Answers
[tex]\large\boxed{Formula:\frac{sum \: of \: interior \: angles}{n}}[/tex]
n means the number of sides.
Sum of interior angles of a dodecagon is 1800°
Let's substitute the values according to the formula.
[tex]\frac{1800}{12}[/tex]
[tex]\large\boxed{ = 150°}[/tex]
Now, we can find the size of one exterior angle.
[tex]\large\boxed{Formula:\frac{360}{n}}[/tex]
n means the number of sides.
A dodecagon has 12 sides.
Let's substitute the values according to the formula.
[tex]\frac{360}{12}[/tex]
[tex]\large\boxed{ = 30°}[/tex]
Hence, the size of 1 interior angle of a dodecagon is 150° and 1 exterior angle is 30°
Related Questions
Please help me with this question!
Answers
Step-by-step explanation:
Yes it is .
7x+9 _> 7•3
7x+9_> 21
7x_> 21 - 9
7x _> 12 divide both side with 7 to find x
then x _> 1.4
which mean x can be any number that is greater than or equal to 1.4 so 2 is correct .
Hi Student!
Looking at the problem statement, we can see that they are asking for us to determine whether x = 2 is a solution of the expression provided or not. The first step that we take is plugging in all the values which means that we take 2 and plug it into all of the x's that we have in the expression that we provided. Then we simplify that expression down on both sides. If the expression in the end results to true then x = 2 is a solution of the expression but if it defaults to false than x = 2 isn't a solution.
Plug in the values
[tex]7x + 9 \ge 7 * 3[/tex][tex]7(2) + 9 \ge 7 * 3[/tex]Simplify both sides
[tex]14 + 9 \ge 7 * 3[/tex][tex]23 \ge 21[/tex]The final expression states that 23 is greater than or equal to 21 which is true. Therefore, x = 2 is a solution of the expression that was provided in the problem statement.
The graph below shows how many cookies can be made depending on how many cups of flour are used. How many cookies will be made if 18 cups of flour are used?
192 cookies
96 cookies
48 cookies
288 cookies
Answers
Answer:
288
Step-by-step explanation:
Find the 18 on the x axis. Go up to the line. Then go left and you will be at 288 on the y axis.
You can also divide a known coordinate to find the rate of change, since the graph is proportional. Use (6, 96). y/x = rate of change
96/6 = 16.
Now multiply 18 and 16 to get the number of cookies.
18 x 16 = 288
the price of a barrel oil currently cost $120. Next month if the price increases by 1/12 of the current cost, then what would be the new cost of a barrel of oil?
Answers
Answer:
$130
Step-by-step explanation:
120 x (1 + 1/12) = 120 x 13/12 = 130
John has four times as much money as his sister Debbie who has half as much as their friend David. Together the three children have $105. a) How much money does Debbie have? Answer b) How much money does John have? Answer.. c) How much money does David have? Answer.. (1)
Answers
Let's say that the money that each person has is equal to a letter:
A=Debbie, B=John, C=David.
Now we can write some equations.
"John has four times as much money as his sister Debbie who has half as much as their friend David."
B = 4A
A = 0.5C
"Together the three children have $105"
A+B+C=105
This is now a system of equations problem. Substitute to solve.
A + (4A) + C = 105
(0.5C) + 4(0.5C) + C = 105
3.5C = 105, so C = 30.
Plug this into the previous equations to get A=15 and B=60
So Debbie has $15, John has $60, and David has $30
00:57
Learn with an example
What is the volume of this cone?
Use ≈ 3.14 and round your answer to the
nearest hundredth.
19 ft
12 ft
Answers
The volume of the given cone.
Solution:[tex]\large\boxed{Formula:V= \frac{1}{3}\pi{r}^{2}h}[/tex]
[tex]\large\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}[/tex]
Let's solve!
Substitute the values according to the formula.
[tex]V=\frac{1}{3}×3.14×{12}^{2}×19[/tex]
[tex]\large\boxed{V=2863.68 \: {ft}^{3}}[/tex]
Therefore, the volume of the given cone is 2863.68 cubic feets.
A. Saving money at the grocery store by using unit pricing.
a. Toilet paper A is 6 mega rolls for $4.59.
b. Toilet paper B is 12 mega rolls for $9.02.
Answers
In order to save money, the person should buy Toilet paper B.
Which option is cheaper?In order to determine the unit price of each option, divide the total cost by the number of rolls. The option that would save money is the cheaper option.
Unit cost = total cost / number of rolls
$4.59 / 6 = $0.77
$9.02 / 12 = $0.75
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Simplify the following expression:
(3i + 4) - i + 4(6 + 2i)
A. 27 + 11i
B. 28 + 10i
C. 14 + 8i
D. 14 + 4i
Answers
The simplified form of this expression is 28 + 10i
This question is an expression of imaginary numbersImaginary numbers are numbers that are composed of a real number and an imaginary part.
