The value for p will be equal to 3 / 4.
We have the function as:
f(x) = (x - 1)³ + 6(p x + 4) 2
f(x) = x³ - 3 x² + 3 x - 1 + 12 p x + 48
f(x) = x³ - 3 x² + 3 x ( 1 + 4 p) + 47
Now, it is divided by x + 2 and leaves a remainder -3.
This means that if we will subtract 3 from f(x), it will be perfectly divisible by x + 2.
g(x) = x³ - 3 x² + 3 x ( 1 + 4 p) + 47 - 3
g(x) = x³ - 3 x² + 3 x ( 1 + 4 p) + 44
Now put x = -2:
(-2)³ - 3 (-2)² + 3 (-2) ( 1 + 4 p) + 44 = 0
-8 - 12 - 6 ( 1 + 4 p) + 44 = 0
- 20 - 6 - 24 p + 44 = 0
24 p = 18
p = 3 / 4.
Therefore, the value for p will be equal to 3 / 4.
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Answer:
Second option: 
Step-by-step explanation:
You know that "x" represents the Avery's weigth (in pounds).
Let be "y" the weight of Jada in pounds.
Since Jada weighs 18 pounds more than Avery, you can write this expression:
The weight of them together is:
Substituting, you get:
Therefore, the expression that tells how much the two of them weigh together is the one provided in the second option:
The answer would be: n=6.
Answer: Kristina sister's age = 15 years
Step-by-step explanation:
LET the sister's age be rep as x
SO that Kristina = 4/5 of x
Given that Kristina's age = 12 , Then her sister's age can be found using The equation
4/5 x X= 12
4/5 X =12
X = 5 X 12 / 4
=60/4=15
Kristina's sister's age = 15 years.
Answer:
Prime Numbers 2, 3, 5
Divisible by 2 - 2, 4, 6
One is NOT a prime number.
So, there are 5 out of 6 numbers that are even or are prime.
This leaves only 1 number that isn't.
So, the probability is 5/6 that the number rolled will be prime or even.
Step-by-step explanation:
