**When the discriminant of an equation is negative, that means it has no real solutions.**
You can solve these types of problems by plugging it (the equation) into the quadratic formula, and then looking at the discriminant. For this specific problem, since it's asking you to find the greatest integer of m so that there are no real solutions, you will have to make m the biggest it can be, but still making the discriminant less than zero.
Find the largest integer n such that the equation
6x^2 + nx + 3 = 0
has no real solutions.
1. Plug the equation into the discriminant of the quadratic formula (you can also plug it into the formula and then extract the discriminant out, but I'll only plug in the discriminant; you can do either):
n^2 - 4 * 6 * 3 < 0
(I added a '< 0' since the problem wanted me to find the largest integer n that had NO REAL SOLUTIONS.)
2. Simplify what you can, then isolate n:
n^2 < 72
3. Now, it's sort of guess-and-check. Plug in numbers until you find what the question wants you to find; in this case, it wants me to find the GREATEST INTEGER n such that the equation has NO REAL SOLUTIONS. I tried a few numbers, then got 8 as my answer. This is because 8^2 is 64, which is less than 72. If I go up any further, 9^2 is 81, which is greater than 72, so my answer for this example problem is 8.
Good luck, I hope I helped.
( 1 / 6 ) * ( 2 / 5 ) = 1 / 15. This means that 1 / 15 of the boats in the marina are blue.
To get the fraction of the number of red boats in the marina, we can do 1 - ( 1 / 15 ) - ( 5 / 6 ).
1 - ( 1 / 15 ) - ( 5 / 6 ) = 1 / 10, so we know that 1 / 10 of the boats in the marina are red.
Now we know that there are 12 red boats in total, and red boats make up 1 / 10 of all the boats in the marina. All you have to do next is multiply 12 * 10, and you'll get the answer to how many boats are in the marina.
Good luck, and I hope this helps.
Let's suppose the number of adult tickets sold are x, and the number of child tickets sold is y.
If 350 tickets were sold, we can say that for our first equation, x + y = 350.
Since $950 was collected, we can say that our second equation will be 3x + 2y = 950.
Here are our two equations: x + y = 350
3x + 2y = 950.
Since x + y = 350, we know that x = 350 - y.
Plugging this into the second equation, we will get 3 ( 350 - y ) + 2y = 950.
Expanding, we get 1050 - 3y + 2y = 950.
We can then combine the ys together, to get 1050 - y = 950.
Subracting 1050 from each side, we'll get -y = -100.
Finally, flip the negative signs into positive signs, and we'll get y = 100, which means that the number of child tickets sold is 100.
All you have to do now is plug the number of child tickets into the first equation, solve, and then you will get the number of adult tickets sold.
I hope this helps, good luck.