< To resolve this issue, let's remove the first parenthesis:
(3i + 4) - i + 4(6 + 2i)
3i + 4 - i + 4(6 + 2i)
< In the second parentheses, let's apply the distributive property:
3i + 4 - i + 4(6 + 2i)
3i + 4 - i + 4 . 6 + 4 . 2i
3i + 4 - i + 24 + 8i
< Finally, let's just sum the like terms, along with the real terms:
3i + 4 - i + 24 + 8i
10i + 4 + 24
10i + 28
28 + 10i
Therefore, the correct value will be 28 + 10i
There are 9 squares and 6 circles. What is the simplest ratio of circles to squares?
Answers
Answer:
2:3, 2 to 3
Step-by-step explanation:
9 and 6 are both factors of three, so you have to reduce. 3 goes into 9 tree times, and 3 goes into 6 twice. Since it is circles to squares, the 2 comes first then 3.
Hope this helps!
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
(15, 3)
(0,0)
Answers
The required equation of the line is 5y=x.
We are given to find the equation of the line passing through the points (0, 0) and (15, 3).
We know that
What is the slope point form of the line?The equation of a line passing through two points (a, b) and (c, d) is given by
[tex]y-b=\frac{d-b}{c-a}(x-a)[/tex]
Therefore, the equation of the line passing through the points (0, 0) and (15, 3) is given by,
Thus, the required equation of the line is
[tex]y-0=\frac{3-0}{15-0}(x-0)\\y=\frac{3}{15}x\\ y=\frac{1}{5}x\\ 5y=x[/tex]
Thus the required equation of the line is 5y=x.
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To determine how American college students feel about commuting, 100 students at a private
the university was chosen by selecting 50 men and 50 women to participate. They were asked
how far they commute each day (in minutes) to campus.
a. Is this an observational study or experiment?
b. What is the sample?
c. What is the target population?
d. What is the sampling method? (Simple random, stratified, convenient, …)
e. Is the data collected qualitative or quantitative?
f. Why is it unlikely that the results of this study will be valid?
Answers
The nature of the research is called Observational Study while the target Population is American Students.
How to find the sampling method?
1) In study, we survey members of a sample without trying to affect them while in experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive treatment. Thus, this is an observational study.
2) The sample is the 100 students made up of 50 boys and 50 girls.
3) The target Population are American College Students
4) The sampling method is; Simple random Sampling
5) The data is qualitative because it deals with description of feelings rather than dealing with numbers and figures.
6) It is unlikely that the results would be invalid because of sampling bias as it was only done in a private university.
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Consider the halfpipe with a diameter of 7 cm and a height of 20 cm.
Find its volume, rounding to 2 decimal places.
Answers
Answer: 384.85
Step-by-step explanation
Dragon and lion dances are performed in a parade on Chinese New Year. The
dragon costume is 112 feet long. This is 8 times as long as the lion costume.
Which equation can be used to find the length of the lion costume?
Answers
Answer: 112 divided by 8 equals the length of the lion costume
Step-by-step explanation: 112 divided by 8 equals ???
Try and work it out using the bus stop method
Sorry if I wasn’t much help.
Find the sum of the first n terms
using the formula:
a(1-rn)
1-r
85 +85(.9) +85(.9)² + ...
. (5 terms)
Answers
The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.
What is the sum of terms of a geometric sequence?Let's suppose its initial term is a , multiplication factor is r and let it has total n terms,
then, its sum is given as:
[tex]S_n = \dfra[/tex][tex]\dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
Given geometric sequence;
85 +85(.9) +85(.9)² + ...
a = 85
r = 0.9
its sum is given as:
[tex]S_n = \dfra[/tex][tex]\dfrac{a(r^n-1)}{r-1}[/tex]
[tex]S_n = \dfrac{85(0.9^5-1)}{0.9-1}\\\\S_n = \dfrac{85(0.5904-1)}{-0.1}\\\\\\S_n = \dfrac{85(-0.4095)}{-0.1}\\\\S_n = 348.08[/tex]
Thus,
The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.
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hi everyone today is world environment day please give me 100 to 200 word eassy on environment to save nature can anyone help this ~
Answers
The conditions or surroundings in which we all live is called the environment. The main elements of the environment are air, water, temperature, weather conditions and more.
The environment is the base of the life cycle. It is the most precious gift of nature. But now our environment is in danger. Saving the environment is very important for living a comfortable life. It is the biggest challenge for humans to revert the environment to its real state. But nothing is impossible.
We need to take some steps immediately in order to save the environment and revert it back to its original form. Using natural resources efficiently is a powerful way to save our environment.
