A regular octagon is inscribed inside a circle. The perimeter of the octagon is units. A: What is the measure of a side of the octagon? B: What is the measure of a central angle of the octagon? C: What is the approximate measure of the apothem of the octagon (to the nearest hundredth of a unit)? D: Using your answer to part C, what is the approximate area of the octagon (to the nearest whole )?
Answers
Answer:
Explained below.
Step-by-step explanation:
Consider the diagram of a regular octagon is inscribed inside a circle.
Suppose the perimeter if the octagon is 8a.
(a)
Compute the measure of a side of the octagon as follows:
[tex]\text{Perimeter}=8\times side\\\\8\times side=8a\\\\side=a[/tex]
Thus, the side of the octagon is a units.
(b)
The sum of all angles of around a point is 360°.
Consider the point P on the octagon.
The sum of all the angle surrounding P will be 360°.
There are a total of 8 angle surrounding the point P.
Then the measure of central angle is:
[tex]\text{Central Angle}=\frac{360^{o}}{8}=45^{o}[/tex]
Thus, the measure of central angle is 45°.
(c)
The line segment from the center of an octagon to the midpoint of a side, perpendicular to said side, is known as the apothem.
Consider the diagram.
In the diagram the line segment PC is an apothem, that is perpendicular to the AB.
The measure of segment AC = a/2 and the measure of segment PA is r (radius of the circle).
Compute he measure of PC as follows:
[tex]PA^{2}=PC^{2}+AC^{2}\\\\PC^{2}=PA^{2}-AC^{2}\\\\PC=\sqrt{PA^{2}-AC^{2}}[/tex]
[tex]=\sqrt{r^{2}-\frac{a^{2}}{4}}[/tex]
Thus, the measure of the apothem of the octagon is[tex]\sqrt{r^{2}-\frac{a^{2}}{4}}[/tex].
(d)
The area of an octagon is:
[tex]\text{Area}=2(1+\sqrt{2})a^{2}[/tex]
Related Questions
Find the m∠CDE rjrsjrsrjr
Answers
Answer:
m∠CDE = 60°
Step-by-step explanation:
Given that the arc at the center = 2 times the arc at the circumference, we have;
Angle at the center = arc CE = 120°
Whereby the angle at the circumference is given as m∠CDE and it is opposite the circle arc CE
We note that m∠CDE is the acute angle between chord DC and DE
Therefore, we have;
Angle at the center = 120° = 2 times the arc at the circumference = 2 × m∠CDE
120° = 2 × m∠CDE
m∠CDE = 120/2 = 60°
Therefore the angle of m∠CDE is equal to 60°.
write the expression in radical form. (88c)^2/3
Answers
Answer:
[tex]\sqrt[3]{88c^{2} }[/tex]
Step-by-step explanation:
If we have a term to a fractional power, that’s the same as finding the denominator root of the number - if the numerator of the fraction isn’t 1, then the term itself inside the root sign becomes the term to the numerator power.
So - since the denominator of this fraction is 3, we find the cube root of 88c. Since the numerator is 2, we square 88c.
[tex]\sqrt[3]{88c^{2} }[/tex].
Hope this helped! (By the way, this was my 100th answer!)
expand the following (x+3)(x-3)
Answers
Answer:
x² - 9
Step-by-step explanation:
Given
(x + 3)(x - 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x - 3) + 3(x - 3) ← distribute both parenthesis
= x² - 3x + 3x - 9 ← collect like terms
= x² - 9
Answer:
x² - 9Step-by-step explanation:
[tex](x + 3)(x - 3)[/tex]
Multiply each term in the first parentheses by each term in the second parentheses ( FOIL )
[tex]x(x - 3) + 3(x - 3)[/tex]
Calculate the product
[tex] {x}^{2} - 3x + 3x - 3 \times 3[/tex]
Multiply the numbers
[tex] {x}^{2} - 3x + 3x - 9[/tex]
Since two opposites add up to zero, remove them from the expression
[tex] {x}^{2} - 9[/tex]
Hope this helps..
