1)An octagon can be divided into 8 congruent triangles with base angles that are 67.5°. This octagon has a side length that is 8 cm.
2)What is the area of each triangle?
3)What is the area of the octagon?
4) Use your work from above to derive a generic formula for any octagon with side length that is n units.
Answers
Answer:
(a) [tex]Area = 14.7824cm^2[/tex]
(b) [tex]Area = 118.2592cm^2[/tex]
(c) [tex]Area = 4nh[/tex]
Step-by-step explanation:
Given
[tex]\theta = 67.5[/tex]
[tex]b= 8cm[/tex] --- base
[tex]n = 8[/tex] --- triangles
Solving (a) The area of each triangle
First, calculate the height (h) of each triangle using:
[tex]\sin(67.5) = \frac{h}{b/2}[/tex] --- i.e. we consider half of the triangle
[tex]\sin(67.5) = \frac{h}{8/2}[/tex]
[tex]\sin(67.5) = \frac{h}{4}[/tex]
Solve for h
[tex]h =4*\sin(67.5)[/tex]
[tex]h =4*0.9239[/tex]
[tex]h =3.6956[/tex]
The area of each triangle is:
[tex]Area = \frac{1}{2} *b * h[/tex]
[tex]Area = \frac{1}{2} *3.6956 * 8[/tex]
[tex]Area = 14.7824cm^2[/tex]
Solving (b): Area of the octagon
This is calculated as:
Area = 8 * area of 1 triangle
[tex]Area = 8 * 14.7824cm^2[/tex]
[tex]Area = 118.2592cm^2[/tex]
Solving (c): Area of octagon of side length n
In (a), we have:
[tex]Area = \frac{1}{2} *b * h[/tex]
Replace b with n
[tex]Area = \frac{1}{2} *n * h[/tex]
Multiply by 8 (the sides) to get the area of the octagon
[tex]Area = 8 * \frac{1}{2} *n * h[/tex]
[tex]Area = 4nh[/tex]
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Answer:
X4
Step-by-step explanation:
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[tex]\huge{ \mathcal{ \underline{ Answer} \: \: ✓ }}[/tex]
The chords subtended by equal arcs are equal.
Therefore,
[tex]2x + 4 = 18[/tex][tex]2x = 14[/tex][tex]x = 7[/tex]Hence, value of x = 7
_____________________________
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Answer:
huuu wate a few minutes
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Ms. Robinson gave her class 12 minutes to read. Carrie read 51/2 pages in that time. At
what rate, in pages per hour, did Carrie read?
1 1/10
22
27 1/2
66
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Answer:
27 1/2
Step-by-step explanation:
help it's due tomorrow
Answers
Answer:
a) 42
b) 42/120
Step-by-step explanation:
Oof, I was just about done with answering this question but I deleted it all by accident so I had to rewrite it.
Anyways, the first part of it is correct.
The second part of it is a bit harder. See, this is conditional probability, which uses the equation that I've attached below.
For Event A, you'll need the total boys / total students:
0.44166
For Event B, you'll need the total counters / total students:
0.83333
Now, plug these values into the equation. The weird U thingy is called "Union". It basically means "and".
P(A and B) / P(B)
P(0.44166 * 0.8333) / P(0.8333)
0.36803 / 0.8333
This is about 0.44165, or 53/120
The mayor is interested in finding a 98% confidence interval for the mean number of pounds of trash per person per week that is generated in the city. The study included 144 residents whose mean number of pounds of trash generated per person per week was 34.5 pounds and the standard deviation was 7.9 pounds. Round answers to 3 decimal places where possible. a. To compute the confidence interval use a
Answers
Answer:
32.966 ; 36.034)
Step-by-step explanation:
Given :
Sample size , n = 144
Mean, x = 34.5
Standard deviation = 7.9
The confidence interval :
Xbar ± Margin of error
Margin of Error = Zcritical * s/√n
Zcritical at 98% = 2.33
Margin of Error = 2.33 * 7.9/√144 = 1.534
Lower boundary = 34.5 - 1.534 = 32.966
Upper boundary = 34.5 + 1.534 = 36.034
(32.966 ; 36.034)
Which equation can be used to solve for x in the following diagram
Answers
Answer:
10x+10 = 110
Step-by-step explanation:
The two angles are vertical angles and vertical angles are equal
10x+10 = 110
Help please just write the ratio like #1 300: ?