♥happy environment day♥☆...hope this helps...☆
_♡_mashi_♡_
Angles in circles
How many degrees are in a half of a full turn?
Answers
Answer:
180 degrees
Step-by-step explanation:
Because 360 is i full turn around and you can divide 360 by 2 and you will get 180
Hope This Helped
Caroline is looking for a tool to measure the mass of a dictionary. Which tool should she use?
A.
ruler
B.
pan balance
C.
stopwatch
D.
1‐liter container
Answers
[tex]\bold{Q:}[/tex]
Caroline is looking for a tool to measure the mass of a dictionary. Which tool should she use?[tex]\bold{Ans:}[/tex]
B. pan balanceA balance or scale is an instrument used to measure mass.
Hope it helps.
[tex]\bold{Feel \: free \: to \: correct \: me}[/tex]~
Maria has 14 fewer apps on her phone than Orlando. If the total number of apps on both phones is 34, how many apps are on each phone?
Answers
Setting up and equation from the word problem, Orlando has 24 apps on his phone, and Maria has 10 apps on her phone.
How many apps are on each phone?Let's assume that Orlando has x number of apps on his phone. According to the given information, Maria has 14 fewer apps, so the number of apps on Maria's phone would be (x - 14).
The total number of apps on both phones is 34, so we can set up the equation:
x + (x - 14) = 34
Simplifying the equation:
2x - 14 = 34
Adding 14 to both sides:
2x = 48
Dividing both sides by 2:
x = 24
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Can anyone please help me solve this and show how you did it? Thank you so much!
-3(-2w-6)<=10-2(-2w-4.5)
(WILL GIVE OUT 50 POINTS!!)
Answers
More Icon
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "4.5" was replaced by "(45/10)".
Rearrange:
Rearrange the equation by subtracting what is to the right of the less equal sign from both sides of the inequality :
-3*(-2*w-6)-(10-2*(-2*w-(45/10)))≤0
Step by step solution :
STEP
1
:
9
Simplify —
2
Equation at the end of step
1
:
9
(0-(3•(-2w-6)))-(10-(2•(-2w-—))) ≤ 0
2
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 2 as the denominator :
-2w -2w • 2
-2w = ——— = ———————
1 2
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
-2w • 2 - (9) -4w - 9
————————————— = ———————
2 2
Equation at the end of step
2
:
(-4w-9)
(0-(3•(-2w-6)))-(10-(2•———————)) ≤ 0
2
STEP
3
:
STEP
4
:
Pulling out like terms :
4.1 Pull out like factors :
-4w - 9 = -1 • (4w + 9)
Equation at the end of step
4
:
(0 - (3 • (-2w - 6))) - (10 - (-4w - 9)) ≤ 0
STEP
5
:
STEP
6
:
Pulling out like terms :
6.1 Pull out like factors :
-2w - 6 = -2 • (w + 3)
Equation at the end of step
6
:
(0 - -6 • (w + 3)) - (4w + 19) ≤ 0
STEP
7
:
Equation at the end of step
7
:
2w - 1 ≤ 0
STEP
8
:
8.1 Divide both sides by 2
w-(1/2) ≤ 0
Solve Basic Inequality :
8.2 Add 1/2 to both sides
w ≤ 1/2
Inequality Plot :
8.3 Inequality plot for
2.000 w - 1.000 ≤ 0
One solution was found :
w ≤ 1/2
Blake has a points card for a movie theater. He receives 35 rewards points just for signing up. He earns 11.5 points for each visit to the movie theater. He needs 196 points for a free movie ticket. How many visits must Blake make to earn a free movie ticket?
Answers
Answer:
14 visits
Step-by-step explanation:
The total number of points on Blake's card will be the sum of the initial number and the number earned for visits. The number earned for visits is the product of the number of visits and the the points earned per visit.
__
setupThe number of points on Blake's card will be ...
p = 35 +11.5x . . . . . when Blake makes x visits to the theater
We want to find x when p=196, so we have ...
196 = 35 +11.5x
solutionThis 2-step equation is solved in the usual way.
161 = 11.5x . . . . step 1, isolate the variable term by subtracting the constant
14 = x . . . . . . . . step 2, divide by the variable coefficient
Blake must make 14 visits to earn a free movie ticket.
Answer:
A
tyler has a points card for a movie theater.
he receives 75 rewards points just for signing up.
• he earns 10.5 points for each visit to the movie theater.
he needs 180 points for a free movie ticket.
.
a
how many visits must tyler make to earn a free movie ticket?
Step-by-step explanation:
1) Which is the first INCORRECT step in the
solution of the inequality shown below?
