For a quadrilateral ABCD inscribed in a circle of radius 1, let AB : AD = 1 : 2 and ∠BAD = 120°. Also, when the point of intersection of diagonals BD and AC is denoted by E, let BE : ED = 3 : 4. Please find the area of triangle ABD and triangle BCD. (Show work)
Answers
The area of triangle ABD = x² * √3 / 2 and The area of triangle BCD = y * √(5x² + 4y² - 2xy√5)
To find the area of triangle ABD, we can use the formula for the area of a triangle: Area = (1/2) * base * height
In triangle ABD, the base is AD and the height is the perpendicular distance from point B to line AD. Since AB : AD = 1 : 2, we can let AB = x and AD = 2x.
Now, we can use the Law of Cosines to find the length of side BD. In triangle ABD, we have:
BD² = AB² + AD² - 2 * AB * AD * cos(∠BAD)
BD² = x² + (2x)² - 2 * x * (2x) * cos(120°)
Simplifying the equation:
BD² = x² + 4x² - 4x² * (-1/2)
BD² = 5x²
Taking the square root of both sides:
BD = √(5x²) = x√5
Since BE : ED = 3 : 4, we can let BE = 3y and ED = 4y.
Now, we can find the length of side BC. In triangle BCD, we have:
BC² = BD² + CD² - 2 * BD * CD * cos(∠BCD)
BC² = (x√5)² + (2y)² - 2 * (x√5) * (2y) * cos(∠BCD)
BC² = 5x² + 4y² - 4xy√5 * cos(∠BCD)
Since the quadrilateral ABCD is inscribed in a circle, ∠BCD = 180° - ∠BAD = 60°.
BC² = 5x² + 4y² - 4xy√5 * cos(60°)
BC² = 5x² + 4y² - 4xy√5 * (1/2)
BC² = 5x² + 4y² - 2xy√5
The area of triangle ABD is given by:
Area ABD = (1/2) * AB * AD * sin(∠BAD)
Area ABD = (1/2) * x * 2x * sin(120°)
Area ABD = x² * √3 / 2
The area of triangle BCD is given by:
Area BCD = (1/2) * BC * CD * sin(∠BCD)
Area BCD = (1/2) * √(5x² + 4y² - 2xy√5) * 2y * sin(60°)
Area BCD = y * √(5x² + 4y² - 2xy√5)
Further calculations require numerical values for x and y to obtain specific areas.
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Related Questions
Can someone please help me please
Answers
Answer:
5
Step-by-step explanation:
Sarah Turned on the soaker hose in her flower bed. The hose releases 192 gallons of water every 4 hours. If she leaves the hose on for 30 minutes how much water will be used?
Answers
Answer:
24 gallons
Step-by-step explanation:
set up a proportion and cross-multiply:
g = # gallons
192/4 = g/0.5*
4g = 96
g = 24
*30 minutes = 0.5 hours
What is r?
r = one-third
r = 3
r = two-thirds
r = one-half
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Answer:
what is the equation.
Step-by-step explanation:
comment the equation
Answer:
r = r
-incomplete
Step-by-step explanation:
since there is no equation or no limitations along with the question, i cannot say what r can be, if there is an equation or additional info I can better tell you, but rn, r literally is equal to all of those answers
im crying please help me so much
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Answer:
A and D
Step-by-step explanation:
A shoe box has a volume of 693 cubic inches. The area of the base of the shoe box is 126 square inches. What is the height of the shoe box in inches?
Answers
Answer: 5.5
volume formula:
v = bh
693 = 126h
h = 5.5
Function is defined by f(x) = x2 - 4x + 8. The graph of function g is shown.
Let h represent the x-coordinate of the vertex of the graph of y = f(x). Let
represent the x-coordinate of the vertex of the graph of y = g(x). What is the
value of h-j?
Answers
The value of h -j is -5.
We have the function, f(x) = x² -4x + 8
Now, vertex
h = x = -b/2a
h = x = -(-4) / (-2)
h = x = -4/2
h= x = -2
Now, according to the graph
j = x= 3
So, h - j
= -2 - 3
= -5
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An online retailer wants to study whether more lenient return policies increase purchasing behaviors. They
select a random sample of 2000 customers who have made purchases in the past year.
They use a random number generator to select 1000 customer account numbers to assign to the treatment
group. The remaining 1000 customers are assigned to the control group.
What type of experiment design is this?
A) randomized block
B) stratified
C) completely randomized
D) marched pairs
E) cluster
Answers
Answer: Completely Randomized
Step-by-step explanation:
effect of one primary factor rather than many different variables
As per the question the retailer wants to study the return policy that can increase the buying behavior and selects a random sample of 2000.
