College Algebra Quiz 2 Geol 8:30-10

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 this description as they do not intersect and have no common points.

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The given answer is 0. This suggests that the question is asking for a numerical value, and out of the options provided, 0 is the only numerical value.

To find (f/g)(2), we need to substitute 2 into the function f and then divide the result by g(2). Since the question does not provide any information about the functions f and g, we cannot determine the exact values of f(2) and g(2). Therefore, without further context or information, we cannot provide an explanation for the given correct answer of 8/3.

All functions are relations because a function is a specific type of relation where each input has exactly one output. In other words, for every element in the domain of a function, there is a unique element in the range. Therefore, all functions can be considered as relations, but not all relations can be considered as functions if they do not satisfy the one-to-one mapping requirement.

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

The correct answer is {x|x is any real number except 3/2}. This is because the domain refers to the set of values that x can take in a function or equation. In this case, x can be any real number except 3/2, as it is specifically excluded from the set. Therefore, the correct answer is the set of all real numbers except 3/2.

The system of equations will have an empty solution set when it is inconsistent, meaning there are no values for the variables that satisfy all the equations. Additionally, the system will be independent, meaning none of the equations can be derived from the others. Therefore, the correct answer is "inconsistent, independent".

The sum of the zeros of a polynomial is equal to the negative coefficient of the linear term divided by the leading coefficient. In this case, the linear term is 0 and the leading coefficient is 1. So, the sum of the zeros is 0/1 = 0. However, since there is no option for 0 in the given answer choices, the correct answer is NO ANSWER.

The product of the roots of a quadratic equation can be found by multiplying the two roots together. In this case, the roots are -3 and 3. When multiplied, -3 multiplied by 3 gives us -9. Therefore, the product of the roots is -9.

A consistent, dependent system has infinitely many solutions because it represents a situation where the equations are not independent and are essentially the same equation. This means that every value that satisfies the equation will also satisfy the other equations in the system, resulting in an infinite number of possible solutions.

The nature of zeros of a quadratic function can be determined by the discriminant, which is the part of the quadratic formula under the square root. If the discriminant is negative, then the zeros are imaginary conjugates, meaning they are complex numbers of the form a + bi and a - bi. Since the answer states "imaginary conjugates," it suggests that the discriminant is negative, indicating that the zeros of the quadratic function are complex numbers.

The given system of equations has four solutions: (-1,2), (1,-1), (3,-4), and (0,1). However, the answer (0,1) is not a solution to the system.

The correct answer is {x|x is any real number greater than or equal to -6}. This is because the given function states that x can be any real number greater than or equal to -6. The domain of a function refers to the set of all possible input values, and in this case, the input values can be any real number greater than or equal to -6.

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The given answer "no point of intersection" suggests that the system of equations or lines being referred to do not intersect each other. This means that the lines are either parallel or coincident, resulting in no intersection point.

For a correspondence to be a function, the number y must be unique for a specific value of x. This means that each x-value in the set X can only correspond to one unique y-value in the set Y. It is not necessary for the numbers x and y to be different or the same, and the uniqueness requirement applies to the y-value, not the x-value.