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sergij07 [2.7K]
2 years ago
8

Find the number of units in the length of diagonal $DA$ of the regular hexagon shown. Express your answer in simplest radical fo

rm.
Mathematics
1 answer:
LekaFEV [45]2 years ago
6 0

17.32 the number of units in the length of diagonal $DA$ of the regular hexagon.

<h3>How do you find the length of the diagonal of a regular hexagon?</h3>

Six equilateral triangles can be formed from the hexagon. The equilateral triangle has an equal length on each side. The diagonal of the hexagon is formed by joining two of the sum of the lengths of the equilateral triangles. As a result, the hexagon's diagonal is twice as long as its sides.

For a polygon, the SUM of the internal angles is:

(n-2) * 180 (n=6 for hexagon)

(6-2)*180 = 720   Thus EACH angle is :   720/6 = 120 degrees

Therefore, the triangle's main angle is 120 degrees, and its other two angles are equal.

There are 180 degrees in any triangle:  

(180-120) / 2 = 30 degrees for each of the smaller angles.

Now use the law of sines:

10/sin30 = x/(sin120)

10/(.5)  × (sqrt3 )/ 2 = x

10 sqrt 3

10/sin30  ×  sin 120  =  17.32

17.32 is the number of units in the length of diagonal $DA$ of the regular hexagon.

Learn more about hexagon here:

brainly.com/question/28016053

#SPJ4

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EXPAND:
Sladkaya [172]

Answer:

\displaystyle  A) 5\log( {x}^{}   )  +   2 \log( {y}^{} )

Step-by-step explanation:

we would like to expand the following logarithmic expression:

\displaystyle   \log( {x}^{5}  {y}^{2} )

remember the multiplication logarithmic indentity given by:

\displaystyle \rm  \log( \alpha  \times  \beta ) \iff  \log( \alpha ) +  \log( \beta )

so our given expression should be

\displaystyle   \log( {x}^{5}   )  +    \log( {y}^{2} )

by exponent logarithmic property we acquire:

\displaystyle   5\log( {x}^{}   )  +   2 \log( {y}^{} )

hence, our answer is A

5 0
3 years ago
6 1/2 - 3 2/5 please help really need it
tatuchka [14]
Answer is 3 1/10 


6 1/2 - 3 2/5 =
13/2 - 17/5 =
65/10 - 34/10 = 
31/10 = 3 1/10
4 0
3 years ago
What Is 34 in standard form?
mamaluj [8]

Answer:

30+4?

Step-by-step explanation:

4 0
3 years ago
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4-x and y = 2x + 3 intersect are the s
ale4655 [162]
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4-x and y = 2x + 3 intersect are the solutions of the equation 4-x = 2x + 3.

Because the point where the graphs intersect is a point that meets both rules (functions) y = 4 - x and y = 2x + 3 meaning that y from y = 4 - x equals y from 2x + 3 and also both x have the same value.

Part B: Make tables to find the solution to 4-x = 2x + 3. Take the integer values of x between -3 and 3.

x values    4 -x         2x + 3

-3              4-(-3)=7     2(-3)+3 =-3
-2              4-(-2)=6     2(-2)+3 =-1
-1              4-(-1)=5     2(-1)+3 = 1
0                4-0=4        2(0)+3 = 3
1                4-1=3         2(1)+3=5
2                4-2=2        2(2)+3 = 7
3                4-3=1        2(3)+3 = 9

The the solution is between x = 0 and x =1

Part C: How can you solve the equation 4-x = 2x + 3 graphically?

Draw in a same graph both functions  y= 4 - x and y = 2x +3.

Then read the x-coordinates of the intersection point. That is the solution.

3 0
3 years ago
Pls help will mark brainlist if correct !! :))
german

Answer:

its (B)

Step-by-step explanation:

8 0
3 years ago
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