He uses matched pair of designs in his experiment design in which participants of the same traits get grouped in pairs. After which within each pair, one participant gets randomly allotted to either the treatment, and the other is assigned to the other part.Hence the option D is correct.
Learn more about the study whether more.
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Here are summary statistics for randomly selected weights of newborn girls: n=250, x_=32.9 hg, s=6.9 hg. Construct a confidence interval estimate of the mean. Use a 95% confidence level. Are these results very different from the confidence interval 31.9 hg < μ < 34.5 hg with only 19 sample values, x_ = 33.2hg, and s = 2.9 hg?
Answers
Answer:
Step-by-step explanation:
Here are summary statistics for randomly selected weights of newborn girls: n=250, x_=32.9 hg, s=6.9 hg. Construct a confidence interval estimate of the mean. Use a 95% confidence level.
The confidence interval of mean
=32.9 ± 1.96 × 6.9/250
Confidence Interval = 32.9 ± 0.5382
Need answer quick please
Answers
In line 3, it will be 7x to the power 2 not 4.
So, the answer will be
[tex]{7x}^{2} + 2x - 1[/tex]
help with this it is so hard
Answers
Answer:
its 4.8
Step-by-step explanation:
i divided 7.5 by 12.5 and got 0.6 and added 4.2 and got 4.8
Answer:
here is your answerrrrrrrrrrr
A play was attended by 348 people,some adults and some children. Admissions for adults was $1.50 and for children 75 cents. The total amount collected was $390. How many adults attended the play?
Answers
Answer:
172
Step-by-step explanation:
Let adults be x
and children be y
According to the problem,
x + y = 348 . . . (1)
1.5x + 0.75y = $390. . . (2)
From Eq 1, find the value of x:
x = 348 - y
Put this value in Eq 2:
1.5 ( 348 - y ) + 0.75y = 390
522 - 1.5y + 0.75 y = 390
-1.5y + 0.75y = 390 - 522
-0.75y = -132
y= -132/-0.75
y = 176
Put the value of y in Eq 1
x + 176 = 348
x = 348 -1 176
x = 172
No. of children = 176
No. of adults = 172
Which is equivalent to 12^0?
Answers
Answer:
the answer is 1
Step-by-step explanation:
I hope this was helpful
When we raise a number to the zeroth power, that means we multiply itself 0 times. You’re not multiplying anything at all. 0 is the only number such that for any number x,x+0=x
7
Anna and Paddy take part in the same fun run.
Anna completed the fun run in 2 hours.
Her average speed was 6 kilometres per hour.
Paddy completed the fun run in 90 minutes.
(a) Work out Paddy's average speed in kilometres per hour.
Answers
Answer:
I wanna say 4.6 kmph
Step-by-step explanation:
6(average) /2(hr)=3kmph
1.20(hr) / 6 (kmph) = 4.6
If Anna and Paddy take part in the same fun run. Anna completed the fun run in 2 hours. Her average speed was 6 kilometres per hour. Paddy completed the fun run in 90 minutes. Then 4.5 km/h is Paddy's average speed
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Anna and Paddy take part in the same fun run. Anna completed the fun run in 2 hours.
Her average speed was 6 kilometres per hour.
Paddy completed the fun run in 90 minutes.
We need to find paddys average speed in kilometres per hour.
Let us convert 2 hrs to minutes=120 minutes
6/120=x/90
Apply cross multiplication
90×6=120x
540=120x
Divide both sides by 120
x=4.5
Hence 4.5 kilometer per hour is the Paddy's average speed.
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[tex] \frac{x}{ \sqrt[5]{y} {}^{} {7} } [/tex]
Answers
Answer:
Step-by-step explanation:
Find the area please..........................................
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Answer:
Should be 216
Step-by-step explanation:
24:10 simplified Ratio HELP
Answers
Answer:
12:5 is the simplified ratio. Couldn't answer before but here lol
hi can you please help me with my work and please no Link please no Link please
Answers
Answer:
The second one, -11/12
Step-by-step explanation:
I used a website so sorry I don't have an explanation
Please help, test due in 2 hours! Will give good review and brainliest.
Answers
Answer:
B. Ellipse
...............................................
Which of the statements is false about the additive identity?
A. if y is the additive identity, then x+y=x
B. the value of the additive identity is 0
C. Adding the additive identity corresponds to making no movements at all on the number line
D. it is the number you add to another number to get 0
Answers
A BluRay disc normally costs $22. This week it is on sale for 25% off the original price. How much money is discounted from the original price of the BluRay disc?
