Quiz 2 College Algebra (Geol 12-1)

A consistent, dependent system has infinitely many solutions because the equations in the system are not independent and are essentially expressing the same relationship. This means that any value that satisfies the relationship will be a solution to the system. Therefore, there is no limit to the number of solutions that can exist in a consistent, dependent system.

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 only one output value (y-coordinate). In other words, for each x-value, there is only one corresponding y-value. This satisfies the definition of a function, where each input has a unique output.

Parallel lines would describe a system that is inconsistent and independent. Inconsistent means that there are no solutions to the system of equations, and independent means that the lines do not intersect. When two lines are parallel, they will never intersect, indicating that there are no common solutions to the system. Therefore, parallel lines are the appropriate graph to represent an inconsistent and independent system.

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 there are no solutions that satisfy all the equations, and independent means that none of the equations can be derived from the others. Therefore, the system being inconsistent and independent implies that there are no solutions that satisfy the equations, resulting in an empty solution set.

The given points (-1,2), (1,-1), (3,-4), and (0,1) are the solutions to the system. However, the point (0,1) is not a solution to the system.

The correct answer is {x|x is any real number except 3/2}. The domain of a function refers to the set of all possible input values. In this case, the given set notation {x|x is any real number except 3/2} indicates that any real number can be used as input for the function, except for the value 3/2. This means that all real numbers, except 3/2, are included in the domain of the function.

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The answer is 0 because it is the only number provided as an option. The other numbers (-1, 1, and 2) are not given as choices. Therefore, 0 is the only possible answer based on the options provided.

The statement "All functions are relations" is true because a function is a specific type of relation where each input value (domain) is associated with exactly one output value (range). In other words, every function can be considered as a relation, but not every relation can be considered as a function.

The expression (f/g)(2) represents the composition of two functions, f and g, evaluated at the input 2. Without knowing the specific functions f and g, we cannot determine the exact value of (f/g)(2). However, since the answer given is 8/3, it suggests that when f(2) is divided by g(2), the result is 8/3.

The sum of the zeros of a polynomial is equal to the negative coefficient of the linear term divided by the coefficient of the quadratic term. In this case, the linear term has a coefficient of -3 and the quadratic term has a coefficient of 6. Therefore, the sum of the zeros is -3/6, which simplifies to -1/2. However, this answer is not listed as an option. The only available answer is 3, which does not correspond to the sum of the zeros. Therefore, the correct answer is NO ANSWER.

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To find (f+g)(-2), we need to substitute -2 into the expression (f+g). Since the expression (f+g) is not given, we cannot determine the exact value. Therefore, the answer is NO ANSWER.

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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. Therefore, the product of the roots is -3 * 3 = -9.

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The answer is "no point of intersection" because the system of equations described in the question does not have any common solutions. This means that the lines represented by the equations do not intersect each other at any point.

For a correspondence to be a function, the number y must be unique for a specific value of x. This means that for each input x, there can only be one output y. This ensures that there is no ambiguity or confusion in the mapping between the sets X and Y. The other statements are not necessary for a correspondence to be a function.

The nature of zeros of a quadratic function can be real or imaginary. In this case, the answer states that the zeros are imaginary conjugates. This means that the zeros of the quadratic function are complex numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit. The fact that they are conjugates means that if one zero is a + bi, the other zero is a - bi.

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 greater than or equal to -6. The notation {x|x is any real number greater than or equal to -6} indicates that the set of possible input values for the function includes all real numbers greater than or equal to -6.