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
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:
https://brainly.com/question/16879446
How do u do these percentages questions
Answer:
Step-by-step explanation:Determine the initial format of the number to be converted to a percentage. ...
Carry out a mathematical process on the number to be converted to a percentage. ...
Multiply the result of the mathematical process by 100. ...
Find the percentage of the original or real number. ...
Multiply the final number by 100.
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region y=4x^2, y=x^2 + 3
Answer:
Step-by-step explanation:
integrate with respect to x
Area is symmetric so will be twice the integral from zero to 1
( I cannot seem to figure out how to make the lower limit negative in this editor)
[tex]A = 2\int\limits^1_0 {(x^2 + 3) - 4x^2} \, dx[/tex])
[tex]A = 2\int\limits^1_0 {-3x^2 + 3} \, dx[/tex]
[tex]A = 6\int\limits^1_0 {-x^2 + 1} \, dx[/tex]
A = 6(-⅓x³ + x)[tex]\left \| {{x=1} \atop {x=0}} \right.[/tex]
A = 6((-⅓(1)³ + (1)) - (-⅓(0)³ + (0)))
A = 6(⅔)
A = 4 units²
write an equivalent expression for 3(2z+4)
Answer:
6z+12
Step-by-step explanation:
you distribute it
Brent buys a dinning table that costs $150 before tax. The sales tax is 8% . How much tax did he pay?
Answer:
12
Step-by-step explanation:
its just twelve beliebe me
Here’s the question:
Steven earns extra money babysitting. He charges $46.50 for 6 hours and $62.00 for 8 hours. Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges. The equation is y =
I’m stumped. Can you help me find the answer along with an explanation? Thanks.
Answer:
An easy way to solve this problem is divide $23.25 by 3 or $54.25 by 7. Either way, you get $7.75. This number represents the amount of money he makes for 1 hour. So with that in mind, the correct equation is:
$7.75x = y
Step-by-step explanation:
Answer: y = 7.75x
Step-by-step explanation:
Find the difference of charges between 6 hours and 8 hours
62-46.5 = 15.5 for 2 hours
15.5/2 = 7.75/hr
62 = 7.75 x 8
Therefore there is no initial charge, and that the relationship is linear
so y = 7.75x
Can someone help me answer please
Answer:
i dont know sry
Step-by-step explanation:
Divide.
5÷1/4
1/20
4/5
5/4
20
Answer:
20.
Step-by-step explanation:
That's the correct answer
Answer:
20
Step-by-step explanation:
To divide by a fraction, such as 1/4, we invert the fraction and then multiply instead of dividing. Thus:
5÷1/4 = 5*(4/1) =20
ALOT OF POINTS FOR THIS ONE
Admission to the state fair is $12, and each ride ticket costs $3.50. Write an
expression to represent the situation and explain what the variable means.
3.50t + 12 where t represents the number of ride tickets
3.50a + 12 where a represents the cost of admission
12a + 3.50 where a represents the cost of admission
12t + 3.50 where t represents the number of ride tickets
Answer : 3.50t + 12
Step - by - step explanation :
the reason why I think the answer is " 3.50t + 12 " is because . . . since the admission to the state farm is only ONCE - there doesn't need to be a variable there to tell us that it MIGHT repeat more than once. and because we don't know how many ride ticket will be purchased - there is a variable there to tell us unknown.
SOMEBODY HELP NO LINKS PLZ AND THANK YOU
two stores opened on the same day. Both stores have 75 customers by the end of the first week, Store A'S customers doubled each week for six weeks, Store B's customers increased by 200 each week for six weeks. Which store had more customers at the end of week 5 ?
A Store A
B Store B
C They have the same number of customers
D Not enough information
show work plz and thank you
Answer: store b
Step-by-step explanation:
1. Find selling price in the following cases.
a) Market price = Rs 480,discount = Rs 40
b) Market price = Rs 870, discount = Rs 75.
2. Find cost price or selling price in the following cases.
a) cost price = Rs 120, profit = Rs 25
b) selling price = Rs 200, profit = Rs 20
Answer:
1) a. Rs 440.
1) b. Rs 795.
2) a.Rs 145.
2) b. Rs 180.
Step-by-step explanation:
1) a.
Given,
Marked Price = Rs 480
Discount Amount = Rs 40
Selling Price = ?
Now,
Selling Price = Marked Price - Discount Amount
= Rs 480 - Rs 40 = Rs 440.
1) b.
Given,
Marked Price = Rs 870
Discount Amount = Rs 75
Selling Price = ?
Now,
Selling Price = Marked Price - Discount Amount
= Rs 870 - Rs 75 = Rs 795.
2) a.
Given,
Cost Price = Rs 120
Profit = 25
Selling Price = ?
Now,
Selling Price = Cost Price + Profit
= Rs 120 + Rs 25 = Rs 145.
2) b.
Given,
Selling Price = Rs 200
Profit = Rs 20
Cost Price = ?
Now,
Cost Price = Selling price - Profit
= Rs 200 - Rs 20 = Rs 180.
Help help help math math math math
Answer:
66 degrees.
Step-by-step explanation:
angle 4 is 124, and angle 1 and 4 make 180 degrees. that means angle 1 is 56 degrees (180-124). and the total angle in a triangle is also 180 degrees.
Add 56 and 58, you'd get 114.
180-114=66
angle 2=66 degrees.
Answer:
66
Step-by-step explanation:
1. The exterior angle theorem states that the measure of an exterior angle of a triangle is congruent to the sum of the two opposite interior angles.
