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:
56.43
Step-by-step explanation:
52.25 + 4.18 (8% tax)
Answer:
628
Step-by-step explanation:
Deposit means money is going into the bank so add 129 onto 499
(b) writing a cheque means money is coming out of the bank so subtract 24 from your previous answer.
628 - 24 = 604
(c) again, this money is coming out so take 151 away from 604
(d) round 604 to the nearest hundred
(it's between 600 and 610 but which is it closest to?)
Answer:
x = 3.5714
Step-by-step explanation:
14x = 50
Divide 50/14
x = 3.5714
Step 1
Write your problem.
537.95 x 9.5% = ?
Step 2
Convert the % to a decimal:
9.5% to 0.095
Step 3
Rewrite the problem with decimal replacing the percentage.
Now the problem looks like this:
537.95 x 0.095 = 51.11
This problem gives the amount of the tax.
Step 4
Add the original price with the tax amount:
537.95 + 51.11 = $589.06 (total cost)
