Answer:
A. 12 r 1
Step-by-step explanation:
6*12=72
73-72=1
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! :)
Hello there!
The sum of two numbers (x + y) is 8 (=8).
Their product (x * y) is 15 (=15).
x + y = 8
x * y = 15
First, we know that the two number must be positive and under 8, as the product is positive.
Let's list out some numbers that are from 1 to 8 that sum up to 8;
1 + 7
2 + 6
3 + 5
4 + 4
Now, we need to multiply the two numbers that add up to 8, and see which makes a product of 15.
1 * 7 = 7, this does not work.
2 * 6 = 12, this does not work.
3 * 5 = 15, this works!
4 * 4 = 16, this does not work.
Since we are looking for the larger number in our pairs, let's pick the largest one out of the correct pair, which is 5.
The largest number is 5.
I hope this helps!
Answer: 5 games
Step-by-step explanation: They need to win half their games for a .500 record and half or 30 is 15. They already won 10 so they need to win 15- 10 = 5 more games to have a .500 record.
