The quadrilateral abcd is a parallelogram because the slopes of opposite sides are equal.
In the given figure we have a quadrilateral ABCD with A (-2,-2) , B(-3,4), C(2,2)
and D(3,-4).
We know that when the slope of two lines are equal then they are parallel.
In the given figure, Slope of BC= Slope of AD =
⇒ BC and AD are parallel .
Also, Slope of CD= Slope of BA =-6
⇒ CD and BA are parallel .
ABCD is a parallelogram because both pairs of opposite sides are parallel.
Hence, the correct reason for the given space is "slopes of opposite sides are equal"
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To celebrate the holiday season this year, the Gaylord Texan has created an extreme eight-lane, tubing hill
with real snow called the "Kung Fu Panda Awesome SNOW Tubing Ride." The cost of each ticket for one day
is $21. This can be modeled by the function f(x) = 21x. The number of tickets purchased by groups is given
by the domain (4, 6, 103. which would be a reasonable range for the total cost of the tickets the groups
would pay?
The reasonable range for the total cost of the tickets the groups
would pay is {84, 126, 2163}.
What is Domain and Range?The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation.
A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values.
Given:
The Function modeled for the situation is
f(x) = 21 x where x is the number of tickets sold.
So, For x= 4 Tickets
Fare, F(x) = 21 x 4= $84
and, For x= 6 Tickets
Fare, F(x) = 21 x 6 = $126
and, For x= 103 Tickets
Fare, F(x) = 21 x 103 = $2163.
Hence, the range is {84, 126, 2163}.
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When two variables are not correlated at all, the correlation coefficient would be _______. a. -1 b. 0 c. 1 d. -2 e. 0.5
Answer:
B. 0
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There are 40 school days in a 2-month
period. How many times can a boy be
expected to take attendance?
A. 16
B. 20
C. 24
D. 28
If there are 40 school days in a 2-month period. The number of times can a boy be expected to take attendance is: B. 20.
How to find the number of attendance times?Given data:
Number of school days = 40
Number of month = 2
Now let find the number of attendance times
Number of attendance times = Number of school days/ Number of month
Number of attendance times = 40/2
Number of attendance times = 20
Therefore the correct option is B.
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how many eight digit numbers contain the digit 2 once, the digit 3 twice, and the digit 4 thrice. leading 0s are allowed. (
0.0405 is the number that contains the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes, leading 0s are allowed.
based on data gathered from the sources
Suppose the information as shown by
How many eight-digit numbers have more 5s than 3s and contain the digits 2 exactly once, 3 exactly twice, and 4 precisely three times
Let there be more 5s than 3s and more 8-digit numbers with the digits 2 once, 3 twice, 4 three times, and 5s than 3.
2,3,3,4,4,4
after that:
= 8!/2!3!3!4!4!4!
= 8.7.6.5.4!/2×6×6×24×24×4!
= 35/864
Now, 0.405, followed by a digit 2 and 3 make up the eight-digit number.
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How many solutions does 9x+7=8x+7
Answer:
One
Step-by-step explanation:
The equation 9x+7=8x+7 has only one solution. This can be seen by setting the two sides of the equation equal to each other and then solving for x.
First, we set the two sides equal to each other by canceling out the 7 on the right side of the equation:
9x+7 = 8x+7
Then, we move all of the terms that have an x on the same side of the equation, and all of the constant terms on the other side:
9x - 8x = 7 - 7
Next, we combine like terms on the left side of the equation:
x = 0
Finally, we solve for x to find the value of x that makes the equation true:
x = 0
Therefore, the only solution to the equation 9x+7=8x+7 is x=0.
Abdel wants to spend $12 on beans and rice.
- beans, b, cost $5 per pound.
- rice, r, cost $2 per pound.
Answer:
1. 2 pounds of beans and 1 pound of rice
2. 0.6 pounds of beans and 9 pounds of rice
3. b pounds of beans and (12-b)/2 pounds of rice
Step-by-step explanation:
1. You know that 2 pounds of beans costs 2*5 so $10. Then you subtract 12-10 to get 2.
2 pounds of rice
2. You multiply 0.6 by 5, and then you subtract that from 12, getting 9. then you divide by 2 (cost of rice per pound) getting 4.5 pounds of rice
Find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. f(x) =3x^2 + 2x - 3, a = - 0.9 Set the center of the linearization as x = L(X) =
The linearization of the given function near x = -0.9 is approximated by the linear equation -x - 7, with the center of the linearization at x = -1. This equation is obtained by evaluating the function and its derivative at x = -1, then using them to approximate the value of the function at x = -0.9.