Best regards!!
What is the simplified form of -9x+3x
Answers
Answer:
-6x
Step-by-step explanation:
you can combine numbers with the same coefficient like any other number
Answer:
-6x
Step-by-step explanation:
It would be doing the same thing as -9 + 3, but without a variable.
how would you solve #81?
Answers
Example 2
A black die and a white die are thrown at the same
time. Display all the possible outcomes. Find the
probability of obtaining:
a) a total of 5
b) a total of 11
c) a 'two' on the black die and a six' on the white die.
It is convenient to display all the possible outcomes
on a grid. This is called a possibility diagram
It’s example 2 please help:)
Answers
Answer:
Total possible outcomes = 6×6 = 36
a) P(5) = 1/9
b) P(11) = 1/18
c) P(two and six) = 1/36
Step-by-step explanation:
A black die and a white die are thrown at the same time.
Each die has six sides so total possible outcomes are
Total possible outcomes = 6×6 = 36
The possible outcomes are given below:
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
a) Find the probability of obtaining a total of 5
Number of ways to get a total of 5 = (1, 4) (2, 3) (3, 2) (4, 1)
Number of ways to get a total of 5 = 4
The probability is given by
P = Number of desired outcomes/total number of outcomes
P(5) = 4/36
P(5) = 1/9
b) Find the probability of obtaining a total of 11
Number of ways to get a total of 11 = (5, 6) (6, 5)
Number of ways to get a total of 11 = 2
The probability is given by
P(11) = 2/36
P(11) = 1/18
c) a 'two' on the black die and a six' on the white die.
There is only one way to get a two on the black die.
Probability of obtaining a two on the black die = 1/6
There is only one way to get a six on the white die.
Probability of obtaining a six on the white die = 1/6
P(two and six) = 1/6×1/6
P(two and six) = 1/36
express each of the following decimal number in the p/q form (1)0.5 (2)3.8
Answers
Answer:
see explanation
Step-by-step explanation:
(1)
0.5 = [tex]\frac{5}{10}[/tex] = [tex]\frac{1}{2}[/tex]
(2)
3.8 = 3 [tex]\frac{8}{10}[/tex] = [tex]\frac{10(3)+8}{10}[/tex] = [tex]\frac{30+8}{10}[/tex] = [tex]\frac{38}{10}[/tex] = [tex]\frac{19}{5}[/tex]
Can any kind soul help me
Answers
Answer:
a) 4.50m/s²
b) v= 21
c) 11.25m/s
Step-by-step explanation:
a) rate of change of speed in first 2 seconds
= gradient of graph from t=0s to t=2s
The two points are (0,0) and (2,9).
[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]
Rate of change of speed
[tex] = \frac{9 - 0}{2 - 0} \\ = \frac{9}{2} \\ = 4.50m/ {s}^{2} [/tex]
Total distance= area under graph
Distance travelled for first 6s
= area of traingle +area of rectangle
= ½(2)(9) +(6-2)(9)
= 9 + 4(9)
= 9 +36
= 45m
Distance travelled from t=6s to t=12s
= 135 -45
= 90m
Area under graph from t=6s to t=12s =90
Area of trapezium= 90
½(A +B)(h)= 90
½(9+ v)(6)= 90
3(9 +v)= 90 (simplify)
9 +v= 30 (÷3 throughout)
v= 30 -9
v= 21
c) Average speed
= total distance ÷total time
= 135 ÷12
= 11.25 m/s
Maya is interning at a law firm over the summer and is paid by the hour. If her hourly wage is $52, which equation represents the proportional relationship between the wages she earns (w) and the number of hours (h)?
Answers
Answer: w= 52h
Step-by-step explanation:
Given: Maya is interning at a law firm over the summer and is paid by the hour.
Her hourly pay = $52
i.e. She is paid $52 per hour.
Let the wages she earns is denoted by 'w' and the number of hours is denoted by 'h'.
