Use double-angle identities to write each expression, using trigonometric functions of θ instead of 4 θ.
cos 4θ
Answer:
cos4θ=8cos^4θ−8cos^2θ+1
Step-by-step explanation:
A company produces a special new type of TV. The company has fixed costs of $470,000, and it costs $1300 to produce each TV. The company projects that if it charges a price of $2300 for the TV, it will be able to sell 850 TVs. If the company wants to sell 900 TVs, however, it must lower the price to $2000. Assume a linear demand. If the company sets the price of the TV to be $3500, how many can it expect to sell? It can expect to sell TVs (Round answer to nearest integer.)
The company can expect to sell approximately 650 TVs at a price of $3500.
To determine how many TVs the company can expect to sell at a price of $3500, we need to analyze the demand based on the given information.
We are told that the company has fixed costs of $470,000, and it costs $1300 to produce each TV. Let's denote the number of TVs sold as x.
For the price of $2300, the company can sell 850 TVs. This gives us a data point (x1, p1) = (850, 2300).
For the price of $2000, the company can sell 900 TVs. This gives us another data point (x2, p2) = (900, 2000).
Since the demand is assumed to be linear, we can find the equation of the demand curve using the two data points.
The equation of a linear demand curve is given by:
p - p1 = ((p2 - p1) / (x2 - x1)) * (x - x1)
Substituting the known values, we have:
p - 2300 = ((2000 - 2300) / (900 - 850)) * (x - 850)
p - 2300 = (-300 / 50) * (x - 850)
p - 2300 = -6 * (x - 850)
p = -6x + 5100 + 2300
p = -6x + 7400
Now, we can use this equation to determine the expected number of TVs sold at a price of $3500.
Setting p = 3500:
3500 = -6x + 7400
Rearranging the equation:
-6x = 3500 - 7400
-6x = -3900
x = (-3900) / (-6)
x ≈ 650
Therefore, the company can expect to sell approximately 650 TVs at a price of $3500.
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Please help me with this homework
7. Find the value of x.
Help please??
Answer: which one
Step-by-step explanation:
4(4m⁵+2m⁵-5m³+ ... +7m⁵) = 60m⁵-20m³
Answer:
2\(m^{5}\)
Step-by-step explanation:
4(4m⁵+2m⁵-5m³+ ... +7m⁵) = 60m⁵- 20m³
We combine similar terms.
4(13\(m^{5}\) - 5m³ + x) = 60\(m^{5}\) - 20m³
We divided by 4 on both sides.
13\(m^{5}\) - 5m³ + x = 15\(m^{5}\) - 5m³
Move all terms not containing x to the right side of the equation.
x = 2\(m^{5}\)
So, the number fill in the blank is 2\(m^{5}\).
How do you solve supply and demand problems?
Supply and demand problems are typically solved by finding the intersection point of the supply and demand curves to determine the equilibrium price and quantity.
To solve supply and demand problems, we typically use the intersection point of the supply and demand curves to determine the equilibrium price and quantity.
Once the equilibrium price and quantity are determined, we can use them to make predictions about the behavior of the market and the effects of changes in supply and demand. We can also calculate consumer surplus, producer surplus, and total surplus.
Various mathematical and graphical methods can be used to analyze supply and demand, including linear equations, graphs, and calculus techniques.
To solve supply and demand problems, we typically start by identifying the supply and demand curves for the market in question.
Then, we can find the intersection point of these curves, which represents the equilibrium price and quantity. If the market price is above the equilibrium price, there will be a surplus of supply and prices will tend to fall. If the market price is below the equilibrium price, there will be a shortage of supply and prices will tend to rise.
We can also analyze the effects of shifts in the supply and demand curves due to changes in various factors such as taxes, subsidies, technology, or consumer preferences. This can help us understand the market dynamics and make predictions about the future behavior of the market.
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Drag the number cards to fill in each blank so that the values are in order from smallest to largest.
To fill in each blank so that the values are in order from smallest to largest, we have;
4° , 1⁴ = 4, 2² , 3³ , 4³ , 2⁹
What are index forms?
We need to know that index forms are defined as mathematical forms used to represent numbers or variables that are too large or too small in more convenient forms.
These index forms are also known as scientific notation or standard forms.
Some examples of index forms are;
3²
4³
2³
From the information given, we have that;
To arrange the numbers;
4° = 1
1⁴ = 4
2² = 4
3³ = 27
4³ = 64
2⁹ = 512
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Mr. Hare left at 8:00 a.m. and is traveling 50 miles per hour. Mrs. Hare left at 9:00 a.m. and is traveling at 55 miles per hour. If Mr. and Mrs. Hare are traveling the same direction, what time will it be when Mrs. Hare first passes Mr. Hare?