The linearization of the given function f(x) = 3x^2 + 2x - 3 near the point x = -0.9 is a linear equation that approximates the value of the function at the point. To obtain the linearization, we must first choose a suitable integer near -0.9 at which the function and its derivative are easy to evaluate. In this case, we choose x = -1 as the center of the linearization. To obtain the linearization equation, we evaluate the function and its derivative at x = -1, then use them to approximate the value of the function at x = -0.9. This results in the linear equation -x - 7. This equation allows us to approximate the value of the function at x = -0.9 without having to calculate the value of the function directly.
f(-1) = 6
f'(-1) = -1
Linearization: f(x) ≈ f(-1) + f'(-1)(x + 1)
= 6 - 1(x + 1)
= -x - 7
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Select all the true statements.
The angle bisectors of a triangle intersect at the circumcenter.
A circle is circumscribed about a
• triangle if the triangle's vertices are on the circle.
A circle is inscribed in a triangle if
• the sides of the triangle are tangential to the circle.
The perpendicular bisectors of the
• sides of a triangle intersect at the circumcenter.
All statements that are true from the options are:
The angle bisectors of a triangle intersect at the circumcenter.A circle is circumscribed about a triangle if the triangle's vertices are on the circle.A circle is inscribed in a triangle if the sides of the triangle are tangential to the circle.The perpendicular bisectors of the sides of a triangle intersect at the circumcenter.i. To circumscribe a given shape implies drawing a circle outside the a given shape. While to inscribe a given shape means to draw a circle within the boundaries of the shape.
ii. A tangent is a straight line which intersect the the circumference of a circle at a point externally.
iii. A perpendicular bisector is a straight line that divides a given line into two equal halves. And it is at right angle to the given line.
iv. The circumcenter of a triangle is the middle point/ center of the triangle.
Therefore, the statements that are true are:
The angle bisectors of a triangle intersect at the circumcenter.A circle is circumscribed about a triangle if the triangle's vertices are on the circle.A circle is inscribed in a triangle if the sides of the triangle are tangential to the circle.The perpendicular bisectors of the sides of a triangle intersect at the circumcenter.Thus all the given statements are true.
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The temperature of a liquid in an experiment starts at 0 degrees Celsius. The experiment calls for the temperature of the liquid to change at a rate of –0.6 degree Celsius per minute.
How long will it take for the liquid to reach –10.5 degrees Celsius? pls answer quick
Answer:
17.5 or 17 minutes and 30 seconds
Step-by-step explanation:
Write a compound inequality for the graph shown below.
Use x for your variable.
The interval is [4, 6], and the compound inequality equals 4 ≤ x < 6 as indicated on the number line.
Given,
The number line;
A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.
Here,
The blue line runs from 1 to 4 and then to 6.
The solid dot at position 4 denotes inclusion, whereas the hollow dot at position 6 denotes exclusion.
Then,
x ≥ 4 and x < 6
Combindlly 4 ≤ x < 6
Hence "The interval is [4, 6], and the compound inequality on the number line is 4 ≤ x < 6 ."
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Solve the systems of equations: 3x+2y=4
-2x+2y=24
Please show work for how you solved for x and y
Answer:
The solution to the system of equations is x = 28, y = -40.
Step-by-step explanation:
To solve a system of equations, we need to find values for the variables that will make both equations true.One way to do this is to eliminate one of the variables by making the coefficients equal and opposite, then solve for the remaining variable.For example, in this system of equations, we can eliminate the y variable by adding the two equations together:3x + 2y = 4
-2x + 2y = 24
---------
x = 28
Now that we have an equation in terms of x, we can substitute this value back into either of the original equations to solve for y. Let's substitute it into the first equation:3x + 2y = 4
3(28) + 2y = 4
84 + 2y = 4
2y = -80
y = -40
the solution to the system of equations is x = 28, y = -40.
