Mand N are two points on the circumference of a circle
centre O.
The straight line AMB is the tangent to the circle at M.
Angle MON = y
Prove that angle BMN = 1/2 y
Answers
Explanation:
We can make use of the symmetry of the problem and properties of similar triangles.
Here's a "paragraph proof."
Draw line OP perpendicular to chord MN, such that P lies on line MB. Let the point of intersection of OP with chord MN be designated point Q. Line OP bisects angle MON, so has measure y/2.
Triangles OPM and MPQ are similar (by AA similarity; both right triangles contain angle OPM), so angle QMP ≅ angle MOP. As we observed above, angle MOP has measure y/2, so angle QMP has measure y/2.
Angle BMN is another name for angle QMP, so it has measure y/2.
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Additional comments
By the HL congruence postulate, the perpendicular bisector of chord MN divides triangle MON into two congruent right triangles. (OM≅ON, MQ≅NQ). That means ∠MOQ≅∠NOQ, so OQ bisects angle MON, as we say above.
__
Another way to come to the desired conclusion is to recognize that for any point X on long arc MN, angle MXN will have measure y/2. (inscribed angle theorem) This remains true in the limit as X approaches M. As X approaches M, secant XM approaches tangent line MB. So, in the limit, angle BMN is y/2.
Related Questions
1. Determine if the lengths 9 cm, 13 cm, and 23 cm can form a triangle.
a. What are the two shortest side lengths?
acmt 15-24
b. Find the sum of the two shortest side lengths.
c. What is the longest side length?
d. Is the sum of the two shortest side lengths more than the length of the longest side?
e. Can the lengths 9 cm, 15 cm, and 23 cm form a triangle?
f. Fill in the blank so the three lengths will NOT form a triangle. 9 cm, 15 cm,
ст
2. Describe how to determine if three lengths form a triangle.
Answers
Answer:
1. Yes
2. 9 & 13
3. 9+13=22
4. 23
5. no
6. yes same as 1.
7. ????????????????????
the second q.
1.??? tried my best sry
Step-by-step explanation:
150- (2+z) with the exponent 3
Answers
Answer:
Step-by-step explanation:
z = 3+i
AKLM has vertices K(1.-4), L(-3, 3), and M(-5, -1). AKLM is translated so that K'is located at point (-3, 2). State the
coordinates of L'and M', where AK'L'M' is the translation of AKLM
A. L'(-8,6), M'(-8, 2)
B. L'(-7, 9), M'(-9,5)
C. L'(1,9), M'(-1,7)
D. L'(2,6), M'(0,2)
Answers
Point K was moved 4 spots to the left and 6 spots up, so if you do that to the coordinates of L and M then you’d end up with L’(-7,9) and M’(-9,5).
Will give brainliest!!!!
Answers
Answer:
1. 24ft ^3
2. 64in^3
3. 500yd^3
4. 32.832cm^3
Step-by-step explanation:
1. 4 * 3 * 2
= 24ft
2. 4 *4 * 4
= 64in
3. 20*5*5
= 500yd
4. 1.9*3.2*5.4
= 32.832
Which is a negatively skewed distribution?
4 6 8
14
26
O A.
0
2
4
6
8
10
12
14
16
T
18 20 22 24 26 28 30
B.
4 6
10
14 16
HE
O c.
0 2
4
6
8
10 12 14 16 18 20 22 24
26 28
30
Answers
Step-by-step explanation:
0c,02,4,6,8,10,12,14,16,18,20,22,24,26,28,30
The distribution (D) is negatively skewed because more values are concentrated on the right side (tail) of the distribution.
What is Statistic?A statistic is a piece of data derived from a subset of a population. It's the inverse of a parameter — census data, which polls everyone.
Statistics is a method of comprehending data collected about us and the world.
Here, a negatively skewed (also known as left-skewed) distribution is a sort of distribution in which more values are concentrated on the right side (tail) of the distribution graph while the left tail of the distribution graph is longer.
Thus, the distribution (D) is negatively skewed
Hence, the correct answer is an option (D).
Learn more about Statistics here:
brainly.com/question/23091366
#SPJ5
I need help please! It would mean a lot (:
Answers
Answer:
1. x=22 2. x= 28
Step-by-step explanation:
1. The total of angles in a triangle add up to 180˚.
93+65= 158
180-158=22
This means that x = 22
2. Angles on a straight line add up to 180.
180-125=55
180-83=97
55+97=152
180-152=28
This means that x = 28
Hope that this helps you.
What two numbers multiply together to give me -21 and add together to give me 4?
Answers
Answer:
-3 and 7
Step-by-step explanation:
-3 and 7 because
Multiply: 7 × -3 = 21
Add: -3 + 7 = 4
What is the approximate length of RP? Round to the nearest tenth. 5. 6 units 6. 1 units 8. 3 units 9. 8 units.
Answers
The apporoximate length of the RP is 6.1 units, the correct option is B.
What is Pythagoras theorem?The Pythagoras theorem states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of the other two sides of the right-angled triangle.
Given
QR is the tangent to circle P at point Q.
QP = 3 units and QR = 5,.3 units
The length of the RP is given by;
[tex]\rm RP=\sqrt{QP^2+QR^2} \\\\RP=\sqrt{3^2+5.3^2}\\\\ RP=\sqrt{9+28.09} \\\\RP=\sqrt{37.09}\\\\RP= 6.1 \ units[/tex]
Hence, the apporoximate length of the RP is 6.1 units.
To know more about Pythagoras theorem click the link given below.
https://brainly.com/question/11526258
Solve the system of equations.
Answers
Answer:
x = 3.75
Step-by-step explanation:
Replace y with the y equation.
So..
4x - 2(x + 1.75) = 4
Answer:
(3.75, 5.5)
Step-by-step explanation:
Adding x (3.75) to 1.75 gives 5.50 (5.5). If this is correct, then 4 x 3.75 + 2 x 5.5 = 4
A soccer field is a rectangle 100 meters wide and 130 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance? Show your work.
Answers
Answer:
The answer is 164 meters
Step-by-step explanation:
Distance = Sq of 100 + Sq of 130 = 26,900 = Sq root of 26,900 = 164 meters
Pls help nobody had the question i was looking for. Divide 0.8 62 answer needs to be in decimal form. 20 points
Answers
Answer:
7.75
Step-by-step explanation:
I divided it and got the answer as 7.75
What is the volume of the figure? Enter the answer in the box.
Answers
Answer:
1760
Step-by-step explanation:
First Cuboid:
(L×B×H)
= 22×5×8
=880
Second Cuboid:
(L×B×H)
=12×5×8
=880
Total Volume:
880+880 = 1760
Hope This Helps!!!!
PLEASE HELP ME THANKSSSS
Answers
Answer:
(-3,-2)
Step-by-step explanation:
I used a system of equations calculater
You are building a flower bed with a perimeter of 16 feet. The length of the bed is 4 feet longer than the width. What are the dimensions ?
Answers
Answer:
Step-by-step explanation:
The perimeter is basically the outline of the shape. The perimeter of a rectangle is given by P=2l+2w, where l is the length and w is the width. Thus, the perimeter of the flower bed would be given by P=2(3n5o)+2(5n5o).
Determine the value of the variables a, b, and c when simplifying and evaluating the expression. 38 34 = ab = c a = b = c =.
Answers
The values of the variables will be a=3 b=4 and c=81
What will be the values of the variables a, b, and c?It is given that
[tex]\dfrac{3^{8} }{3^{4} } = a^{b}=c[/tex]
now we can write that
[tex]3^{8}\times3^{4} =a^{b}[/tex]
[tex]3^{8-4} = a^{b}[/tex]
[tex]3^{4}=81 = a^{b} =c[/tex]
So from the above expression, we can see that a=3 b=4 and c=81
Thus values of the variables will be a=3 b=4 and c=81
To know more about the Variables follow
https://brainly.com/question/23931018
Answer:
a =
✔ 3
b =
✔ 4
c =
✔ 81
Step-by-step explanation:
just did it
Maya wants to build a bookshelf with a top, a bottom, and two shelves inside. She wants the height of the entire bookshelf to be 4 times the length of each shelf. She has 24 feet of wood to use for her bookshelf. Let x represent the length of a shelf.
Answers
Answer:
96
Step-by-step explanation:
if u times 24x4=96
Write down letters of the circled points and order them by least to greasiest. You will spell a word that describes y way to compare quantities
Answers
One way to compare quantities is with fractional numbers that represent quantities using divided numbers.
What is a fraction?Fractional number is a mathematical concept that refers to a quantity divided by another quantity. Common fractions are made up of: numerator, denominator and dividing line between them (horizontal or oblique bar).
The denominator "b" expresses the number of equal parts that represent the unit.The numerator "a" indicates how many of them are taken.Some examples of fractional numbers are:
[tex]\frac{1}{2}[/tex][tex]\frac{2}{4}[/tex][tex]\frac{3}{4}[/tex][tex]\frac{50}{100}[/tex]Note: This question is incomplete because there is some information missing. However I can answer it based on my general prior knowledge.
