Answer:
The area of the regular hexagon is ![166.3\ units^{2}](https://tex.z-dn.net/?f=166.3%5C%20units%5E%7B2%7D)
Step-by-step explanation:
we know that
The area of a regular hexagon can be divided into 6 equilateral triangles
so
step 1
Find the area of one equilateral triangle
![A=\frac{1}{2}(b)(h)](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%28b%29%28h%29)
we have
![b=r=8\ units](https://tex.z-dn.net/?f=b%3Dr%3D8%5C%20units)
----> is the apothem
substitute
![A=\frac{1}{2}(8)(4\sqrt{3})](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%288%29%284%5Csqrt%7B3%7D%29)
![A=16\sqrt{3}\ units^{2}](https://tex.z-dn.net/?f=A%3D16%5Csqrt%7B3%7D%5C%20units%5E%7B2%7D)
step 2
Find the area of 6 equilateral triangles
![A=(6)16\sqrt{3}=96\sqrt{3}=166.3\ units^{2}](https://tex.z-dn.net/?f=A%3D%286%2916%5Csqrt%7B3%7D%3D96%5Csqrt%7B3%7D%3D166.3%5C%20units%5E%7B2%7D)
I got 36000000 . Hope this helps
Answer:
The two step equation that we can use to find michael's age is x = (f-2)/4 where f = 30. So Michael is 7 years old.
Step-by-step explanation:
In order to solve this problem we will attribute variables to the ages of Michael and his father. For his father age we will attribute a variable called "f" and for Michael's age we will attribute a variable called "x". The first information that the problem gives us is that Michael's dad is 30 years of age, so we have:
f = 30
Then the problem states that the age of the father is 2 years "more" than four "times" Michaels age. The "more" implies a sum and the "times" implies a product, so we have:
f = 2 + 4*x
We can now find Michael's age, for that we need to isolate the "x" variable. We have:
f - 2 = 4*x
4*x = f - 2
x = (f-2)/4
x = (30 - 2)/4 = 7 years
The two step equation that we can use to find michael's age is x = (f-2)/4 where f = 30. So Michael is 7 years old.
To acquire a given product. Insofar as the amount people are prepared to pay for a product represents its value, price is also a measure of value.
Answer:
![\displaystyle x \approx 8.2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20%5Capprox%208.2)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Trigonometry</u>
[Right Triangles Only] SOHCAHTOA
[Right Triangles Only] sinθ = opposite over hypotenuse
Step-by-step explanation:
<u>Step 1: Identify Variables</u>
Angle θ = 23°
Opposite Leg = <em>x</em>
Hypotenuse = 21
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute in variables [sine]:
![\displaystyle sin(23^\circ) = \frac{x}{21}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20sin%2823%5E%5Ccirc%29%20%3D%20%5Cfrac%7Bx%7D%7B21%7D)
- [Multiplication Property of Equality] Isolate <em>x</em>:
![\displaystyle 21sin(23^\circ) = x](https://tex.z-dn.net/?f=%5Cdisplaystyle%2021sin%2823%5E%5Ccirc%29%20%3D%20x)
- Rewrite:
![\displaystyle x = 21sin(23^\circ)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20%3D%2021sin%2823%5E%5Ccirc%29)
- Evaluate:
![\displaystyle x = 8.20535](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20%3D%208.20535)
- Round:
![\displaystyle x \approx 8.2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%20%5Capprox%208.2)