Answer:
x³ - 8x² - 11x + 148
Step-by-step explanation:
Given that x = 6 + i is a root then x = 6 - i is also a root
Complex roots occur as conjugate pairs.
The factors are therefore (x - (6 + i)) and(x - (6 - i))
Given x = - 4 is a root then (x + 4) is a factor
The polynomial is the product of the factors, that is
p(x) = (x + 4)(x - (6 + i))(x - (6 - i))
= (x + 4)(x - 6 - i)(x - 6 + i)
= (x + 4)((x - 6)² - i²)
= (x + 4)(x² - 12x + 36 + 1)
= (x + 4)(x² - 12x + 37) ← distribute
= x³ + 4x² - 12x² - 48x + 37x + 148
= x³ - 8x² - 11x + 148
Answer:
C. 2 × 7 × 11
Step-by-step explanation:
2 × 7= 14
14 × 11= 154
The answer is 5
Here are the steps:
First off, we will be using the distance formula of

So we have the ordered pairs of (3,1) and (6,5)
Once you plug them into the formula it should look like this:

Now we do the math inside the parenthesis and end up with:

Then you multiply by the power and simplify to get:

And the

=5
So your answer is
5
Answer:
Step-by-step explanation:
This is a special die. Its six sides bear the numbers {9, 10, 11, 12, 13, 14}.
There are three possibilities for getting a multiple of two: {10, 12, 14}, and
there is only one possibilities for getting a multiple of ten: {10, 12, 14}
The probability here of getting a multiple of two is 3/6, and that of getting a multiple of ten is 1/6. But one of the outcomes is found in both result sets: 10. Getting a multiple of 10 is already included in the event that the outcome is a multiple of two. My answer here would be 3/6, or 1/2.