College Algebra Quiz 2 Nursing

An inconsistent system means that there are no solutions that satisfy all of the equations or inequalities in the system. An independent system means that each equation or inequality in the system provides new information and is not redundant. Therefore, an inconsistent, independent system has no solutions and each equation or inequality in the system is necessary.

Parallel lines describe a system that is inconsistent and independent because they never intersect. In an inconsistent system, there are no solutions that satisfy all the equations simultaneously, while in an independent system, there is exactly one solution. Therefore, parallel lines, which never intersect, represent a system that is both inconsistent and independent.

A consistent, dependent system has infinitely many solutions because the equations in the system are not independent and can be expressed as multiples of each other. This means that any value that satisfies one equation will also satisfy the others, resulting in an infinite number of solutions.

The set of ordered pairs {(2,2),(3,2),(1,2),(0,2)} is a function because each input value (x-coordinate) is paired with exactly one output value (y-coordinate). In other words, for every x-value, there is only one corresponding y-value.

The product of the roots of a quadratic equation can be found by multiplying the constant term by the coefficient of the quadratic term. In this case, the constant term is -3 and the coefficient of the quadratic term is 1. Therefore, the product of the roots is -3.

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The answer is 0 because it is the only number given as an option. The question is incomplete and does not provide any context or information to determine what is being referred to.

The correct answer is {x|x is any real number greater than or equal to -6}. This is because the function is defined for all real numbers that are greater than or equal to -6. The domain of a function represents the set of all possible input values, and in this case, any real number greater than or equal to -6 can be used as an input for the function.

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For the correspondence to be a function, the number y must be unique for a specific value of x. This means that each value of x in the set X should correspond to only one value of y in the set Y. It ensures that there is no ambiguity or multiple outputs for a single input, which is a requirement for a function.

The given system of equations consists of four coordinate pairs. To determine which one is not a solution, we can substitute the values of each coordinate pair into the equations of the system. If the values satisfy all the equations, then it is a solution. However, if the values do not satisfy any of the equations, then it is not a solution. In this case, when we substitute the values (0,1) into the equations, it does not satisfy any of them. Therefore, (0,1) is not a solution to the system.

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The expression (f/g)(2) represents the composition of functions f and g, evaluated at the input value of 2. To find this value, we first need to evaluate g(2), which is not given in the options. Therefore, an explanation cannot be provided for the given correct answer.

The correct answer is {x|x is any real number except 3/2}. This is because the domain of a set refers to the possible values that x can take. In this case, x can take any real number except 3/2. Therefore, the set {x|x is any real number except 3/2} accurately represents the domain of the given set.

The nature of zeros of a quadratic function can be determined by the discriminant, which is the value under the square root in the quadratic formula. If the discriminant is negative, the zeros are imaginary and occur in conjugate pairs. Therefore, the correct answer is "imaginary conjugates".

The sum of the zeros of a quadratic equation is equal to the negative coefficient of the linear term divided by the coefficient of the quadratic term. In this case, the quadratic equation is not given, so we cannot determine the sum of the zeros. Therefore, the correct answer cannot be determined based on the information given.

All functions are relations because a function is a specific type of relation where each input has exactly one output. In other words, every function can be represented as a relation, but not every relation can be represented as a function. Therefore, the statement "All functions are relations" is true.

The given answer "no point of intersection" suggests that the system does not have any common solution or intersection point. This means that the equations or objects being referred to in the system do not intersect or meet each other at any point.