A regular m-gon has 3 times as many sides as a regular k-gon.
The measure of an interior angle of the regular m-gon is 14/3 times
the measure of an exterior angle of the regular k-gon.
Algebraically find the values of k and m.

Answers

Answer 1

9514 1404 393

Answer:

k = 10m = 30

Step-by-step explanation:

The interior angle of the m-gon is ...

  m-interior = 180 -360/m

The exterior angle of the k-gon is ...

  k-exterior = 360/k

The required relationships are ...

  m = 3k

  m-interior = 14/3(k-exterior)

Substituting for m, we can write the latter relation as ...

  (180 -360/(3k)) = 14/3(360/k)

Multiplying by 3k/180, we have ...

  3k -2 = 28

  k = (28 +2)/3 = 10

The values of k and m are 10 and 30, respectively.

_____

Check

The interior angle of the m-gon is 180 -360/30 = 168 degrees.

The exterior angle of the k-gon is 360/10 = 36 degrees.

The angle ratio is 168/36 = 14/3 as required.


Related Questions

4. The average speed of an Express train between New Delhi and Kota is 97 km/hr. The train
takes 4 hr to travel from New Delhi to Kota. Find the distance between New Delhi and Kota.

Answers

Answer:

Distance between New Delhi and Kota = 388 kilometers

Step-by-step explanation:

Given that:

Average speed of express train = 97 kilometer per hour

Time taken to travel  = 4 hours

Distance between New Delhi and Kota = Speed * Time

Distance = 97 * 4

Distance = 388 kilometers

Hence,

Distance between New Delhi and Kota = 388 kilometers

On Sunday, Sheldon bought 4 1/2 kg of plant food. He used 1 2/3 kg on his strawberry plants and used 1/4 kg for his tomato plants.



How many kilograms of plant food did Sheldon have left?

Answers

Answer:

Sheldon had 2 7/12 kg left

4 1/4 - 1 2/3 = 3 1/4 - 2/3

= 3 3/12 - 8/12

= 2 15/12 - 8/12

= 2 7/12

Hope this helps! have an amazing day :)

A town's population of children increased from 376 to 421 during the past year. Which equation shows how to find the percent increase? a p=421−376376 b p=421−376421 c p=376421−376

Answers

Answer:

a. p=421−376/376

Step-by-step explanation:

Computation for Which equation shows how to find the percent increase

Percentage increase=421-376/376*100

Percentage increase=45/376*100

Percentage increase=11.968%

Percentage increase=11.97% (Approximately)

Based on the above calculation The equation that will shows how to find the percent increase of the town's population of children from 376-421 during the past year will be:p=421-376/376

Ashley charges 25.00 pesos for every page for
encoding. In addition, she charges 5 pesos per
page of printed output. How many page/s
did she encode
and print if she receives
amount of 960.00 pesos?
a. 10
c. 30
b. 20
d. 32​

Answers

first add 25 and 5 and divide 960 by 30

Help with these two they have to be Decimal or fraction form rounded all the way!!

Answers

Answer:

x=1/2 I'm not sure it may be wrong

Answer:

The question to the question provided is

[tex] \frac{1}{2} [/tex]

What’s 2 1/4 + 3 2/3

Answers

Answer:

The correct answer is 5 11/12

Step-by-step explanation:

HAVE A GOOD DAY!

Help! I’ll mark brainliest! Show your work.

Answers

the perimeter is 16 units


Find the slope of the
equation below and show the work.
X=4

Answers

Answer:

Undefined

Step-by-step explanation:

If a linear equation is organized in the form x=[a number], we know straight away that this line is a vertical line. This form is actually [tex]x=d[/tex], where [tex]d[/tex] is the x-intercept of the line. Vertical lines do not have a y-intercept because they are parallel to the y-axis.

The slope of vertical lines is undefined.

I hope this helps!

6 m 11m in area

10yrd 8yd in area

5in 7in in area

4cm 6cm 10cm in area

Please I need answers for all of them

Answers

66,80,35,24000
Those are the answers if I’m correct

Can anyone help me solve this is a worksheet extra credit

Answers

Answer:

11. Coordinates of the meeting point 18,24

12.equation for line R, y= -2x/5-4

equation for line E,y=2x/5+12

13. 1,3, 4,5,10,13 ,15

14.70°

15. AC= 47

Step-by-step explanation:

I'm pretty sure about the answers. Please consider making brainliest. Thank you

How many different positive four-digit integers can be created if the four digits 1,
3,5, and 6 must be used to create each integer?

