in the given figure ,o is the centr of the circle, ab is the diameter and do is perpendicular to ab. prove that angle AEC= ANGLE ODA
Answers
The given triangles ΔDOA and ΔABC are right triangles that have a
common vertex at point A.
ΔDOA is similar to ΔABC, and ∠AEC is equal to ∠ABC, therefore, ∠AEC = ∠ODAReasons:
The given parameters are;
The diameter of the circle with center O = AB
DO ⊥ AB (DO is perpendicular to AB)
Required:
Prove that ∠AEC = ∠ODA
A two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
1. AB is the diameter of circle [tex]{}[/tex] 1. Given
2. DO is perpendicular to AB [tex]{}[/tex] 2. Given
3. ∠DOA = 90° [tex]{}[/tex] 3. Definition of DO ⊥ AB
4. ∠BCA = 90° [tex]{}[/tex] 4. Thales theorem
5. ∠BCA ≅ ∠BCA [tex]{}[/tex] 5. Reflexive property
6. ΔDOA ~ ΔABC [tex]{}[/tex] 6. AA similarity postulate
7. ∠ABC ≅ ∠ODA [tex]{}[/tex] 7. CASTC
8. ∠ABC = ∠ODA [tex]{}[/tex] 8. Definition of congruency
9. ∠AEC ≅ ∠ABC [tex]{}[/tex] 9. Angles in the same segment
10. ∠AEC = ∠ABC [tex]{}[/tex] 10. Definition of congruency
11. ∠AEC = ∠ODA [tex]{}[/tex] 11. Transitive property of equality
In statement 6, ΔDOA is similar to ΔABC by Angle-Angle, AA, similarity
postulate, therefore, the three angles of ΔDOA are congruent to the three
angles of ΔABC.
Therefore ∠ABC ≅ ∠ODA by Corresponding Angles of Similar Triangles
are Congruent, CASTC.
Learn more about circle theorem here:
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Related Questions
Solve system of equations y=3/4x+2 5x+4y=-24
Answers
Answer:
[tex]\left \{ {{y=-1} \atop {x=-4}} \right.[/tex]
Step-by-step explanation:
[tex]\left \{ {{y=\frac{3}{4} x+2} \atop {5x+4y=-24}} \right. <=> \left \{ {{y=\frac{3}{4}x+2 } \atop {5x+4*(\frac{3}{4}x+2)=-24 }} \right. <=>\left \{ {{y=\frac{3}{4}x+2 } \atop {5x+3x+8=-24}} \right. <=> \left \{ {{y=\frac{3}{4}x+2 } \atop {8x=-32}} \right. \\<=>\left \{ {{y=\frac{3}{4}x+2 } \atop {x=-4}} \right. <=> \left \{ {{y=\frac{3}{4}*(-4)+2 } \atop {x=-4}} \right. <=> \left \{ {{y=-3+2} \atop {x=-4}} \right. =>\left \{ {{y=-1} \atop {x=-4}} \right.[/tex]
How are the two triangles congruent? If not congruent, select not
congruent.
