x = 132
22/5x = 132
22x = 660
x = 30.
That means that the breadth of the rectangle is 30 meters, and the length is (6/5) * 30 = 6 * 6 = 36 meters.
The formula for the area of the rectangle is the breadth times the length, so the area is 36 * 30 = 1,080 meters squared.
Hope this helps!
A manufacturing company is expected to pay a dividend of br. 1.25 per share at the end of the year (D1=br.1.25). The stock sells for br. 32.50 per share and its required rate of return is 10.5%. The dividend is expected to grow at some constant rate forever. What is the growth rate
Answers
Answer:
the equilibrium expected growth rate is 6.65%
Step by step Explanation:
We were given stock sold per share of $32.50
Dividend per share =$1.25
Required Return rate = 10.5%
Then we can calculate Percentage of Dividend for share as;
dividend of br. 1.25 per share at the end of the year (D1=br.1.25)
= 1.25×100= 125
Let the dividend percentage = y
stock sold per share × y= 125
125= 32.50y
y = 125/32.50
y= 3.85
y= 3.85*100%
Then the Dividend percentage = 3.85%
Growth rate=(required rate of return -Dividend percentage)
= 10.5 - 3.85 = 6.65
Therefore, the equilibrium expected growth rate is 6.65%
HELP SOMEONE PLEASE!!!!! Factor completely 10x2 + 2x − 8. 2
(5x − 1)(x + 4) 2(5x − 4)(x + 1) 2(5x + 2)(x − 2) 2(5x − 2)(x + 2)
Answers
Answer:
2(5x - 4)(x + 1)
Step-by-step explanation:
10x^2 + 2x − 8 =
First, factor out the GCF of all terms which is 2.
= 2(5x^2 + x - 4)
5x^2 factors into 5x and x.
= 2(5x )(x )
-4 factors into -4 and 1, -1 and 4, and -2 and 2. Use the set of two factors in the proper positions that will give the middle term.
= 2(5x - 4)(x + 1)
Answer:
[tex]\large \boxed{2(5x-4)(x+1)}[/tex]
Step-by-step explanation:
[tex]10x^2 + 2x - 8[/tex]
Rewrite 2x as 10x - 8x.
[tex]10x^2 + 10x-8x - 8[/tex]
Factor out the two groups.
[tex]10x(x+1)-8(x+1)[/tex]
Take x+1 as a common factor.
[tex](10x-8)(x+1)[/tex]
Factor 10x - 8.
[tex]2(5x-4)(x+1)[/tex]
(4) The Highest Common Factor of 35pq^2, -14pq^2 and -21p^2q^3 is
Answers
[tex]35pq^2=5\cdot7\cdot p\cdot q^2\\-14pq^2=-1 \cdot 2\cdot 7\cdot p \cdot q^2\\-21p^2q^3=-1\cdot 3\cdot 7\cdot p^2 \cdot q^3\\\\\text{hcf}(35pq^2,-14pq^2,-21p^2q^3)=7\cdot p \cdot q^2=7pq^2[/tex]
Rearrange the equation so x is the independent variable. y+6=5(x-4)
Answers
Answer:
x = (y + 26)/5
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
y + 6 = 5(x - 4)
Step 2: Distribute
y + 6 = 5x - 20
Step 3: Isolate x
y + 26 = 5x
Step 4: Isolate variable x
(y + 26)/5 = x
Step 5: Rewrite
x = (y + 26)/5
Answer:
y = 5x - 26
Step-by-step explanation:
Since x is the independent variable, you have to solve for y.
y + 6 = 5(x-4)
Now distribute:
y + 6 = 5x - 20
subtract the 6 from both sides
y + 6 - 6 = 5x - 20 - 6
y = 5x - 26
The average monthly rainfall for 6 months was 28.5 mm. If it had rained 1mm more each month what would the average have been? By how much would the total have been increased in six months and by how much would average have been increased per month? What's the answer??
Answers
Answer:
29.5 mm
Step-by-step explanation:
We are told that the average monthly rainfall for 6 months was 28.5 mm.
Thus, total for the 6 months = 28.5 × 6 = 171 mm
Now, we are told that it rained 1 mm extra each month.
So extra for the six months = 1 × 6 = 6mm
New total for 6 months = 171 + 6 = 177 mm
So, new average for 6 months = 177/6 = 29.5 mm
cuantos son 4 elevado a 4???
Answers
Answer:Answer and Explanation:
When a number is said to be 'to the fourth power,' that just means that you need to multiply the number by itself four times. For example, 7 to the...
