Using the diagram of a regular hexagon, fill in the blanks for the steps to solve for the area of a hexagon with sides equal to 8 cm. (1) How many equilateral triangles are there? _

(2) What is the measure of each of the three angles in the equilateral triangle? _

(3) If we cut an equilateral triangle down the middle (green line), what special right triangle do you create? _

(4) What is the vocabulary word for the green line? _

(5) What is the length of the short side of one 30-60-90 triangle? _

(6) What is the length of the hypotenuse of one 30-60-90 triangle? _

(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg. _

(8) What is the height of the equilateral triangle? _

(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. _

(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.