1 point
SSS
SAS
ASA
AAS
ОО
Not congruent
Answers
Answer:
SAS
Step-by-step explanation:
there are vertical angles in the middle and the sides are already marked
6^9+6^8)/(6^8*6^-9)
HELP PLS
Answers
Step-by-step explanation:
Question:-To simplify the expression Expression:-[tex] \frac{( {6}^{9} + {6}^{8} )}{( {6}^{8} \times {6}^{ - 9} )} [/tex]Solution :-[tex] = \frac{( {6}^{9} + {6}^{8} )}{( {6}^{8} \times {6}^{ - 9} )} [/tex]
[In numerator we take 6^8 common][tex] = \frac{ {6}^{8} ( {6} + 1)}{( {6}^{8} \times {6}^{ - 9} )} [/tex]
[On Simplification][tex] = \frac{( {6}^{8} \times 7)}{( {6}^{8} \times {6}^{ - 9} )} [/tex]
[In denominator as we know, a^x × a^y = a^(x+y)][tex] = \frac{( {6}^{8} \times 7)}{( {6}^{8 + ( -9)} )} [/tex]
[On Simplification][tex] = \frac{( {6}^{8} \times 7)}{( {6}^{ - 1} )} [/tex]
[As we know, 1/a^-1 = a ][tex] = {6}^{8} \times 7 \times 6[/tex]
[On further multiplying of 6][tex] = {6}^{9} \times 7[/tex]
Result:-In exponential form:
[tex] = {6}^{9} \times {7}^{1} (ans)[/tex]
In numerical form:
70,543,872 (Ans)
[tex] \huge \: \bf \: Question:—[/tex]
[tex] \sf \longmapsto6^9+6^8)/(6^8 \times 6^{-9})[/tex]
[tex]\huge\bf Solution:—[/tex]
[tex]\sf \longmapsto \: \dfrac{ {6}^{9} + {6}^{8} }{ {6}^{8} \times {6}^{ - 9} } [/tex]
[tex]\sf \longmapsto \dfrac{10077696 + {6}^{8} } { {6}^{8} \times {6}^{ - 9} } [/tex]
[tex]\sf \longmapsto \dfrac{10077696+1679616}{ {6}^{8} \times {6}^{ - 9} } [/tex]
[tex]\sf \longmapsto \: \dfrac{11757312}{{6}^{8} \times {6}^{ - 9}} [/tex]
[tex]\sf \longmapsto \dfrac{11757312}{1679616(6 {}^{ - 9} )} [/tex]
[tex] \boxed{\bf \: As \: a^{-n} = 1/a(n) \: ,}[/tex]
[tex]\sf \longmapsto \dfrac{11757312}{1679616 \bigg(\dfrac{1}{10077696} \bigg )} [/tex]
[tex]\sf \longmapsto \dfrac{11757312}{ \dfrac{1}{6} } [/tex]
[tex]\sf \longmapsto \: \: 70543872[/tex]
[tex] \boxed{\bf \: \: \: Convert\: 70543872 \: to\: scientific \: notation}[/tex]
[tex] \sf \longmapsto \: 7.0543872 × 10 {}^{7} [/tex]
[tex]\boxed{ \bf \: \: Convert\: 70543872 \: to\: exponent}[/tex]
[tex]\sf\longmapsto {6}^{9} \times 7 [/tex]
_________________________________
[tex] \boxed{\bf \: Answer\: in\: Number}:—[/tex]
[tex] \boxed{\bf \: 70543872}[/tex]
[tex]\boxed{ \bf \: Answer\: in\: Exponent:—}[/tex]
[tex] \boxed{\bf \: {6}^{9} \times 7}[/tex]
[tex]\boxed{\bf Answer\: in\: Scientific\: Notation:—}[/tex]
[tex]\boxed{ \bf \: 7.0543872 × 10 {}^{7} }[/tex]
Suppose a group of 100 women aged 60-64 got a new flu vaccine in 2004, and 5 of them died the following year. Is this event unusual? Specifically, how likely is it that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year? Know the chance of dying of a woman aged 60-64 getting a new flu vaccine in the next five years is 0.009.
Answers
Therefore, the probability that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year is 0.0000000059049%, making the event absolutely unusual.
Given that a group of 100 women aged 60-64 got a new flu vaccine in 2004, and 5 of them died the following year, to determine if this event is unusual, and specifically, how likely is it that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year knowing that the chance of dying of a woman aged 60-64 getting a new flu vaccine in the next five years is 0.009, the following calculation must be performed:
0.009 x 0.009 x 0.009 x 0.009 x 0.009 = X 0.000000000059049 = X 0.000000000059049 x 100 = X 0.0000000059049% = X
Therefore, the probability that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year is 0.0000000059049%, making the event absolutely unusual.
