A chef has 13 brands of hot sauce. In how many ways can the chef pick 4 to mix into a gumbo. Simplify your answer.

715 ways

Step-by-step explanation:

The order in which the brands are chosen 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:

4 from a set of 13. So

715 ways

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

step-by-step explanation: