Answer:
Statement: <em>m<</em>ABC = <em>m<</em>CBD
Reason: <em>m<</em>ABC + <em>m<</em>CBD = 52°
Step-by-step explanation:
Hi Lauren! I hope you’re fine!
Well, the exercise defines that segment BC is the bisector of angle ABD (m<ABD). As you may already know, a bisector is a segment that divides the angle (in this case m<ABD) into two equal angles (m<ABC and m<CBD).
The exercise ask you to prove that the angle <em>m<</em>ABC = 26 °
To arrive at this answer, you must first declare that the ABC and CBD angles are the same (this is your statement).
Then, you must apply the data they give you in the slogan as the reason. That is, you know that the greater angle ABD measures 52 ° and is the sum of the angles ABC and CBD. Therefore, in the reason column you must put m<ABC + m<CBD = 52°
So your statement is: m<ABC = m<CBD (Let's call this equation 1)
And your reason is: m<ABC + m<CBD = 52° (And let's call this equation 2)
<u>Here is the prove:
</u>
Let's start with equation 2
m<ABC + m<CBD = 52° (WE REPLACE WITH EQUATION 1 WHERE m<ABC = m<CBD)
m<ABC + m<ABC = 52°
2 * m<ABC = 52°
m<ABC = 52°/2
m<ABC = 26°
I hope I've been helpful!
Regards!
We know that we can take 4 out of (-16x + 8) [ we know this because we can divide 16 by 4 ( to get 4 ) and we can divide 8 by 4 ( to get 2 ) ]
we can factor out a 4 then from the parentheses to get 4(-4x + 2), but since we are multiplying by 1/4 we get
1/4(4)(-4x + 2), and since 1/4 * 4 = 1, our final answer is
-4x + 2
Answer:
![(-4, -1)](https://tex.z-dn.net/?f=%28-4%2C%20-1%29)
Step-by-step explanation:
![6x-y=-23](https://tex.z-dn.net/?f=6x-y%3D-23)
Add y to both sides:
![6x-y+y=-23+y\\6x=-23+y](https://tex.z-dn.net/?f=6x-y%2By%3D-23%2By%5C%5C6x%3D-23%2By)
Divide both sides by 6:
![\frac{6x}{6}=-\frac{23}{6}+\frac{y}{6}\\x=\frac{-23+y}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B6x%7D%7B6%7D%3D-%5Cfrac%7B23%7D%7B6%7D%2B%5Cfrac%7By%7D%7B6%7D%5C%5Cx%3D%5Cfrac%7B-23%2By%7D%7B6%7D)
Substitute this into the second equation given:
![2*\frac{-23+y}{6}+5y=-13](https://tex.z-dn.net/?f=2%2A%5Cfrac%7B-23%2By%7D%7B6%7D%2B5y%3D-13)
![\frac{-23+16y}{3}=-13](https://tex.z-dn.net/?f=%5Cfrac%7B-23%2B16y%7D%7B3%7D%3D-13)
Multiply both sides by 3:
![-23+16y=-39](https://tex.z-dn.net/?f=-23%2B16y%3D-39)
Add 23 to both sides:
![-23+16y+23=-39+23\\16y=-16](https://tex.z-dn.net/?f=-23%2B16y%2B23%3D-39%2B23%5C%5C16y%3D-16)
Divide both sides by 16:
![\frac{16y}{16}=\frac{-16}{16}\\y=-1](https://tex.z-dn.net/?f=%5Cfrac%7B16y%7D%7B16%7D%3D%5Cfrac%7B-16%7D%7B16%7D%5C%5Cy%3D-1)
We know that
.
Thus, ![x=\frac{-23-1}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-23-1%7D%7B6%7D)
![x=-4](https://tex.z-dn.net/?f=x%3D-4)
![(x, y) = (-4, -1)](https://tex.z-dn.net/?f=%28x%2C%20y%29%20%3D%20%28-4%2C%20-1%29)
Your answer would be B, all you need to do is look at the first point plotted and match it with the number you see on the x and y axis and then look at what each number means