Basically, exterior angle = opposite interior angle + opposite interior angle2. Now, let's see what information we have so far, and what we don't have.
m∠4 is 124 degrees, is the exterior angleThe angle with 58 degrees is one of the opposite interior angles∠2 is the other opposite interior angle, but we don't know its measure3. Now, let's set up the equation and solve it.
Step 1: Set up the equation.
[tex]124 = x + 58[/tex]Step 2: Subtract 58 from both sides.
[tex]124-58=x+58-58[/tex] [tex]66 = x[/tex]Step 3: Check if solution is correct.
[tex]124=66+58[/tex] [tex]124=124[/tex]Therefore, the answer is 66.
Plz solve this its urgent
Options are 6cm
3cm
1.5cm
ΔPQR has: PM is a median
So: MR = QM = 3 cm
ANSWER: MR = 3 cm
Ok done. Thank to me :>
What is the probability of randomly selecting a month pf year and not getting a month that ends in y?
Answer:
2/3
Step-by-step explanation:
The months whose names end in 'y' include Jan, Feb, May, Jul. The probability of randomly selecting a month whose name ends in 'y' is 4/12 (remember that there are 12 months in a year), or 1/3.
Thus, the probability of selecting a month whose name does NOT end in 'y' is 8/12, or 2/3. Note that this event is the 'complement' of the first event:
P(name does not end in 'y') = 1 - P(name does not end in 'y') = 1 - 1/3 = 2/3
50 mm = how many cm?
Answer:
5cm
Step-by-step explanation:
50mm ÷ 10 = 5cm
-6x+6y=9 (1/2,2) please helppppp
Answer:
Not a solution.
Step-by-step explanation:
[tex]-6x + 6y = - 9\\\rule{150}{0.5}\\-6(\frac{1}{2}) + 6(2) = -9\\\\-3 + 12 = -9\\\\9 =-9[/tex]
The final result is a contradiction. It is not a solution to the equation, and therefore, will not be on the line.
if 7 men and 5 womean have applied for job and 3 applicants are randomly selected from the probability that 2 are men
The probability that 2 men are selected is 49/144
Probability is the likelihood or chance that an event will occur.
If 7 men and 5 women have applied for job, the total number of people that applied will be 12 people
Pr(2 men are selected) = 7/12 * 7/12Pr(2 men are selected) = 49/144Hence the probability that 2 men are selected is 49/144
Learn more on probabaility here:https://brainly.com/question/24756209
helppppppppppppppp me
Answer:
I think it is A hope this helps
Step-by-step explanation:
If a = − 3 and b=−i, then find the value of a^ 3b in fully simplified form.
Answer:
27i.
Step-by-step explanation:
a^3b = (-3)^3 * -i
= -27 * -i
= 27i.
A tire company paid $4,992 for 64 tires. Which is the most reasonable estimate for the cost of each tire?
can anyone slove this
Δ PQR has: PM is a median
so: MR = QM = 3 cm
ANSWER: MR = 3 cm
Ok done. Thank to me :>
WILL GIVE BRAINLIEST
Answer:
its the 2nd and the 6th one
Step-by-step explanation:
On which number line -9 and its opposite shown?
Answer:C TRUST MEEE
Step-by-step explanation:
mark as brainliest
Use the graph method to solve the system of linear equations:
2x + y = 3 and x + y = 3
A) (-1.5, 0)
B) (0, -1.5)
C) (0,3)
D) (3,0)
Answer:
C) (0,3)
Step-by-step explanation:
It would be that answer because I found the answer in a website. Its Math-way
Answer:
C) (0,3)Step-by-step explanation:
Graph each line on the same plane and take the point of their intersection.
Given linear equations:
2x + y = 3 and x + y = 3See the attached to confirm the answer is the point (0, 3)
Dylan is knitting a scarf, and he wants the final product to be 4 inches wide and 63 inches long. Each skein of yarn will knit a rectangle that is 4 inches by 9 inches. How many skeins should Dylan buy?
Answer:
7
Step-by-step explanation:
63 / 9 = 7
Answer asap! Need help before I go to sleep.
Answer:
Step-by-step explanation:
Parallel lines have identical slopes
4x - 7y = 9
7y = 4x - 9
y = (4/7)x - 9/7
so the parallel line has form
y = (4/7)x + b
plug in the point on the line
3 = (4/7)7 + b
b = -1
y = (4/7)x - 1
As you did not tell us where you live and what time you intend to go to bed, we have NO way of knowing your actual deadline
Principal = $ 15000, rate = 10% p.a. and time
21/5 years
PLS HELP ASAP
Answer:
Simple Interest: A=P(1+rt)
A=15000(1+(0.1*4.2))
A=$21,300
Compound Interest:A=P(1+r/n)^nt
A=15000(1+0.1/4.2)^1*4.2
A=$64,500
Step-by-step explanation:
4+2g+5g=-66
help me
plsss
pls
Sam earns $12 per hour. The store offers him a raise--a 6% increase per hour. After the raise,
how much will Sam make per hour?
Answer:
Solution here
Earning=$12 per hour
Raise=6%
The amount earned by Sam after raise=6×12/100
=72/100
=$0.72
The total amount made by Sam after the raise = $12+$0.72
=$12.72
What is the slope of the line (1,4) (3,2)
Step-by-step explanation:
the slope is the ratio of "y coordinate change / x coordinate change".
so, in our case here
x changes by +2 (from 1 to 3).
y changes by -2 (from 4 to 2).
so, the slope is -2/2 = -1.