Learn more about fractional numbers in: https://brainly.com/question/13398430
Answer:
The word is RATIO.
Step-by-step explanation:
Your problem is incomplete. However, I came across the same problem and solved it (Lesson 23, question 220c). Use the coordinates ONLY from the previous question and compare from there.
PLEASE ANSWER QUICKLY! WILL GIVE BRAINIEST! ONE QUESTION! ANSWER CORRECTLY TYSM! <333
Answers
Answer:
B
Step-by-step explanation:
All real numbers
Let me know if this helped <3
Does anyone know the answer? I’ll give 20 points
Answers
Answer:
infinite, or A
Step-by-step explanation:
you can put x as any number.
infinite or A
Step-by-step you can put an x by any number
A man bought a bow and arrow for £700, paying three times as much for the bow as for the arrow. How much did the bow cost?
Answers
Answer:
2,100 im pretty sure
700×3=2,100
Help please I will give Brainly!
Answers
Answer:
24
Step-by-step explanation:
Add them up
Orlando, Florida is approximately 61 square
miles less than the size of Tampa, Florida. If
Orlando is 114
square miles, find the size of
Tampa.
Answers
Answer:
sanaol alam ang sagot
Step-by-step explanation:
salamat sa points
Please help! I have listed the question below.
Answers
good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
the rest of the rows on the chart are 4,5,6,7,8,9.
Answers
Answer:
[tex]-\dfrac{27}{4}[/tex] % per hour
or -6.75 % per hour (if you want the answer as a decimal)
Step-by-step explanation:
From the table:
f(0) = 100
f(4) = 73
Average rate of change:
[tex]\dfrac{f(b)-f(a)}{b-a}=\dfrac{73-100}{4-0}=-\dfrac{27}{4}[/tex]
Find the circumference of the object. Use $3.14 or 22/7
for Pi. Round to the nearest hundredth if necessary.
Answers
Answer:
18.84
Step-by-step explanation:
Circumference = 2πd
where d = diameter
the shape given has a diameter of 6
to find the circumference we simply plug in the value of the diameter as well as π into the formula
formula : C = πd
π = 3.14 and d = 6
C = 3.14(6) = 18.84cm
Please help!! Behind x
Answers
Answer:
A''( -3,-18)
B"(0,-27)
C"(-12,-30)
Step-by-step explanation:
First, shift everything to the left 3 units and down 8 units so the points are
A'(-1,-6)
B'(0,-9)
C'(-4,-10)
Next we multiply everything by 3,
A''( -3,-18)
B"(0,-27)
C"(-12,-30)
What is the simplify of 8/16
Answers
Answer:
1/2
Step-by-step explanation:
8/16 divide by 8
equals 1/2
Answer:
1/2
Step-by-step explanation:
you can divide both the top and bottom by 8
What is the slope between (14,-8) and (7,-6)
Answers
Answer:
[tex] - \frac{2}{7} [/tex]
Step-by-step explanation:
Slope formula:
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
where (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate
Slope
[tex] = \frac{ - 8 - ( - 6)}{14 - 7} [/tex]
[tex] = \frac{ - 8 + 6}{7} [/tex]
[tex] = - \frac{2}{7} [/tex]
You have a bouquet of flowers. All but two are roses, all but two are daisies, and all but two are tulips. How many flowers do you have
Answers
Answer: THE answer is 3
Step-by-step explanation: ^^^^
Emma and Paul each invest $2,000 into accounts that earn 6% interest. If Emma’s account earns simple interest and Paul’s account earns compound interest, which is the value of each person’s account after 8 years?
a. Emma - $2,960; Paul - $1,187. 70
b. Emma - $960; Paul - $1,187. 70
c. Emma - $2,960; Paul - $3,187. 70
d. Emma - $960; Paul - $3,187. 70
Answers
[tex]~~~~~~ \stackrel{\textit{\Large Emma}}{\textit{Simple Interest Earned Amount}} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &8 \end{cases} \\\\\\ A=2000[1+(0.06)(8)]\implies A=2000(1.48)\implies \boxed{A=2960} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \stackrel{\textit{\Large Paul}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &8 \end{cases}[/tex]
[tex]A=2000\left(1+\frac{0.06}{1}\right)^{1\cdot 8}\implies A=2000(1.06)^8\implies \boxed{A\approx 3187.70}[/tex]