tertre

I see now! Thanks for the explanation, CPhill!

Discriminant is used to find the number of real roots of a quadratic equation and also the nature of the roots of a quadratic equation. Discriminant analysis is used to analyze relationships between a non-metric dependent variable and metric or dichotomous independent variables.

For a quadratic equation of the form ax^2 + bx + c = 0 with real number coefficients and a not equal to 0, the expression b^2 - 4ac is called the discriminant and can be used to determine the number and type of the solution of the equation.

So, the answer is \(\boxed{-23}\)

This should be easy enough.

Plugging in the value of y, we have 0=15-3x. Taking 15 to the other side, we get -15=-3x, so x=-15/-3=5

We can use the Euclidean Algorithm. \(\begin{align*} &\text{gcd}\,(a^2+9a+24,a+4) \\ &\qquad=\text{gcd}\,(a^2+9a+24-(a+5)(a+4),a+4)\\ &\qquad=\text{gcd}\,(a^2+9a+24-(a^2+9a+20),a+4)\\ &\qquad=\text{gcd}\,(4,a+4). \end{align*}\) Since \(4\) is a factor of \(a\) and thus \(a+4\) , the greatest common divisor is \(\boxed{4}\).

Thank you, CPhill! 

Thanks, EP! Amazing!

Amazing, hectictar!

Very good! Amazing, CPhill!

1.) - Salmon                Trout        Halibut
       /       |           \        /   |  \         /   |  \
   Fries Carrots Slaw  F   C  S     F  C   S
-There is 9 different options, assuming that since its a combination problem and not a sequence problem, order doesn't matter.

There are 4 kings in a deck of cards, and 13 hearts in a deck of cards. So, the answer is 4/52*13/51, if there are no replacements.