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Men to women working for a company is 2 to 3 if there are 80 employees total how many men work for the company
Answers
Answer:
48
Step-by-step explanation:
because if there is 48 men there is 32 women therefor making 80 employees
1038*472 please help
Answers
Answer:
443,226
Step-by-step explanation:
Given f(x) = x + 2, describe how setting k = 4 affects the slope and y-intercept of the graph of g compared to the graph of f.
g(x) = (4x) + 2
g(x)=4(x+2)
Answers
Answer:
g(2)=(4x) +2=7y
g(3)=4(x+2)
please help me in this question
3(x-2)=2x+10
Answers
Answer:
[tex]3(x-2)=2x+10\\3x-6=2x+10 | +6\\3x=2x+16 | -2x\\x = 16[/tex]
30.
a) [tex]180^{0} - 134^0-22^0=24^0[/tex]
[tex]r=24^0[/tex]
b)
[tex]90^0=2x^0+3x^0\\90^0=5x^0 |:5\\x^0=18^0[/tex]
[tex]2x^0= 2* 18^0=36^0[/tex]
[tex]3x^0=3*18^0=54^0[/tex]
Take care!
calculate the quotient below and give your answer in scientific notation
Answers
Answer:
the answer is 95
Please hurry!! This assignment is almost due!!
Answers
Answer:
x = 23
Step-by-step explanation:
8x-27 = 7x-4
8x-7x = -4+27
x = 23
Can someone help me plssssssssss
Answers
It’s saying is 5 times the original number. 200/5=40
Which inequality represents the phrase below? a number more than 72 A. x < 72 B. x > 72 C. x > 71 D. x = 72
Answers
Answer:
the answer is. C.i hope this helps sorry if im wrong
In ΔABC, m∠1=70° and m∠4=35°. What is m∠3?
Answers
Answer:
75
Step-by-step explanation:
A triangle can only have 3 angles that add up to 180 degrees. Subtract 70 and 35 from 180 to get 75.
180=x+70+35
180-(70+35)=x
a recipe for one batch of Holliday cookies uses 6 tablespoons of frosting for every 16 cookies please awnser quick
Answers
Recently, your parents read in the newspaper that American factory worker jobs have the lowest income ra
What is the best explanation for this fact?
A A factory worker does not need a lot of education
B Companies are relocating factories to other parts of the world.
C Factories are always in poor areas.
D A computer can do the work a factory worker currently does
Answers
Answer:
A. A factory worker does not need a lot of education.
Step-by-step explanation:
The answer is " A " which is a factory worker does not need a lot of education. since most people don't have a PHD degree or anything higher education, it results in a lot of people joining due to the benefit of the factory worker doesn't need a lot of worker which makes it low in demand too.
For the trig function f(0)=sin(0) whats the input variable
For the trig function g(0)=cos(0) whats the input variable
Answers
For the function f(0)=sin(0), 0 is the input variable while f(0) is the output.
For the function g(0)=cos(0), 0 is the input variable while g(0) is the output.
The standard form of representing trigonometry functions is f(x) = sinx or f(x) = cos x
From the functions:
x is the input variable (also known as the domain)y is the output variable also known as the range;Given the trig function f(0)=sin(0), compared with the general equation, we can see that 0 is the input variable while f(0) is the output.
Similarly for the function g(0)=cos(0), 0 is the input variable while g(0) is the output.
Learn more on input variables here: https://brainly.com/question/11451813
| 2n+2g = 5
3x + 3y = 7
How many solutions does the system of equations above have?
Answers
Answer:
The following equation has no / zero solution.
Step-by-step explanation:
The slope of both the equations is proportional which means that the lines are parallel to each other. Thus, the given equation has no solutions.
Solve for x, y, and z
Answers
Step-by-step explanation:
[tex]x = 46.16 \\ y = 23.00 \\ z = 55.7[/tex]
help with this please
Answers
y=-2*0+12 —> y=0+12 —> y=12
so you would put that 12 in the first box. that gives you the points (0,12) on the graph and that’s where you would put your first dot…
you repeat this process for all the other x values
WILL GIVE BRAINLIEST
Answers
Answer:
the y intercept is 5/3
the y intercept is 3/5
An article when sold at a profit of 5% yields Rs 50 more than when sold at a loss of 5%. What was the cost price of the article?
