10 students are competing in a dance competition. How many was can you award first, second, and third place?

Given:

Total number of students = 10

To find:

How many was can you award first, second, and third place?

Solution:

Total number of students is 10. So, the total possible ways for the first award is 10.

We know that one student can hold only one place. So, after giving the first award, the number of remaining students is 9 and the total possible ways for the second award is 9.

Similarly, the total possible ways for the third award is 8.

Now, the total number of ways to award first, second, and third place is:

Therefore, the total number of ways to award first, second, and third place is 720.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

srry idk

step-by-step explanation: