a convex octagon inscribed in a circle has four consecutive sides of length 3 and 4 consecutive sides of length 2. find the area of the octagon if if you solve this question I will mark you as brainliest answer
Answers
Answer:
13 + 12√2
Step-by-step explanation:
Not sure if there's an easier way, but here's my method:
Draw the radius lines from the center of the circle to each vertex of the octagon. This will divide the octagon into 8 isosceles triangles, 4 big and 4 small.
Draw the height of one of the big triangles. Define the angle between the height and the radius as A. Similarly, draw the height of one of the small triangles. Define the angle between the height and the radius as B.
Using trig, we can say:
sin A = 1.5 / r
sin B = 1 / r
The vertex angle of the large isosceles triangle is 2A, and the vertex angle of the small isosceles triangle is 2B. Therefore:
4(2A) + 4(2B) = 360
A + B = 45
If we substitute into the first trig equation:
sin(45 − B) = 1.5 / r
sin 45 cos B − cos 45 sin B = 1.5 / r
1/√2 cos B − 1/√2 (1/r) = 1.5 / r
cos B − 1/r = 1.5√2 / r
cos B = (1 + 1.5√2) / r
If we substitute into the second trig equation:
sin(45 − A) = 1 / r
sin 45 cos A − cos 45 sin A = 1 / r
1/√2 cos A − 1/√2 (1.5/r) = 1 / r
cos A − 1.5/r = √2 / r
cos A = (1.5 + √2) / r
Using SAS area of a triangle, the area of the large triangle is:
Area = ½ r² sin(2A)
Area = ½ r² (2 sin A cos A)
Area = r² sin A cos A
Area = (r sin A) (r cos A)
Area = (1.5) (1.5 + √2)
Area = 2.25 + 1.5√2
Similarly, the area of a small triangle is:
Area = ½ r² sin(2B)
Area = ½ r² (2 sin B cos B)
Area = r² sin B cos B
Area = (r sin B) (r cos B)
Area = (1) (1 + 1.5√2)
Area = 1 + 1.5√2
So the total area is:
Area = 4(2.25 + 1.5√2) + 4(1 + 1.5√2)
Area = 9 + 6√2 + 4 + 6√2
Area = 13 + 12√2
Related Questions
I need help please
Answers
Answer:
Its out of A and C srry couldn't help much
Identify the sampling method that was used. a local restaurant collects business cards in a bowl by the register. a free dinner is given to the person whose business card is drawn.
Answers
Correct answer is C. Based on the given information, the sampling method used in this scenario is simple random sampling.
Simple random sampling is a method where each member of the population has an equal chance of being selected. In this case, the business cards are collected in a bowl, and a free dinner is given to the person whose card is drawn. Since all the business cards are placed in the same bowl and there is an equal chance for any card to be drawn, this represents a simple random sampling approach.
Therefore, the correct answer is C. Based on the given information, the sampling method used in this scenario is simple random sampling.
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Complete question is below
Identify the sampling method that was used. A local restaurant collects business cards in a bowl by the register. A free dinner is given to the person whose business card is drawn.
Stratified
Systematic
Random
Cluster
A mixture of purple paint contains (6 teaspoons of red paint and (5 teaspoons of blue
paint. To make the same shade of purple paint using 35 teaspoons of blue paint, how
much red paint would you need? Use the double number line diagram to help if
needed.
Answers
If the 35 teaspoons of blue paint are there. Then for the purple paint, we need to add 42 teaspoons of red paint.
What are ratio and proportion?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two things are equal.
A mixture of purple paint contains 6 teaspoons of red paint and 5 teaspoons of blue paint.
To make the same shade of purple paint using 35 teaspoons of blue paint, then the amount of the red paint that you need will be
Let x be the amount of the red color needed.
Then we have
\(\rm \dfrac{x}{35} = \dfrac{6}{5}\\\\\\x \ \ = \dfrac{6 \times 35}{5}\\\\\\x \ \ = 6 \times 7\\\\\\x \ \ = 42 \ spoons\)
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Can anyone help out?
Answers
What is the missing length
Answers
Answer:
14
Step-by-step explanation:
Since the two 't' values are the same
we could just do:
\(\sqrt{196}\)
which is 14
Fill out the function table below f(x) = 3(2 – x) –2
Answers
The value of (x,y) on the given points of the function will be (-2,10),(-1,7),(0,4),(1,1), and (2,-2).
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
As per the given function,
f(x) = 3(2 – x) –2
Put x = -2
f(-2) = 3(2 + 2) - 2 = 10 thus, (-2,10)
Put x = -1
f(-1) = 3(2 + 1) - 2 = 7 thus, (-1,7)
Put x = 0
f(0) = 3(2 - 0) - 2 = 4 thus, (0,4)
Put x = 1
f(1) = 3(2 - 1) - 2 = 1 thus, (1,1)
Put x = 2
f(2) = 3(2 - 2) - 2 = -2 thus, (2,-2)
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Let f(x)=4x2 6. The function g(x) is f(x) translated 4 units down. What is the equation for g(x) in simplest from? Enter your answer by filling in the box. G(x) =.
Answers
The G(x) is the new function of the f(x) which is translated 4 units down is 4x²+2.
What is Function?A function assigns the value of each element of one set to the other specific element of another set.
The given function can be transformed from the initial position of the new position by subtracting the 4 from the initial function.
We know that in the initial function y=4x²+6, y is the output, while x is the input for the function f(x).
As the G(x) is the new function of the f(x) which is translated 4 units down. therefore,
\(G(x) = f(x)-4\\\\G(x) = 4x^2+6-4\\\\G(x) =4x^2+2\)
hence, the G(x) is the new function of the f(x) which is translated 4 units down is 4x²+2.
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14. Suppose that 1 out of every 10,000 doctors in a certain region is infected with the SARS virus; in the same region, 20 out of every 100 people in a particular at-risk population also are infected with the virus. A test for the virus gives a positive result in 99% of those who are infected and in 1% of those who are not infected. A randomly selected doctor and a randomly selected person in the at-risk population in this region both test positive for the disease. Who is more likely to actually have the disease?
Answers
Answer:
The person in the at-risk population is much more likely to actually have the disease
Step-by-step explanation:
The probability of a randomly selected doctor having the disease is 1 in 1,000 (P(I)=0.0001).
The probability that a doctor is infected with SARS, given that they tested positive is:
\(P(I|+)=\frac{P(I)*0.99}{P(I)*0.99+(1-P(I))*0.01}\\P(I|+)=\frac{0.0001*0.99}{0.0001*0.99+(1-0.0001)*0.01}\\P(I|+)=9.9*10^{-3}\)
The probability of a randomly selected person from the at-risk population having the disease is 20 in 100 (P(I)=0.20).
The probability that a person in the at-risk population is infected with SARS, given that they tested positive is:
\(P(I|+)=\frac{P(I)*0.99}{P(I)*0.99+(1-P(I))*0.01}\\P(I|+)=\frac{0.2*0.99}{0.2*0.99+(1-0.2)*0.01}\\P(I|+)=0.962\)
Therefore, the person in the at-risk population is much more likely to actually have the disease
please help, no need to show work :))
Answers
Answer:
incenter
Step-by-step explanation:
It is the center of the circle that can be inscribed in the triangle, making the incenter equidistant from the three sides of the triangle.
Answer:
it creates the point of concurrency called the incenter
B.) incenter
under what circumstances will the chi-square test for goodness of fit produce a large value for chi-square?
Answers
The chi-square test for goodness of fit will produce a large value for chi-square under the circumstances where the observed frequencies significantly deviate from the expected frequencies based on the null hypothesis.
The chi-square test for goodness of fit is used to determine if there is a significant difference between the observed frequencies in a sample and the expected frequencies based on a specified distribution.
The test compares the observed frequencies in different categories or groups with the expected frequencies under the null hypothesis.
A large value for chi-square indicates a significant discrepancy between the observed and expected frequencies, suggesting that the null hypothesis is not supported.
This can occur in several circumstances.
First, if the sample size is large, even small differences between observed and expected frequencies can lead to a significant chi-square value.
Second, if there are substantial deviations between the observed and expected frequencies in one or more categories, the chi-square value will be large. This could indicate a lack of fit between the observed data and the expected distribution.
Additionally, if the assumptions of the chi-square test are violated, such as independence of observations or expected frequencies being sufficiently large, it can lead to inflated chi-square values.
These violations can distort the results and lead to a larger chi-square value.
In summary, the chi-square test for goodness of fit produces a large chi-square value when the observed frequencies significantly deviate from the expected frequencies, indicating a lack of fit between the observed data and the expected distribution.
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formula for volume of a pyramid with a triangular base
Answers
The formula for finding the volume of a pyramid with a triangular base is:
V = (1/3) * A * h
Where:
V represents the volume of the pyramid,
A represents the area of the triangular base, and
h represents the height of the pyramid.
To find the volume, we multiply the area of the triangular base by the height and then divide the result by 3.
To calculate the area of the triangular base (A), you can use different formulas depending on the available information about the triangle. Here are a few common scenarios:
1. If you know the base and height of the triangular base:
A = (1/2) * base * height
2. If you know the lengths of all three sides (a, b, c) of the triangular base:
You can use Heron's formula to find the area:
\(A = \sqrt{(s * (s - a) * (s - b) * (s - c))\)
where s represents the semiperimeter of the triangle, given by s = (a + b + c)/2.
Once you have determined the area of the triangular base, you can substitute it into the volume formula along with the height of the pyramid to calculate the volume.
It's important to ensure that the base and height measurements are in the same unit of measurement for accurate calculations. Remember that the resulting volume will be expressed in cubic units, corresponding to the unit of length used for the base and height.
By using the formula V = (1/3) * A * h, you can calculate the volume of a pyramid with a triangular base, provided you have the necessary measurements.
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a box of donuts containing 2 maple bars, 6 chocolate donuts, and 4 custard filled donuts is sitting on a counter in a work office. kelsi comes along and decides to eat two in a row. what is the probability that kelsi will eat a custard filled donut and then a chocolate donut? round your answer to 4 decimal places.
Answers
The probability that Kelsi will eat a custard filled donut and then a chocolate donut is approximately 0.1455.
How calculate the probability of Kelsi eating a custard filled donut?To calculate the probability of Kelsi eating a custard filled donut and then a chocolate donut, we need to use the concept of conditional probability.
The probability of Kelsi eating a custard filled donut first is 4/12 (since there are 4 custard filled donuts out of a total of 12 donuts).
After Kelsi eats a custard filled donut, there are only 11 donuts left, and 6 of them are chocolate donuts. So the probability of Kelsi eating a chocolate donut second, given that she already ate a custard filled donut, is 6/11.
To find the probability of both events happening together (Kelsi eating a custard filled donut first and a chocolate donut second), we multiply the probabilities:
P(custard first and chocolate second) = P(custard first) * P(chocolate second | custard first)
P(custard first and chocolate second) = (4/12) * (6/11)
P(custard first and chocolate second) = 0.1455
Rounding to 4 decimal places, we get:
P(custard first and chocolate second) ≈ 0.1455
Therefore, the probability that Kelsi will eat a custard filled donut and then a chocolate donut is approximately 0.1455.
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Is -8/4 rational or irrational? please help need this for tmr!
Answers
Answer:
its rational!
Step-by-step explanation:
suppose that for budget planning purposes the city in exercise 12 needs a better estimate of the mean daily income from parking fees. a) someone suggests that the city use its data to create a 95% confidence interval instead of the 90% interval first created. how would this interval be better for the city?
Answers
A 95% confidence interval is wider than a 90% confidence interval and so provides a better estimate of the population mean.
A confidence interval represents the range of values within which the population mean is estimated to lie with a certain degree of confidence. The wider the interval, the more certain we can be that the population mean lies within it. In other words, a 95% confidence interval provides a better estimate of the population mean than a 90% interval because it is wider and therefore more likely to contain the true population mean.
This increased accuracy is particularly important for the city in their budget planning as it allows them to make more informed decisions based on a more reliable estimate of their expected daily income from parking fees.
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Solve the equation for w.
w divided by 4.4 minus 2.8 equals 11.5
62.92
38.28
3.25
1.97
Answers
Answer:
62.92
Step-by-step explanation:
Liz earns a salary of $2,300 per month, plus a commission of 3% of her sales. She wants to earn at least $2,500 this month. Enter an inequality to find amounts of sales that will meet her goal. Identify what your variable represents. Enter the commission rate as a decimal.
Answers
Answer:
she needs 200 more$
Step-by-step explanation:
Harry fills up his Jeep with gasoline and notes that the odometer reading is 23,408.1 miles. The next time he fills up his Jeep, he pays for 15.5 gallons of gasoline. He notes his odometer reading is 23,684 miles. How many miles per gallon did he get? (Round the answer to the nearest tenth, if necessary.)
Answers
First let's find how many kilometers the jeep traveled, by subtracting the odometer readings:
\(23684-23408.1=275.9\)Now, to find the miles per gallon, we just need to divide the kilometers by the amount of gallons of gasoline:
\(\frac{275.9}{15.5}=17.8\)So Harry got 17.8 miles per gallon with the Jeep.
Use the Extension of the Power Rule to Explore Tangent Lines Question Find the equation of the tangent line to the graph of the function f(x)-91/3+5 at z 27. Give your equation in slope-intercept form y- mz + b. Use improper fractions for m or b if necessary.
Answers
The equation of the tangent line to the graph of f(x) at x = 27 is y = (1/3)x + 23 in slope-intercept form.
To find the equation of the tangent line to the graph of the function f(x) = \(9x^{1/3} + 5\) at x = 27, we need to determine the slope of the tangent line and the y-intercept.
First, let's find the derivative of the function f(x) using the power rule. The power rule states that if \(f(x) = cx^n\), then \(f'(x) = cnx^{(n-1)}\)
For (x) = \(9x^{1/3} + 5\) , the derivative f'(x) is given by:
\($f'(x) = \frac{1}{3} \cdot 9 \cdot x^{-\frac{2}{3}} = 3x^{-\frac{2}{3}}$\)
Next, we evaluate f'(x) at x = 27 to find the slope of the tangent line:
\($m = f'(27) = 3 \cdot 27^{-\frac{2}{3}} = \frac{3}{27^{\frac{2}{3}}}$\).
To simplify the expression, we can rewrite \(27^{(2/3)}\) as \((3^{3})^{(2/3)}\), which equals \(3^2 = 9\):
m = 3/9 = 1/3
Now that we have the slope of the tangent line, we can determine the y-intercept. Since the line passes through the point (27, f(27)), we substitute x = 27 into the original function:
f(27) = \(9(27)^{(1/3)}\) + 5 = 9 × 3 + 5 = 27 + 5 = 32.
Therefore, the point on the tangent line is (27, 32).
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is a point on the line, we can substitute the values we found:
y - 32 = (1/3)(x - 27).
To write the equation in slope-intercept form y = mx + b, we simplify the equation:
y - 32 = (1/3)x - 9.
Finally, adding 32 to both sides, we obtain:
y = (1/3)x + 23.
Therefore, the equation of the tangent line to the graph of f(x) at x = 27 is y = (1/3)x + 23 in slope-intercept form.
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An office manager orders reams of office paper according to the price diagram. Write an equation that describes the proportional relationship between r, the number of reams purchased, and c, the total cost. Diagram of reams of paper purchased; 4 reams correspond with 11.88 dollars and 6 reams correspond with 17.82 dollars.
Answers
By solving linear equation we get total cost C = 2.97 r
Where r is a number of reams and C is the total cost.
What is a linear equation?A linear equation in one variable is one that is written in the form ax + b = 0, where a, and b are real numbers and the coefficients of x and constant, i.e. a and b, are not equal to zero.
Given:
Writing on linear equations that represent the proportional relationships
y = mx
Where y = total cost
m = unit cost
x = number of reams
So as per the question linear equation will be,
For 4 reams = 11.88
So, 1 ream = 11.88/4
= 2.97
Similarly for 6 reams = 17.82
So, 1 ream = 17.82/ 6
= 2.97
By solving linear equation we get total cost C = 2.97 r
Where r is the number of reams and C is the total cost.
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What is the solution to this system of equations?
( __ , __ )
Answers
Answer:
x = 5
y = 3
(5,3)
Step-by-step explanation:
use substitution...
4x -3(2x-7) = 11
-2x + 21 = 11
x = 5
y = 3
Is the following expression greater than, less than, or equal to zero? (a^2+b^2)/(a^2+b^2+1)
Answers
Answer:
the answer is Equal to zero
Step-by-step explanation:
hope it's help correct me if I'm wrong <3
Answer:
≥0
Step-by-step explanation:
This one may seem tricky. The denominator is ALWAYS one more than the numerator. So, let's take a look at some examples.
-2/-1
This is >0. And even if you keep going to a number as high as -10000/-9999, it will ALWAYS be >0.
0/1
Hmm...this one is equal to 0. Seems like we have ≥0 right now.
2/3
>0, right? Well, since we have expression ≥0, that's your answer!
Hope it helps!
Which expression is equivalent to -66.1 - (-55.6)?
Answers
Answer:
subtracting a negititive is the same as adding so -66.1+55.6
Hope This Helps!!!
The following regression was obtained by a real estate broker for a certain neighborhood predicting the price of a house in 1000's) based on age, squared footage (in 100's) and whether the house has or does not have a pool:Y^= 100-0.5(age)+10(square footage)+30 (pool).Explain the coefficient of age of the house:Group of answer choicesA. For an additional year of age, price of the house will decrease by 5000 dollars on average holding squared footage and pool constant.B. For an additional year of age, price of the house will decrease by 500 dollars on average holding squared footage and pool constant.C. For an additional year of age, price of the house will increase by 5000 dollars on average holding squared footage and pool constant.D. For an additional year of age, price of the house will increase by 5000 dollars holding squared footage and pool constant.
Answers
B. For an additional year of age, price of the house will decrease by 500 dollars on average holding squared footage and pool constant. is the answer.
What is regression equation?This equation helps to predict the value of the dependent variable based on the values of the independent variables.
This is because the coefficient of age of the house group is -0.5.
This means that for an additional year of age, the predicted price of the house will decrease by
0.5*1000 = 500 dollars on average,
holding squared footage and pool constant.
This is because the coefficient of age in the regression equation is negative, indicating that as the age of the house increases, the predicted price of the house decreases.
Thus, for an additional year of age, the price of the house will decrease by 500 dollars on average holding squared footage and pool constant.
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Which of the following analytic techniques covered so far in class is an essential part of the weighted ranking method?
A. Pairwise Ranking
B. Eight Elements of Thought
C.Ratio Method
Answers
Answer:
A. Ratio MethodRatio Method means that ICE Futures Europe will determine and disclose the adjustment ratio if known or the equation necessary to calculate the ratio. The adjustment ratio will be rounded, using normal mathematical rounding conventions, to five decimal places.
A) Pairwise ranking is an essential part of the weighted ranking method.
Pairwise ranking is one of the analytic techniques covered so far in class that is an essential part of the weighted ranking method.
Pairwise ranking, also known as pairwise comparison, is a process for comparing different options. Each option is compared to every other option to determine which one is better.
This is done by considering two options at a time and evaluating which one is preferred over the other, and then assigning a value to each option based on how many times it was chosen over the others.
The weighted ranking method, also known as the analytic hierarchy process (AHP), is a decision-making method that involves breaking down a complex problem into smaller, more manageable pieces, prioritizing them, and then making a decision based on the priorities.
Pairwise ranking is an essential part of this process because it helps to determine the relative importance of each option and thus how much weight should be given to each option in the final decision.
Hence, Pairwise Ranking is an essential part of the weighted ranking method.
