Questions and Answers
Simplify the expression $7 - 2 * 5 + 9 + 3$ using order of operations.
Which of the following describes the domain of the function $ƒ(x) = \frac{s - 5}{x + 6}$?
Which of the following expressions is in standard form for complex numbers?
Find the distance between the points (-2, 2) and (1, 6).
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Find the midpoint between the points (-2, 2) and (1, 6).
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Let x and y be inversely related. If y = 3 when x = 4, find y when x = 6.
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Identify the type of transformation for the parabola $ƒ(x) = x^2 - 6$.
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What would the dimensions of the matrix be if a 2x4 matrix and a 4x2 matrix were multiplied?
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Read the information below and identify the objective function: Mrs. Drake is selling 38 skirts and 12 dresses. However, she has only enough space to display 42 of these. The expected profit of each skirt is $5 while the expected profit of each dress is $12. Use x to represent skirts and y to represent dresses.
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Which of the following best describes the matrix $[¹₀ ⁰₁]$?
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Solve the equation $x^2 - 6x = 5$. (show your work)
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Solve the equation $x^3 - 3x^2 - 4x + 12 = 0$. (show your work)
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Solve the equation $x^4 - 2x^2 - 3 = 0$. (show your work)
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Solve and graph the solution: $x^2 + 4x - 12 ≥ 0$. (show your work)
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Solve and graph the solution: $|2x - 3| - 5 ≤ 8$. (show your work)
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Write the combination $(fg)(x)$ for $f(x) = x^2 + 2x$, $g(x) = x - 3$. (show your work)
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Write the composition $(f ullet g)(x)$ for $f(x) = x^2 + 2x$, $g(x) = x - 3$. (show your work)
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Graph the parabolic function $f(x) = (x - 2)^2 + 3$. (show your work)
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Graph the solutions to the inequality $2x - 3y$. (show your work)
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Study Notes
Simplification and Functions
- To simplify the expression 7 - 2*5 + 9 + 3 using order of operations results in 0.
- The domain of the function ƒ(x) = (x - 5)/(x + 6) is all real numbers except x = -6, represented as (-∞, -6) and (-6, ∞).
- The standard form for complex numbers is exemplified by 7 - 4i.
Geometry and Midpoint Calculations
- The distance between the points (-2, 2) and (1, 6) is 5 units.
- The midpoint between the points (-2, 2) and (1, 6) is (-½, 4).
Inverse Relations
- Inversely related variables show that if y = 3 when x = 4, then y = 2 when x = 6.
Transformations in Functions
- The parabola f(x) = x² - 6 undergoes a vertical translation.
Matrix Operations
- The resulting dimensions when multiplying a 2x4 matrix by a 4x2 matrix yield a 2x2 matrix.
Profit Maximization Problem
- The objective function representing expected profit in a sales context is P = 5x + 12y, where x represents skirts and y represents dresses.
Matrix Types
- The matrix [¹₀ ⁰₁] is classified as an identity matrix.
Solving Equations
- Several equations require solutions or graphing, but specific solutions are pending for x² - 6x = 5, x³ - 3x² - 4x + 12 = 0, and x⁴ - 2x² - 3 = 0.
Inequalities and Graphing
- Solutions to inequalities such as x² + 4x - 12 ≥ 0 and |2x - 3| - 5 ≤ 8 require intervals and graphical representation.
Function Composition
- Function combinations include the product (fg)(x) and composition (f(g))(x) using f(x) = x² + 2x and g(x) = x - 3.
Graphing Functions
- The function f(x) = (x - 2)² + 3 can be graphed using translational graphing techniques.
Additional Notes
- Gaps exist in showing work for solving equations and graphing inequalities; these should be addressed for complete understanding.
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Description
Test your knowledge of Algebra 2 concepts with these flashcards focused on order of operations, domain of functions, and complex numbers. Perfect for 10th-grade students preparing for their test. Challenge yourself and see how well you understand these key topics!
