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)

For A Quadrilateral ABCD Inscribed In A Circle Of Radius 1, Let AB : AD = 1 : 2 And BAD = 120. Also,

Answers

Answer 1

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.

For more such questions on area of triangle

https://brainly.com/question/28470545

#SPJ8


Related Questions

3/7 in decimal form rounded to the nearest thousandth

Answers

Answer:

3/7=0.4285

Step-by-step explanation:

0.4285

= 0.429

Multiply [-1 3/5 x (-6)] x (-3 3/4) x 10

Answers

Answer:

-360

Step-by-step explanation:

hope this helps!

Answer:

-360

Step-by-step explanation:

[-1 3/5 × (-6)] × (-3 3/4) × 10

= [-8/5×-6] × -15/4×10

= 48/5×-15/4×10

= -360

(b) A number increased by -8 is greater than 12

Answers

Answer:

x+-8 > 12 Hope this helps.

Please help with the homework please thanks

Answers

I have written the answers and the steps on a piece of paper.

-4 times what equals 3x ?

Answers

Answer:

[tex]\large\boxed{\tt-\frac{3}{4} x}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to identify the missing number for our equation.}[/tex]

[tex]\textsf{First, we should translate our \underline{word form} equation into \underline{numerical form}.}[/tex]

[tex]\tt \underset{-4}-4 \ \underset{\times}{times} \ \underset{?}{what} \ \underset{=}{equals} \ \underset{3x}{3x}?}[/tex]

[tex]\tt -4 \times \ ? = 3x[/tex]

[tex]\large\underline{\textsf{Identifying Ways of Solving;}}[/tex]

[tex]\textsf{We know that the unknown value is multiplied by -4 to equal 3x.}[/tex]

[tex]\textsf{-4 will equal the quotient of 3x and the unknown number.}[/tex]

[tex]\textsf{Hence, the unknown number will equal the quotient of 3x and 4.}[/tex]

[tex]\large\underline{\textsf{Solving For the Unknown Number;}}[/tex]

[tex]\tt \frac{3x}{-4} = Unknown \ Number[/tex]

[tex]\underline{\textsf{Multiply the Numerator and Denominator by the Reciprocal of -4;}}[/tex]

[tex]\textsf{The Reciprocal is a fraction where the numerator and denominator flip.}[/tex]

[tex]\tt Reciprocal \ of \ -4 \ is; -\frac{4}{1} \rightarrow \boxed{-\frac{1}{4}}[/tex]

[tex]\mathtt{ \frac{-\frac{1}{4} \times3x}{-\frac{1}{4} \times -4} \rightarrow \frac{\frac{-3}{4}x }{1} \rightarrow \large\boxed{\tt-\frac{3}{4} x}}[/tex]

Solve for z

Please help me, thank u!!!

Answers

-3.6

Step-by-step explanation:

z/(-2) + -5 = -3.2 → times -2

z + 10 = 6.4

z = 6.4 - 10

z = -3.6

2. $12.00 for 6 ounces of soda

Answers

Answer:

The answer is $2.00 per ounce of soda.

Step-by-step explanation:

Hope this helps!

Answer:

$2.00 per ounce of soda. please mark me brainliest :)

Step-by-step explanation:

which number produces a rational number when multiplied by 0.5?

Answers

Answer:

2.22

Step-by-step explanation:

PLEASE HELP ME ITS ALGEBRA TWO THANK YOUUUU

Answers

Answer:

20 kilograms of paper will be recycled in Sean's office after 10 weeks.

Write the equation of the line with x-intercept of -4 and y-intercept of 2. Hint:With those intercepts, (-4,0) and (0,2) are points on the line.

1.) -4x + 2y = 8
2.) 4x – 2y = -8
3.) 2x + 4y = 8
4.) 2x – 4y = -8

Answers

Answer

2.) 4x - 2y = -8

The equation of the line having an x-intercept of -4 and y-intercept of 2 is 2x - 4y = -8 so, option 4 is correct.

What is line?

A simple line in Euclidean geometry. A line, according to Euclid, is the distance between two points and can stretch forever in either direction. While Euclid's initial definition is now regarded as a line segment, such an extension in both directions is now thought of as a line.

