A person has 5 tickets for a concert and she wants to invite 4 of her 8 best friends. How many choices does she have, if two of her friends do not get along and cannot be both invited?

55

Step-by-step explanation:

Combinations formula is used to make choice of 'R' out of 'N' options =

N(C)R = N ! / [ R ! . (N-R)! ]

Total choices to choose 4 out of 8 friends = 8C4

= 8! / (4! 4!)  

= 70

Choices for calling them 2 together = 2C2 x 6C2

= 1 x [ 6! / (2! 4!)]

= 15

So : Number of choices that the 2 friends are not called together = Total choices - choices they are called together

= 70 - 15 = 55

0=3x^2+17x-160

Step-by-step explanation:

Area = Width × Length

Width = x + 5

Length = 3x + 2

(x + 5) × (3x + 2)

use rainbow method

3x × x = 3x^2

3x × 5 = 15x

2 × x = 2x

2 × 5 = 10

3x^2 + 17x + 10 = 170

subtract 170 from both sides

3x^2 + 17x + 10 - 170 = 0

0 = 3x^2 + 17x - 160