Answers
2) 25:31
3) 9:21 = 3:7
4) 5:21
5) 5:13
6) 15:14
The sum of three numbers is 910. One of the numbers, x, is 60% greater than the sum of the other two numbers. What is the value of x?
Answers
Answer:
I don't know I'm sorry I tried to found answers but I couldn't
Can someone help me
Answers
Answer:
y= -2/5x + 5
Step-by-step explanation:
Answer:
y=-2/5x+5
is the answer
HOPE IT HELPEDPLEASEEEEEE IM BEGGING SOMEONE PLEASEEEE HELPPPP PLEASEEEEE PLEASEEEEE SOEMONE HELPPPP PLEASEEEEEEEEEEEEEEEEEEEE
Answers
Answer:
8 nachos and 5 hot dogs
Step-by-step explanation:
Let x equal number of nachos
let y equal number of how dogs
1.5x + 2y = 22
x + y = 13
y = 13 - x
1.5x + 2(13 - x) = 22
1.5x + 26 - 2x = 22
1.5x - 2x = 22 - 26
-0.5x = - 4
x = -4/-0.5
x = 8
y = 13 - x
y = 13 - 8
y = 5
5
Select the correct answer.
Which number has a repeating decimal form?
A. 15
OB.
11
25
3
20
C. D.
2
ODIN
Answers
Answer:
C=6.6666666666666666666666666
Answer:
[tex]D.\frac{2}{6}[/tex]
Step-by-step explanation:
√15 = 3.87298334621
11/25 = 11 ÷ 25 = 0.44
3/20 = 3 ÷ 20 = 0.15
2/6 = 2 ÷ 6 = 0.33333333333
solve for ,"a" in 3(a+2)/4 +3/2=0
Answers
Answer:
a=-4
Step-by-step explanation:
3(a+2)=-6
3a+6-6=-6-6
3a/3=-12/3
can you help me solve for x.
Answers
Answer:
x=4
Step-by-step explanation:
Find the value of x. Round your answer to the nearest tenth.
Answers
Answer:
x = 9.7
Step-by-step explanation:
Reference angle (θ) = 68°
Opposite = 24
Adjacent = x
Apply, the trigonometric function, TOA which is:
[tex] tan (/theta) = \frac{Opp}{Adj} [/tex]
Plug in the values
[tex] tan 68 = \frac{24}{x} [/tex]
Multiply both sides by x
[tex] x*tan 68 = 24 [/tex]
Divide both sides by tan 68
[tex] x = \frac{24}{tan 68} [/tex]
x = 9.69662942
x = 9.7 (nearest tenth)
I NEED HELP ASAP: Figure ABCD is reflected across the x-axis. What are the coordinates of A' , B' , C' , and D' ? Enter your answer by filling in the boxes.
A' ( ___, ___ )
B' ( ___, ___ )
C' ( ___, ___ )
D' ( ___, ___ )
Answers
Answer:
A - 1,4
B -5,8
C -5,4
D -4,2
Step-by-step explanation:
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Answer:
A' ( -1, -4 )
B' (-5, -8 )
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D' ( -4, -2 )
Step-by-step explanation:
I took the test
|x| > - 16 what is the value of x
Answers
9514 1404 393
Answer:
x ∈ all real numbers
Step-by-step explanation:
The given inequality is true for any value of x. The absolute value of a quantity is always greater than any negative number.
A baseball team has won 50 games of 75 played. The team has 45 remaining games to play. How many of the remaining games must a team win in order to win 60% of the total games played during the season?
A. 20
B. 21
C. 22
D. 23
Answers
Answer:
C. 22
Step-by-step explanation:
The team played 75 games and 45 remaining.
75+45=120
60% of 120 = 0.6×120= 72
The team must win 72 games and they already won 50 games so the team has to win 72-50=22 games more.
7+2x/3=5
what is x ?
Answers
Answer:
x = -3
Step-by-step explanation:
7 + 2x/3 = 5
7*3 + 2x = 5*3 ( we multiply by 3 to remove the denominator )
21 + 2x = 15
2x = 15 - 21
2x = -6
x = -6/2
x = -3
Answer:
X=4
Step-by-step explanation:
Times both side by 3
then you get 7+2x=15
then minus 7 from both sides
2x=8
divide by 2
x=4
Convert the following angle from degrees to radians. Express your answer in simplest
form.
