Podcast
Questions and Answers
Simplify the expression $7 - 2 * 5 + 9 + 3$ using order of operations.
Simplify the expression $7 - 2 * 5 + 9 + 3$ using order of operations.
Identify the objective function for Mrs. Drake's sales of skirts and dresses.
Identify the objective function for Mrs. Drake's sales of skirts and dresses.
Which of the following describes the domain of the function $f(x) = \frac{s - 5}{x + 6}$?
Which of the following describes the domain of the function $f(x) = \frac{s - 5}{x + 6}$?
Find the distance between the points $(-2, 2)$ and $(1, 6)$. (show your work)
Find the distance between the points $(-2, 2)$ and $(1, 6)$. (show your work)
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Which of the following expressions is in standard form for complex numbers?
Which of the following expressions is in standard form for complex numbers?
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If $y$ is inversely related to $x$, and $y = 3$ when $x = 4$, find $y$ when $x = 6. (show your work)
If $y$ is inversely related to $x$, and $y = 3$ when $x = 4$, find $y$ when $x = 6. (show your work)
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Find the midpoint between the points $(-2, 2)$ and $(1, 6)$. (show your work)
Find the midpoint between the points $(-2, 2)$ and $(1, 6)$. (show your work)
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What would the dimensions of the matrix be if a $2x4$ matrix and a $4x2$ matrix were multiplied?
What would the dimensions of the matrix be if a $2x4$ matrix and a $4x2$ matrix were multiplied?
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Identify the type of transformation for the parabola $f(x) = x² - 6$.
Identify the type of transformation for the parabola $f(x) = x² - 6$.
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Which of the following best describes the matrix $[¹₀ ⁰₁]$?
Which of the following best describes the matrix $[¹₀ ⁰₁]$?
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Solve the equation: $x^4 - 2x^2 - 3 = 0$.
Solve the equation: $x^4 - 2x^2 - 3 = 0$.
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Solve the equation: $x^2 - 6x = 5$.
Solve the equation: $x^2 - 6x = 5$.
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Solve the equation: $x^3 - 3x^2 - 4x + 12 = 0$.
Solve the equation: $x^3 - 3x^2 - 4x + 12 = 0$.
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Solve and graph the solution. Write the solutions in interval notation: $|2x - 3| - 5 ≤ 8$.
Solve and graph the solution. Write the solutions in interval notation: $|2x - 3| - 5 ≤ 8$.
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Solve and graph the solution. Write the solutions in interval notation: $x^2 + 4x - 12 ≥ 0$.
Solve and graph the solution. Write the solutions in interval notation: $x^2 + 4x - 12 ≥ 0$.
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Write the product of the functions $f(x) = x^2 + 2x$, $g(x) = x - 3$ and show your work.
Write the product of the functions $f(x) = x^2 + 2x$, $g(x) = x - 3$ and show your work.
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Write the composition $(f ∘ g)(x)$ for $f(x) = x^2 + 2x$, $g(x) = x - 3$ and show your work.
Write the composition $(f ∘ g)(x)$ for $f(x) = x^2 + 2x$, $g(x) = x - 3$ and show your work.
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Graph the parabolic function using translational graphing: $f(x) = (x - 2)² + 3$.
Graph the parabolic function using translational graphing: $f(x) = (x - 2)² + 3$.
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Graph the solutions to the inequality $2x - 3y$.
Graph the solutions to the inequality $2x - 3y$.
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Study Notes
Simplifying Expressions
- To simplify 7 - 2 * 5 + 9 + 3, apply order of operations: 7 - 10 + 9 + 3 = 0.
Objective Function
- For Mrs. Drake selling skirts and dresses, the profit function is P = 5x + 12y, where x represents skirts and y represents dresses.
Domain of Functions
- The domain of the function ƒ(x) = (s - 5) / (x + 6) excludes x = -6, giving the domain: (-∞, -6) and (-6, ∞).
Distance Between Points
- The distance between points (-2, 2) and (1, 6) calculates to 5, using the distance formula.
Standard Form of Complex Numbers
- The standard form for complex numbers is represented as a + bi; 7 - 4i fits this definition.
Inverse Relationships
- Given y = 3 when x = 4, y can be determined when x = 6. The result is y = 2.
Midpoint Calculation
- The midpoint between points (-2, 2) and (1, 6) is (-1, 4), calculated by averaging the x and y coordinates.
Matrix Dimensions
- Multiplying a 2x4 matrix by a 4x2 matrix results in a 2x2 matrix.
Transformations of Functions
- The transformation of the parabola represented by ƒ(x) = x² - 6 is a vertical translation.
Matrix Identification
- The matrix [¹₀ ⁰₁] is identified as an identity matrix.
Solving Equations
- The equation x⁴ - 2x² - 3 = 0 yields solutions x = ±i and x = ±√3.
- For x² - 6x = 5, solutions are x = 3 ± √14.
- The cubic equation x³ - 3x² - 4x + 12 = 0 has solutions x = 2, -2, 3.
Absolute Value Inequalities
- The solution to |2x - 3| - 5 ≤ 8 includes all values in the interval [-5,8].
Graphing Solutions
- The inequality x² + 4x - 12 ≥ 0 yields solutions in intervals (-∞, -6] and [2, ∞).
Function Operations
- For functions f(x) = x² + 2x and g(x) = x - 3, the product (fg)(x) results in x³ - x² - 6x.
- The composition (f ⁰ g)(x) yields x² - 4x + 3.
Graphing Parabolas
- The graph of f(x) = (x - 2)² + 3 has its vertex at (2, 3), with significant points at (4, 12) and (5, -7).
Inequalities
- Graphing the solution for the inequality 2x - 3y requires further specification for x and y ranges.
Studying That Suits You
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Description
Prepare for your Algebra 2 Test with this set of review flashcards. These flashcards cover key topics such as simplifying expressions and identifying objective functions, ensuring you grasp essential concepts leading up to the test. Brush up on your skills and feel confident on exam day!
