1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Svetllana [295]
3 years ago
14

The area of a regular octagon is 35 cm^2. What is the area of a regular octagon with sides five times as long?

Mathematics
1 answer:
Marat540 [252]3 years ago
3 0
So... let's say the smaller regular octagon has sides of "x" long, then the larger octagon will have sides of 5x.

\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&Sides&Area&Volume\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array} \\\\
-----------------------------\\\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\
-------------------------------\\\\

\bf \cfrac{small}{large}\quad \stackrel{area~ratio}{\cfrac{s^2}{s^2}}\implies \stackrel{area~ratio}{\cfrac{x^2}{(5x)^2}}\implies \stackrel{area~ratio}{\cfrac{x^2}{5^2x^2}}\implies \stackrel{area~ratio}{\cfrac{\underline{x^2}}{25\underline{x^2}}}=\stackrel{area~ratio}{\cfrac{35}{a}}
\\\\\\
\cfrac{1}{25}=\cfrac{35}{a}\implies a=\cfrac{25\cdot 35}{1}
You might be interested in
A softball backstop that is 10 feet high casts an 8-foot shadow at the same time a light pole casts a 20-foot shadow. The height
Sedbober [7]

I'm just getting points

Step-by-step explanation:

just getting points

8 0
2 years ago
For a consumer to obtain a 10% discount, he must spend an amount
DENIUS [597]

Answer:

the answer is 180 dollars

Step-by-step explanation:

20 is 10% of 200 so just subtract that

3 0
2 years ago
How do you turn a percent into a decimal?
olchik [2.2K]

Answer:multiply the percent times 100

Step-by-step explanation:

8 0
3 years ago
Show that ifAB=IandAC=I, then it follows that B=C. Explain how this proves thatthe inverse of the matrix A is unique.
Anna007 [38]

Answer with Step-by-step explanation:

Suppose that a matrix has two inverses B and C

It is given that AB=I and AC=I

We have to prove that Inverse of matrix is unique

It means B=C

We know that

B=BI where I is identity matrix of any order in which number of rows is equal to number of columns of matrix B.

B=B(AC)

B=(BA)C

Using associative property of matrix

A (BC)=(AB)C

B=IC

Using BA=I

We know that C=IC

Therefore, B=C

Hence, Matrix A has unique inverse .

6 0
3 years ago
An English teacher has 6 short stories, 4 novels, and 23 poems to choose from. How many ways can he assign one of each to his cl
Karolina [17]

Answer:

552

Step-by-step explanation:

This is a problem of permutation which can be solved by rule of fundamental counting principle.

This principle states that if there "m" ways of doing one thing and "n" ways of doing other. Then no. of ways in which both the things can be done together is "m*n". This can be extended for m, n, p,r, s things and so on.

example: if there are 5 shirts and 3 trousers then number of ways in which the shirts and trousers can be worn is 5*3 = 15 ways.

_____________________________________________

The given problem is on similar concepts.

here  6 short stories, 4 novels, and 23 poems have to be assigned to his class.

Thus it can be done in 6*4*23 = 552 ways.

5 0
3 years ago
Other questions:
  • Ms. Higgins would like for her homework assignments to have three addition problems for every five subtraction problems. If she
    6·1 answer
  • The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she d
    5·1 answer
  • A mother is currently 7 times older than her son. In 3 years time, she will be 5 times older than her son. Let x and y be the pr
    11·2 answers
  • Triangle LMN is similar to triangle PQR. Which of the following sets of side lengths could be those of triangle LMN.
    6·2 answers
  • It takes 2 hours for a boat to travel 28 miles downstream.The same boat can travel 18 miles upstream in 3 hours .Find the rate o
    6·1 answer
  • Please answer ASAP<br><br><br>y=5/8b+10 for b, ill give brainliest and show work plz
    11·1 answer
  • Sally is 140cm tall and Tara is 160cm. What is the ratio of their<br> heights (in its lowest terms)
    6·1 answer
  • Triangle ABC has angle measures as shown.
    11·2 answers
  • I need answer immediately!!!!!!
    14·1 answer
  • PLS HELP!!!!!!!!!!!!! math related
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!