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Questions and Answers
Select all of the irrational numbers.
Select all of the irrational numbers.
Which inequality and graph represent all possible solutions of: |−3x|≤6?
Which inequality and graph represent all possible solutions of: |−3x|≤6?
{-2≤x≤2}
What is the probability of tossing heads using Jeff and Kevin's results?
What is the probability of tossing heads using Jeff and Kevin's results?
11/20
What is the correct solution mentioned in the problem?
What is the correct solution mentioned in the problem?
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Select all sets of numbers that √31 belongs to.
Select all sets of numbers that √31 belongs to.
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What is the value of 1/6 ÷ (-3/18)?
What is the value of 1/6 ÷ (-3/18)?
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What is the value of 4(3h-6)/1+h for h = -2?
What is the value of 4(3h-6)/1+h for h = -2?
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What is the opposite and the reciprocal of 500?
What is the opposite and the reciprocal of 500?
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What is the solution to 3y+20= 3+2y?
What is the solution to 3y+20= 3+2y?
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What does the graph represent for: −6≤2x≤6?
What does the graph represent for: −6≤2x≤6?
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Which points represent the graph for y = 2x + 1?
Which points represent the graph for y = 2x + 1?
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What is the slope of the line represented by the equation 3x + 5y = -15?
What is the slope of the line represented by the equation 3x + 5y = -15?
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Choose the set of ordered pairs that represents a function.
Choose the set of ordered pairs that represents a function.
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Which ordered pair is a solution to the equation represented by the graph?
Which ordered pair is a solution to the equation represented by the graph?
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What is the slope of the line passing through the points (-8,3) and (-7,-5)?
What is the slope of the line passing through the points (-8,3) and (-7,-5)?
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Select all true statements about the graph.
Select all true statements about the graph.
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What are the slope and y-intercept of the line given by 12x - 4y = -96?
What are the slope and y-intercept of the line given by 12x - 4y = -96?
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What is the vertex of the equation y = |x + 2| - 4?
What is the vertex of the equation y = |x + 2| - 4?
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What is the y-intercept of the line 9x + 6y + 1 = 0?
What is the y-intercept of the line 9x + 6y + 1 = 0?
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What is the solution set for the system of equations: x + 2y + z = 5, 2x - 6 + 5z = 3, x + 3z = 3?
What is the solution set for the system of equations: x + 2y + z = 5, 2x - 6 + 5z = 3, x + 3z = 3?
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What is the solution set for the equations: x - y + z = -1, x + y + 3z = -3, 2x - y + 2z = 0?
What is the solution set for the equations: x - y + z = -1, x + y + 3z = -3, 2x - y + 2z = 0?
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What is the solution set for the equations: 6x + y = 7, x + 12y = 13?
What is the solution set for the equations: 6x + y = 7, x + 12y = 13?
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What is the solution set for the equations: 2x + 3y = 12, 3x + 4y = 17?
What is the solution set for the equations: 2x + 3y = 12, 3x + 4y = 17?
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What is the solution set for the system of equations: x + 2y + z = 4, 2x - y + 4z = -8, -3x + y - 2z = -1?
What is the solution set for the system of equations: x + 2y + z = 4, 2x - y + 4z = -8, -3x + y - 2z = -1?
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What is the solution set for the equations: 5z + 4y = 4, 3x - 2y = 0, x + 3z = -8?
What is the solution set for the equations: 5z + 4y = 4, 3x - 2y = 0, x + 3z = -8?
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What is the solution set for the equations: 4x - y + z = -5, -x + y - z = 5, 2x - z - 1 = y?
What is the solution set for the equations: 4x - y + z = -5, -x + y - z = 5, 2x - z - 1 = y?
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What is the solution set for the equations: 2x + 7y = 15, 3x - 6y = 6?
What is the solution set for the equations: 2x + 7y = 15, 3x - 6y = 6?
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What is the solution set for the equations: x - y + z = -1, x + y + 3z = -3, 2x - y + 2x = 0?
What is the solution set for the equations: x - y + z = -1, x + y + 3z = -3, 2x - y + 2x = 0?
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What is the answer to the video game word problem?
What is the answer to the video game word problem?
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Identify the vertex and the y-intercept of the function y = -3(x + 2)^2 + 5.
Identify the vertex and the y-intercept of the function y = -3(x + 2)^2 + 5.
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Write in the vertex form: y = 2x^2 + 12x + 8.
Write in the vertex form: y = 2x^2 + 12x + 8.
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What is the vertex and y-intercept of the function y = 2(x - 2)^2 - 4?
What is the vertex and y-intercept of the function y = 2(x - 2)^2 - 4?