Answers

Answer:

You have 4 digits with which to work. The digits can be placed:

1st position: 4 possible digits

2nd position 3 possible digits

3rd position 2 possible digits

4th position 1 possible digit

Total permutations equal

4 * 3 * 2 * 1

which equals

24

Step-by-step explanation:

A pair of jeans is on sale for 25% off the original price. The sale price is $78. What is the original price

A.
$59

B.
$103

C.
$104

D.
$312

Answers

Answer: C (104)

Step by step explanation:

To find this answer, you would multiply all the answer choices by 25% and then add the answer to 78 and if the answer is that number, then its correct

104 times 25%=26

78+26=104

does anyone know how to solve 2x+3y=7 and 4x-5y=25 using substitution to solve the system of equations. PLEASE HELP ONLY IF YK IT

Answers

Answer:

x = 5, y = -1

Step-by-step explanation:

2x+3y=7

4x-5y=25

Keep the second equation the same, but change the first equation so you have something to substitute into.

3y= -2x+7

y= -2/3x + 7/3

substitute into second equ.

4x + 10/3x - 35/3 = 25

put the variables on one side, and the numbers on the other.

22/3x = 110/3

divide by 3

22x = 110

x = 5

Substitute x = 5 into the first equation,

10 + 3y = 7

move numbers to one side, and variables to the other.

3y = -3

y = -1

Answer:

x = 5, y = - 1

Step-by-step explanation:

2x + 3y = 7

4x - 5y = 25

In the second equation, solve for y in terms of x:

4x - 5y = 25

- 5y = 25 - 4x

- y = 5 - 4x/5

y = - 5 + 4x/5  Now substitute this for y in equation 2x + 3y = 7

2x + 3(-5 + 4x/5) = 7

2x - 15 + 12x/5 = 7

10x/5 - 15 + 12x/5 = 7

22x/5 = 7 + 15

22x/5 = 22  Now multiply both sides by 5/22 to isolate :

x = 5

Now substitute this value (x = 5) into 4x - 5y = 25 to solve for y:

4(5) - 5y = 25

20 - 5y = 25

- 5y = 5

y = - 1

You can check that these are correct by substituting x = 5 and y = -1  into the above equations to make sure they check out.

Polygon ABCD has the following vertices:

A(−4, 2), B(3, 2), C(3, −5), and D(−4, −2)

Calculate the area of the polygon.

28 units squared
38.5 units squared
40.5 units squared
49 units squared

Answers

9514 1404 393

Answer:

  (b)  38.5

Step-by-step explanation:

The polygon is a trapezoid with bases 4 and 7 and height 7. Its area is given by the formula ...

  A = (1/2)(b1 +b2)h

  A = (1/2)(4 +7)(7) = 77/2

  A = 38.5 . . . . square units

Give the other person brainiest pls because they were right I know because I took test and they helped me :)

ok i can drag what goes in what

Answers

Answer:

The equation should look like c=1.59 times a

Step-by-step explanation:

if it cost 1.59 dollars per pound of apple it is going to be a multiplication problem so then you fill in the blanks, A standing for per pound of apples and C representing total cost

is the relation a function? why

Answers

Answer:

no its not

Step-by-step explanation:

x-11 is only supposed to have one y.

if its a funtion then x should only have one line comming out of it. if its not a finction then x has two lines coming out of it.

Answer: no because the x axis dont equal or match up with the y axis and because theres not a certain amount of numbers for it to equal to or match to.

Step-by-step explanation:

A function is a relation in which each input has only one output. In the relation , y is a function of x, because for each input x (1, 2, 3, or 0), there is only one output y. x is not a function of y, because the input y = 3 has multiple outputs: x = 1 and x = 2.            please give me brainliest

write a real word problem that you could represent 3+ x =10

Answers

Answer:

A class has 10 science students, both of Physics and Biology.

If Biology group has 3 students, what's the number of students in the Physics group?


A line has this equation: -5y = 4x+40
Write an equation for the perpendicular line that goes through (8,5).

Answers

Answer:

The equation of the second line is;

y = 4x - 27

Step-by-step explanation:

Firstly, we need the slope of the first line

To get the slope, we need the equation in the general form of ;

y = mx + c

where m is the slope of the line

Thus, we have in this case, to divide through by -5

That will give the slope value as -5/20 = -1/4

If two lines are perpendicular, the product of their slopes is -1

The slope of the line we want to calculate, let us call it m

m * -1/4 = -1

-m = -4

m = 4

So we want to write the equation of a line with slope 4 and point (8,5)

We proceed to use the point-slope form

That will be;

y-y1 = m(x-x1)

y-5 = 4(x-8)

y-5 = 4x-32

y = 4x -32 + 5

y = 4x -27

quadratic equations
m^2-12=m

Answers

Step-by-step explanation:

m² -12 = m

m² = m + 12

m = [tex]\sqrt{m + 12\\}[/tex]

Substitute the known value of x​ into y=4x+20​. Then solve for y entering the equation in simplest form

Answers

Answer:

[tex]y=24,[/tex] when [tex]x=1[/tex].

