Step-by-step explanation:
The quadratic equation is x² + (p - 5)x + 2q = 0.
By Vieta's Formula,
we have SOR = -b/a and POR = c/a.
=> (-3) + (6) = -(p - 5) and (-3)(6) = 2q.
=> 3 = 5 - p and -18 = 2q
Hence, p = 2 and q = -9.
Alternate Method:
We have (x + 3) and (x - 6) as factors of the quadratic equation x² + (p - 5)x + 2q = 0.
=> (x + 3)(x - 6) = x² - 3x - 18.
By Comparing Coefficients,
(p - 5) = -3 and 2q = 18.
Hence p = 2 and q = -9.
Answer:
5.55
is already rounded to the nearest thousandth.
Step-by-step explanation:
The answer is 35 centimetres
Answer:
There are 24 ways to select one book of each type.
Step-by-step explanation:
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:

It is provided that there are 6 different biographies and 4 different mystery novels on a bookshelf.
Compute the number of ways to select a biography as follows:
Number of ways to select a biography =

There are 6 ways to select a biography.
Compute the number of ways to select a mystery novel as follows:
Number of ways to select a mystery novel =

There are 4 ways to select a mystery novel.
Then the total number of way to select one book of each type is:

Thus, there are 24 ways to select one book of each type.