Step-by-step explanation: In geometry, a vertex is where two rays share a common endpoint or where they interest each other.
The rays are called the sides of the angle and
common endpoint is called the vertex.
The vertex is very important when naming angles because
the vertex is always at the center when naming the angle.
Below is an example of two rays that share a
common endpoint which is called the vertex.
Explanation
As you can see all the possible answers have the same form:
![g(x)=ax^2](https://tex.z-dn.net/?f=g%28x%29%3Dax%5E2)
By looking at the picture you'll notice that the graph of g(x) has to pass through the point (2,1). Remember that the points in the graph of g(x) have the form (x,g(x)). Since (2,1) is part of the graph of g(x) then we have the following:
![\begin{gathered} (2,1)=(x,g(x)) \\ x=2 \\ g(2)=1 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%282%2C1%29%3D%28x%2Cg%28x%29%29%20%5C%5C%20x%3D2%20%5C%5C%20g%282%29%3D1%20%5Cend%7Bgathered%7D)
So let's evaluate the expression for g(x) that we wrote before at x=2. This way we'll obtain an equation for the number a:
![\begin{gathered} g(2)=1=a\cdot2^2 \\ 1=4a \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20g%282%29%3D1%3Da%5Ccdot2%5E2%20%5C%5C%201%3D4a%20%5Cend%7Bgathered%7D)
Then we can divide both sides by 4:
![\begin{gathered} \frac{1}{4}=\frac{4a}{4} \\ a=\frac{1}{4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B1%7D%7B4%7D%3D%5Cfrac%7B4a%7D%7B4%7D%20%5C%5C%20a%3D%5Cfrac%7B1%7D%7B4%7D%20%5Cend%7Bgathered%7D)
Then we get:
![g(x)=\frac{1}{4}x^2=(\frac{1}{2}x)^2](https://tex.z-dn.net/?f=g%28x%29%3D%5Cfrac%7B1%7D%7B4%7Dx%5E2%3D%28%5Cfrac%7B1%7D%7B2%7Dx%29%5E2)
Answer
Then the answer is option A.
4.555
4.556
4.557
4.558
4.559
4.561
4.562
4.563
4.564
1 Decimeter = 10 Centimeters
4 x 10 = 40 Centimeters
Answer:
The answer is
<h2>
![( - 5 \: , \: - \frac{15}{2} )](https://tex.z-dn.net/?f=%28%20-%205%20%5C%3A%20%2C%20%5C%3A%20%20-%20%20%5Cfrac%7B15%7D%7B2%7D%20%29)
</h2>
Step-by-step explanation:
The midpoint M of two endpoints of a given line segment can be found by using the formula
<h3>
![M = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )](https://tex.z-dn.net/?f=M%20%3D%20%28%20%5Cfrac%7Bx1%20%2B%20x2%7D%7B2%7D%20%20%2C%20%5Cfrac%7By1%20%2B%20y2%7D%7B2%7D%20%29)
</h3>
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-4, -9), (-6, -6)
The midpoint is
<h3>
![M = ( \frac{ - 4 - 6}{2} , \: \frac{ - 9 - 6}{2} ) \\ = ( - \frac{10}{2} , - \frac{15}{2} )](https://tex.z-dn.net/?f=M%20%3D%20%28%20%5Cfrac%7B%20-%204%20-%206%7D%7B2%7D%20%20%2C%20%5C%3A%20%20%5Cfrac%7B%20-%209%20-%206%7D%7B2%7D%20%29%20%5C%5C%20%20%3D%20%28%20-%20%20%5Cfrac%7B10%7D%7B2%7D%20%2C%20-%20%20%5Cfrac%7B15%7D%7B2%7D%20%29)
</h3>
We have the final answer as
<h3>
![( - 5 \: , \: - \frac{15}{2} )](https://tex.z-dn.net/?f=%28%20-%205%20%5C%3A%20%2C%20%5C%3A%20%20-%20%20%5Cfrac%7B15%7D%7B2%7D%20%29)
</h3>
Hope this helps you