Answer:
P(x) = x³ - 3x² - 5x + 15
Step-by-step explanation:
∵ The roots of the polynomial are -√5 , √5 , 3
∴ The polynomial has 3 factors:
(x - √5) , (x + √5) , (x - 3)
∴ P(x) = (x - √5)(x + √5)(x - 3)
= (x² + √5x - √5x - 5)(x - 3)
= (x² - 5)(x - 3) = x³ - 3x² - 5x + 15
∴ P(x) = x³ - 3x² - 5x + 15
Answer:
1/26
Step-by-step explanation:
There is only one 6 of hearts and only one ace of diamonds.
The probability of selecting the 6 of hearts is thus 1/52, and that of selecting the ace of diamonds is also 1/52.
The probability of selecting the 6 of hearts or the ace of diamonds is the SUM of these two results: 1/52 + 1/52 = 2/52 = 1/26.
Answer:
Step-by-step explanation:
Write and solve an equation:
Total earnings = $782.75 = s(40 hrs) + 1.5*s*(7 hrs)
Then 782.75 = 40s + 10.5s = 50.5s
Dividing both sides by 50.5: s = 15.5. The attendant's regular hourly wage was $15.50.
Remark
The proof is only true if m and n are equal. Make it more general.
m = 2k
n = 2v
m + n = 2k + 2v = 2(k + v).
k and v can be equal but many times they are not. From that simple equation you cannot do anything for sure but divide by 2.
There are 4 combinations
m is divisible by 4 and n is not. The result will not be divisible by 4.
m is not divisible by 4 but n is. The result will not be divisible by 4.
But are divisible by 4 then the sum will be as well. Here's the really odd result
If both are even and not divisible by 4 then their sum is divisible by 4