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SOMEONE HELP ASAP PLEASE
Answers
Answer:3/4
Step-by-step explanation:
in 5-8, find each reciprocal. 5/9 8 7/3 1/12
Answers
the answer
155
324
5/9 (87/3(1/12)= 155/324
5n+6-9n=3-(4n+6) I need help lol
Answers
Answer:
No solution
Step-by-step explanation:
5n + 6 - 9n = 3-(4n+6)
5n + 6 - 9n = 3 + 4n - 6
5n + 4n - 9n = 3 - 6 - 6
0 = -9
Answer:
5n+6-9n=3-(4n+6)
Step-by-step explanation:
;]
simplify this problem\( \frac{9x}{4x - 4} + \frac{ {x}^{2} + 6x }{ {x}^{2} + 5x - 6} \)
Answers
1. Factor the denominators as follow:
\(\begin{gathered} 4x-4=4(x-1) \\ \\ \\ x^2+5x-6 \\ =x^2+6x-x-6 \\ =x(x+6)-(x+6) \\ =(x-1)(x+6) \\ \\ \\ \\ \\ \frac{9x}{4(x-1)}+\frac{x^2-6x}{(x-1)(x+6)} \end{gathered}\)2. Write the expresion with the less common denominator:
Multiply the first fraction by (x+6) (both parts, numerator and denominator):
\(\frac{9x}{4(x-1)}\cdot\frac{x+6}{x+6}=\frac{9x(x+6)}{4(x-1)(x+6)}\)Multiply the second fraction by 4 (both parts, numerator and denominator):
\(\frac{x^2-6x}{(x-1)(x+6)}\cdot\frac{4}{4}=\frac{4(x^2-6x)}{4(x-1)(x+6)}\)Rewrite the expression with the less common denominator:
\(\begin{gathered} \frac{9x(x+6)}{4(x-1)(x+6)}+\frac{4(x^2-6x)}{4(x-1)(x+6)} \\ \\ =\frac{9x(x+6)+4(x^2-6x)}{4(x-1)(x+6)} \end{gathered}\)3. Remove parentheses and simplify:
\(\begin{gathered} \frac{9x^2^{}+54x+4x^2-24x}{(4x-4)(x+6)} \\ \\ =\frac{13x^2+30x}{4x^2+24x-4x-24} \\ \\ =\frac{13x^2+30x}{4x^2+20x-24} \end{gathered}\)Then, the given expression simplified is:\(\frac{9x}{4x-4}+\frac{x^2-6x}{x^2+5x-6}=\frac{13x^2+30x}{4x^2+20x-24}\)![simplify this problem[tex] \frac{9x}{4x - 4} + \frac{ {x}^{2} + 6x }{ {x}^{2} + 5x - 6} [/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/3FEf63pRqLXeuugCPzvxJcejYts4in3X.png)
-4j-1-5j+6= pls help me
Answers
Hello
Answer:
-9j+5
Step-by-step explanation:
=-4j-1-5j+6
=-4j-5j+6-1
=-9j+5
Find the first four nonzero terms in a power series expansion about x0 for a general solution to the given differential equation. 0
Answers
Answer:
Start with equation,
y''(x) = f(x) = 6y/(10x-x²) about point x₀ = 5
Then,
y(x) = a₀ + a₁(x-5) + a₂(x-5)²+ a₃(x-5)³ + a₄(x-5)⁴...….
by inspection,
y(5) = a₀ and y'(5) = a₁
then,
y''(5) = 6a₀/(50-25) = 6a₀/25
y'''(x) = 6y'/(10x-x2) - 6y(10-2x)/(10x-x2)2
then,
y'''(5) = 6a₁/25 - 0 = 6a₁/25
y''''(x) = 6y''/(10x-x2) -12y'(10-2x)/(10x-x2)² + 12y/(10x-x2)² + 12y(10-2x)2/(10x-x2)³
then,
y''''(5) = (6/25)(6a₀/25) + 0 + 12a₀/625 + 0
= 48a₀/625
So,
y(x) = f(x) = f(5) + f'(5)(x-5) + f''(5)(x-5)2/2! + f'''(5)(x-5)3/3! + f''''(5)(x-5)4/4! …
or
y(x) = f(x) = a₀ + a₁(x-5) + (6ao/25)(x-5)2/2! + (6a1/25)(x-5)3/3! + (48a₀/625)(x-5)4/4!...
or
y(x) = f(x) = a₀ + a₁(x-5) + (3a₀/25)(x-5)²+ (a₁/25)(x-5)³+ (2a₀/625)(x-5)⁴.....
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