O is the center of the regular octagon below. Find its area. Round to the nearest tenth
if necessary.
Answers
The following solution is arrived at by using the formula for the area of a regular octagon in relation to its Apotem which in this case is 18. Hence the area of the Octagon given is 1,446.
What is an Apothem?An apothem is defined as a line from the center of a regular polygon at right angles to any of its sides.
What is the area of a Regular Octagon?The calculation for this shape using only it's apothem has some curved bends. In order to derive the area, we have to divide the octagon into triangles.
When we find the area of the triangles we can then multiply by the total number to get the area of the Octagon.
Hence we can say that the area of the Octagon (A) = (1/2b*h)n
Where b = base
h = height
n = number of triangles.
Recall that the total angle in a circle is 360°, hence given that all the triangles are equal, we must divide 360° by 8 triangles to get the angle in the vertex of each triangle.
Thus, 360°/8 = 45°
So we have The angle of our triangle which is opposite the base.
Recall that the triangle is split in two so that each of the triangles are right-angled triangle,
Hence, the angle opposite the base for each right angle triangle is given as:
45°/2 = 22.5°
So to get the length of the opposite side (x), we use the law of tangents:
Which means:
x = 18 Tan 22.5°
= 18 * 0.55785173935
≈ 10.04
So if x is ≈ 10.04, then area of that triangle is
= 1/2 * 10.04 * 18 (that is 1/2bh)
= 90.3792
From the above, we can state that the Area of the triangle with the Apothem is
= 90.3792 * 2
= 180.74
Recall our formula for finding the area of the octagon:
A = (1/2bh)n
A = (108.74) *8
A = 1,445.95
≈ 1,446
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Related Questions
Solve the picture for n
Answers
The two angles shown are vertical angles which men they equal each other:
9n = 8n + 8
Subtract 8n from both sides:
N = 8
->Solution
i) 9n = 8n+8 [ V.O.A. vertically opposite angles ]
or, 9n - 8n = 8
or, n = 8
therefore, value of n is 8
Now,
ii) 9n = 9 X n = 9 X 8 = 72 degrees
iii) 8n + 8 = 8 X 8 + 8 = 64 + 8 = 72 degrees
for the following question, true or false.
Answers
Answer:
False
Step-by-step explanation:
You can't add without first doing the terms of 2^3---(PENDAS)
Enter the correct answer in the box. Write your answer in the form y = mx + b, using the appropriate inequality symbol in place of the equal sign.
What inequality is shown in the graph?
Answers
Answer:
y ≥ -x - 4
Step-by-step explanation:
[tex]\sf let (x_1,y_1)=(-4,0)\\\\let (x_2,y_2)=(0,-4)[/tex]
[tex]\sf slope \ (m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-0}{0-(-4)}=-1[/tex]
Slope-point form of linear equation:
[tex]\sf \implies y-y_1=m(x-x_1)[/tex]
[tex]\sf \implies y-0=-1(x-(-4))[/tex]
[tex]\sf \implies y=-x-4[/tex]
For ≤ or ≥ graph a solid line
For < or > graph a dashed line
For shading above the line: y ≥ or y >
For shading below the line: y ≤ or y <
Therefore, as the line is solid and shading is above the line:
[tex]\sf y\geq -x-4[/tex]
Answer: y ≥ -x - 4
Step-by-step explanation:
helpppppp meeeee pleaseeeeeeeee thanksssssss :)))))))
Answers
Answer:
815.76 is your answer
Step-by-step explanation:
The area of a rectangle is 5 x cubed + 19 x squared + 6 x minus 18 with length x + 3. using synthetic division, what is the width of the rectangle?
5 x squared + 4 x minus 6
5 x squared + 34 x + 108 + startfraction 306 over x + 3 endfraction
5 x cubed + 4 x squared minus 6 x
5 x squared + 34 x + 108 + startfraction 306 over x minus 3 endfraction
Answers
A rectangle is a 2-dimensional shape having 4 sides. The width of the rectangle is 5x^2 + 4x - 6
How to find the quotient of a function using synthetic division?A rectangle is a 2-dimensional shape having 4 sides
The formula for calculating the area of the rectangle is given as:
A = lw
Given the following
Area = 5x^3+19x^2+6x-18
Length = x + 3
Using the synthetic division:
5x^2 + 4x - 6
x + 3 | 5x^3+19x^2+6x-18
5x^3 + 15x^2
________________________
4x^2 + 6x
4x^2 + 12x
__________________________
-6x - 18
-6x - 18
Hence the width of the rectangle is 5x^2 + 4x - 6
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Answer:
A
Step-by-step explanation:
When planning space exploration, scientists face many
challenges. One issue is the weight of the items being
transported. They can use the engineering design process
to help minimize the weight of materials on board a
spacecraft.
