T. J. is hosting a dinner party. T. J. greets the first guest and they shake hands. The second guest arrives and shakes hands with T. J. and the first guest. The third guest arrives and shakes hands with T. J., the first guest, and the second guest. This pattern continues. How many handshakes have taken place after the ninth guest arrives?

45 Handshakes

Step-by-step explanation:

45 Handshakes have taken place all together

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

5

step-by-step explanation: