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: I think the answer is 173.25
Step-by-step explanation:
To find that you have to times them.
15.0*11.55 = 173.25
You proofread 2 pages per minute so you divide 96 by 2 to get 48 minutes which is the answer
Answer:
The value of g(f(1)) is 84/5
Step-by-step explanation:
To find the answer to a composite function, start with the function on the inside, which is f(1). So, we input 1 into the f(x) equation and evaluate.
f(x) = 6x + 2
f(1) = 6(1) + 2
f(1) = 6 + 2
f(1) = 8
Now that we have the answer of 8, we can input that in for x in the outside function, which is g(x).
g(x) = 2x + 4/5
g(8) = 2(8) + 4/5
g(8) = 16 + 4/5
g(8) = 84/5
Answer:
c
Step-by-step explanation:
it is because in (a) the square root of 112. is 10.58 which is in between 10 and 11
(B) the square root of 180 is 13.42 which is between 13&14
(c) the square root of 12 is 3.46 which is not between 4&5