Given:

The lines with an x-intercept of -4 and y-intercept of 2,

The coordinates can be written as (-4,0) and (0,2),

Write the equation of the line as shown below,

y - 2 = (2 - 0) / (0 - (-4)) (x - 0)

y - 2 = 2 / 4 x

y - 2 = 1 / 2 x

2y - 4 = x

x - 2y = -4 or 2x - 4y = -8

Thus, the equation of the line is 2x - 4y = -8.

To know more about the line:

https://brainly.com/question/2696693

#SPJ2

Shashi Rimoko earns $620 per week as a chef. He has group
medi Shashi Rimoko earns $620 per week as a chef. He has group
medical and dental insurance. Medical coverage costs $9,560
a year and dental coverage costs $172 a year. The restaurant
pays 80% of the medical and 65% of the dental insurance. How
much is deducted each week for insurance

Answers

Out of the weekly amount that Shashi Rimoko makes, a deduction of $37.93 is made for insurance.

The total Medical cost is $9,560 and out of this, the amount paid by Shashi per year is:

= Amount x (1 - percentage paid by restaurant)

= 9,560 x ( 1 - 80%)

= $1,912

The amount he pays for Dental coverage is:

= Amount x (1 - percentage paid by restaurant)

= 172 x (1 - 65%)

= $60.20

The total amount he pays for insurance per year is:

= Medical + Dental

= 1,912 + 60.20

= $1,972.20

The weekly deduction is:

= Year amount / No. of weeks in year

= 1,972.20 / 52

= $37.93

In conclusion, $37.93 is deducted from his paycheck every week.

Find out more at https://brainly.com/question/16711490.

-48 divided by what equals 6

Answers

Answer: the answer is -8

Step-by-step explanation:

halp now if u pro i will give brainli

Answers

The answer is the orange line.

Answer:

The orange line is the actual answer because it is moving at constant velocity

Step-by-step explanation:

Write the equation of the line passing through the points (2,-5) and (7,-3).

Answers

Answer:

5y·2x=21

[tex] \frac{y - y1}{y2 - y1} = \frac{x - x1}{x2 - x1} [/tex]

Step-by-step explanation:

using the formula above,you will find the equation 5y–2x=21

In ∆PQR, m P = 60°, m Q = 30°, and m R = 90°. Which of the following statements about ∆PQR are true? Check all that apply.

A. PQ = √3 • PR

B. PQ = 2 • PR

C. QR = 2 • PR

D. QR = √3/2 • PQ

E. QR = √3 • PR

F. PR = √3/2 • PQ​

Answers

Answer:

C. QR = 2 • PR

Step-by-step explanation:

According to given information we can draw a right triangle with angle measures as follows :

30-60-90 and for this special right triangle the side length would follow as:

The side length that sees angle measure 30 = a

The side length that sees angle measure 60 = a[tex]\sqrt{3}[/tex]

The side length that sees angle measure 90 = 2a

following this information the:

PR(sees 30 degrees) = a (can be represented as PR in this case)

and so

QR(sees 90 degrees) = 2a (2*PR  in this case)

PQ(sees 60 degrees) = a[tex]\sqrt{3}[/tex] ([tex]\sqrt{3}[/tex] *PQ in this case)

The correct option is C. QR = 2 • PR

Find the x-and y-intercepts.
3x - 5y = -15

Answers

The x intercepts is 5 and the y intercepts is -3
x intercept (-5,0)
y intercept (0,3)

If x=0.8 and y=0.25, find y when x=0.125

Answers

Answer:

0.0390625

Step-by-step explanation:

by the equation then x=y*(16/5)

then when x=0.125 , y = 0.0390625

Which of the following ordered pairs make this equation true?

Y=x-1

A) (3,2)

B) (1,4)

C) (4,5)

D) (0,1)

Answers

Answer: A

Step-by-step explanation:

Replace x by 3, and y by 2

Answer:

A. (3, 2)

Step-by-step explanation:

x = 3 , y = 2

• Y= x - 1

• 2 = 3-1

• 2 = 2

Evaluate. {1−[−3−(5+4)]}⋅(−6)

Answers

Answer:

-78

Step-by-step explanation:

So we start with the innermost parentheses

(5+4) = 9

{1−[−3−(9)]} x -6

-3 - 9 = -12

{1 - [-12]}

Whenever you subtract a negative, the subtraction and negative cancel each other out, so it turns into addition

1 + 12 = 13

13 x -6 = -78

Mona is decorating a bulletin board. She has 32 butterflies and wants to put them in 4 rows. Which picture shows how many she should put in each row?

