What is the size of an interior angle of a regular hexagon

Which of the following is a solution to sin(x/2) = radical 3/2

Vinvika [58]

Answer:

sin ( x/ 2 ) = - √ 3 /2

Take the inverse sine of both sides of the equation to extract x

from inside the sine.

x/ 2 = arcsin ( − √ 3/ 2 )

The exact value of arcsin ( − √ 3 /2 ) is − π /3 .

/x 2 = − π /3

Multiply both sides of the equation by 2 .

2 ⋅ x /2 = 2 ⋅ ( − π /3 )

Simplify both sides of the equation.

x = − 2 π /3

The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from 2 π , to find a reference angle. Next, add this reference angle to π to find the solution in the third quadrant.

x /2 = 2 π + π/ 3 + π

Simplify the expression to find the second solution.

x = 2 π /3

4 π

Add 4 π to every negative angle to get positive angles.

x = 10 π /3

The period of the sin ( x /2 ) function is 4 π so values will repeat every 4 π radians in both directions.

x =2 π /3 + 4 π n , 10 π/ 3 + 4 π n , for any integer n

Exclude the solutions that do not make sin ( x /2 ) = − √ 3/ 2 true.

x = 10 π /3 + 4 π n , for any integer n

4 0

3 years ago

( 100 pts and brainliest )Which graph shows?

Rashid [163]

Answer

Try looking up answer sheets for this question I don't know the answer but i would help you if i could.

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Write a simplified expression to find the perimeter of a square with a side length of 3y units.

Murrr4er [49]

Answer:

Perimeter= 12y units

3y(4) = 12y

Step-by-step explanation:

3y + 3y + 3y + 3y= 12y

4 0

2 years ago

An experience bricklayer can construct a small wall in 3 hours. An apprentice can complete the job in 5 hours. Find how long it

Over [174]

Answer:

Step-by-step explanation:

If the bricklayer can construct the wall in its entirety in 3 hours, then he can get 1/3 of the job done in an hour.

If the apprentice can get the whole job done in 5 hours, then he can get 1/5 of the job done in an hour. If they both work together on said job, the equation is

$\frac{1}{3}+\frac{1}{5}=\frac{1}{x}$ and now we solve for x. Multiply everything by the LCM to get rid of the fractions. That would be 15x:

$15x(\frac{1}{3}+\frac{1}{5}=\frac{1}{x})$ and doing that gives us

5x + 3x = 15 and

8x = 15 so

x = 1.875 hours which is 1 7/8 hours which is also 1 hour and 52 1/2 minutes.

3 0

3 years ago

If the original square had a side length of

irina [24]

Answer:

Part a) The new rectangle labeled in the attached figure N 2

Part b) The diagram of the new rectangle with their areas in the attached figure N 3, and the trinomial is $x^{2} +11x+28$

Part c) The area of the second rectangle is 54 in^2

Part d) see the explanation

Step-by-step explanation:

The complete question in the attached figure N 1

Part a) If the original square is shown below with side lengths marked with x, label the second diagram to represent the new rectangle constructed by increasing the sides as described above

we know that

The dimensions of the new rectangle will be

$Length=(x+4)\ in$

$width=(x+7)\ in$

The diagram of the new rectangle in the attached figure N 2

Part b) Label each portion of the second diagram with their areas in terms of x (when applicable) State the product of (x+4) and (x+7) as a trinomial

The diagram of the new rectangle with their areas in the attached figure N 3

we have that

To find out the area of each portion, multiply its length by its width

$A1=(x)(x)=x^{2}\ in^2$