a large university is divided into six colleges, with most students graduating from four of these colleges. the following bar chart gives the distribution of the percent graduating from the four most popular colleges in 2003. the percent of students graduating from either engineering or business is:
A.) ~30%
B.) ~40%
C.) ~50%
D.) Over ~60%
The percentage of students graduating from engineering or business
is ~50%
as per given in the questions
An university is divided into 6 colleges
with which the most of the students graduating from the four of the colleges given in the graph below
the percentage of students who are interested in biological science colleges are 20%
the percentage of students who are interested in mathematics colleges are 10%
the percentage of students who are interested in Engineering colleges are 20%
the percentage of students who are interested in business colleges
are 30%
from the graph, graduating from either Engineering or Business
is = 20% + 30% = 50%
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Write the point-slope form of the equation of a line that passes through the point (−1, 6)and is parallel to the line that passes through the points (6, 2) and (2, 4).
y-6=-1/2(x+1)
1. the point-slope form is y-y1=m(x-x1)
x1 and y1 are the coordinates of the point (-1,6) because the line we are looking for its equation passes through it. "m" is the slope.
2. plug in the point (-1,6) in the form from step 1
y-6=m(x+1)
3. to find the slope of this line, the question tells us that this line is parallel to another line that passes through two given points. Any parallel lines, their slopes are the same. That means we have to find the slope of the 2nd line and use it for the 1st line.
The slope formula is m=(y2-y1)/(x2-x1)
plug in the two points m=(4-2)/(2-6), which is equal to -1/2
4. plug in "m" value in the equation from step 2.
Done
A rocket motor is manufactured by bonding together two types of propellants, an igniter and a sustainer. The shear strength of the bond (y) is thought to be a linear function of the age of the propellant (X) when the motor is cast. Twenty observations are shown in the following table.
A) find the least squares estimated of the slope and intercept in the linear regression model
B) find the estimate of (?^2)
C) estimate the mean shear strength of a motor made from propellant that is 20 weeks old
A- The fitted line or the fitted linear regression model is:[tex]y=2625.385462-36.96179663*x[/tex]
B- [tex]s^{2} = 9811.21237[/tex]
C- [tex]y_{20} = 1886.14953[/tex]
A fundamental and widely used form of predictive analysis is linear regression. Regression analysis' main goal is to look at two things: (1) Is it possible to accurately forecast an outcome (dependent) variable using a set of predictor variables? (2) Which individual variables—as shown by the size and sign of the beta estimates—are highly important predictors of the outcome variable, and how do they affect the outcome variable? The link between one dependent variable and one or more independent variables is explained using these regression estimations.
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Write a system of equations for the problem below. You do not have to solve the system. Use x for the number of one-dollar bills, y for the number of five-dollar bills, and z for the number of ten-dollar bills. Top equation: Molly has one-dollar bills, five-dollar bills, and ten-dollar bills in her wallet that are worth a total of . 96 Second Equation: If she had one more one-dollar bill, she would have just as many one-dollar bills as she has fives and tens combined. Third Fquation: She has bills total
In view of Molly's three types of bills
Therefore the first equation is [tex]1x+5y+10z=96[/tex]
Therefore the second equation is [tex]x+1=y+z[/tex]
Therefore the third equation is [tex]x+y+z=23[/tex]
As per the details share in the above question as as follow,
x for the no, of $1 bills
y for the no. of $5 bills.
z for the no. of $10 bills.
We have to find the first, second and third equations.
Therefore worth of x $1 bills is [tex]1 \times x[/tex]
So of y for the no. of $5 bills is [tex]5 \times y[/tex]
And z for the no. of $10 bills is [tex]10 \times z[/tex]
The total worth in molly wallet is $96.
So the equation will be,
[tex]1x+5y+10z=96[/tex]
Now further is molly has one more $1 bill then the number of $1 bill will be same as.
Therefore the second equation is [tex]x+1=y+z[/tex]
Now she had 23 bills,
We also know that she has one-dollar, five-dollar, and ten-dollar notes, with x denoting the quantity of each, Y the number of the five-dollar bill, and Z the number of the ten-dollar bill.
