The answer is for (6x^2-6x-5)(7x^2+6x-5) is B
The best way to multiply complicated problems mentally* is to break them into chunks.
Start with 20 times 8 to get 160, and then 8 times 5 to get 40. Add these together to get 200. 200 times 3 is 600, and 20 times 200 is 4000. Add these together to get your final answer, 4600.
In other words 8 x 20 + 8 x 5 = 200 200 x 3 + 200 x 20 = 4600
*I assumed you meant mentally, because otherwise you'd just multiply longhand, multiplying two of the three numbers and then multiplying their product with the third.
If (-1, -1) is an extremum of , then both partial derivatives vanish at this point.
Compute the gradients and evaluate them at the given point.
The first and third functions drop out.
The second function depends only on . Compute the second derivative and evaluate it at the critical point .
This indicates a minimum when . In fact, since this function is independent of , every point with this coordinate is a minimum. However,
for all , so (-1, 1) and all the other points are actually <em>global</em> minima.
For the fourth function, check the sign of the Hessian determinant at (-1, 1).
The second derivative with respect to is -2/(-1) = 2 > 0, so (-1, -1) is indeed a local minimum.
The correct choice is the fourth function.
Mark the entries in the table that are even. Those values are: 2, 4, 6, 8, 10, 12
There are 1+3+5+5+3+1 = 18 cases where this happens
Now mark the entries that are 5 or 10. There are multiples of 5. There are 4+3 = 7 cases of either 5 or 10.
If we add up 18 and 7, we get 18+7 = 25. Now subtract out the cases where we get both an even number AND a multiple of 5. So the three tens are counted twice. We go from 25 to 25-3 = 22
Divide this value (22) over the total number of outcomes (6*6 = 36). Doing this gets us
22/36 = 11/18
The answer is choice A
Answer:
r=-39
Step-by-step explanation:
-6(2r + 8)= -10(r-3) solve -6(2r+8)
-12r-48= -10(r-3) solve -10(r-3)
-12r-48= 10r+30
+48 +48
-12r=-10r+78
+10r +10r
-2r=78
-2r/-2=78/-2
r=-39