Answers
Answer:
$7.33
Step-by-step explanation:
22=3/4x
22/.75=22*4/3=29.3333333
$29.33-$22=$7.33
A discounted from the original price of the Blu-ray disc will be $5.5.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
Cost of a Blu-ray disc = $22
The sale on the cost of a Blu- ray = 25%
Now,
Find the discounted price of a Blu-ray as;
Discounted price = 25% of $22
= 25 x $22 / 100
= $550/100
= $5.5
Thus, A discounted from the original price of the Blu-ray disc will be $5.5.
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Determine if 0.875 is rational or irrational and give a reason for your answer.
Answers
I had $370.00. My Mom gave $150.00. My Dad gave $150.00. My Aunt and Uncle gave me $100.00. I had another $30.00. How much did I have?
Willie Buggs Jr
Answers
Answer: You have $800.
Step-by-step explanation:
Find the value of x that makes A || B.
1
2
B
4
3
5
L2 = 3x – 10 and Z3 = x + 30
x = [ ? ]
Answers
Answer:
x=20
Step-by-step explanation:
3x-10=x+30
2x-10=30
2x=40
x=20
Answer:
X=20
Step-by-step explanation:
So their alternate interior angle which is equal
3x-10=x+30
Solve and you would get 20
giving brainliest *easy*
Answers
Answer:
1256
Step-by-step explanation:
PLEASE HELP :DDDDDDDDDD
Answers
A=11 x 11= 121 cm^2
Next find the area of one triangle and the equation is A=1/2bh
A=1/2(11)(10)
A=55 cm^2
Multiply the area of one triangle by 4 since there are four triangles and it should equal to 220 cm^2. You then add this to the base and the final answer should be 341 cm^2.
I hope this helps
Answer:
341 cm²
Step-by-step explanation:
A=11 x 11= 121 cm²
A=1/2(11)(10)
A=55 cm²
Multiply the area of one triangle by 4 since there are four triangles.
=220 cm²
220+121=341cm²
write each of the following expression without using absolute value.
|6m-54|, if m<9
Answers
9514 1404 393
Answer:
54 -6m
Step-by-step explanation:
For values of m < 9, the argument of the absolute value function is less than 0. Then the expression evaluates to ...
-(6m -54) = 54 -6m
The National Center for Health Statistics interviewed 5409 adult smokers in 2015, and 2626 of them said they had tried to quit smoking during the past year. Consider this to be a random sample. Find a 95% confidence interval for the proportion of smokers who have tried to quit within the past year. (Round the final answers to three decimal places.)
Answers
Answer:
95% of the confidence interval for the proportion of smokers who have tried to quit within the past year
(0.47228 , 0.49868)
Step-by-step explanation:
Step(i):-
Given that the National Center for Health Statistics interviewed 5409 adult smokers in 2015
and 2626 of them said they had tried to quit smoking during the past year
proportion
[tex]P = \frac{x}{n} = \frac{2626}{5409} =0.48548[/tex]
Q = 1-P = 1 - 0.48548 = 0.5146
Step(ii):-
95% of the confidence interval for the proportion of smokers who have tried to quit within the past year
[tex](P - Z_{\alpha } \sqrt{\frac{PQ}{n} } , P+ Z_{\alpha } \sqrt{\frac{PQ}{n} } )[/tex]
[tex](0.48548 - 1.96 \sqrt{\frac{0.48548 X 0.51452}{5409} } , 0.48548+ 1.96\sqrt{\frac{0.48548 X 0.51452}{5409} } )[/tex]
( 0.48548 - 0.0132 , 0.48548 +0.0132)
(0.47228 , 0.49868)
Final answer:-
95% of the confidence interval for the proportion of smokers who have tried to quit within the past year
(0.47228 , 0.49868)
Find the value of x to the nearest degree.
A. 58
B. 52
C. 38
D. 32
Answers
Answer:
52⁰
Step-by-step explanation:
Cos x⁰ = adjacent/hypotenus
Cos x⁰ = 8/13
Cos x⁰ = 0.615
x⁰ = cos^-1 (0.615)
x⁰ = 52⁰
A DVD player costs a store $185 to purchase from the manufacturer. They mark the price of the DVD player up by 20% for profit. How much do they charge for the DVD player?
Answers
Answer:
$222
Step-by-step explanation:
$185 x 1.2 = $222
Answer:
222
Step-by-step explanation:
Hi! So marking up means to raise the price or increase it.
185 is the whole, a whole is 100
and we need to raise it by 20% so add these two together to get 120%, turn this into a decimal is 1.2, now to find and increase we multiply it by the original price.
1.2 x 185 = 222
Very sorry if it is wrong.
Which expression represents the perimeter of the of the figure below?
Answers
Answer:
10x - 20
Step-by-step explanation:
Hello! Remember you have to write complete questions in order to get good and exact answers. Here I'll help you assuming some things. First of all, for a two dimensional shape, the perimeter is defined as the distance around it. Suppose we have a rectangle whose dimensions are: