Answer:
x = 8.69
Step-by-step explanation:
we know that the perimeter of the dodecagon is 54, so each edge will be 54/12
54/12 = 4.5 cm
if we draw the lines to remove 6 vertices and form a hexagon, 6 triangles with 2 sides of 4.5 cm are formed.
we know that the angle of each vertex is 150 ° because it is a dodecagon
if we apply the law of cosines we can take the other side of the triangle, since we only need 2 side and the opposite angle to the side we want to know
a would be our x
b = 4.5
c = 4.5
A = 150°
a^2 = b^2 + c^2 - 2bc * cos (A)
x^2 = 4.5^2 + 4.5^2 - 2 * 4.5 * 4.5 * cos (150)
x^2 = 20.25 + 20.25 - 40.50 * -0.866
x^2 = 40.50 + 35.07
x = √ 75.57
x = 8.69
Answer:
The first number is 20, the second one is 11
Step-by-step explanation:
Let the first number be x and the second number be y
Since it says "9 is the difference between two numbers", the first equation will be x-y=9
It also says that "their sum is 31". That means the second equation will be x+y=31
here are the two equations:
x-y=9
x+y=31
You can solve this any way you like, but I'll show elimination
add the two equations
x-y=9
x+y=31
2x=40
divide by 2
x=20
Substitute 20 as x in one of the equations
20+y=31
subtract 20 from both sides
y=11
That means the two numbers are 20 and 11
Hope this helps!