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Factor the expression: -15x^2 + 15x + 20.
Factor the expression: -15x^2 + 15x + 20.
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Select an equivalent expression to x^2 + 10x + 16.
Select an equivalent expression to x^2 + 10x + 16.
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Select an expression equivalent to 3x^2 + 14x + 16.
Select an expression equivalent to 3x^2 + 14x + 16.
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Write 3 + √-49 in the form of a + bi.
Write 3 + √-49 in the form of a + bi.
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Write -3 - √-180 in the form of a + bi.
Write -3 - √-180 in the form of a + bi.
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Find the absolute value of |-5 + i|.
Find the absolute value of |-5 + i|.
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Simplify (3i)(-i).
Simplify (3i)(-i).
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Given the function y = 2x^2 - 8x + 4, find the y-intercept and the vertex.
Given the function y = 2x^2 - 8x + 4, find the y-intercept and the vertex.
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Enter the value equivalent to (-3 + 4i) - (2 + 6i).
Enter the value equivalent to (-3 + 4i) - (2 + 6i).
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Simplify (-4 - 4i)(3 + 2i).
Simplify (-4 - 4i)(3 + 2i).
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Indicate whether the equation 5/20x = 1/4x has solutions.
Indicate whether the equation 5/20x = 1/4x has solutions.
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Indicate whether the equation 3x = 4x + 5x has solutions.
Indicate whether the equation 3x = 4x + 5x has solutions.
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Indicate whether the equation √2x + 3 + 6 = 0 has solutions.
Indicate whether the equation √2x + 3 + 6 = 0 has solutions.
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How long will it take the stone to hit the ground as modeled by y = −16t^2 + 358?
How long will it take the stone to hit the ground as modeled by y = −16t^2 + 358?
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Study Notes
Irrational Numbers
- Examples include √2, √34, and π.
- √31 belongs to irrational and real numbers.
Inequalities
- The inequality |−3x|≤6 translates to the solution set {-2≤x≤2}.
- The graph for −6≤2x≤6 corresponds to {-3≤x≤3}.
Probability
- The probability of tossing heads, based on Jeff and Kevin's coin toss results, is 11/20.
Mistakes in Solutions
- In a multi-step problem, the first mistake occurs in step 1; the correct solution is 7.
Algebraic Evaluations
- The value of 1/6 ÷ (-3/18) is -1.
- For h = -2 in the expression 4(3h-6)/(1+h), the result is 48.
Opposites and Reciprocals
- The opposite of 500 is -500, and the reciprocal is 1/500.
Graph Representations
- The graph of the equation y = 2x + 1 passes through points (-1,0) and (0,2).
- The slope of the line defined by 3x + 5y = -15 is -3/5.
Function and Ordered Pairs
- The ordered pairs {(-3,-5), (-5,-3), (-7,-7)} represent a function.
- The ordered pair (0,-1) is a solution to the equation represented by the graph.
Slope Calculations
- The slope of the line through points (-8,3) and (-7,-5) is -8.
- For the equation 12x - 4y = -96, the slope is 3 and the y-intercept is 24.
Vertex and Intercepts
- The vertex of y = |x+2| -4 is at (-2,-4).
- The y-intercept of 9x + 6y + 1 = 0 is -1/6.
Systems of Equations Solutions
- For x + 2y + z = 5, 2x - 6 + 5z = 3, x + 3z = 3, the solution set is (0, 2, 1).
- The systems of equations yield solutions (4,2,-3), (1,1), and (3,2) for other specified sets.
Polynomial Factoring and Forms
- Vertex form of the polynomial y = 2x² + 12x + 8 is y = 2(x + 3)² - 10.
- (x^2 + 10x + 16) can be factored to (x+2)(x+8) and (3x^2 + 14x + 16) to (x+2)(3x+8).
Complex Numbers
- Convert 3 + √-49 to the form a + bi gives 3 + 7i.
- Simplifying -3 - √-180 results in -3 - 6i√5.
Absolute and Imaginary Values
- The absolute value of |-5 + i| is √26.
- Simplifying (3i)(-i) results in 3.
Graph Heights and Time
- In the function y = −16t² + 358, it models the height of a stone dropped from a cliff. The time to hit the ground can be calculated using a quadratic equation setup.
Solutions Types for Equations
- The equation 5/20x = 1/4x has infinitely many solutions.
- The equation 3x = 4x + 5x has one real solution.
- The equation √(2x+3) + 6 = 0 has no real solutions.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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Test your knowledge with these flashcards covering topics from Algebra 2, Quarter 1. Each card challenges you on key concepts such as irrational numbers, inequalities, and probability. Perfect for revision or self-assessment before your upcoming exam!
