FILL IN THE BLANK PLEASE HELP 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 (red line), what special right triangle do you create? _

(4) What is the vocabulary word for the red 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. _

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

sasaasasa

step-by-step explanation:

sasasdfubisdbjvkzc

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)

step-by-step explanation:

6