2(x+1)-(3-x) ≤ -4:
Step 1: 2x + 2-3+x≤-4;
Step 2: 3x - 1≤-4;
Step 3: 3x
-3;
Step 4: x>-1
(a) Step 1
(b) Step 2
(c) Step 3
(d) Step 4
Answers
Step-by-step explanation:
we are missing the inequality sign in step 3.
step 1 and step 2 are correct.
step 4 is wrong.
the correct step 3 looks like
3x <= -3
if your original step 3 says the same, then the first wrong step is step 4.
if your original step 3 does not say the same, then the first wrong step is step 3.
What part of the circle below is highlighted in red?
A. Radius
OB. Chord
O C. Diameter
OD. Center
Answers
Hi Student!
Let's go through each of the options that were provided to the question stating what part of the circle was highlighted in red and talk about what they mean.
First off, radius is the distance from the outer line to the middle which perfectly incapsulates what the red line is. Therefore, the correct answer would be option A, Radius.
However, if you want to understand the rest of the definitions you can follow with the bullets provided.
Chord - This isn't a math termDiameter - This term is actually quite similar to that of radius but instead this is the length from one side of the outer line to the other side of the outer line. This would cause the diameter to be twice the length of the radius and so if we want to determine the radius using the diameter we can just divide it by 2Center - This just description the dot in the middle of the circle3) Find an estimated product.
59 x 42 = ?
Oa.) 50 x 40 = 2500
Ob.) 60 x 50 = 3500
Oc.) 60 x 40 = 2400
Answers
Answer:
c.
Step-by-step explanation:
we estimate by rounding the factors to "easy numbers". that means numbers we can easily calculate even in our heads, and we get at just a ballpark number as result for orientation.
59 is much closer to 60 than to 50.
42 is much closer to 40 than to 50.
of course, we round to the closest "round numbers", so that the loss of precision through the rounding is as little as possible, so that the estimation still gives a much value as possible.
and the sum of the differences of the factors should be as close to 0 as possible.
so, 60×40 is the closest and therefore best estimation.
the sum of the factor differences is (+1 - 2) = -1.
compare to the real result :
59×42 = 2,478
answer a and b are by the way not correct :
50×40 = 2000 (and not 2500)
60×50 = 3000 (and not 3500)
FYI - in this case 50×50 = 2500 would be the closest estimation.
and the sum of the factor differences would be (-9 + 8) = -1.
normally, this wide "jumping" (-9 to +8) would make it only second choice.
If y = 9 inches, z = 14 inches, h = 5 inches, and w = 4 inches, what is the area of the object?
Answers
Answer:
126
Step-by-step explanation:
x − y = 12
x + 2y = 21
Answers
Answer: x=15, y=3
Step-by-step explanation:
Subtracting the two equations, we get -3y=-9, meaning y=3.
Substituting this into the first equation, we get that x-3=12, and thus, x=15.
Triangle JKL is reflected across the y-axis to create ∆J' K' L' . Are the two figures are congruent
Answers
pls help me with this problem :)
The areas of two similar triangles are 9 cm² and 49 cm². One of the sides of the first
triangle is 2 cm. What is the length of the corresponding side of the other triangle?
Answers
Answer:
I believe it should be rounded to 11, if not decimal would be 10.88
Step-by-step explanation:
49 divided by 9 equals 5.44 which is the amount times the 49cm^2 triangle is compared to the 9cm^2. So then the side is 2cm, multiply by the amount times bigger the other triangle is which would be 10.88. Hopefully I'm not wrong:)
Answer:
The answer is 4 and 2/3 cm²
Step-by-step explanation:
Take the square root of 49 and 9 and you'll get 7 and 3 since the scale factor is the large area over the small area.
The large area would be √49 cm²
The small area would be √9 cm²
7 x cm
------ = ----------, cross multiply
3 2 cm
7 × 2 = 3 × x
14 = 3x
x = 14/3, x = 4 and 2/3
what is the volume of the composite
Answers
3/x=2
How do you solve this without get a loop
Answers
Answer:
x= 3/2
Step-by-step explanation:
3/x=2
Multiply x both sides so,
3 =2x
Divide 2 to get the value of x so,
x= 3/2
X=
08
09
0 10
4
10 X
Answers
Answer:
8
Step-by-step explanation:
Intersecting Chords Formula:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
5*x = 4*10
5x = 40
Divide by 5
5x/5 = 40/5
x = 8
A triangle has side lengths 9 cm, 12 cm, and 16 cm.
Answers
Answer:
https://www.calculator.net/triangle-calculator.html?vc=&vx=16&vy=9&va=&vz=12&vb=&angleunits=d&x=54&y=24
Step-by-step explanation:
I went to this website
https://www.calculator.net/triangle-calculator.html
put in what I knew of the triangle and got all the information you may need.