The domain of the function is the set of all the values of x that would allow the function to have real values. Since the radicand is x - 3, the value of x cannot be less than 3 because that would make the value of sqrt (x - 3) an imaginary number. Thus, the domain should be all numbers GREATER than or equal to 3.
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Answer: -2</h3>
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Explanation:
We use the remainder theorem. This is the idea where if we divide P(x) over (x-k), then the remainder is P(k).
Comparing x+1 to x-k shows that k = -1
It might help to rewrite x+1 as x-(-1) to get it into the form x-k better.
Plug this k value into the function
f(x) = 2x^6 + 3x^5 - 1
f(-1) = 2(-1)^2 + 3(-1)^5 - 1
f(-1) = 2(1) + 3(-1) - 1
f(-1) = 2 - 3 - 1
f(-1) = -1 - 1
f(-1) =-2
The remainder is -2
We can confirm this through synthetic division or polynomial long division.
Answer:
Step-by-step explanation:
Problem 4a
You have 6 numbers on the cube, a bag with 4 letters and a spinner with 3 letters
The total number of results is
6 * 4 * 3 = 72
Problem 4b
P(A,3,Q) = (1/3)(1/6)(1/4) = 1/72
Problem 4c
A and Q remain the same. 1/3 and 1/4
Not rolling a 6 is a little different. Success will result in a 1 2 3 4 5 being thrown. That's 5/6
So the results are 1/3 * 1/4 * 5/6 = 5/72
Regroup terms:
y - 2/9 ≤ 5/9
Add 2/9 to both sides:
y ≤ 5/9 + 2/9
Simplify 5/9 + 2/9 to 7/9:
y ≤ 7/9
5x2=10
5+2= 7
Answer: 5 and 2