Step-by-step explanation:
We have two fractions, \dfrac{1}{6} 6 1 start fraction, 1, divided by, 6, end fraction and \dfrac{3}{8} 8 3 start fraction, 3, divided by, 8, end fraction, and we want to rewrite them so that they have a common denominator (and whole number numerators). What numbers could we use for the denominator? Choose 2 answers: Choose 2 answers: (Choice A) A 121212 (Choice B) B 242424 (Choice C) C 161616 (Choice D) D 4848
Answers
Answer:
B) 24
D) 48
Step-by-step explanation:
Given:
Two fractions
[tex]\dfrac{1}6 \\and\\\dfrac{3}8[/tex]
To find:
Number that can be chosen as Common denominator such that numerator is also a whole number ?
Solution:
Common denominator for two fractions [tex]\frac{p}{q}[/tex] and [tex]\frac{r}{s}[/tex] is chosen as LCM or multiple of LCM of (q, s).
OR
Common denominator for two fractions is chosen as the Least Common Multiple or multiple of LCM of denominators of the two fractions.
The denominators of the given fractions are 6 and 8.
Let us factorize and try to find the LCM of 6 and 8.
[tex]6 = \underline2 \times 3\\8 = \underline2 \times 2\times 2[/tex]
Common part of the denominators (as underlined) will be taken only once.
So, [tex]LCM = 2 \times 3 \times 2 \times 2 =24[/tex]
Multiples of LCM, 24 = 48
So, the correct answers are:
B) 24 and
D) 48
pls help. A granola mix sells for $8.99 a pound. Tung wants to buy a bag of granola mix that weighs 7.8 pounds. The bag of granola mix will cost about $16. $17. $63. $72.
Answers
Answer:
about 72 dollars
Step-by-step explanation
"about" tells us to round our numbers. Therefore, 7.8 becomes 8. As each pound is $8.99, we multiply the two and get 71.92, which is "about" 72.
Answer:
$72
Step-by-step explanation:
To find the cost, multiply the price per pound by the number of pounds.
8.99(7.8)
= 70.12
This is closest to $72
Which of the following is the solution of 5x – 6 = 44?
O x=-10
38
X=--
5
38
X = 10
Answers
Answer:
x = 10
Step-by-step explanation:
5x - 6 = 44
Add 6 on both sides of the equation.
5x = 50
Divide by 5 on both sides of the equation.
x = 10
So, the value of x is equal to 10
Answer:
x=10
Step-by-step explanation:
5x-6=44
grouping constants and numbers with coefficient of x we get
5x=44+6
5x=50
5x/5=50/5
x=10
(x - y) + 2y + x3, when x = -3 and y=7
plss help
Answers
Solve for x. 7x+38=45
Answers
Answer:
x=1
Step-by-step explanation:
subtract 38 from both sides:
7x=7
divide both sides by 7 to isolate x:
x=1
HOPE THIS HELPS!!!! :)
Camila llama a cuatro compañeras y les informa sobre una campaña de recoleccion de alimentos. Cada una de estas amigas llama a otras cuatro amigas para contarles sobre la campaña, y luego estas llaman a 4 nuevas amigas.¿cuantas amigas se enteran de este llamado?
Answers
Answer:
El total de amigos que se enteran del es 84 amigos.
Step-by-step explanation:
Camila llama a cuatro acompañantes y les informa sobre una colecta de alimentos. Cada uno de estos amigos llama a otros cuatro amigos para contarles sobre la campaña, y luego llaman a 4 nuevos amigos. ¿Cuántos amigos se enteran de esta llamada?
El número de compañeros que llamó Camila = 4 amigos
Cada uno de los cuatro amigos llamó a otros cuatro amigos para hacer = 4 × 4 = 16 amigos
Cada uno de los dieciséis amigos llamó a otros cuatro amigos para hacer = 16 × 4 = 64 amigos
Por lo tanto, el número total de amigos que se enteran de la llamada para dar información sobre una colecta de alimentos = 4 + 16 + 64 = 84 amigos.
Murphy purchases two bags of rice of weights 56 kg and 72 kg. Find the maximum value of weight which can measure the weight of the rice exact number of times.
Answers
Answer:
8
Step-by-step explanation:
In order to answer this question we need to find the greatest common divisor of the two quantities which will give us the maximum number by which both can be divided.
The greatest common divisor of a group of integers is the largest common divisor that divides each of the integers. The first step to find it is write down the integers as a product of primes, so we have:
[tex]56=(28)(2)=(14)(2)(2)=(7)(2)(2)(2)= 2^3[/tex]·[tex]7[/tex]
[tex]72=(24)(3)=8(3)(3)=2^3[/tex]·[tex]3^2[/tex]
Now, in order to find the gcd we are going to take the factors that they have in common. In this case they both share the [tex]2^3[/tex].
Thus, [tex]2^3=8[/tex] is the greatest common divisor and therefore the maximum value of weight which can measure the weight of the rice exact number of times.