Now, (Total wages earned) = (hourly pay) x (Number of hours)
w = (52) (h)
⇒ w= 52h
Hence, the equation represents the proportional relationship between the wages she earns (w) and the number of hours (h): w= 52h
Answer:52h
Step-by-step explanation: tried got it right
A professor is grading the final exam. He notices that the mean test score is 61, and the standard deviation is 10. The test scores were normally distributed. if there were 450 students in the data sample, how many would have a test score between 61 and 71? *Round your answer to the nearest full value.
Answers
Answer:
66666699999
Step-by-step explanation:
aljebra questions anum counted the money she had in her purse and money box . When she doubbled the amount in her purse and add it to the amount in money box she gets rs 1700 . When she triples the amount in her purse and add in to money box she gets rs 2200. How much money does she have in her purse
Answers
Answer:
Money in her purse is Rs. 500.
Step-by-step explanation:
Let the money in her purse = Rs. [tex]x\\[/tex]
Let the money in her Money box = Rs. [tex]y[/tex]
As per question statement,
Double the money in her purse (i.e. [tex]2 \times x[/tex]) and add it to the amount in money box, she gets Rs. 1700.[tex]2x+y=1700[/tex] ........ (1)
Triple the money in her purse (i.e. [tex]3\times x[/tex]) and add it to amount in money box ([tex]y[/tex]), she gets Rs. 2200.[tex]3x+y=2200[/tex] ....... (2)
To find: Money in her purse = ? i.e. [tex]x=?[/tex]
Let us solve for [tex]x[/tex] using the two linear equations.
We can use substitution method here i.e. find value of one variable from one equation and then substitute that value in other equation.
Using equation (1), we get the value of [tex]y[/tex] as follows:
[tex]y=1700-2x[/tex]
Now, let us put this value of y in equation (2) to find the value of [tex]x[/tex]:
[tex]3x+1700-2x=2200\\\Rightarrow x+1700 = 2200\\\Rightarrow x=2200-1700\\\Rightarrow x = Rs.\ 500[/tex]
Money in her purse is Rs. 500.
I have a lot of questions like this, and I know the formula but I still get it wrong!
Answers
Answer: 4
Step-by-step explanation: use pick’s theorem to solve.
I+B/2-1.
We can substitute the variables with our information from the graph:
0+10/2-1=5-1=4 that’s the answe
Hope this helps
A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answers
Answer:
4/25 = 0.16
Step-by-step explanation:
The shortest stick must be between 0 and 5/3. The probability that it is longer than 1 is therefore:
(5/3 − 1) / (5/3 − 0)
(2/3) / (5/3)
2/5
So the probability that both of the shortest sticks are longer than 1 is (2/5)² = 4/25.
I need someone to answer this immediately please. ... The area of a piece of land is 50cm square. Fi d the value of x, if the length
and breadth are given as (x+2) and (x-3)m respectively
options. A. 3
B. 5
C. 7
D. 8
Answers
Answer:
x=8
Step-by-step explanation:
Area is equal to
A = l * w
50 = ( x+2) ( x-3)
FOIL
50 = x^2 -3x+2x -6
Combine like terms
50 = x^2 -x -6
Subtract 50 from each side
0 = x^2 -x -56
Factor
What two numbers multiply to -56 and add to -1
-8*7 = -56
-8+7 = -1
0 = ( x-8) ( x+7)
Using the zero product property
x-8 =0 x+7 =0
x = 8 x=-7
Since the length cannot be negative x cannot be negative
x=8
Answer:
8
Step-by-step explanation:
put the 50 under area and continue with like that
5/8 of the staff are male. 5/12 of the staff works part time at the aquarium.What fraction of the staff is female?
Answers
Answer:
3/8
Step-by-step explanation:
If 5/8 of the staff is male, then 8/8 is the total number of staff.
8/8 - 5/8 = 3/8
3/8 of the staff is female.
Hope this has helped. If the question has more to it, then please specify.
what is 1 add 1 please help!!!!!!!!!!!!!!!PS first person to get it correct gets brainiest
Answers
Answer: 2
Step-by-step explanation:
Answer:
2...........