Answers

Answer:

8

Step-by-step explanation:

you do 32/4 which is 8 so the anwer should be 8

The marksobtained by a group of students in science test are
90, 49, 87, 74,80, 85, 49
Find the
a) Median
b) Mode
c) Range

Answers

The answer is AI think

A repair team is responsible for a stretch of oil pipeline 2 miles long. The distance (in miles) at which any fracture occurs can be represented by a uniformly distributed random variable, with probability density function f(x) = 0.5.
What is the probability that the next fracture will occur in the last half mile of the two mile interval?

Answers

Using the uniform distribution, it is found that there is a 0.25 = 25% probability that the next fracture will occur in the last half mile of the two mile interval.

The uniform distribution has two bounds, a and b.  

The probability of finding a value above x is:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

In this problem, the distribution is uniform over 2 miles, thus [tex]a = 0, b = 2[/tex].

The probability of a failure on the last half-mile is P(X > 1.5), thus:

[tex]P(X > 1.5) = \frac{2 - 1.5}{2 - 0} = 0.25[/tex]

0.25 = 25% probability that the next fracture will occur in the last half mile of the two mile interval.

A similar problem is given at https://brainly.com/question/17088600

Help me please……………….

Answers

Answer:

8 or [tex]\frac{8}{1}[/tex]

Step-by-step explanation:

[tex]\frac{4}{\frac{1}{2}}[/tex] can also be written as;

4 ÷ 0.5

(0.5 is the 1/2 in decimal form)

4 ÷ 0.5 = 8

Consider the quadratic function f(x)=8x2−7x+6. What is the constant of the function?

Answers

Answer:

6  is the constant :

because it is never going to change

f(x), and others that contain x will change based on the value x

Since 6 doesn’t have the c with it it will be constant

Can someone help me pls.....

Answers

Answer:

the first one is equivalent and the second one is not equivalent

Step-by-step explanation:

In the first one do the distributive property first by distributing the the -2.

[tex]3x - 4.6x - 5 = 1.6x - 5[/tex]

collect like terms on the left side

[tex] - 1.6x - 5 = - 1.6x - 5[/tex]

they are equivalent.

The second equation do the distributive property first by multiplying by -3.

[tex]5 + 4.8x + 6.3 = 4.8x - 1.3[/tex]

collect like terms on the left.

[tex]4.8x + 11.3 = 4.8x - 1.3[/tex]

not equivalent

Find f( -7) if f(x) = 3 - 2x.A)-24B)-11C)17D)23

Answers

Answer:

C) 17

Step-by-step explanation:

f(-7) = 3 - 2(-7)

f(-7) = 3 + 14

f(-7) = 17

Hope this helps! Pls give brainliest!

Answer:

C) 17

Step-by-step explanation:

Hope it helps

Peace Out

Hope you have a good day

NO LINKS/ NO ASSESSMENTS!!!

Part 1: Write a rule to describe each transformation​

Answers

Answer:

(x, y) → (-x, y)

Step-by-step explanation:

We can observe the figures are mirrored over y- axis.

This is a reflection and the rule is:

(x, y) → (-x, y)

plz i need help walk me through it, thanks​

Answers

Answer:

[tex]p=36^{\circ}[/tex]

Step-by-step explanation:

We can prove that a tangent will always be perpendicular to the radius touching it. So, the other angle in the diagram is [tex]90^{\circ}[/tex].

Because all the angles of a triangle sum to [tex]180^{\circ}[/tex], we have that [tex]p+54+90=180[/tex].

We combine like terms on the left side to get [tex]p+144=180[/tex].

We subtract [tex]144[/tex] on both sides to get [tex]p=36[/tex].

So, [tex]\boxed{p=36^{\circ}}[/tex] and we're done!

