Determine the measures of the apothem, the radius, and the perimeter of the regular octagon.
a. a = 14.4, r = 15.6, p = 96
b. a = 14.4, r = 15.6, p = 12
c. a = 15.6, r = 14.4, p = 96
d. a = 10, r = 15.6, p = 96
Answers
we know that
A) a regular Octagon has all its eight sides congruent
B) all the eight interior angles are also congruent
C) the measure of each angle = 135º
therefore
see the attached figure
∠ alfa=135°/2--------> 67.5°
AP=12/2---------> 6 units
cos (alfa)=AP/AO----------> AO=AP/cos (alfa)
AO=6/cos(67.5)---------> 15.68 units
the radius= distance AO----------> 15.68 units
radius=15.68 units
the apothem=distance OP
sin(alfa)=OP/AO---------> OP=sin(alfa)*AO
OP=sin(67.5°)*15.68-------> 14.49 units
the apothem=14.49 units
perimeter=12*8--------> 96 units
perimeter=96 units
the answers Part A), B) and C) are
apothem=14.49 units
radius=15.68 units
perimeter=96 units
therefore the option is the a.) a = 14.4, r = 15.6, p = 96
Answer:
a.) a = 14.4, r = 15.6, p = 96
Related Questions
ANSWER NOW PLEASE! EXTRA POINTS!
1) Martha is covering this trapezoid-shaped board with fabric. How many square feet of fabric does Martha need?
2) A garden in the shape of a regular hexagon has sides that are each 5 meters long. If the height of each of the congruent triangles within the hexagon is about 4.33 meters,what is the area of the garden?
Answers
2. About 64.95meters or technically 64.95191
hope this helps!! :)
In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 5 cm?
Enter your answer in the box.
Answers
10cm
Because (The 30-60-90 Triangle Theorem)
In a 30-60-90 triangle, the length of the hypotenuse is TWICE the length of the shorter leg.
Thanks Shellbag101
The length of the hypotenuse is 10cm
SOH CAH TOA identityGiven a 30-60-90 triangle where:
Length of the shorter leg = 5cm (adjacent)
The hypotenuse is what we need.
[tex]cos \theta = \frac{adj}{hyp} \\ [/tex]
Substitute the given parameters
[tex]cos 60 = \frac{5}{h}\\ h =\frac{5}{cos 60}\\ h = \frac{5}{0.5}\\ h = 10cm[/tex]
Hence the length of the hypotenuse is 10cm
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whats the answer to 8n−15=41
Answers
8*7=56
56-15=41
Hope this helped☺☺
+15 +15
8n=56 DIVIDE BY 8
/8 /8
n=7 FINAL ANSWER
What is the least common Multiple of 9 and 10? Use prime factorization to solve.
Answers
......................
The areas of two similar octagons are 112 in.² and 63 in.². What is the ratio (larger to smaller) of their perimeters?
16/3
4/9
16/9
4/3,
Answers
For the area:
A1 = (k ^ 2) * A2
For the perimeter
P1 = k * P2
Note: The factor k is the same in both cases
Where,
k = growth factor (k> 1) or reduction (k <1)
Substituting values we have:
12 = (k ^ 2) * 63
Let's clear k:
k = root (112/63)
k = 4/3
Answer:
The ratio (larger to smaller) of their perimeters is:
k = 4/3
k = growth factor (k> 1) or reduction (k <1)
Area1= (k ^ 2) * Area2Perimeter1 = k * Perimeter2
Substitute: 12 = (k ^ 2) * 63 k = sqaure root (112/63) k = 4/3
Explain why increasing the sample size tends to result in a smaller sampling error when a sample mean is used to estimate a population mean.
A. The above statement is incorrect, the sample size has no effect on the sampling error.
B. The larger the sample size, the more closely the possible values of \bar{x} cluster around the mean of \bar{x}
C. If the sample size is larger, the possible values of \bar{x} are farther from the mean of \bar{x},
Answers
Sampling error is inversely proportional to the sample size which means if the sample size increases the sampling error decreases. Then option B is correct.
What is sampling error?The amount of inaccuracy in the estimating value appears due to the smaller sample size.
The sample size tends to result in a smaller sampling error when a sample mean is used to estimate a population mean.
We know that the formula of the sampling error
[tex]\rm Sampling \ error = z \times \dfrac{\sigma}{\sqrt{n}}[/tex]
Sampling error is inversely proportional to the sample size which means if the sample size increases the sampling error decreases.
More about the sampling error link is given below.
https://brainly.com/question/15375591
Pls help.
Solve (6x^3-1x^2+1)/(2 x+1)
a. -3x^2+2x-1
b. 3x^2-2x+1
c. -3x^2+2x-1
d. 3x^2+2x-1,
Answers
PLEASE HELP ME ON THIS
BRAINLIEST AVAILABLE IF YOU ANSWER CORRECTLY
Answers
The ratios are, for Beverly:
1.0171.0321.0541.058
for Lowell
1.051.051.051.05
So obviously Beverly is not exponential and Lowell is.
prove this trigonometric equation;
- tan^2x + sec^2x = 1,
Answers
- tan²x + sec²x = 1 or 1 + tan²x = sec²x
sin²x + cos²x = 1
Divide the whole by cos²x
[tex] \frac{sin^2x}{cos^2x} + \frac{cos^2x}{cos^2x} = \frac{1}{cos^2x} [/tex]
[tex] \frac{sinx}{cosx} = tanx[/tex] so [tex] \frac{sin^2x}{cos^2x} = tan^2x[/tex]
and
[tex] \frac{1}{cosx} = secx [/tex] so [tex] \frac{1}{cos^2x} = sec^2x[/tex]
Therefore,
tan²x + 1 = sec²x
Take tan²x to the other side {You will have the same answer}
1 = - tan²x = sec²x or sec²x - tanx = 1
Which of the following expression expressions is equivalent to cos3x/sinxcosx?
A.) cscxcos2x-secxsin2x
B.) secxcos2x-cscxsin2x
C.) secxcosx-cscxsinx
D.) cscxcosx-secxsinx
Answers
Answer:
A.) cscxcos2x-secxsin2x
Step-by-step explanation:
I'm sorry I really do not know how to solve this but I just did the quiz and b was not correct.
Final answer:
To find an expression equivalent to cos3x/sinxcosx, we use trigonometric identities and simplification to arrive at cscx - secx. Option D, cscx cosx - secx sinx, when expanded and simplified, is equivalent to cscx - secx, thus it is the correct answer.
Explanation:
The question asks us to find an expression equivalent to cos3x/sinxcosx. To start, let's simplify the given expression using trigonometric identities.
We can write cos3x as cos(2x+x), which by using the angle addition formula for cosine gives us cos(2x+x) = cos2x cosx - sin2x sinx. Now our expression looks like this: (cos2x cosx - sin2x sinx) / (sinx cosx).
The next step is to split the numerator to have two separate fractions: cos2x/sinx - sin2x/cosx. We can then recognize that cos2x/sinx is equivalent to 1/sinx or cscx, and -sin2x/cosx is equivalent to -1/cosx or -secx. Therefore, the equivalent expression is cscx - secx.
Comparing this result to the options given, option D, cscx cosx - secx sinx, expands to 1/sinx × 1 - 1/cosx × sinx, which can be simplified to cscx - secx. Thus, option D is the correct answer.
Dyann takes a bus to work every day. On Monday the trip took 34 minutes. On Tuesday the trip took 36 minutes. On Wednesday the trip took 35 minutes. On Thursday the trip took 34 minutes. Dyann determines that the trip to work on Friday will take about 35 minutes.
Does her conclusion use inductive, or deductive reasoning?
Answers
Answer:
inductive reasoning
In this question, the conclusion is that the trip to work on Friday will take about 3535 minutes. This conclusion is based on observation of specific examples instead of scientific research.
Therefore, the type of reasoning used is inductive reasoning.
The sum of three consecutive odd integers is − 105 . find the numbers.
Answers
x+(x+2)+(x+2+2)=105
3x+2+2+2=105
3x+6=105
3x=99
x=33
so the answers would be 33, 35 and 37
Personal Finance is a dead group.
How does the availability of credit in a community affect the housing market there?