A. 7:00 p.m.
B. 8:00 p.m.
C. 9:00 p.m.
D. 10:00 p.m.
Answer: B 8:00pm
Step-by-step explanation:
the selling price for a pair of jeans is 39.98. There is a 4.5% sales tax on all purchases. How much would it cost to buy the jeans?
Answer:
$41.78
Step-by-step explanation:
tax is 4.5% on top of original price of 39.98
so multiplying 39.98 by 1.045 gives us 41.78
you multiply by 1.045 because 4.5% is the same as 0.045 and the 39.98 represents 100% of the price so it is 1 and you are paying 104.5% of that price for it when tax is included
You deposit $2,000 into a bank account that will bay you 4. 8% interest APR ("annual percentage rate") compounded monthly. How much money will you have in 10 years?
\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 4.8\%\to \frac{4.8}{100}\dotfill &0.048\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &10 \end{cases} \\\\\\ A=2000\left(1+\frac{0.048}{12}\right)^{12\cdot 10}\implies A=2000(1.004)^{120}\implies A\approx 3229.06\)
(-0.2)(0.4 I don’t know how to do this question
Answer:
-0.08
Step-by-step explanation:
Multiply.
-0.2
x 0.4
_____
0 0 8
Each number you started out with has 1 space between the last number and the decimal, so your final answer will have 2 spaces.
Also, since you multiplied a negative and a positive, your final answer will be negative.
Find the Next 3 Letters in J F M A M J J A
What are the next 3 letters in the sequence J F M A M J J A?
The next three letters in the sequence J F M A M J J A are S, O, N.
To find the next three letters in the sequence J F M A M J J A, we need to identify the pattern or rule that governs the sequence. In this case, the sequence follows the pattern of the first letter of each month in the year.
The sequence starts with 'J' for January, followed by 'F' for February, 'M' for March, 'A' for April, 'M' for May, 'J' for June, 'J' for July, and 'A' for August. The pattern repeats itself every 12 months.
Therefore, the next three letters in the sequence would be 'S' for September, 'O' for October, and 'N' for November.
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The next three letters in the sequence "J F M A M J J A" are "S O N", indicating the months of September, October, and November.
The given sequence "J F M A M J J A" represents the first letters of the months in a year, starting from January (J) and ending with August (A). To find the next three letters in the sequence, we need to continue the pattern by considering the remaining months.
The next month after August is September, so the next letter in the sequence is "S". After September comes October, represented by the letter "O". Finally, the month following October is November, which can be represented by the letter "N".
Therefore, the next three letters in the sequence "J F M A M J J A" are "S O N", indicating the months of September, October, and November.
It is important to note that the given sequence follows the pattern of the months in the Gregorian calendar. However, different cultures and calendars may have different sequences or names for the months.
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Q1: Factor the polynomial 6x4 + 24x3 − 72x2 completely by first factoring out the GCF, and then factoring the rest of the expression. Q2: Consider the polynomial 6x4 + 24x3 − 72x2. What is the greatest common factor (GCF) of the terms of the polynomial?
Answer:
After factorizing the given polynomial we get 6x^2 (x+6)(x-2)
Step-by-step explanation:
Given Polynomial:
6x^4+24x^3−72x^2
We need to completely factorize the polynomial.
Consider,
6x^4+24x^3−72x^2
GCF = 6x^2, By taking it common out
= 6x^2 (x^2+4x-12)
= 6x^2 (x^2+6x-2x-12)
= 6x^2 (x(x+6)-2(x+6))
= 6x^2 (x+6)(x-2)
Therefore, After factorizing the given polynomial we get 6x² ( x + 6 ) ( x - 2 )
Please mark me Brainliest.
Consider the equation below. 6x2 − y + 3z2 = 0 Reduce the equation to one of the standard forms. Classify the surface. ellipsoid elliptic paraboloid hyperbolic paraboloid cone hyperboloid of one sheet hyperboloid of two sheets
The standard form of the equation is:
\(\frac{(x-\frac{3}{2})^2 }{\frac{3}{2} } +\frac{(z-\frac{\sqrt{3} }{2})^2 }{\frac{5}{2} } - \frac{y}{\frac{45}{4} } = 1\)
This is the standard form of an ellipsoid, since the equation has positive coefficients for both the x² and z² terms.
To reduce the equation 6x² - y + 3z² = 0 to one of the standard forms, we can complete the square for x and z and move the constant term to the other side of the equation.
