Leanne is picking out some movies to rent, and she is primarily interested in children's movies and comedies. She has narrowed down her selections to 18 children's movies and 7 comedies. Step 2 of 2 : How many different combinations of 3 movies can she rent if she wants at least one comedy

If she wants at least one comedy, there are 1484 different combinations.

Step-by-step explanation:

The order in which she wants to pick the movies is not important. So, we use the combinations formula to solve this question.

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

In this question:

She wants combinations of 3 movies, with at least one comedy. The easiest way to find this is finding the total number of combinations of 3 movies, from the set of 25(18 children's and 7 comedies), and subtract by the total number without comedies(which is 3 from a set of 25). So

Total:

3 from a set of 25.

Without comedies:

3 from a set of 18.

At least one comedy:

If she wants at least one comedy, there are 1484 different combinations.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

good job you smart son of a gun you are smarter that einstein. 7