Answer:
The fraction is 1/4
Step-by-step explanation:
we know that
The area of an equilateral triangle, using the law of sines is equal to
where
x is the length side of the triangle
In this problem
Let
b ----> the length side of the regular hexagon
2b ---> the length side of the equilateral triangle
step 1
Find the area of the six triangles
Multiply the area of one triangle by 6
![A=6[x^{2}\frac{\sqrt{3}}{4}]](https://tex.z-dn.net/?f=A%3D6%5Bx%5E%7B2%7D%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B4%7D%5D)
we have
substitute
step 2
Find the area of the regular hexagon
Remember that, a regular hexagon can be divided into 6 equilateral triangles
so
The area of the regular hexagon is the same that the area of 6 equilateral triangles
we have
substitute
step 3
To find out what fraction of the total area of the six triangles is the area of the hexagon, divide the area of the hexagon by the total area of the six triangles
You can solve by subtracting: 500-330
but I like to use mental math and think this way:
she has 330
70 more will give her 400
and 100 more will give her 500
100 + 70 is 170.
Answer:
It is a function.
Step-by-step explanation:
You can test if a graph is a function if you draw a vertical line anywhere on the graph and you see it hits two points.
This is the table for the graph.
![\left[\begin{array}{ccc}x&y\\-3&0\\0&1\\3&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%26y%5C%5C-3%260%5C%5C0%261%5C%5C3%262%5Cend%7Barray%7D%5Cright%5D)
Remember these rules:
- Each x value, or input, has its unique y value, or output
- If you draw a vertical line anywhere on the graph, it should only go through one point
We can check these two rules for this graph:
- Does each x value have its own, unique y value? Yes
- If you draw a vertical line anywhere on the graph, does it only go through one point? Yes, there are no overlaps
Keep in mind that two different x-values can have the same y value.
Figure 1:
It has two x values with the same y-values.
Figure 2 and 3:
The vertical line goes through two points. So the same x-value has two different y-values.
-Chetan K
F(x) = x²
g(x) = x - 3
g(-2) = (-2) - 3 = -5
f(-5) = (-5)² = 25
Answer : <span>(fog)(-2) = 25</span>