The engineering design process starts with a statement of the problem to be
solved. Which sentence best states the problem described above?
O A. Metal is stronger than plastic, but it is also much heavier.
OB. Space vessels must carry heavy equipment but also minimize
weight.
O C. The longer a space flight will last, the more equipment must be
carried
D. Lower gravity on the Moon means that objects weigh less on the
Moon than on Earth.
Answers
Answer: Space vessels must carry heavy equipment but also minimize weight.
Step-by-step explanation:
i got it right on a p e x
Une bouteille cylindrique de 12 cm de hauteur a une capacité de 1 L quel est le rayon de sa base
Answers
Answer:
≈5.15 [cm].
Step-by-step explanation (English version):
1) Capacity - V - 1000 cm³;
height - h - 12 cm;
radius - r - ?
2) the initial formula is:
V=π*r²*h, where π=3.1415;
then final formula of the required r is:
[tex]r=\sqrt{\frac{V}{\pi *h}};[/tex]
3) [tex]r=\sqrt{\frac{1000}{3.1415*12}} =\sqrt{26.5266} =5.15[cm].[/tex]
The pressure on a scuba diver at sea level is 14.7 pounds per square inch (psi). The pressure increases 0.445 psi for each foot of depth. Suppose the pressure on a diver is 41.4 psi. How deep is she?
Answers
Answer:
14.7÷41.4=0.355
the answer is 0.355
9. Determine if x + 1 is a factor of x ^ 4 - 4x ^ 2 - 4x - 1 Justify your answer.
Answers
Answer:
No
Step-by-step explanation:
x + 1 is not a factor of the polynomial because the remainder is 2 and not 0
Ms. Pearson kept track of student absences versus final average grades in her math dass for one semester, The
data is shown in the table below
Answers
The correct statement about the data collected by Ms. Pearson is that there is no association between a student's absences and the final average grades.
When do variables have a linear relationship?The equation that represents a linear relationship is: a + bx
Where x represents the rate of increase. Thus, for linear equations, the functiion increases by a constant term.
Looking at the table, the average final grade does not increase by a constant term.
To learn more about linear functions, please check: https://brainly.com/question/26434260
6+8 divided by 2 simplify the expression
Answers
Answer:
6+8 is 14 and 14/2 is 7.
Step-by-step explanation:
the answer is 7
14/2
7
The answer is 7
59+55+854+456+456+7894
Answers
Answer :
59+55+854+456+456+7894=9,774
7/6 x 4/5 = in simplest form
Answers
Answer:
heyy do you still need help
Step-by-step explanation:
Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value tα/2, (b) find the critical value zα/2, or (c) state that neither the normal distribution nor the t distribution applies.
The confidence level is 99%, σ is not known, and the histogram of 56 player salaries (in thousands of dollars) of football players on a team is as shown.
Answers
Considering that we have the standard deviation for the sample, the t-distribution will be used, and the critical value is t = 2.6682.
When should the t-distribution and the z-distribution be used?If we have the standard deviation for the sample, the t-distribution should be used.If we have the standard deviation for the population, the z-distribution should be used.In this problem, σ is not known, hence we get the standard deviation of the sample from the histogram and the t-distribution is used.
Using a t-distribution calculator, considering a confidence level of 99% and 56 - 1 = 55 df, the critical value is t = 2.6682.
More can be learned about the t-distribution at https://brainly.com/question/16162795
I need answers NOW!
BRAINLIEST FOR WHO CAN ANSWER!
Answers
Write an equation in slope intercept for for the like with slope -3/5 and
y-intercept -3
Answers
Answer:
An equation for the slope and y-intercept would be y=-3/5x-3
Step-by-step explanation:
Remember the formula for this, y=mx+b, in which the m stands for the slope and the x would be next to the slope always because the slope is ever changing, and the b stands for the y-intercept or in other words, where the line crosses the y-axis not the x-axis.
Answer:
y = -3/5x - 3
Explanation:
The format of slope-intercept is:
[tex]\sf{y = mx + b}[/tex]
Where:
m = slopeb = y-interceptSo to write the equation, I just plug the data into y = mx + b:
[tex]\sf{y=-\dfrac{3}{5}x+(-3)}\\\\\sf{y=-\dfrac{3}{5}x-3}[/tex]
Hence, the equation is y = -3/5x - 3.
select exponential growth or decay for each function:
PLEASE HELP, 24 BRAINLY POINTS REWARD
Answers
Answer:
1. growth
2. decay
3. growth
4. decay
Answer:
Step-by-step explanation:
Growth: anything in the parenthesis that is greater than 100% or 1 | > 1
Decay: anything in the parenthesis that is less than 100% or 1 | < 1
(1 + r) = growth
(1 - r) = decay
r = rate of growth
[tex]f(x)=485(1.98)^t < ==|(1+0.98=1.98)| > 1= > growth\\[/tex]
[tex]f(x)=\frac{1}{4}(0.18)^t < ==|(1-0.82=0.18)| < 1= > decay[/tex]
[tex]f(x)=46(1.001)^t < ==|(1+0.001=1.001)| > 1= > growth[/tex]
[tex]f(x)=0.08(0.34)^t < ==|(1-0.66=0.34)| < 1= > decay\\[/tex]
Hope this helps!
Dogs lap water to drink it. Every 3 minutes a dog laps water, it gets 30 ounces. If a dog needs 155 ounces per day, predict how many minutes the dog will lap water.
Answers
Answer:
15 minutes and 51 seconds
Step-by-step explanation:
155/30 = 5.17
5.17 x 3 = 15.51
It will take the dog approximately 15.5 minutes to lap enough water to consume 155 ounces.
Here, we have to predict how many minutes a dog will lap water to consume 155 ounces per day, we can set up a proportion based on the given information:
1 dog laps water every 3 minutes and gets 30 ounces.
Therefore, in 1 minute, a dog laps 30/3 = 10 ounces.
Now, we want to find out how many minutes it takes for the dog to consume 155 ounces:
Let x be the number of minutes the dog laps water to consume 155 ounces.
Proportion:
(Ounces lapped in x minutes) / (Ounces lapped in 1 minute) = (Total ounces needed) / (Ounces lapped in 1 minute)
(10x) / 10 = 155 / 1
Simplify the equation:
10x = 155
Now, solve for x:
x = 155 / 10
x = 15.5
So, it will take the dog approximately 15.5 minutes to lap enough water to consume 155 ounces.
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What is the reason for statement 3 in the proof below?
Given: ABCD is a parallelogram
Prove:
Answers
Answer: Alternate interior angles theorem
Step-by-step explanation:
Which rule dilates a figure in the coordinate plane by a scale factor of 5?
Answers
Dilation involves changing the size of a figure
The dilation rule of a figure in the coordinate plane by a scale factor of 5 is (b) (x,y) [tex]\to[/tex] (5x,5y)
How to determine the dilation rule?The scale factor (k) is given as:
k = 5
Assume the coordinates of the figure is (x,y)
The dilation rule would be:
(x,y) [tex]\to[/tex] k(x,y)
Substitute 5 for k
(x,y) [tex]\to[/tex] 5(x,y)
Expand
(x,y) [tex]\to[/tex] (5x,5y)
Hence, the dilation rule is (b) (x,y) [tex]\to[/tex] (5x,5y)
Read more about dilation at:
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If the coordinate plane is dilated by a scale factor of 5, hence the resulting coordinate of the preimage will be (5x, 5y)
Dilation of coordinateDilation is a transformation technique that changes the size and shape of an object in an xy plane
If the coordinate point (x, y) is dilated by a factor of "k", the resulting coordinate of the preimage will be (kx, ky)
If the coordinate plane is dilated by a scale factor of 5, hence the resulting coordinate of the preimage will be (5x, 5y)
Learn more on dilation here: https://brainly.com/question/10253650
Please help!!!!!!!!!!!!!!!!1
Answers
Answer:
The correct answer is C: [tex]t\leq 58[/tex]
Step-by-step explanation:
In order to solve this problem, start by first creating an inequality to represent the situation above. The price of the hours and the supply fee can't go over $1,500, so you can set the representative inequality as [tex]25t+50\leq 1500[/tex]. Now solve the inequality, and you will get [tex]25t+50\leq 1500[/tex] => [tex]25t\leq 1450[/tex] => [tex]t\leq 58[/tex] hrs. So C is the correct answer.
Answer:
The answer is C.t is less than or equal to 58.
Step-by-step explanation:
Let x = Number of tutoring sessions
Supplies + tutoring cost = total cost
50 + 25x = 1500
Now need to solve:
Subtract 50 from both sides and simplify
50/ + 25x - 50 = 1500 - 50
25x = 1450
Divide both sides by 25 and simplify
25x/25 = 1450/25
Therefore,
[tex]x\leq 58[/tex]
The 25th term of an arithmetic series is 44.5
The sum of the first 30 terms of this arithmetic series is 765
Find the 16th term of the arithmetic series.
Show your working clearly.
