María, Natalia, Carlos y juan, 4 compañeros de colegio que comparten su gusto por la naturaleza, deciden ir juntos al estreno de un documental sobre el cuidado del medio ambiente y compran las boletas para hacerse en una fila con 4 puestos contiguos numerados. Si María y Natalia siempre están sujetas, entonces la cantidad de formas diferentes en que se pueden ubicar en los 4 puestos, los 4 compañeros mencionados es?: 12 10 16 24

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

If x is 6, then 7x= a. 13 b. 42 c. 42x d. 76

How is the equation of this circle written in standard form? x2 + y2 - 6x + 14y = 142 a) (x - 3)2 + (y + 7)2 = 200 b) (x+ 3)2 + (y - 7)2 = 200 (x - 6)2 + (y + 14)2 = 142 d) (x+6)2 + (y- 14)2 = 142