The availability of credit has no affect on the housing market.
The less credit available, the higher the cost of housing.
The availability of credit determines whether or not people put their homes up for sale.
The more credit available, the higher the cost of housing.,
Answers
What is the quotient of 78.3 ÷ 3.48?
Answers
Good luck with your work!
make w the subject of the formula y-aw=2w-1
Answers
Solution step by step:
1) given formula: y-aw=2w-1
2) transpose aw and - 1
2w + aw = y + 1
3) common factor w:
w (a + 2) = y + 1
4) divide both sides by (a + 2):
w = [ y + 1] / [a + 2]
To make w the subject of the formula y-aw=2w-1, rearrange the equation as follows: add aw to both sides, factor out w on the right side, add 1 to both sides, and then divide by (a+2). The final equation is w=(y+1)/(a+2).
Explanation:The question is asking to rearrange the given formula y-aw=2w-1 to solve for the variable w. We can follow these steps:
Add aw to both sides of the equation to eliminate it on the left side. This gives us y=aw+2w-1. Factor out w from the right side. This gives us y=w(a+2)-1. Add 1 to both sides of the equation to eliminate it on the right side. This gives us y+1=w(a+2). Divide both sides of the equation by (a+2) to isolate w. This gives us w=(y+1)/(a+2).
Therefore, in the formula y-aw=2w-1, w=(y+1)/(a+2) when solved for w.
Learn more about Rearranging Equations here:https://brainly.com/question/10945620
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Domain -1,4,5,3,-5 Range n,w,y,n,w is this a function
Answers
If you apply the vertical line test, none of the xs have 2 ys. It does not matter if 2 xs have the same y value.
Please help asap!!! 19 pts
Answers
How many triangles exist with the given angle measures? 32°, 51°, 97°
Answers
We need to check if these angles satisfy that condition:
32°+51°+97°=180°
They do satisfy. Now we check if any angle has value that is not possible.
32° and 51° angles are OK.
97° angle is also OK. It is obtuse angle.
For each angle measures exactly one triangle exists. In this example we have an obtuse-angle triangle.
The correct answer is 1.
To determine if a set of three angles can form a triangle, we need to check if the sum of the three angles is equal to 180°. If the sum is 180°, then the angles can form a triangle; otherwise, they cannot form a triangle.
Given angles: 32°, 51°, 97°
we can represent the calculation as follows:
[tex]\text{Sum of the given angles} &= 32^\circ + 51^\circ + 97^\circ&= 180^\circ[/tex]
Since the sum of the three given angles is equal to 180°, these angles can form a triangle.
To determine the number of triangles that exist with these angle measures, we need to consider the permutations of the angles. Since the order of the angles does not matter in a triangle, we have:
[tex]\text{Number of triangles} = \frac{3!}{3} = 1[/tex]
Therefore, there exists only one triangle with the given angle measures of 32°, 51°, and 97°.
40 POINTS! + BRAINLIEST
What is the measure in radians for the central angle of a circle whose radius is 6 cm and intercept arc length is 5.4 cm?
Make sure to show all calculations.
Answers
Answer:
6.5
Step-by-step explanation:
1. calculate using the equation
PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER
Answers
This circle graph shows the results of a survey that asked people to identify their favorite type of music.
What percent of people chose rock or country as their favorite type of music?
9%
35%
45%
55%
A circle graph with 5 sections. The first section is labeled Rock 27 percent. The second section is labeled Hip Hop 28 percent. The third section is labeled Jazz 19 percent. The fourth section is labeled Country 18 percent. The fifth section is labeled Other 14 percent.
Answers
Country or rock would be found by adding the two percentages:
18+27 = 45.
(Side note: the percentages on this circle graph add up to 106%....)
Answer: C) 45
Hope Thsi Helps ^_^
Which property justifies the following statement? If x=2,and y=3x-11, then y=3•2-11
Answers
Solve for x under the assumption that x > 0. Enter your answer in interval notation using grouping symbols.
x−24/x<10,
Answers
The solution for the set would be: x is (0,12).
What is the solution?
To arrive at the solution, we would first move the constant term to the right side as follows;
x - 24/x < 10
x < 10 + 24/x
We then multiply both sides by x to eliminate the fraction:
x² < 10x + 24
Collect all terms to one side;
x² - 10x - 24 < 0
Factorize
(x - 12)(x + 2) < 0
So, x - 12 is positive when x > 12 and negative when x < 12.
x + 2 is positive for all values of x > 0.
In Mr. Sheldon’s physical education class, each student plays at most 1 sport.
A total of 20 students play soccer or basketball.
Given that 1/3 of the students play soccer, and 8 play basketball, how many students in Mr. Sheldon’s class play neither soccer nor basketball?
I have no idea how to calculate. I will reward the right answer along with explanation of how it was figured. (I attached a pic of the multiple choices) Thanks!
Answers
Given that 1/3 of the students play soccer you can conclude that 1\3 is equal 12 student, then in class totally are 12*3=36 students.
36-20=16 students play neither soccer nor basketball
Answer: Correct choice is B.
Please help simple math problem
Answers
When 2 lines intersect, they make vertical angles.
Vertical angles are congruent (equal).
Vertical angles are opposite one another.Supplementary angles add up to 180º = 40 degrees + 140 degrees = 180 degrees. Adjacent and Supplementary Angles = 120 + 60 = 180 degreesAdjacent angles are “side by side” and share a common ray. 130 degrees and 50 degrees.Complementary angles add up to 90º. = 60 degrees + 30 degrees = 90 degrees.
The area of a rectangle is 54 m^2 , and the length of the rectangle is 3m more than twice the width. find the dimensions of the rectangle.
Answers
Read the word problem. Hershel buys 5 bags of cookies, 3 bags of granola, and several bags of fruit snacks from a bake sale. In total, he buys 10 bags from the bake sale. How many bags of fruit snacks did Hershel buy? Which type of word problem is shown? part-whole comparison multiplication division
Answers
Final answer:
Hershel bought 2 bags of fruit snacks in a part-whole comparison word problem, where the total (10 bags) minus the sum of known parts (5 bags of cookies and 3 bags of granola) equals the unknown part.
Explanation:
The word problem presented asks how many bags of fruit snacks Hershel bought if he bought a total of 10 bags, including 5 bags of cookies and 3 bags of granola. To solve this, we subtract the known quantities from the total: 10 total bags - 5 bags of cookies - 3 bags of granola = 2 bags of fruit snacks.
The type of word problem shown is a part-whole comparison because it involves figuring out a missing part of a whole based on the other known parts.
At Devon's new job he spent $12.99, $10.50, $9.89, $6.90, and $7.58 on lunch the first week.
In the second week, he spent $2 more in total for the 5 lunches than the first week.
What is the increase in the mean for the second week compared to the first?
Round the answer to the nearest penny.
Enter your answer in the box.
$
Answers
$0.40.
Explanation:
To find the mean of the lunch costs for the first week, we first add together all of the amounts he spent on lunch that week:
$12.99+$10.50+$9.89+$6.90+$7.58 = $47.86.
Now we divide this by the number of lunches, 5:
47.86/5 = $9.572 ≈ $9.57.
The second week he spends a total of $2 more on lunch. Adding this to the first week's total, we have:
47.86+2 = $49.86.
To find the mean, we divide this by the number of lunches in the second week, 5:
49.86/5 = $9.972 ≈ $9.97.
The mean increased from the first week to the second week by 9.97-9.57 = $0.40.
The increase in the mean for the second week compared to the first with the given parameters is; $0.40
Let us first find the mean of the lunch costs for the first week;
Mean for first week = ($12.99 + $10.50 + $9.89 + $6.90 + $7.58)/5 = $9.572
We are told that he spends a total of $2 more on lunch in the second week.
Second week total = $12.99 + $10.50 + $9.89 + $6.90 + $7.58 + $2 = $49.86.
Mean of second week = 49.86/5 = $9.972
The increase in the mean for the second week compared to the first is;
9.972 - 9.572 = $0.40
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A simple question I can't answer thnks yall
Answers
so the answer would be A
which value is a solution of the equation 2-8x=-6 ? ( 1point )
A. 1
B. 1/2
c. -1
d. 8,