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:
A and C
Step-by-step explanation:
Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring.
Options B and D give events which are most likely to be dependent, because if a driver texts while driving affects the possibility that the driver can get into the accident and if a woman lives in Alaska affects she can have a heavy winter coat.
Options A and C are two sets of most likely independent events, because the girl's singing does not affect on her wish to become a lawyer and a man's hair doesn't depend on where his father lives.
Answer:
I'll setup the problem and you can compute the answer
Step-by-step explanation:
The formula for simple:
I = P*r*t
I = interest
P = loan amount
r = interest rate per period (period = days)
n = number of periods
P = 10,170
r = .0764/365
t = 272
Take a picture of the table
3x -1/2y = -7/2
x = -2y + 1
3 (-2y + 1) -1/2y = -7/2
-6y +3 -1/2y = -7/2
-13/2y = -13/2
y = 1
x = -2(1) + 1
x = -1
Answer = (-1, 1)