Step-by-step explanation:

Given: [tex]y=4x+20[/tex]

To find: Value of [tex]y[/tex], substituting the known value of [tex]x[/tex]

We have,

[tex]y=4x+20 ...(i)[/tex]

Putting [tex]x=1[/tex] in equation [tex](i)[/tex], we get

[tex]y=4(1)+20[/tex]

[tex]\implies y=4+20[/tex]

[tex]\implies y=24[/tex]  

Hence, the value of [tex]y[/tex] is [tex]24[/tex], when the value of [tex]x[/tex] is [tex]1[/tex].

The ratio of cats to dogs at April's Animal Shelter was 3 to 2. How many dogs were in the shleter if there were a total of 75 cats and dogs in the
shelter?
A 30
B 25
c 50
d 150

Answers

Answer:

A:30

Step-by-step explanation:

because 3+2(the ratio) =5

75(the total number or both) divide by 5

so 1 ratio=15

15 x 2(the ratio of dogs)

=30

3 less than 8 times w

Answers

Answer:

8w-3

Step-by-step explanation:

Is that what you were looking for?

Evaluate the expression when a = 17 and c = 7.
²
a+c
a-2c

Answers

A+c
17+7=24
a-2c
17-2(7)=3

Answer:

Step-by-step explanation:

a + c = 17 + 7 = 24.

a - 2c = 17 - 2(7) = 3.

Bryan and his parents went to dinner at their favorite restaurant. The bill came to $130. His parents left a 15% tip. How much TIP did they leave? *

Answers

Answer:

$19.50

Step-by-step explanation:

Turn the %15 into a decimal

130 x 0.15 = 19.50

They left $19.50 as their tip.

Find the quotient. -275/-25

Answers

Answer:

5

Step-by-step explanation:

-275/-25 is 11 because a negative and a negative equal a positive and then you just divide. :)

pls help with this :(​

Answers

Answer:

is it 8x

i'm not sure

Step-by-step explanation:

Answer:

( E ) = 18x

Step-by-step explanation:

According to question,

2/3 ( E ) = 12x [ Here ( E ) is the expression]

2 ( E ) = 36x

( E ) = 36/2 x

( E ) = 18x

Hope it helps.......

Phillip wanted to leave a 15% tip. He thought to himself that 15% = 10% plus half of 10%. Which of the following equations will help Phillip estimate the tip on a $36.00 bill correctly?
A.
$3.60 + $3.60 = $7.20

B.
$3.60 + $0.36 = $3.96
C.
$1.80 + $1.80 = $3.60
D.
$3.60 + $1.80 = $5.40

Answers

3.00 that Ian’s kiwi wow

Answer: 36.00

Step-by-step explanation:

Divide 36.00 by 10 and You Simply Get 3.60

Hope this Helps :DD

The school store received a shipment of notebooks and pens. There are 10 cartons of notebooks and 25 boxes of pens. Each carton of notebooks costs $72 and contains 48 notebooks. Each box of pens costs $12.60 and contains 36 pens. The school wants to make a 10% profit.

question What is the cost of one notebook? What amount must be added on to the notebook's cost to account for a 10% markup? What will be the retail price (price the school is charging) for the notebook?

Answers

Answer:

cost of one notebook:  72/48 = $1.50

10% mark up = $1.50 x 0.10 = 0.15 cents

retail price = $1.65

Step-by-step explanation:

Mr bell bought a freezer in a sale where all goods were 20% off. what was the original price of the freezer?

Answers

Answer:

First, you did not exactly state what the original price was or maybe that's how the question is worded, but in this scenario the original price of the freezer would be x because they did not tell us.

Step-by-step explanation:

A 20 percent discount is 0.20 in decimal format. For example if the original price was $20, then you would multiply 0.2 by $20 to get $4.00. In this question i would say the original price would be x, so then it would be 0.2x.

Hope this helps:)

Mrs. Rawlings is preparing to celebrate National Cone Appreciation Day! She will paint 100 cones like the one shown to the right. Approximately how much paint will she need? (Use 3.14 for n.)

Answers

Answer:

Step-by-step explanation:

8+5+9.4= 22.4

100n+22.4

100(3.14)+22.4= 336.4

I gave you this to help you, if you know how much is in each paint cans, than divide that number with 336.4, and you'll get your answer.

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