Answers
Answer:
[tex]a_{16}=26.5[/tex]
Step-by-step explanation:
Arithmetic series: [tex]a_n=a+(n-1)d[/tex]
Sum of arithmetic series: [tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
(where a is the first term and d is the common difference)
Given:
[tex]a_{25}=44.5[/tex][tex]S_{30}=765[/tex][tex]\implies a_{25}=44.5[/tex]
[tex]\implies a+(25-1)d=44.5[/tex]
[tex]\implies a+24d=44.5[/tex]
[tex]\implies S_{30}=765[/tex]
[tex]\implies \dfrac{30}{2}[2a+(30-1)d]=765[/tex]
[tex]\implies 30a+435d=765[/tex]
Rewrite [tex]a+24d=44.5[/tex] to make a the subject:
[tex]\implies a=44.5-24d[/tex]
Substitute found expression for a into [tex]30a+435d=765[/tex] and solve for d:
[tex]\implies 30(44.5-24d)+435d=765[/tex]
[tex]\implies 1335-285d=765[/tex]
[tex]\implies 285d=570[/tex]
[tex]\implies d=2[/tex]
Substitute found value of d into [tex]a=44.5-24d[/tex] and solve for a:
[tex]\implies a=44.5-24(2)=-3.5[/tex]
Therefore:
[tex]\implies a_{16}=-3.5+(16-1)2=26.5[/tex]
what type of line is this
Answers
~Denki Kaminari here~
Answer:
its a best fit line
Step-by-step explanation:
because it is in-between the blue and yellow points, that is what i assume the answer is.
hope this helps :D
Answer:
oblique line.
Step-by-step explanation:
hops this helps
Factor using the greatest common factor
25n ² - 5n
32n ² + 28n - 20
Answers
Answer:
this is my answer
5n (5n - 1)
4n (8 + 7) - 20
You deposit 2,000$ in a savings account earning 5% simple interest. How long will it take for ythe balance of the account to be 3,800$
Answers
Answer:
1 year and a half or 18 months
Step-by-step explanation:
If ABCD is dilated by a factor of 1/2, the coordinate of D' would be:
Answers
Answer:
D'=(1,-1)
Step-by-step explanation:
If you dialate by 1/2 then all you have to do, is find half of point D. so point D sits at (2,-2) and half of 2 would be (1,-1).
The dilated coordinates of D(2,-2) = D'(1,-1).
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.
From the graph,
we interpreted the coordinates of D (2,-2).
Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.
To find the dilation of transformation
The basic formula to find the scale factor of a dilated figure is:
Scale factor = coordinates of the new shape ÷ coordinates of the original shape.
That means,
multiply the factor to the coordinates.
D' = (2 x 1/2, -2 x 1/2)
D' = (1, -1)
Therefore, the coordinates after the dilation D' (1,-1).
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Can anyone help me on this?
Answers
Answer:
Out of the two sums, B is the closest to the value to 1/2.
Steps for A:
Change 1/3 to 5/15
2+5/15
= 7/15
7/15 as a decimal: 0.46
0.50 - 0.46 = 0.04
Steps for B:
Change 6/7 to 18/21
Change 1/3 to 7/21
18-7/21
= 11/21
11/21 as a decimal: 0.52
0.52 - 0.50 = 0.02
help me with this question please
Answers
Answer:
I'm sorry I don't know wish I could help you out
Helppp plssssss!!!!!!
Answers
Because the triangle DEF only corresponds in triangle XYZ so it means that EDF will only correspond in YXZ.
PLSS I NEED HELP!!
1). To make a full rotation, 59 days, 19 h, and 45 min goes by for Mercury. It only takes Earth 1 day! How many hours does it take Mercury to complete a full rotation? Show your work using the correct conversion factors.
2). Some plants grow quickly. An invasive weed species can grow quickly. One variety grows up to 0.89 ft per day. How fast in inches per hour can this weed grow? Show your work using the correct conversion factors.
3). David’s watch broke. He decides to get it fixed instead of replacing it. The total cost to repair the watch can be represented by 0.07(45h) + 45h, where h represents the number of hours it takes to repair the watch.
a). What part of the expression represents the cost of the repair before tax?
b) Explain what your answer in Part A means in the context of the problem.
Answers
1) It takes 1435.75 hours for Mercury to complete a full rotation.
2) The weed can grow at 0.445 inches per hour.
Time calculation1) Given that to make a full rotation, 59 days, 19 h, and 45 min goes by for Mercury, to determine how many hours does it take Mercury to complete a full rotation, the following calculation must be performed:
59 x 24 + 19 + 0.75 = X1416 + 19.75 = X1435.75 = X2) Given that a plant grows up to 0.89 ft per day, to determine how fast in inches per hour can this weed grow, the following calculation must be performed:
0.89 / 24 = ft per hour0.037 = ft per hour1 ft = 12 inches0.037 x 12 = 0.445Learn more about time calculation in https://brainly.com/question/14695611
Answer:
1) It takes 1435.75 hours for Mercury to complete a full rotation.
2) The weed can grow at 0.445 inches per hour.
Step-by-step explanation: