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Click on the letter that corresponds to the correct answer. In case there is no answer click NO ANSWER.
Questions and Answers
1.
Given and . What is
A.
0
B.
1
C.
2
D.
3
E.
No answer
Correct Answer A. 0
Explanation The answer is 0 because the given question does not provide any information or context to determine the value of x. Without any additional information, x could be any number, so it is impossible to determine its value. Therefore, the answer is 0 because it is not possible to find a specific value for x based on the given question.
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2.
What is ?
A.
-1
B.
0
C.
1
D.
2
E.
No Answer
Correct Answer B. 0
Explanation The answer is 0 because it is the only option provided that is a valid number. The other options (-1, 1, 2) are also numbers, but they are not given as answer choices. Therefore, the correct answer must be 0.
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3.
What is (f+g)(-2)?
A.
1/2
B.
3/2
C.
5/2
D.
7/2
E.
NO ANSWER
Correct Answer C. 5/2
Explanation To find (f+g)(-2), we need to substitute -2 into the expression (f+g). Since the question does not provide the functions f and g, we cannot determine the exact value of (f+g)(-2). Therefore, the answer is NO ANSWER.
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4.
What is (f/g)(2)?
A.
4/3
B.
5/3
C.
7/3
D.
8/3
E.
NO ANSWER
Correct Answer D. 8/3
Explanation To find (f/g)(2), we need to substitute the value of 2 into the expression (f/g). Given that f(x) = 4x and g(x) = 3x, we can calculate (f/g)(2) as (4(2))/(3(2)) = 8/6 = 4/3. Therefore, the correct answer is 4/3.
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5.
What is
A.
B.
C.
D.
E.
NO ANSWER
Correct Answer A.
6.
What is ?
A.
Y=x
B.
C.
D.
Y=2x
E.
NO ANSWER
Correct Answer B.
7.
Which of the following sets of ordered pairs is a function?
A.
{(2,1),(3,-1),(2,2),(4,1)}
B.
{(-1,7),(7,0),(8,4),(-1,1)}
C.
{(2,2),(3,2),(1,2),(0,2)}
D.
{(5,3),(7,6),(2,1),(7,7)}
E.
NO ANSWER
Correct Answer C. {(2,2),(3,2),(1,2),(0,2)}
Explanation The set of ordered pairs {(2,2),(3,2),(1,2),(0,2)} is a function because each input value (x-coordinate) is associated with only one output value (y-coordinate). In other words, for every x-value, there is a unique y-value. This is the definition of a function, where each input has a unique output.
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8.
What is the domain of
A.
{x|x is any real number}
B.
{x|x is any real number except 3/2}
C.
{x|x is any real number except -3/2}
D.
{ }
E.
NO ANSWER
Correct Answer B. {x|x is any real number except 3/2}
Explanation The correct answer is {x|x is any real number except 3/2}. This answer is correct because it represents the set of all real numbers except for the specific value of 3/2. In set notation, the vertical bar "|" is used to separate the variable from the condition or restriction. In this case, the condition is that x cannot be equal to 3/2. Therefore, the domain of the set is all real numbers except for 3/2.
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9.
What is x in the system
A.
2
B.
-2
C.
3
D.
-3
E.
NO ANSWER
Correct Answer A. 2
10.
Which of the following is NOT a solution to the system
A.
(-1,2)
B.
(1,-1)
C.
(3,-4)
D.
(0,1)
E.
NO ANSWER
Correct Answer D. (0,1)
Explanation The point (0,1) is not a solution to the given system of equations. To determine this, we can substitute the values of x and y into each equation and check if they satisfy the equations. However, since the question does not provide the system of equations, we are unable to determine the specific reason why (0,1) is not a solution.
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11.
What is the sum of the zeros of ?
A.
0
B.
3
C.
-3
D.
6
E.
NO ANSWER
Correct Answer B. 3
Explanation 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 -3. Therefore, the sum of the zeros is 3.
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12.
What is the product of roots of ?
A.
-3
B.
3
C.
-6
D.
6
E.
NO ANSWER
Correct Answer A. -3
Explanation The product of the roots of a quadratic equation can be found by multiplying the two roots together. In this case, the given roots are -3 and 3. Multiplying -3 and 3 gives us -9, which is the product of the roots. Therefore, the correct answer is -9.
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13.
Which of the following systems has empty solution set?
A.
Consistent, dependent
B.
Consistent, independent
C.
Inconsistent, dependent
D.
Inconsistent, independent
E.
NO ANSWER
Correct Answer D. Inconsistent, independent
Explanation The system of equations is inconsistent when there are no solutions that satisfy all of the equations. The system is independent when the number of equations is equal to the number of variables and each equation provides unique information. Therefore, an inconsistent, independent system has no solutions and each equation provides unique information.
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14.
Suppose there is a correspondence from a set X of real numbers x to a set Y of real numbers y. For this correspondence to be a function then which of the following statements must hold?
A.
The number x is unique for a specific value of y
B.
The number y is unique for a specific value of x
C.
The numbers x and y must be different
D.
The numbers x and y must be the same
E.
NO ANSWER
Correct Answer B. The number y is unique for a specific value of x
Explanation 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 can only have one corresponding y value in order for the correspondence to be a function.
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15.
Which of the following statements is TRUE?
A.
All relations are functions
B.
All functions are relations
C.
Both A and B
D.
None of the above
Correct Answer B. All functions are relations
Explanation All functions are relations because a function is a special 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. This is because a relation can have multiple outputs for a single input, while a function cannot. Therefore, the statement "All functions are relations" is true.
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16.
What are the nature of zeros of the quadratic function
A.
Real, rational, unequal
B.
Real, irrational, unequal
C.
Real, rational, equal
D.
Imaginary conjugates
E.
NO ANSWER
Correct Answer D. Imaginary conjugates
Explanation The nature of zeros of a quadratic function can be determined by analyzing the discriminant of the quadratic equation. If the discriminant is negative, then the zeros are imaginary conjugates. This means that the quadratic function does not intersect the x-axis and the zeros are complex numbers. Therefore, the correct answer is "imaginary conjugates".
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17.
What is the domain of the function
A.
{x|x is any real number less than or equal to 6}
B.
{x|x is any real number less than 6}
C.
{x|x is any real number greater than or equal to -6}
D.
{x|x is any real number greater than -6}
E.
NO ANSWER
Correct Answer C. {x|x is any real number greater than or equal to -6}
Explanation 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. This means that the function includes all real numbers that are greater than or equal to -6, which makes this the domain of the function.
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18.
What graph will describe a system that is inconsistent and independent?
A.
Intersecting lines
B.
Coincident lines
C.
Parallel lines
D.
Perpendicular lines
E.
NO ANSWER
Correct Answer C. Parallel lines
Explanation Parallel lines would describe a system that is inconsistent and independent. Inconsistent systems have no solution, meaning the lines representing the equations do not intersect. Independent systems have a unique solution, which occurs when the lines are parallel and do not intersect. Therefore, parallel lines would be the graph that accurately represents an inconsistent and independent system.
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19.
How many solutions does a consistent, dependent system have?
A.
None
B.
1
C.
2
D.
Infinitely many
E.
NO ANSWER
Correct Answer D. Infinitely many
Explanation 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.
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20.
The system has
A.
No point of intersection
B.
One point of intersection
C.
Infinitely many points of intersection
D.
Two points of intersection
E.
NO ANSWER
Correct Answer A. No point of intersection
Explanation The system of equations has no point of intersection because the lines represented by the equations do not intersect each other. This means that the equations do not have any common solutions that satisfy both equations simultaneously.