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:
1.6627 (money wise, $1.66)
Step-by-step explanation:
Since its 130%, you know there was already a whole increase. So first you would do 1.279 + 1.279, which would give you 2.558. Then you need to calculate 30% of 1.279 for the rest of the increase. That gives you 0.3837 Add 2.558 and 0.3837 together, which would give you 2.9417. To get the INCREASE, you would have to subtract the new total from the original price, so 2.9417 - 1.279. This would give you 1.6627.
5(2x^2 - 5x - 3) = 5(2x + 1)(x - 3)
hope this helps :)
Answer:
the answer would be 16
Step-by-step explanation:
12 1/2 - -4 1/2=??? 1/2 - 1/2= 0 so 12 - -4=16
hope this helps