Starting with 6x² - y + 3z² = 0, we can complete the square for x by factoring out a 6 from the x² term and adding and subtracting (6/2)² = 9 to get:
6(x² - 3x + 9/4) - y + 3z² = 0 + 54/4
Simplifying, we get:
6(x - 3/2)² - y + 3z² = 27/2
Similarly, we can complete the square for z by factoring out a 3 from the z² term and adding and subtracting (3/2)² = 9/4 to get:
6(x - 3/2)² - y + 3(z² - 3/4) = 27/2 - 9/4
Simplifying, we get:
6(x - 3/2)² - y + 3(z - √(3)/2)² = 45/4
Therefore, the standard form of the equation is:
\(\frac{(x-\frac{3}{2})^2 }{\frac{3}{2} } +\frac{(z-\frac{\sqrt{3} }{2})^2 }{\frac{5}{2} } - \frac{y}{\frac{45}{4} } = 1\)
This is the standard form of an ellipsoid, since the equation has positive coefficients for both the x² and z² terms.
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(write using exponent) I’ll give brainliest !! Pls help
Answer:
\(\frac{1}{4^{21} }\)
Step-by-step explanation:
\(4^{-3*7}\)
\(4^{-21}\)
\(\frac{1}{4^{21} }\)
It's really important, please help
The question isn't complete. This is just part of the question
So please send the whole question together.
Answer:
98 mins
Step-by-step explanation:
147.5 +x = 245.5
x = 245.5-147.5
x= 98 mins
The three angle measures in a triangle are congruent. The angles are equiangular! What is the measurement of one of the angles?
Answer:
60 degrees per angle.
Step-by-step explanation: a triangle has a total of 180 degrees, and the number of sides determine the number of angles it has. in this case, it's an equilateral triangle. 180/3 = 60. all triangles have 3 sides if you didn't know that ;)
suppose that each party must select a speaker and a vice speaker. how many ways are there for the speaker and vice speaker to be selected in the demonstrators party?
There are n x (n-1) number of ways for the speaker and vice speaker to be selected in the demonstrator's party, where n is the number of members in the party.
For the demonstrator's party, the first position of the speaker can be filled by any of the n members. After the speaker is chosen, there are n-1 members left to select from for the position of vice speaker. Therefore, the total number of ways the speaker and vice speaker can be selected is n x (n-1).
For example, if the demonstrator's party has 4 members, there are 4 choices for the speaker position. After the speaker is chosen, there are 3 choices left for the position of vice speaker. So, the total number of ways to select a speaker and vice speaker in the party is 4 x 3 = 12.
This formula can be applied to any size of the party to determine the total number of possible ways to select a speaker and vice speaker.
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A pipefitter must connect two pipes as shown. The run is 32 feet while the set is 21 feet. How long a pipe will he need, and what will be the connecting angles? Round tothe nearest hundredth.
In order to determine how long the pipe connector must be, we can use the Pythagorean Theorem.
\(c^2=a^2+b^2\)where "a" and "b" are either run or set in the diagram while "c" is the length of the pipe.
Let's say "a" is run which is 32 ft and "b" is the set which is 21 ft. Let's plug this into the formula above.
\(c^2=32^2+21^2\)Then, solve for c.
\(\begin{gathered} c^2=1024+441 \\ c^2=1465 \end{gathered}\)Get the square root on both sides of the equation.
\(\sqrt{c^2}=\sqrt{1465}\Rightarrow c=38.275\approx38.28ft\)Hence, the pipe connector must be 38.28 ft.
To determine the angle, we can use either the cosine or sine functions.
For angle "a", we can use the sine function and we use the set and the length of the pipe connector.
\(\theta=sin^{-1}\frac{21}{\sqrt{1465}}\)Using the calculator, the value of angle theta is:
\(\theta=33.274\approx33.27\degree\)The measure of angle "a" is approximately 33.27°.
For angle "b", we can use the sine function and we use the run and the length of the pipe connector.
\(\theta=sin^{-1}\frac{32}{\sqrt{1465}}\)\(\theta=56.725\approx56.73\degree\)The measure of angle "b" is approximately 56.73°.
Answer:
See below
Step-by-step explanation:
Run and rise and x form a right triangle ...use pythag theorem
x^2 = 32^2 + 21^2 shows x = 38.28 ft
Right triangle tan (angle ) = opposite leg / adjacent leg
angle a = arctan ( 21/32) = 33.27° angle b = arctan (32/21) = 56.73°
How many square meters are in 280 square centimeters
We can perform a change of units to see that 280 square centimeters is equivalent to 0.028 square meters.
How many square meters are in 280 square centimeters?We want to perform a change of units between square centimeters and meters.
Remember the relation:
100cm = 1m
Now we can square both sides of that equation, then we will get:
(100 cm)^2 = (1m)^2
10,000 cm^2 = 1m^2
Then if we have a measure in square centimeters, to transform it into square meters we need to divide that measure by 10,000.
Then:
280 cm^2 = (280/10,000) m^2 = 0.028 m^2
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Juice box has 20% more juice in its new packaging. The original packaging held 12 fluids ounces. How much juice does the new packaging hold?
Answer: 14.4
Step-by-step explanation:
There are 14.4 fluids ounces juice does the new packaging hold.
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.
Given that;
Juice box has 20% more juice in its new packaging.
And, The original packaging held 12 fluids ounces.
Now,
Since, The original packaging held 12 fluids ounces.
Hence, The amount of juice does the new packaging hold is;
⇒ 12 + 20% of 12
⇒ 12 + 20/100 × 12
⇒ 12 + 2.4
⇒ 14.4
Thus, There are 14.4 fluids ounces juice does the new packaging hold.
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Which linear inequality is represented by the graph?
1: y ≥ One-thirdx – 4
2: y ≤ One-thirdx – 4
3: y ≤ One-thirdx + 4
4: y ≥ One-thirdx + 4
Answer: option B
(B) y ≤ 1/3x – 4 <========+ 100%
Step-by-step explanation:
Find the equation of the line that
is parallel to y = 4x + 1 and
contains the point (1, 1).
y = [? ]X + [ ]
The equation of a line is:
\( \displaystyle \large{y - y_1 = m(x - x_1)}\)
Since the line has to be parallel to line y = 4x+1. Hence, m = 4.
\( \displaystyle \large{y - y_1 = 4(x - x_1)}\)
Given point is (1,1). Let this be the following:
\( \displaystyle \large{(x_1,y_1) = (1,1)}\)
Substitute the point in.
\( \displaystyle \large{y - 1 = 4(x - 1)}\)
Convert the equation in a slope-intercept form or function form.
First, distribute 4 in the expression.
\( \displaystyle \large{y - 1 = 4x - 4}\)
Add 1 on both sides.
\( \displaystyle \large{y - 1 + 1 = 4x - 4 + 1} \\ \displaystyle \large{y = 4x - 3}\)
Hence, the line that is parallel to y = 4x+1 and passes through (1,1) is y = 4x-3
The following triangle is and
isosceles
scalene
equilateral
——————
right
acute
obtuse
Answer:
isosceles
right
Step-by-step explanation:
The two legs (not the hypotenuse) are marked as equal. So the triangle is at least isosceles (choice of the top three)
The square in the bottom left corner is used as the symbol for a right angle. So this triangle is a right triangle.
I’m confused on what number 4 means. Can someone please help?
According to the given dot plot there are 18 students in the class.
3. From the given dot plot, we can see there are 18 students in the class.
4. In the class there are 18 students, survey is done on what kind of music each student like and what kind of Music CDs each student brought.
Therefore, according to the given dot plot there are 18 students in the class.
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write an explanation comparing constant percentage change to constant rate of change. 2. what are some key words in a verbal description that indicate an exponential function can be used to model the situation? what is meant by such words?'
Percentage Change = (ΔV/IV₁I) × 100
Constant rate of Change = (y₂ - y₁)/ (x₂ - x₁)
Constant Percentage Change:
This means that after t period the something has grown to \(g^{t} = 1.10^{t}\) it original value .
percentage change formula equals the change in value divided by the absolute value of the original value multiplied by 100.
Constant rate of Change:
In which the rate does not change between different points in the function. in short, constant rate of change refers to the comparison of the way two quantities changes. in equation, the constant rate of change can be seen as a slope.
An exponential function is a function that changes at a constant percentage rate.
An exponential function y of t is characterized by the following property:
when t increases by 1 to find the new value of y the current value by the base.
y- value for t +1 = Base of y - value for t
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James ordered a large pizza that was cut into 8 equal portions. Of the 8 slices, only 3 of the slices were eaten. James believed that there was 0.75 pi radians left of the pizza. Which of the following correctly
describes James' claim?
A) James in incorrect because he calculated the number of slices of pizza that were eaten instead of the number of slices of pizza that were left. James needed to divide 360 by the appropriate number of
slices of pizza, 8. He then would have needed to multiply the result by 5 in order to find how many degrees of pizza was left over. After that, James would have needed to divide by 180 and multiply by TT
to get 1.257 radians as the amount of pizza that was left.
