You put the 15x + 100 on the angle CEB instead of CED. If you put it in the right spot, it should work out fine since they are vertical angles.
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
There are 11 numbers on cards.
6 cards contain even numbers.
Answer: p(even) = 6/11
There is only one card with a 7. After the first card is picked and returned, there are 11 cards in the bag again.
p(even then 7) = p(even) * p(7) = 6/11 * 1/11 = 6/121
Answer: p(even then 7) = 6/121
Answer:
y-1=
(x+8)
Step-by-step explanation:
1. y-y1=m(x-x1) (point slope form)
2. y1 is the y of your given point and x1 is the x of your given point
3. m is the slope
Step-by-step explanation:
By Completing the Square,
![\begin{align}f(x)&=-2x^2+4x+6\\&=-2(x^2-2x)+6\\&=-2(x^2-2x+1)+8\\&=-2(x-1)^2+8 \end{align}](https://tex.z-dn.net/?f=%5Cbegin%7Balign%7Df%28x%29%26%3D-2x%5E2%2B4x%2B6%5C%5C%26%3D-2%28x%5E2-2x%29%2B6%5C%5C%26%3D-2%28x%5E2-2x%2B1%29%2B8%5C%5C%26%3D-2%28x-1%29%5E2%2B8%20%5Cend%7Balign%7D)
Since the first tern is at most zero, the maximum value occurs when
![x=1, f(x)=8](https://tex.z-dn.net/?f=x%3D1%2C%20f%28x%29%3D8)
Answer:
The correct option is (b).
Step-by-step explanation:
The solution of the given polynomial is :
![(-\dfrac{1}{3},4)](https://tex.z-dn.net/?f=%28-%5Cdfrac%7B1%7D%7B3%7D%2C4%29)
x = 1/3 and y = -4
i.e.
Sum of roots = (1/3-4) = -11/3
Product of roots = (1/3)(-4) = -4/3
The quadratic equation is as follows :
![x^2+(\text{sum of roots})x+\text{Product of roots}=0](https://tex.z-dn.net/?f=x%5E2%2B%28%5Ctext%7Bsum%20of%20roots%7D%29x%2B%5Ctext%7BProduct%20of%20roots%7D%3D0)
Put all the values,
![x^2+\dfrac{-11}{3}x+\dfrac{-4}{3}=0\\\\3x^2-11x-4=0](https://tex.z-dn.net/?f=x%5E2%2B%5Cdfrac%7B-11%7D%7B3%7Dx%2B%5Cdfrac%7B-4%7D%7B3%7D%3D0%5C%5C%5C%5C3x%5E2-11x-4%3D0)
So, the correct option is (b).