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KATRIN_1 [288]
3 years ago
9

Please help me with #7

Mathematics
1 answer:
Dominik [7]3 years ago
8 0

Step-by-step answer:

This is a regular heptagon, means it has 7 <em>congruent</em> sides and 7 <em>congruent </em>vertex angles.

To work with polygons, there is a very important piece of information that you must know to solve the majority of related problems.

This is:

sum of exterior angles of polygons = 360 degrees.

If you don't remember the 360 degrees, think of the sum of exterior angles of an equilateral triangle, which is 3*(180-60)=3*120=360!  It works!

For a regular heptagon, c = 360/7=51.43 degrees approx.

This means that each vertex angle measures

vertex angle = 180-c

So since 2d+the vertex angle = 360, we have

2d+(180-c)=360

solve for d:

2d=360-(180-c)=180+c

d=(180+c)/2=90+c/2=115.71 degrees. (approx.)

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<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%20%2B%201%20%7D%7B2%7D%20%20%3D%20%20%5Cfrac%7B7x%20-%203%7D%7B2%7D%20" id="Tex
MAVERICK [17]

Answer:

\sf x =\dfrac{2}{3}

Explanation:

\sf \rightarrow \dfrac{x+1}{2} = \dfrac{7x-3}{2}

cross multiply

\sf \rightarrow 2(x+1) = 2(7x-3)

divide both sides by 2

\sf \rightarrow x + 1 = 7x-3

isolate variables

\sf \rightarrow x -7x = -3-1

simplify

\sf \rightarrow -6x = -4

divide both sides by -6

\sf \rightarrow \dfrac{-6x}{-6}  = \dfrac{-4}{-6}

simplify

\sf \rightarrow x =\dfrac{2}{3}

4 0
1 year ago
Read 2 more answers
Taking finals pls help
Shtirlitz [24]

Answer:

It should be B $250 - - - - -

3 0
3 years ago
Factor 4n^2 - 5n -6​
Allushta [10]

Answer:

(n-2) • (4n+3)

Step-by-step explanation:

4n2-5n-6  

Final result :

 (n - 2) • (4n + 3)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (22n2 -  5n) -  6

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  4n2-5n-6  

The first term is,  4n2  its coefficient is  4 .

The middle term is,  -5n  its coefficient is  -5 .

The last term, "the constant", is  -6  

Step-1 : Multiply the coefficient of the first term by the constant   4 • -6 = -24  

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -5 .

     -24    +    1    =    -23  

     -12    +    2    =    -10  

     -8    +    3    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  3  

                    4n2 - 8n + 3n - 6

Step-4 : Add up the first 2 terms, pulling out like factors :

                   4n • (n-2)

             Add up the last 2 terms, pulling out common factors :

                   3 • (n-2)

Step-5 : Add up the four terms of step 4 :

                   (4n+3)  •  (n-2)

            Which is the desired factorization

Final result :

 (n - 2) • (4n + 3)

3 0
3 years ago
What is the point of intersection when the system of equations below is graphed on the coordinate plane?
olya-2409 [2.1K]

Answer:

I.M.S. infinite many solutions

Step-by-step explanation:

this will come out to be the same line.

6 0
3 years ago
The initial count of a certain type of bacteria in a culture is 350. If the bacteria grows at the rate of 20% per hour, which fu
raketka [301]
I think it is 350(1.2)^t because you take the starting amount (350) and then multiple it by the growth rate (which is 20%, but when added to 100 and the put into a decimal is 1.2) raised by the number of hours (t).
I hope this helps.
4 0
3 years ago
Read 2 more answers
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