255°
Answers
Answer:
(17/12)π radians
Step-by-step explanation:
π radians = 180º
255 * (π/180) = (17/12)π
What is the common ratio of the geometric sequence 4, 16, 64, 256? * please help
Answers
Answer:
4
Step-by-step explanation: 16/4=4
Shelia is baking a few cakes for the bake sale for her school. Each cake requires 5/6 cups of sugar. How many cakes can she bake if she has 7 1/2 cup of sugar?
Answers
15/2 / 5/6
15/2 x 6/5
90/ 10
= 9
9 cups can be baked if she has 7 1/2 cup of sugar in
It took 45 seconds to fill an 18 gallon container. At this rate how long will it take to fill a 40 gallon container
Answers
Answer:
[tex]18 \: gallons = 45 \: seconds \\ 40 \: gallons = ( \frac{40}{18} \times 45) \: seconds \\ = 100 \: seconds[/tex]
Convert.
2 mi = _ yd
Answers
Answer: 2 mi = 3520.00 yd
Answer:
2 mi= 3520 yd
Step-by-step explanation:
To convert a mile measurement to a yard measurement, multiply the length by the conversion ratio.
1 mile is equal to 1,760 yards
multiply the length value by 1760 to get your answer
2 x 1760 = 3520
a- You roll a regular die (one dice). What is the probability of rolling a 4? SIMPLIFY,
IF NECESSARY.
Answers
Answer:
1/6th chance
Step-by-step explanation:
Answer:
1/6
Step-by-step explanation:
there's only one 4 on a normal 1 to 6 die
An air-conditioning fan makes 125 revolutions per second. How many revolutions will it make if it runs for 30 minutes?
Answers
Answer:
225,000 revolutions
Step-by-step explanation:
An air conditioning fan makes 125 revolutions per second
The number of revolution in 30 minutes can be calculated as follows
60 secs= 1 min
x= 30 min
= 30×60
= 1800 secs
1800×125
= 225,000
Hence the airconditioning makes 225,000 revolutions in 30 minutes
Please help me!!!
Find the measure of angle x in the figure below:
Answers
Answer:
Step-by-step explanation:
Please can someone help me I’m confused and lost
Answers
Answer: the answer is the third one
Step-by-step explanation:
well first of all how u get 3is because u have to divide 6 by 2 or u have todo the square root of 6 and 2 and u get 3
Sara can weed a garden in 30 minutes. When her brother Hamdan helps her, they can weed
the same garden in 20 minutes. How long would it take Hamdan to weed the garden if he
worked by himself?
Answers
Step-by-step explanation:
Hello!The answer is:It will take 42.35 minutes to weed the garden together.
Why?
To solve the problem, we need to use the given information about the rate for both Laura and her husband. We know that she can weed the garden in 1 hour and 20 minutes (80 minutes) and her husband can weed it in 1 hour and 30 minutes (90 minutes), so we need to combine both's work and calculate how much time it will take to weed the garden together.
So, calculating we have:
Laura's rate:
\frac{1garden}{80minutes}
80minutes
1garden
Husband's rate:
\frac{1garden}{90minutes}
90minutes
1garden
Now, writing the equation we have:
Laura'sRate+Husband'sRate=CombinedRateLaura
′
sRate+Husband
′
sRate=CombinedRate
\frac{1}{80}+\frac{1}{90}=\frac{1}{time}
80
1
+
90
1
=
time
1
\frac{1*90+1*80}{7200}=\frac{1}{time}
7200
1∗90+1∗80
=
time
1
\frac{170}{7200}=\frac{1}{time}
7200
170
=
time
1
\frac{17}{720}=\frac{11}{time}
720
17
=
time
11
\frac{17}{720}=\frac{1}{time}
720
17
=
time
1
\frac{17}{720}*time=1
720
17
∗time=1
time=1*\frac{720}{17}=42.35time=1∗
17
720
=42.35
Hence, we have that it will take 42.35 minutes to weed the garden working together.
Have a nice day!Maya and Zack built the tent below in their backyard how much material did they use to build the tent
Answers
Answer:
[tex]Area = 279ft^2[/tex]
Step-by-step explanation:
Given
See attachment for tent
Required
The material needed
This implies that we calculate the surface area of the tent.
This is calculated as:
Area = 2 * Area of Congruent triangles + 2 * Area of Congruent Rectangles + Area of Base Rectangle
So, we have:
[tex]Area = 2 * \frac{1}{2} * 6 * 8 + 2 * 10.5 * 7 + 10.5 * 8[/tex]
[tex]Area = 48 + 147 + 84[/tex]
[tex]Area = 279ft^2[/tex]