Hello from MrBillDoesMath!
Answer:
All real x
Discussion:
Take any real number, say, P. Then solve
f(x) = (x-2)2 + 2 = P => (subtract 2 from both sides)
(x-2)2 = P -2 => (divide both sides by 2)
(x-2) = (1/2) (P-2) => (add 2 to both sides)
x = (1/2)(P-2) + 2
Conclusion: for any real number range value, P, there is an x (given by the above formula) such that f(x) = P. In other words, the range of f is all real numbers x
Regards,
MrB
-9x(5 - 2x) Distribute/multiply 9x into (5 - 2x)
(-9x)5 - (-9x)2x
-45x - (-18x²) 2 negative signs cancel each other out and become +
-45x + 18x² Your answer is A ( the first option)
Answer:
The fourth term of the expansion is -220 * x^9 * y^3
Step-by-step explanation:
Question:
Find the fourth term in (x-y)^12
Solution:
Notation: "n choose k", or combination of k objects from n objects,
C(n,k) = n! / ( k! (n-k)! )
For example, C(12,4) = 12! / (4! 8!) = 495
Using the binomial expansion formula
(a+b)^n
= C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + C(n,3)a^(n-3)b^3 + C(n,4)a^(n-4)b^4 +....+C(n,n)b^n
For (x-y)^12, n=12, k=3, a=x, b=-y, and the fourth term is
C(n,3)a^(n-3)b^3
=C(12,3) * x^(12-3) * (-y)^(3)
= 220*x^9*(-y)^3
= -220 * x^9 * y^3
I guess tht was the answer, im i right?