The sum of three numbers is 69. the second number is equal to the first diminished by 8, and the third number is 5 times the first.

if x represents the first number, then which of the following equations could be used to determine the values of all of the numbers?

a x= 6x-8
b 69=6x-8
c 69=7x-8

Consider the system: y = 3x + 5 y = ax + b what values for a and b make the system inconsistent? what values for a and b make the system consistent and dependent? explain

1- 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.2- 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 the first question?

What is the value of the discriminant of the quadratic equation -2x = -8x + 8 and what does its value mean about thenumber of real number solutions the equation has?