Therefore the third equation is [tex]x+y+z=23[/tex]
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c) For the high jump, each competitor receives multiple opportunities to clear the bar at
each height. On average, Shane completes 3 out of 3 jumps on the lowest bar, 5 out of
6 jumps on the middle bar, and 3 out of 4 jumps on the highest bar. What is
Shane’s overall average number of jumps completed? (2 points)
d) If Shane’s average number of jumps completed is greater than one-half, then the eighth
graders earn 50 points. Which grade should be awarded 50 points**? (1 point)
PLEASE QUICK!
c) Shane’s overall average number of jumps completed is of 2.458275.
d) As Shane's overall average number is greater than one half, then the eight graders will be awarded the 50 points.
How to obtain the average number of jumps completed?The jumps that Shane takes are given as follows:
Lowest bar: 100% probability of completed, as 3/3 = 100.Middle bar: 0.8333 = 83.33% probability, as 5/6 = 0.8333.Highest bar: 0.75 = 75% probability, as 3/4 = 0.75.Then the probabilities for each number are given as follows:
One jump -> only the lowest: 1 x (1 - 0.8333) = 0.1667.Two jumps -> lowest and middle: 1 x 0.8333 x (1 - 0.75) = 0.208325.Three jumps -> all -> 1 x 0.8333 x 0.75 = 0.624975.Then the distribution of the number of jumps completed is given as follows:
P(X = 1) = 0.1667.P(X = 2) = 0.208325.P(X = 3) = 0.624975.The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability, hence:
E(X) = 1 x 0.1667 + 2 x 0.208325 + 3 x 0.624975 = 2.458275.
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tell me the answer to pls 40 divided by m
The expression of the statement 40 divided by m is 40/m
How to determine the expressionFrom the question, we have the following parameters that can be used in our computation:
40 divided by m
The above statement is a mathematical statement
The mathematical statement can be expressed as an expression
Recall that, we have
40 divided by m
The term "divided by" means a quotient expression
To divide is represented as / i.e. quotient
So, the expression that represents 40 divided by m is 40/m
Hence, the complete expression is 40/m
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if a linear function is increasing, explain mathematically why the reciprocal function must be decreasing
If a linear function is increasing, the reciprocal function must be decreasing, mathematically because the reciprocal function is the inverse of the linear function
The reciprocal function of a linear function is given by the formula:
f(x) = 1/x
If a linear function is increasing, then its slope (m) is positive. This means that the slope of the reciprocal function must be negative. The slope of the inverse of a linear function is the negative reciprocal of the slope of the linear function, meaning that the slope of the reciprocal function must be negative for the linear function to be increasing.
To illustrate this, we can consider a simple example of a linear function, f(x) = 2x. This linear function has a positive slope (2), so its reciprocal function, f(x) = 1/x, must have a negative slope (-1). This means that the reciprocal function is decreasing.
In general, if a linear function is increasing, then its reciprocal function must be decreasing, as the slope of the reciprocal function must be the negative reciprocal of the slope of the linear function.
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the sum of a number, 1/6 of that number, and 7 is 121/2 find the number
Answer:
The number is:
321/7
Step-by-step explanation:
a + a/6 + 7 = 121/2
6a/6 + a/6 + 42/6 = 363/6
6a + a + 42 = 363
7a = 363 - 42
7a = 321
a = 321/7
Check:
321/7 + (321/7)/6 + 7 = 121/2
321/7 + 321/42 + 7 = 121/2
1926/42 + 321/42 + 294/42 = 2541/42
1926 + 321 + 294 = 2541
Find the value of the test statistic for testing whether there is a linear relationship between the and the estimated number. Round your answer to two decimal places, if necessary.
the value of the test statistic for testing whether there is a linear relationship between the and the estimated number is 0.3506905
Using a correlation Coefficient calculator, the correlation Coefficient, r for the data = 0.127
The test statistic :
T = r² / √(1 - r²) / (n - 2)
Sample size, n = 10
Hence,
T = 0.127² / √(1 - 0.127²) / (10 - 2)
T = (0.016129 / 0.3506905)
T = 0.3506905
The value of the test statistic to 2 decimal places is 0.35
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according to carfax, the value of a new vehicle can drop by 20 percent after the first 12 months of ownership. then, for the next four years, you can expect your car to lose roughly 10 percent of its value annually. use the depreciation rates listed by carfax to find the value of a brand new ford f-150 valued at 63,580 after 5 years. round to the nearest dollar.
The value of the brand new Ford F-150 after five years is approximately 32,435 dollars. Rounded to the nearest dollar, the value of the Ford F-150 after five years is 32,000 dollars.
The value of a new vehicle after the first 12 months of ownership is given by the equation:
value after 12 months = value at time of purchase × (1 - depreciation rate)
In this case, the value of the vehicle at the time of purchase is 63,580, and the depreciation rate is 20%. Plugging these values into the equation gives us:
value after 12 months = 63,580 × (1 - 0.20) = 50,864
The value of the vehicle after five years is given by the equation:
value after 5 years = value after 12 months × [tex](1 - depreciation rate)^n[/tex]
where n is the number of years after the first 12 months of ownership. In this case, n is 4 (5 years - 1 year).
Plugging the values for the value after 12 months, the depreciation rate, and n into the equation gives us the following:
value after 5 years = 50,864 × [tex](1 - 0.10)^4[/tex] = 32,435
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A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 14 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area.
The radius of the cylinder that produces the minimum surface area is 1.34cm and this can be determined by using the formula area and volume of cylinder and hemisphere.
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder.
The total volume of the solid is 10 cubic centimeters.
The volume of a cylinder is given by:
V = πr²h
The total volume of the two hemispheres is given by:
V = 2 x 2/3 πr³
Now, the total volume of the solid is given by:
V total = πr²h + 2 x 2/3πr³
Now, substitute the value of the total volume in the above expression and then solve for h.
10 = πr²h + 4/3πr³
h = 10/πr² + 4r/3
Now, the surface area of the curved surface is given by:
A = 2πrh
Now, the surface area of the two hemispheres is given by:
A' = 2 x 2πr²
A' = 4πr²
Now, the total area is given by:
A total = 2πrh + 4πr²
Now, substitute the value of 'h' in the above expression.
A total = 2πr(h = 10/πr² + 4r/3) + 4πr²
Simplify the above expression.
dA = -20/r + 4πr²/3
Now, differentiate the total area with respect to 'r'.
dA/dr = 20/r + 8πr/3
Now, equate the above expression to zero.
0 = -20/r² + 8πr/3
Simplify the above expression in order to determine the value of 'r'.
8πr³ = 60
r = 1.34 cm
Therefore, the radius of the cylinder that produces the minimum surface area is 1.34cm
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The Shaffer family started on a trip in their car with 18 gallons of gasoline. The car uses 2 gallons of gasoline every hour. If t represents the number of hours spent driving and g represents the number of gallons of gasoline left in the car, which equation could be used to calculate the value of g, if 0 ≤t ≤9
Multiple Choice
g = 18 - 2t
g = 18t - 2
g = 2t - 18 g = 2t + 18
Answer:
g = 18 - 2t
Step-by-step explanation:
They start with 18 gal.
To find how much gas they use while driving:
(2 gal/hr)(t hr)
Subtract that amount from the 18 gal they had in the tank to start with.
g = 18 gal - (2 gal/hr)(t hr)
Line 1 passes through the points (-20, -4) and (-11,-4).
Line 2 is perpendicular to Line 1 and passes through the
point (-17, -14).
What is the equation of Line 2?
something noteworthy is that, the y-coordinate for Line 1 is the same, well that simply means that Line 1 is a horizontal line, anything perpendicular to a horizontal line is simply a vertical line, Check the picture below.
onvert the integral below to polar coordinates and evaluate the integral. instructions: please enter the integrand in the first answer box, typing theta for . depending on the order of integration you choose, enter dr and dtheta in either order into the second and third answer boxes with only one dr or dtheta in each box. then, enter the limits of integration and evaluate the integral to find the volume. a
As per the polar coordinates, the limits of the integration is written as ∬Df(rcos(θ),rsin(θ))rdrdθ.
What is meant by polar coordinates?
In math, polar coordinates refer a pair of coordinates locating the position of a point in a plane, the first being the length of the straight line ( r ) connecting the point to the origin, and the second the angle ( θ ) made by this line with a fixed line.
Here we have the limits of integration and evaluate the integral to find the volume. for the polar coordinates.
Here we have the polar representation of a point P is the ordered pair (r,θ) where r is the distance from the origin to P and θ is the angle the ray through the origin and P makes with the positive x-axis.
Then the polar coordinates r and θ of a point (x,y) in rectangular coordinates satisfy
=> r=x² + x² and tan(θ)=yx;
Here the rectangular coordinates x and y of a point (r,θ) in polar coordinates satisfy and x=rcos(θ) and y=rsin(θ).