B) James is incorrect because he did not need to use TT when solving for radians. The amount of pizza left over is only 0.75.
C) James is incorrect because he did not divide 360 by the appropriate number of slices of pizza, 5, in order to find how many degrees of pizza was left. James would have then needed to divide by 180
and multiply by TT to get 0.4π radians as the amount of pizza that was left.
As per central angle theorem, James in incorrect because he calculated the number of slices of pizza that were eaten instead of the number of slices of pizza that were left. James needed to divide 360 by the appropriate number of slices of pizza, 8. He then would have needed to multiply the result by 5 in order to find how many degrees of pizza was left over. After that, James would have needed to divide by 180 and multiply by π to get 1.257 radians as the amount of pizza that was left.
Define central angle theorem?The central angle is the angle that a circle's arc occupies in its center. The arms of the central angle are formed by the radius vectors.
In other words, it's an angle whose vertex is the center of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's center subtends is known as the central angle.
Here,
out of 8 slices 5 are left.
So 360/8
= 45
5 × 45 = 225°
Now 225° = 225× π/180
= 3.927 Rad
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James ordered a large pizza cut into eight equal pieces. Of the 8 slices, only 3 were edible. James thought the rest of the pizza was 0.75 pi radians. Option A) correctly describes James' claim.
Define central angle theorem?The central angle is the angle an arc of a circle makes at its center. The central angle arm is formed by the radius vector. That is, the angle at which the arms with the apex at the center of the circle and the arms at his two radii of the circle intersect at two different positions. Combining these two points forms an arc. The angle that this arc makes at the center of the circle is called the central angle.
Here,
out of 8 slices 5 are left.
So 360/8
= 45
5 × 45 = 225°
Now 225° = 225× π/180
= 3.927 Rad
According to the central angle theorem, James is wrong because he calculated the number of pizza slices eaten, not the number of pizza slices left. James had to divide his 360 by 8, the number of pizza slices. Then he had to multiply the result by 5 to see how many pizzas were left. Then James had to divide him by 180 and multiply by π, so he got 1.257 radians as the remaining amount of pizza.
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Michelle has four white socks two black socks and two gray socks in her drawer she pulled that one sock on the drawer without looking she's not put it back then Michelle Pulls a second Sock from the drawer .what is the probability that Michelle pulls two white socks from the drawer a.3/14 b. 3/16 c. 1/16 d. 1/2
Answer:
3/14
Step-by-step explanation:
prob for the 1st sock=4/8=1/2
prob for the 2nd sock=3/7(there's 7 socks left now and only 3 were white since she pulled one out and didn't put it back)
so the prob of both being white is 1/2*3/7=3/14
In January a baby elephant weighs 180kg. By March the weight of the baby elephant had increased by ⅜. Work out the weight of the baby elephant in March
The weight of th baby elephant in the month of March would be 247.5 Kg.
What is weight?Weight of a body is the force exerted by the earth on the body on the surface of the earth towards its center.
Given is that in January a baby elephant weighs 180kg. By March the weight of the baby elephant had increased by ⅜.
Assume the weight of the baby elephant in March would be {x} Kg. We can write -
{x} = 180 + 3/8 of 180
{x} = 180 + 3/8 x 180
{x} = 180 + 67.5
{x} = 247.5 Kg
Therefore, the weight of th baby elephant in the month of March would be 247.5 Kg.
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In the given figure ABCD, prove that
angleBCD= angleBAD+ angle ABC+angle ADC.
[Hint: Join A and C then extended AC to the point E]
We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.
To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:
Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.
Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.
Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).
Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.
Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).
Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.
Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.
Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.
Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.
Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.
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Given: Quadrilateral \(\displaystyle\sf ABCD\)
To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)
Proof:
1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).
2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).
3. In triangle \(\displaystyle\sf ACD\):
- \(\displaystyle\sf \angle ACD = \angle BAD + \angle ADC\) (Angles of a triangle add up to \(\displaystyle\sf 180^\circ\)).4. In triangle \(\displaystyle\sf BCE\):
- \(\displaystyle\sf \angle BCE = \angle BAD + \angle ABC\) (Angles of a triangle add up to \(\displaystyle\sf 180^\circ\)).5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):
- \(\displaystyle\sf \angle BCE = \angle BCD\).6. Combining the equations from steps 3 and 4:
- \(\displaystyle\sf \angle BCD = \angle ACD = \angle BAD + \angle ADC\). - \(\displaystyle\sf \angle BCD = \angle BCE = \angle BAD + \angle ABC + \angle ADC\).Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).
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