Answers
Answer:
Rs 500
Step-by-step explanation:
For cost c, the price that gives a 5% profit is ...
c + 5%·c = 1.05c
The price that gives a 5% loss is ...
c -5%·c = 0.95c
The difference of these prices is Rs 50:
1.05c -0.95c = 50
0.10c = 50 . . . . simplify
c = 500 . . . . . . . divide by 0.1
The cost price of the article is Rs 500.
100 POINTS WILL AWARD BRAINLIEST PLEASE HELP
(IMAGE INCLUDED)
In the image below, the m
Answers
Answer: 67°.
Step-by-step explanation:
1) m∠PMR=m∠LMN=3x+19°;
2) m∠LMN+m∠LMP=180°, it can be written as 3x+19+9x-31=180;
3) if to solve the equation 3x+19+9x-31=180, then x=16;
4) m∠PMR=3x+19=48+19=67°.
Find x
Linear pairs are supplementary
9x-31+3x+19=18012x-12=180x-1=15x=15+1=16So
opposite angles are equal
m=9(16)-31=144-31=113°For what values of r will the area of the shaded region be greater than or equal to 12 square units? Write your answer as an inequality.
Answers
Answer:
r>=12
Step-by-step explanation:
Matthew had $12m. He spent 80¢ every day. How much did he have left
after 2 weeks? Give your answer in dollars.
Answers
Answer:
11999988.80 or .80
Step-by-step explanation:
12,000,000-(.80*14)=11999988.80
12-(.80*14)=.80
Determine if the two triangles are congruent. If they are, state how you know
Answers
Answer:
yes the two triangles are congruent by the SSS theorum.
Step-by-step explanation:
it is given that two of the sides are congruent. they also share a side making that side also congruent. so, all three sides are equal, making the two triangles congruent by SSS/side-side-side theorum.
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $1,000, annual interest: 6%, interest periods: 6, number of years: 14 more than the investment compounded annually.
After 14 years, the investment compounded periodically will be worth $ ____(Round to two decimal places as needed.)
Answers
After 14 years, the investment will be worth $ 2,306.72.
Given that an investment has a $ 1000 principal, 6% annual interest, 6 interest periods and 14 years of investment, to determine, after 14 years, how much the investment will be worth, the following calculation must be performed:
1000 x (1 + 0.06 / 6) ^ 14x6 = X 1000 x 1.01 ^ 84 = X 1000 x 2.3067 = X 2,306.72 = X
Therefore, after 14 years, the investment will be worth $ 2,306.72.
Learn more about maths in https://brainly.com/question/15603792
PLS HELP PLEASSSS ILL MARK U AS BRAIN KING THINGY WTV U CALL IT
Answers
Answer: infinitley many solutions
Step-by-step explanation:
Given the function f (x) = 3x — 2, what is the value of f (3)?
Answers
Answer:
7
Step-by-step explanation:
Simply plug in 3 for x. 3 times 3 is 9 and 9 minus 2 is 7.
Which of the following is a geometric sequence with a common ratio of 2?
A) 14, 28, 56, 112, ...
B) 64, 32, 16, 8, ...
C) 87, 85, 83, 81, ...
D) 14, 16, 18, 20, ...
Answers
Answer:
A
Step-by-step explanation:
Geometric sequences involve multiplication and the ratio of 2 means each number is multiplied by 2 to get the next number.
M is the midpoint of the segment. Find the length of XM.
Answers
Answer:
x=2 and XM=11
Step-by-step explanation:
because M is the midpoint of the line, you know that both XM and ZM are equal and you know an expression for the lengths of both of these.
set these expressions equal and solve:
4x+3=3x+5 so by subtracting the 3x from the right side, moving it over to the left and subtracting 3 from the left side to move it over to the right, you get:
x=2
then to find XM, plug in this value of x to get XM=11
4(2)+3=11