Answer:
8.5
Step-by-step explanation:
it would technically round to 9, but given the answer choices its A) 8
Any tangent line to
![y=x^2-x](https://tex.z-dn.net/?f=y%3Dx%5E2-x)
at a point
![(a,b)=(a,a^2-a)](https://tex.z-dn.net/?f=%28a%2Cb%29%3D%28a%2Ca%5E2-a%29)
will have slope
![y'(a)=2x-1\bigg_{x=a}=2a-1](https://tex.z-dn.net/?f=y%27%28a%29%3D2x-1%5Cbigg_%7Bx%3Da%7D%3D2a-1)
. Such a line has equation
![y-(a^2-a)=(2a-1)(x-a)\implies y=(2a-1)x-a^2](https://tex.z-dn.net/?f=y-%28a%5E2-a%29%3D%282a-1%29%28x-a%29%5Cimplies%20y%3D%282a-1%29x-a%5E2)
For this (these) line(s) to pass through (2, -3), you must have
![-3=(2a-1)\times2-a^2\implies a^2-4a-1=0\implies a=2\pm\sqrt5](https://tex.z-dn.net/?f=-3%3D%282a-1%29%5Ctimes2-a%5E2%5Cimplies%20a%5E2-4a-1%3D0%5Cimplies%20a%3D2%5Cpm%5Csqrt5)
So the two lines in questions are
![y=(2a-1)x-a^2](https://tex.z-dn.net/?f=y%3D%282a-1%29x-a%5E2)
for these values of
![a](https://tex.z-dn.net/?f=a)
.
To show there is no tangent line that passes through (2, 7), you have to show there is no solution for
![a](https://tex.z-dn.net/?f=a)
in
![7=(2a-1)\times2-a^2](https://tex.z-dn.net/?f=7%3D%282a-1%29%5Ctimes2-a%5E2)
You have
![a^2-4a+9=0](https://tex.z-dn.net/?f=a%5E2-4a%2B9%3D0)
but this has no real solutions, so no such tangent line exists.
Note: The values in the table are not correct because the sum of the probability of all events is not equal to one. The should be 0.13 and 0.33 instead of 0.113 and 0.133 respectively.
Given:
The probability distribution for a random variable x is given in the table.
x : -5 -3 -2 0 2 3
P(x) : 0.17 0.13 0.33 0.16 0.11 0.10
To find:
The probability of -2.
Solution:
From the given probability distribution for a random variable x, it is clear that the value of the probability is 0.33 corresponding to -2.
![P(-2)=0.33](https://tex.z-dn.net/?f=P%28-2%29%3D0.33)
Therefore, the probability of -2 is 0.33.
Answer:
y = -3x + 6
Step-by-step explanation:
Two lines that are parallel will have the same slope. All we need to do is find the new y-intercept.
-3 = -3(3) + b
-3 = -9 + b
6 = b
Now we can input the stuff we know and solved for back into the original formula [ y = mx + b ].
y = -3x + 6
Best of Luck!
Uncle Tom's Cabin was written by an abolitionist who had first hand knowledge of the atrocities inflicted on slaves. The novel began as a 40 week series, published in The National, and was read weekly by people who knew the author and her family. The onslaught of disgraceful realities shamed those involved with slavery and the cultural tide began to turn at the timing of the authors pen.