For the dinner special at a restaurant, the customer must choose an appetizer, a salad, an entree, a side dish, and a dessert. Here are the items to choose from. Choice Possible items Appetizer Chicken strips, Shrimp cocktail, Buffalo wings, Potato skins Salad Garden, Caesar Entree T-bone steak, Pot roast, Lamb Side dish Corn, Rice, French fries, Baked potato, Pinto beans Dessert Chocolate cake, Brownies, Ice cream, Apple pie How many dinner specials are possible

The number of possible dinner specials are 4368.

Step-by-step explanation:

The number of dinner specials = 5

They include appetizer, a salad, an entree, a side dish, and a dessert.

Possible items to choose from = 16.

They are 1. Appetizer Chicken strips, 2. Shrimp cocktail, 3. Buffalo wings, 4. Potato skins, 5. Salad Garden, 6. Caesar Entree T-bone steak, 7. Pot roast, 8. Lamb Side dish Corn, 9. Rice, 10. French fries, 11. Baked potato, 12. Pinto beans, 13. Dessert Chocolate cake, 14. Brownies, 15. Ice cream, 16. Apple pie

This is a combination problem requiring a combination solution with the following formula and steps:

C (n, r) =? C (n, r) = ?

n choose r

n (objects) =  16

r (sample) =  5

C (n, r) =? C (n, r) = ?

C (n, r) =C (14,5) C (n, r) =C (16,5)

=16! (5! (16−5)!) =16! (5! (16−5)!)

= 4368

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