Step-by-step explanation:
1 + 1 = 2............
Explain how you would decide whether to use a dot plot or a box plot to display a data set. Give some strengths and weaknesses of each type of display to support your explanation.
Answers
Answer:
A box plot should be used in a situation when you need the median and quartiles. A dot plot should be used when you need exact numbers. The strengths of a box plot is that it shows a big data sets into a rounded form. The strengths of a data set is that you can show the exact numbers but it would work best with small numbers.
Hope this helped?
if cos 0=2/3, what are the values of sin 0 and tan 0?
Answers
Answer:
Below
Step-by-step explanation:
● cos O = 2/3
We khow that:
● cos^2(O) + sin^2(O) =1
So : sin^2 (O)= 1-cos^2(O)
● sin^2(O) = 1 -(2/3)^2 = 1-4/9 = 9/9-4/9 = 5/9
● sin O = √(5)/3 or sin O = -√(5)/3
So we deduce that tan O will have two values since we don't khow the size of O.
■■■■■■■■■■■■■■■■■■■■■■■■■
●Tan (O) = sin(O)/cos(O)
● tan (O) = (√(5)/3)÷(2/3) or tan(O) = (-√(5)/3)÷(2/3)
● tan (O) = √(5)/2 or tan(O) = -√(5)/2
PLEASE HELP Jane has twice as many cousins as James. Bryan has 5 cousins, which is 11 less that Jane has. How many cousins does James have?
Answers
Answer:
James has 8 cousins
Step-by-step explanation:
Bryan =5
Jane =Bryan + 11=5+11=16 ( Bryan has 11 cousins less than Jane)
James: 1/2 Jane=16/2=8 cousins ( Jane has twice as James)
(05.02 LC)What is the area, in square inches, of the figure shown here? A parallelogram with a height of 4inches is shown. The height of the parallelogram is used to divide the side of the parallelogram into 5 inches, which is the length (or side) of the rectangle, and into 4 inches, which is the base of the triangle formed by the division. 20 in2 24 in2 32 in2 36 in2
Answers
Answer:
36 in²
Step-by-step explanation:
The figure that is been described is a Parallelogram.
The area of a Parallelogram is = Base × Height
From the question, the Height of the Parallelogram = 4 inches
The Base of the Parallelogram is calculated as the Length or base of the rectangle + base of the triangle
= 5 inches + 4 inches
= 9 inches
Area of the Parallelogram = 9 inches × 4 inches
= 36 square inches or 36 in²
Answer:
20 INCHES SQUARED
Step-by-step explanation:
If a test has 40 questions and you get 200 points for the whole test, how many points are each question worth?
Answers
Answer:
5
Step-by-step explanation:
To find the points for each question, you must divide the number of points (200) by the number of questions (40) to get the number of points for each question
[tex]\frac{200}{40}[/tex]
Divide 200 by 40 to get
[tex]\frac{5}{1}[/tex] or [tex]5[/tex]
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day!
Answer:
5 points
Step-by-step explanation:
200points / 40 questions = 5points/1question
then:
1 questión worths 5 points
find the coordinates of the point satisfying lying on x axis at a distance of 5 units to the right of x axis lying on y axis at a distance of 3 units below the orgin
Answers
Answer:
(5, -3)
Step-by-step explanation:
Coordinates are located on Cartesian planes (more like locating a point on a graph). Cartesian coordinates can be two dimensional or three dimensional in nature depending on the number of axis we are considering. For the question, the dimension of the required coordinate is 2-dimensional i.e (x,y).
On the Cartesian plane, we have the x axis along the horizontal plane and y axis along the vertical.
Note that positive values lies towards the right of the x-axis and also up the y-axis. The negative values lies towards the left of the x-axis and also down the y-axis.
According to the question, if a point is lying on x axis at a distance of 5 units to the right of x axis, then the value of x will be +5 i.e x = +5
Also, if a point lies on the y axis at a distance of 3 units below the origin, then the value of y will be -3 i.e y = -3.
Hence, the coordinates satisfying this points (x,y) is (5, -3)
2^2(3-8)÷5-1 please help
Answers
Answer:
-5
Step-by-step explanation:
2^2*(3-8)÷5-1
4*(-5)÷4
-20÷4
=-5
Answer:
-5
Step-by-step explanation:
Firstly 2^2=4, 4(3-8)=4*(-5)= -20, -20/5 -1= -4-1= -5
Together, two apples have 1/5 gram of fat. How many apples have a total of 4 grams of a
apples
Answers
Answer:
40 apples
Step-by-step explanation:
2 apples= [tex]\frac{1}{5}[/tex] grams
x apples= 4 grams
8/[tex]\frac{1}{5}[/tex] = 8 x 5/1=40
Answer:
40
Step-by-step explanation:
edu instruction correct
Figure ABCD is a parallelogram. Parallelogram A B C D is shown. Angle A is (4 p + 12) degrees and angle C is 36 degrees. What is the value of p? 6
Answers
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
i checked on edge
An annual salary is $45000. His tax free allowances total $13000. He has to pay a tax of 20% on his taxable income.
The tax payable is?
Answers
Answer:
6400
Step-by-step explanation:
Taxable amount=45000-13000=32000
tax=32000*20/100
=6400
Coffee is sold in two different sized canisters. The smaller canister has a diameter of 9 cm and a height of 12 cm. The larger canister is double the size of the small canister. Calculate the volume and surface area of each canister and compare the results of doubling the dimensions.
Answers
Answer:
volume 1 =763 cm3
volume 2 = 6,104 cm3
Second volume is 8 times greater than the first volume.
Surface area 1 = 466 cm2
surface area 2 =1,865 cm2
second surface area is 4 times greater than the first surface area .
Step-by-step explanation:
Volume of a cylinder: π radius^2 x height
Radius = diameter /2 = 9/2 = 4.5
V = 3.14 x 4.5^2 x 12 = 763 cm3
Surface area: (3.14 r^2)2 + 2(π x radius x height)
Sa = (3.14 x 4.5^2 )2 + 2(3.14 x 4.5 x 12 )=466 cm2
Since the second canister is double the size:
Radius = 4.5 x 2 = 9
Height = 12 x 2 =24
V = 3.14 x 9^2 x 24 = 6,104 cm3
Sa = (3.14 x 9^2 )2 + 2(3.14 x 9 x 24 )=1,865 cm2
Dividing the second volume by the first one:
6,104/ 763 = 8
Second volume is 8 times greater than the first volume.
Dividing the second surface area by the first one:
1865/466 = 4
second surface area is 4 times greater than the first surface area .
30. A rectangular prism has a volume of
285.6 cubic feet. The prism is
12 feet long and 3.4 feet wide. What is
the height of the prism?
A 7 ft
C 19 ft
B 15 ft
D 22 ft
Answers
Answer:
The answer is a
Step-by-step explanation:
my brother is very smart
Can someone tell me the answer it would really help 3(x−2)+1 =
Answers
Step-by-step explanation:
3(x-2)+1
= 3x-6+1
= 3x-5
Answer:
Step-by-step explanation:
3(x-2)+1=
Then distribute, and now you get:
3x-6+1=
Now combine like terms, and now you get:
3x-5=
There is nothing much to do because there isn't a answer for it
Jason considered two similar televisions at a local electronics store. The generic version was based on the brand name and was three eighths the size of the brand name. If the generic television set is 12 inches by 24 inches, what are the dimensions of the brand name television
Answers
Answer:
32 inches by 64 inches
Step-by-step explanation:
Since the generic television is [tex]\frac{3}{8}[/tex] the size of the brand name.
Then the brand name is [tex]\frac{8}{3}[/tex] the size of the generic, thus
[tex]\frac{8}{3}[/tex] × 12 = 32
[tex]\frac{8}{3}[/tex] × 24 = 64
Thus dimensions are 32 inches by 64 inches
Answer:
The dimensions are 32 inches by 64 inches