Answer:
x = 12
Step-by-step explanation:
The hexagonal tile given here is made up of 6 triangles with equal bases and heights.
So, area of hexagonal tile will be equal to 6 times the area of one triangle.
Therefore,
![18 \sqrt{3} = 6 \times \frac{1}{2} \times 2 {( \sqrt{3)} }^{ \frac{x}{12} } . {( \sqrt{3)} }^{ \frac{x}{6} } \\ \\ 18 \sqrt{3} = 6 {( \sqrt{3)} }^{ \frac{x}{12} } . {( \sqrt{3)} }^{ \frac{2x}{12} } \\ \\ \frac{18 \sqrt{3} }{6} = {( \sqrt{3)} }^{ \frac{x}{12} + \frac{2x}{12} } \\ \\ 3 \sqrt{3} = {( \sqrt{3)} }^{ \frac{3x}{12} } \\ \\ 3. {3}^{ \frac{1}{2} } = {3}^{ \frac{3x}{24} } \\ \\ {3}^{1 + \frac{1}{2} } = {3}^{ \frac{x}{8} } \\ \\ {3}^{ \frac{3}{2} } = {3}^{ \frac{x}{8} } \\ (bases \: are \: equal \: so \: exponents \: \\ will \: also \: be \: equal) \\ \implies \frac{3}{2} = \frac{x}{8} \\ \\ x = \frac{3 \times 8}{2} \\ \\ x = 3 \times 4 \\ \\ x = 12](https://tex.z-dn.net/?f=18%20%5Csqrt%7B3%7D%20%20%3D%206%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes%202%20%7B%28%20%5Csqrt%7B3%29%7D%20%7D%5E%7B%20%5Cfrac%7Bx%7D%7B12%7D%20%7D%20.%20%7B%28%20%5Csqrt%7B3%29%7D%20%7D%5E%7B%20%5Cfrac%7Bx%7D%7B6%7D%20%7D%20%20%5C%5C%20%20%5C%5C%2018%20%5Csqrt%7B3%7D%20%20%3D%206%20%20%7B%28%20%5Csqrt%7B3%29%7D%20%7D%5E%7B%20%5Cfrac%7Bx%7D%7B12%7D%20%7D%20.%20%7B%28%20%5Csqrt%7B3%29%7D%20%7D%5E%7B%20%5Cfrac%7B2x%7D%7B12%7D%20%7D%20%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B18%20%5Csqrt%7B3%7D%20%20%7D%7B6%7D%20%20%3D%20%7B%28%20%5Csqrt%7B3%29%7D%20%7D%5E%7B%20%5Cfrac%7Bx%7D%7B12%7D%20%20%2B%20%20%5Cfrac%7B2x%7D%7B12%7D%20%7D%20%20%5C%5C%20%20%5C%5C%203%20%5Csqrt%7B3%7D%20%20%3D%20%20%7B%28%20%5Csqrt%7B3%29%7D%20%7D%5E%7B%20%5Cfrac%7B3x%7D%7B12%7D%20%7D%20%5C%5C%20%20%5C%5C%203.%20%7B3%7D%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%20%3D%20%20%7B3%7D%5E%7B%20%5Cfrac%7B3x%7D%7B24%7D%20%7D%20%20%5C%5C%20%20%5C%5C%20%20%7B3%7D%5E%7B1%20%2B%20%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%20%3D%20%20%7B3%7D%5E%7B%20%5Cfrac%7Bx%7D%7B8%7D%20%7D%20%20%5C%5C%20%20%5C%5C%20%7B3%7D%5E%7B%20%5Cfrac%7B3%7D%7B2%7D%20%7D%20%20%3D%20%20%7B3%7D%5E%7B%20%5Cfrac%7Bx%7D%7B8%7D%20%7D%20%20%5C%5C%20%28bases%20%5C%3A%20are%20%5C%3A%20equal%20%5C%3A%20so%20%5C%3A%20exponents%20%5C%3A%20%20%5C%5C%20will%20%5C%3A%20also%20%5C%3A%20be%20%5C%3A%20equal%29%20%5C%5C%20%5Cimplies%20%20%5Cfrac%7B3%7D%7B2%7D%20%20%3D%20%20%5Cfrac%7Bx%7D%7B8%7D%20%20%5C%5C%20%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B3%20%5Ctimes%208%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20x%20%3D%203%20%5Ctimes%204%20%5C%5C%20%20%5C%5C%20x%20%3D%2012)
The answer is 40 you do 10 times 4 I hope it helped you you only need to multiply
<span>speed limit < = 60
I don't really remember how to graph it though sorry
</span>
Answer:
x=2
Step-by-step explanation:
In order to solve this problem, you need to find the scale factor. This is done through cross multiplying proportions. In this instance, you have to cross multiply x/4 by 3.5/7. When you multiply x and 7, you get 7x. When you multiply 3.5 and 4, you get 14. Simplify by isolating the variable, and you get 2.
Answer:
x-intercept (s):
For this case h (x) = 0
x2 - 2x - 8 = 0
(x-4) * (x + 2) = 0
x1 = 4
x2 = -2
y-intercept:
For this case x = 0
h (0) = (0)2 - 2 (0) - 8
h (0) = - 8
vertex:
We derive the equation:
h '(x) = x2 - 2x - 8
h (x) = 2x - 2
We match zero:
2x-2 = 0
x = 2/2
x = 1
We evaluate the function for x = 1
h (1) = (1)2 - 2 (1) - 8
h (1) = 1 - 2 - 8
h (1) = -9
The vertex is:
(1, -9)
axis of symmetry of the function:
x = 1
Step-by-step explanation:
hope it helps