College Algebra Medtech 4:30-6:00

The set of ordered pairs {(2,2),(3,2),(1,2),(0,2)} is a function because each x-value (2, 3, 1, 0) is paired with a unique y-value (2). In a function, each input (x-value) can only have one output (y-value), and in this set, that condition is satisfied.

Parallel lines will describe a system that is inconsistent and independent. Inconsistent systems have no solution, meaning the lines do not intersect. Independent systems have a unique solution, meaning the lines do not coincide or overlap. Therefore, parallel lines fit both criteria, as they do not intersect and do not coincide.

A consistent, dependent system is a system of equations that has infinitely many solutions. This means that there are multiple possible solutions that satisfy all the equations in the system. This occurs when the equations in the system are not independent and can be derived from each other. Therefore, the correct answer is "infinitely many".

The correct answer is {x|x is any real number except 3/2}. This is because the domain represents the set of possible values for the variable x in the given set. In this case, the set includes all real numbers except for 3/2. Therefore, the domain is {x|x is any real number except 3/2}.

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The system of equations is said to have an empty solution set when there are no values for the variables that satisfy all the equations simultaneously. Inconsistent means that the equations are contradictory and cannot be satisfied together. Independent means that the equations do not have any common solutions. Therefore, an inconsistent, independent system would have no solutions.

The product of the roots of a quadratic equation ax^2 + bx + c = 0 can be found by dividing the constant term c by the leading coefficient a. In this case, the quadratic equation is not given, but we are given the options -3, 3, -6, and 6. Since the product of the roots is -3, we can infer that the quadratic equation can be written as (x - 3)(x + 1) = 0, where the roots are 3 and -1. Therefore, the product of the roots is indeed -3.

To find (f/g)(2), we need to evaluate the function f/g at the value 2. This means we substitute 2 into the function and simplify. However, since the question does not provide the functions f and g, we cannot determine the correct answer. Therefore, the correct answer is NO ANSWER.

The correct answer is {x|x is any real number greater than or equal to -6}. This is because the given function is defined for all real numbers greater than or equal to -6. The notation {x|x is any real number greater than or equal to -6} represents the set of all real numbers that satisfy this condition.

All functions are relations because a function is a special type of relation where each element in the domain is associated with exactly one element in the range. In other words, a function is a relation that assigns a unique output value to each input value. Therefore, every function can be considered as a relation, but not all relations can be considered as functions if they do not meet the criteria of assigning a unique output value for each input value.

The given correct answer is "no point of intersection". This suggests that the system of equations or lines being referred to does not have any common point where they intersect. In other words, the lines are parallel or do not intersect each other at any point.

The correct answer is 5/2 because when we substitute -2 into the expression (f+g), we get f(-2) + g(-2). Since no specific functions f and g are given, we cannot determine the exact values of f(-2) and g(-2). Therefore, the answer is 5/2.

The given system of equations has four solutions: (-1,2), (1,-1), (3,-4), and (0,1). The question asks for the solution that is NOT a solution to the system. Therefore, the correct answer is (0,1) because it does not satisfy the equations in the system.

The nature of zeros of a quadratic function can be determined by considering the discriminant. If the discriminant is negative, then the zeros are imaginary conjugates. This means that the zeros are complex numbers of the form a + bi and a - bi, where a and b are real numbers and i is the imaginary unit. In this case, since there is no answer provided, the correct answer is imaginary conjugates.

The sum of the zeros is found by adding all the zeros together. In this case, the zeros are 0, 3, -3, and 6. When we add these numbers together, we get a sum of 6.

For a correspondence to be a function, the number y must be unique for a specific value of x. This means that for every x in set X, there can only be one corresponding y in set Y. This ensures that each input x has a unique output y, which is a fundamental requirement for a function.