Then the area element dA in polar coordinates is determined by the area of a slice of an annulus and is given by dA=rdrdθ.
Here we have to convert the double integral ∬Df(x,y)dA to an iterated integral in polar coordinates,
Now, we have to substitute rcos(θ) for ,x, rsin(θ) for ,y, and rdrdθ for dA to obtain the iterated integral
=> ∬Df(rcos(θ),rsin(θ))rdrdθ.
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A cube of 9cm wan filled with 405cubic centimeters of water what is the height of water in the cube
Answer:
The answer 700 centimeters cubic.
3. Solve the equation. Show your work. Express your answer as both a simplified mixed number and as a decimal.
Answer:
Use interval notation to express the set of real numbers x that satisfies the inequality -2 <= x < 5.
To express the set of real numbers x that satisfies the inequality -2 ≤ x < 5, we used the Interval notation method and got the solution set as [-2,5).
Interval Notation Method :Interval notation is a way of representing intervals on the number line. That is, how to write a subset of the real number line. Intervals include numbers between two specific numbers. We can use this notation to express inequalities.
Generally, we read about the three types of intervals :
Open intervals : This type of interval does not contain the endpoints of the inequality. For example, for set {x | -a< x < b}, the open interval notation is (-a, b).Closed Intervals: This type of interval contains the endpoints of the inequalities. For example, for set {x | -a≤ x ≤ b} the closed interval notation is [-3,1].Half-Open Interval: This type of interval contains only one endpoint of the inequality. For example, for set {x| -a ≤ x < b} the half-open interval notation is [-3,1).We have given an inequality as -2 ≤ x < 5
We have to express the set of real numbers x that satisfies the given inequality.
Let's started, The first thing we'll want to ask ourselves is if we're going to use parentheses or brackets when we write this.
y = { x | -2 ≤ x < 5 }
We see that the lower value of x is -2 or greater than -2 and higher value of x is less than 5. We're just going to write it down. Using the interval notation, the lower side x is greater than and equal to -2 so, we use closed bracket here and the upper side x is less than 5 that is we use parentheses or open bracket here.
Thus, in interval notation y = x , x∈[-2, 5)
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Write the equation of the line in fully simplified slope-intercept form.
The equation of the line in fully simplified slope-intercept form is y = -x/3 -1
The slope-intercept form of a straight line is used to find a line's equation. We need to know the slope of the line and the intercept where the line crosses the y-axis in order to use the slope-intercept formula.
Consider a straight line with y-intercept b and slope m. For a straight line with slope "m" and y-intercept "b,"
The slope intercept form equation is: y = mx + b.
According to the question,
The line is passing through (3,-2) and (-3 ,0)
Slope of any line passing through two points = y2-y1 / x2-x1
Slope of required line: m = 0 - (-2) / -3 - 3
=> m = -2/6
=> m = -1/3
Equation of line => y = -1/3 x + b -----(1)
As we know this line is passing through (-3,0)
Substituting the value in equation(1)
=> 0 = 1 + b
=> b = -1
Hence , The equation of line is y = -1/3 x -1
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Find the area of a regular 12-gon inscribed in a unit circle.
The required area of the regular 12-gon is obtained as 3 square units.
What is a regular polygon?A regular polygon can be defined as a polygon having all of its sides and angles equal to one another. The expression for each angle of a regular polygon is 180(n - 2)/n.
The angle between two sides of regular 12-gon is given as below,
180(12 - 2)/12 = 150°.
Now, the area of regular 12-gon is equivalent to the area of sum of 12 triangles.
The angle for the triangle will be 150/2 = 75°.
The diagram for such a triangle is given as below,
Now, OC = 1 × Sin B
⇒ OC = Sin 75°
And, BC = 1 × Cos B
⇒ BC = Cos 75°
Then, AB = 2BC = 2Cos 75°
Area of the triangle is given as,
1/2 × base × height
⇒ 1/2 × Sin 75° × 2Cos 75°
⇒ 0.25
Now, the area of the regular 12-gon inscribed in a unit circle is given as,
12 × 0.25 = 3 square units.
Hence, the area of a regular 12-gon inscribed in a unit circle is 3 square units.
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