Answer:
Step-by-step explanation:
x²- y² = (x+y) (x-y)
x² + xy = x(x+y)
x² + 2xy + y² = (x+y) (x+y)
You use the FOIL method, and how you do this is -
(x - 7) (x + 8)
Multiply the first x by both numbers in the second factor. Which means, you multiply x by x and 8, the two in (x + 8).
With this, you get -
x^2 + 8x
Then do the same thing with -7.
-7x - 56
Then combine the two.
x^2 + 8x - 7x - 56
Combine like terms.
x^2 + x - 56
So now, 7 x 8 is 56
And -7 + 8 would be 1. And that is the value of “x” which is b in the form a^2x + bx + c.
Now with this, you take those two numbers and make the factors =
(x + 8) (x - 7)
Then you set these equal to 0.
x + 8 = 0
Subtract the 8 from both sides.
x = -8
————
x - 7 = 0
Add the 7 on both sides.
x = 7
Answer: A
Find rates of change until you find a constant.
dy/dx=1,2,3,4,5,6
d2y/dx2=1,1,1,1,1
So the acceleration, d2y/d2x, is constant. This means that this is a quadratic sequence of the form a(n)=an^2+bn+c. So we can set up a system of equations to solve for the values of a,b, and c. Using the first three points, (1,1), (2,2), and (3,4) we have:
9a+3b+c=4, 4a+2b+c=2, and a+b+c=1 getting the differences...
5a+b=2 and 3a+b=1 and getting this difference...
2a=1, so a=1/2 making 5a+b=2 become:
2.5+b=2, so b=-1/2, making a+b+c=1 become:
1/2-1/2+c=1, so c=1 so the rule is:
a(n)=0.5x^2-0.5x+1 or if you prefer to not have decimals
a(n)=(x^2-x+2)/2
the first two professors did not know if everyone wanted coffee because the third professor had to choose yes or no if he wanted coffee. the first two professors were waiting for the third to say something, and when he said no, they knew he did not want coffee. if one of the first two professors said no, the answer would be no.
Answer:
d. (x+2)/(-x²-5)
Step-by-step explanation
ƒ(x) = x + 2/(2x²)
The function is undefined when x = 0.
b. ƒ(x) = (2x + 4)/(3x + 3)
The function is undefined when 3x + 3 = 0, i.e., when x = -1.
c. ƒ(x) = (6x - 5)/(x² - 7)
The function is undefined when x² - 7 = 0, i.e., when x = √7.
d. ƒ(x) = (x+2)/(-x²-5) = -(x+2)/(x² + 5)
The function would be undefined if x² + 5 = 0, i.e., if x² = -5. However, the square of a real number cannot be negative.
This function has no excluded values.
