Answer: A is the correct option.Segment AD is 3 and segment AE is 2.
Step-by-step explanation:
Given : A triangle ABC where AC=4 and AB=6
then to prove segment DE is parallel to segment BC and half its length.
the length of AD and AE must divide AC and AB respectively to get the same ratio of 2:1
To apply converse of basic proportionality theorem.
If we take first option Segment AD is 3 and segment AE is 2 then
![\frac{AB}{AD}=\frac{6}{3}=\frac{2}{1},\frac{AC}{AE}=\frac{4}{2}=\frac{2}{1}\\\Rightarrow\frac{AB}{AD}=\frac{AC}{AE}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7BAD%7D%3D%5Cfrac%7B6%7D%7B3%7D%3D%5Cfrac%7B2%7D%7B1%7D%2C%5Cfrac%7BAC%7D%7BAE%7D%3D%5Cfrac%7B4%7D%7B2%7D%3D%5Cfrac%7B2%7D%7B1%7D%5C%5C%5CRightarrow%5Cfrac%7BAB%7D%7BAD%7D%3D%5Cfrac%7BAC%7D%7BAE%7D)
Therefore by converse of basic proportionality theorem
DE is parallel to segment BC and half its length.
Therefore A is correct option.
Answer:
Number of games won = 110
Step-by-step explanation:
Given:
Total games played = 154
The ratio of number of games won to number of games lost = ![\frac{5}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%7D)
Solution:
Let the number of games won be = ![5x](https://tex.z-dn.net/?f=5x)
Thus, number of games lost = ![2x](https://tex.z-dn.net/?f=2x)
The total games played can be given as = ![5x+2x=7x](https://tex.z-dn.net/?f=5x%2B2x%3D7x)
Thus, we have:
![7x=154](https://tex.z-dn.net/?f=7x%3D154)
Dividing both sides by 7.
![\frac{7x}{7}=\frac{154}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B7x%7D%7B7%7D%3D%5Cfrac%7B154%7D%7B7%7D)
∴ ![x=22](https://tex.z-dn.net/?f=x%3D22)
So, number of games won = ![5\times 22 = 110](https://tex.z-dn.net/?f=5%5Ctimes%2022%20%3D%20110)
To reflect a function across the y-axis you have to change
![x\mapsto -x](https://tex.z-dn.net/?f=x%5Cmapsto%20-x)
So, the function becomes
![f(x)=-2x^2+5x-3 \mapsto f(-x)=-2(-x)^2+5(-x)-3=-2x^2-5-3](https://tex.z-dn.net/?f=f%28x%29%3D-2x%5E2%2B5x-3%20%5Cmapsto%20f%28-x%29%3D-2%28-x%29%5E2%2B5%28-x%29-3%3D-2x%5E2-5-3)