Answer:
See proof below
Step-by-step explanation:
We have to verify that if we substitute 
in the equation 
the equality is true.
Let's substitute first in the right hand side:
Now we use the distributive laws. Also, note that 
(this also works when the power is n-2).
then the sequence solves the recurrence relation.
Let's solve the equation 2k^2 = 9 + 3k
First, subtract each side by (9+3k) to get 0 on the right side of the equation
2k^2 = 9 + 3k
2k^2 - (9+3k) = 9+3k - (9+3k)
2k^2 - 9 - 3k = 9 + 3k - 9 - 3k
2k^2 - 3k - 9 = 0
As you see, we got a quadratic equation of general form ax^2 + bx + c, in which a = 2, b= -3, and c = -9.
Δ = b^2 - 4ac
Δ = (-3)^2 - 4 (2)(-9)
Δ<u /> = 9 + 72
Δ<u /> = 81
Δ<u />>0 so the equation got 2 real solutions:
k = (-b + √Δ)/2a = (-(-3) + √<u />81) / 2*2 = (3+9)/4 = 12/4 = 3
AND
k = (-b -√Δ)/2a = (-(-3) - √<u />81)/2*2 = (3-9)/4 = -6/4 = -3/2
So the solutions to 2k^2 = 9+3k are k=3 and k=-3/2
A rational number is either an integer number, or a decimal number that got a definitive number of digits after the decimal point.
3 is an integer number, so it's rational.
-3/2 = -1.5, and -1.5 got a definitive number of digit after the decimal point, so it's rational.
So 2k^2 = 9 + 3k have two rational solutions (Option B).
Hope this Helps! :)
Answer:
one
Step-by-step explanation:
3x-7=4+6+4x
3x=7+4+6+4x
3x=17+4x
3x-4x=17
-x=17
x=-17
Answer:
There are a 25% probability that Christine fails the course.
Step-by-step explanation:
We have these following probabilities:
A 50% probability that Christine finds a tutor.
With a tutor, she has a 10% probability of failling.
A 50% probability that Christine does not find a tutor.
Without a tutor, she has a 40% probability of failing.
Probability that she fails:
10% of 50%(fail with a tutor) plus 40% of 50%(fail without a tutor). So
There are a 25% probability that Christine fails the course.
Answer:
Step-by-step explanation:
The magnitude of vector 
is given by 
The magnitude of vector 
is 
.
The magnitude of vector 
is 
.
Therefore,
