Step-by-step explanation:
With reference to the regular hexagon, from the image above we can see that it is formed by six triangles whose sides are two circle's radii and the hexagon's side. The angle of each of these triangles' vertex that is in the circle center is equal to 360∘6=60∘ and so must be the two other angles formed with the triangle's base to each one of the radii: so these triangles are equilateral.
The apothem divides equally each one of the equilateral triangles in two right triangles whose sides are circle's radius, apothem and half of the hexagon's side. Since the apothem forms a right angle with the hexagon's side and since the hexagon's side forms 60∘ with a circle's radius with an endpoint in common with the hexagon's side, we can determine the side in this fashion:
tan60∘=opposed cathetusadjacent cathetus => √3=Apothemside2 => side=(2√3)Apothem
As already mentioned the area of the regular hexagon is formed by the area of 6 equilateral triangles (for each of these triangle's the base is a hexagon's side and the apothem functions as height) or:
Shexagon=6⋅S△=6(base)(height)2=3(2√3)Apothem⋅Apothem=(6√3)(Apothem)2
=> Shexagon=6×62√3=216
Answer:
A Solution is a value we can put in place of a variable (such as x) that makes the equation true.
Step-by-step explanation:
Answer:
(-2a, -2b)
Step-by-step explanation:
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A nonlinear system of equation is a system of equation that has at list one nonlinear equation
A nonlinear system of equations that has one linear function that never intersects the quadratic function has; <u>No solution</u>
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The reason the option selected for the number of solutions is correct is as follows;
Required:
The number of solutions a system of nonlinear equations that do not intersect have
Solution:
The given system of equation is presented as follows;
Linear function: f(x) = m·x + c
Quadratic function: f(x) = a·x² + b·x + c
Given that the linear function never touches the quadratic function, we have;
a·x² + b·x + c ≠ m·x + c
Therefore, the equations are never equal hand they have no common solution
Therefore, the correct option is <u>No solution</u>
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Learn more about nonlinear system of equations here:
brainly.com/question/11650202
brainly.com/question/10571443
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