Find the midpoint of the segment with the given endpoints.
(-10,- 6) and (-3,7)

Answers

Step-by-step explanation:

in essence, these 2 points are the Hypotenuse of a right-angled triangle. the legs are the coordinate differences between the 2 points creating the 3rd point of that triangle at (-10, 7) : the x coordinate of one point, and the y coordinate of the other.

now, we are looking for the midpoint. this midpoint cuts the original line/hypotenuse in half creating a scaling factor of 1/2.

when we create now a similar triangle based on that "half- Hypotenuse", we need to use the same scaling factor also on the legs (the coordinate differences).

so, when we cut the coordinate differences also in half, we get the coordinates for the midpoint on the main line.

xm, ym are the coordinates of the midpoint.

xm = (x1 + x2)/2 = (-10-3)/2 = -13/2 = -6.5

ym = (y1 + y2)/2 = (-6+7)/2 = 1/2 = 0.5

so, the midpoint is (-6.5, 0.5)

there are 76 milligrams of sodium in a 3ounce serving at skinless chicken how much sodium would be in 8 ounce of skinless chicken to the nearest tenth

Answers

Answer:

202.7 milligramsHope this helped :)

Answer:

202.7

Step-by-step explanation:

76 divided by 3 to see how many milligrams of sodium is in 1 once of chicken, so it would be 25.33... (or you xould simplify to 25.4.) Then you times by 8 to see how much is in 8 ounces

Other Questions
Each ____has its own agency that is responsible for determining and enforcing the licensing laws and regulations for social workers in that area what is metabolism meaning Translate this sentence to English No links PLEASE HELP!!!Vicente, para llegar a la biblioteca, tienes que doblar a la izquierda en la carretera 3b. Para en la seal de alto. No dobles a la izquierda enla calle 18, dobla a la derecha en la avenida 4 oeste. La biblioteca queda a la derecha, entre la plaza y el restaurante. Acabas de llegar a labiblioteca What are the domain and range of the function A skateboarder rolls off a horizontal ledge that is 1.32 m high and lands 1.88 m from the base of the ledge what was his initial velocity Use Gausss approach to find the following sums a.1+2+3+4++99b.1+3+5+7++101 Can anyone help ASAP!!!! Thanks which layer of the epidermis is not present in thin skin? What is the reason for the widespread use of fins on surfaces? Group of answer choices Decreasing the rate of heat transfer from a surface by increasing the heat transfer surface area Decreasing the rate of heat transfer from a surface by decreasing the heat transfer surface area Increasing the rate of heat transfer from a surface by decreasing the heat transfer surface area Increasing the rate of heat transfer from a surface by increasing the heat transfer surface area The endpoints of AC are A(-8, 9) and C (1, -3). Point B(-2, 1) lies on AC. Whatis the ratio AB: BC?A 1:2B1:1C) 2:1D) 3:1 Pls Answer This Ill Rate 3 stars and giva a thanks if u answer and btw this is a 15 point questions PLS ANSWER I BEG Will the lizard make it to the other side of the road before the car gets there?yes or no the melting point of a substance is also the same as the: which statements best describe the relationship between political machines and local communities in the late nineteenth century? Select two correct answers. APolitical machines worked with labor unions to expand their influence in local communities.B Political machines emerged among immigrant groups in rural communities.C Political machines used a system of patronage to gain the support of voters and their communities. D Political machines provided aid to urban communities in exchange for votes. E Political machines worked with voters to eliminate corruption in government. sus componentes no se distinguen a simple vista , aun utilizando. microscopio Where did potuks father wish for potuk to be ? David is a wealthy business owner with no children and is very close with his only niece, Allie. He would like to give her alarge gift for her 18th birthday as a token of his affection for her. After much consideration, he finally decides to buy her abrand new Corvette convertible. To deliver the gift, David puts the convertible keys on a keychain and hides them in hercoat pocket. He then tells her that her gift is in her coat pocket and the car is hers immediately. She finds the keys and isdelighted. Allie's parents, however, are hardworking and proud and as such, they are hesitant to allow her to accept thegift. After much pressure from her parents, Allie decides not to accept the gift from her uncle because she does not wantto feel obligated to him. She would feel more comfortable with a less expensive birthday present.Go through the requirements that a gift must have to be valid. Does the Corvette in question qualify as a gift?How many elements are necessary for this type of gift to be valid? An entrepreneur is a person who__a business venture.assumes the risk fororganizesdoes not get involved inoperates First Day how setting similar to main character please helpppppppppppppppppppppppp