The correct answer is C.
You can tell this by factoring the equation to get the zeros. To start, pull out the greatest common factor.
f(x) = x^4 + x^3 - 2x^2
Since each term has at least x^2, we can factor it out.
f(x) = x^2(x^2 + x - 2)
Now we can factor the inside by looking for factors of the constant, which is 2, that add up to the coefficient of x. 2 and -1 both add up to 1 and multiply to -2. So, we place these two numbers in parenthesis with an x.
f(x) = x^2(x + 2)(x - 1)
Now we can also separate the x^2 into 2 x's.
f(x) = (x)(x)(x + 2)(x - 1)
To find the zeros, we need to set them all equal to 0
x = 0
x = 0
x + 2 = 0
x = -2
x - 1 = 0
x = 1
Since there are two 0's, we know the graph just touches there. Since there are 1 of the other two numbers, we know that it crosses there.
Answer: A compound event is the combination of two or more simple events (with two or more outcomes).
Step-by-step explanation:
Answer:
80/81
Step-by-step explanation:
If a head is twice as likely to occur as a tail, then the probability of getting heads is 2/3 and the probability of getting tails is 1/3.
The probability of getting at least 1 head involves 4 scenarios:
1) 1 Head and 3 Tails
2) 2 Heads and 2 Tails
3) 3 Heads and 1 Tail
4) 4 Heads
Instead of calculate all these scenarios, you could calculate the opposite scenario: 4 Tails. The sum of all possible scenarios is 1, so:
P(at least one head) + P(no heads) = 1
Then, P(at least one head) = 1 - P(no heads)
The probability of 4 tails is:
P(no heads) = P(TTTT) = (1/3)(1/3)(1/3)(1/3)=1/81
Then, P(at least one head) = 1 - 1/81=80/81
Answer:
-9
Step-by-step explanation:
x² -16 = (x -4)(x +4)
This magnitude of this product can only be prime if one of the factors is ±1. Any other integer value of x will produce a composite number (or zero).
... For x-4 = ±1, x = 3 or 5
... For x+4 = ±1, x = -3 or -5
The values of x that are ±3 both give |x²-16| = 7, a prime.
The values of x that are ±5 both give |x²-16| = 9, not a prime.
The two values of x that are of interest are x=-3 and x=3. Their product is ...
... (-3)·(3) = -9
Answer:
x = 6, -8
Step-by-step explanation:
If (x - 6)(x + 8) = 0, that would imply that either (x - 6) or (x + 8) would equal zero. Using this, we can find that solving the two equations:
x - 6 = 0
and
x + 8 = 0
would yield the two solutions to the equation.
x - 6 = 0
Add 6 to both sides of the equation.
x = 6
So one of the solutions would be x = 6.
x + 8 = 0
Subtract 8 from both sides of the equation.
x = -8
So the other solution would be x = -8.
The two solutions are x = 6 and x = -8.
I hope you find my answer and explanation to be helpful. Happy studying.
