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)
Answer:
im not really sure but i think its b
Step-by-step explanation:
Answer:
a) 21
Step-by-step explanation:
If the columns are labeled a, b, c, d left to right, it appears that we have ...
![\sqrt{a}\times(b-c)=d\\\\\sqrt{49}\times(10-7)=21](https://tex.z-dn.net/?f=%5Csqrt%7Ba%7D%5Ctimes%28b-c%29%3Dd%5C%5C%5C%5C%5Csqrt%7B49%7D%5Ctimes%2810-7%29%3D21)
The value of M is 21.
_____
Questions like this require that you try different combinations of operations on the numbers shown to see if you can find a relationship. Here, the left column is a perfect square, so that is a clue. The difference of the numbers in the middle columns is a factor of the number in the right column -- another clue. It takes a certain amount of creative thought and familiarity with arithmetic facts. There is no "step-by-step" for a problem like this.
Answer:
![3 \frac{1}{3}](https://tex.z-dn.net/?f=3%20%5Cfrac%7B1%7D%7B3%7D)
Hope this helps.
Step-by-step explanation:
Answer:
1.2 laps per minute
Step-by-step explanation:
divide laps/minutes.