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Questions and Answers
Evaluate the expression: k + 9 when k = 7.
Evaluate the expression: k + 9 when k = 7.
16
Evaluate the expression: $\frac{1}{3}(7 - 5.5)^2$.
Evaluate the expression: $\frac{1}{3}(7 - 5.5)^2$.
0.75
Translate into expression: ¾ of a number m.
Translate into expression: ¾ of a number m.
¾m
Translate into expression: 6 more than 3 times a number n.
Translate into expression: 6 more than 3 times a number n.
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Solve: d - 13 = 25.
Solve: d - 13 = 25.
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Evaluate: -√36.
Evaluate: -√36.
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What is $\sqrt{250}$?
What is $\sqrt{250}$?
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Solve: 8 = m - 13.
Solve: 8 = m - 13.
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Solve: 12w - 5 - 3w = 40.
Solve: 12w - 5 - 3w = 40.
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Rewrite in y-intercept form: 10x − y = 20.
Rewrite in y-intercept form: 10x − y = 20.
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Solve: y − 2 > 3.
Solve: y − 2 > 3.
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Solve: $\frac{5}{6}(12p - 24) > \frac{2}{5}(25p - 25)$.
Solve: $\frac{5}{6}(12p - 24) > \frac{2}{5}(25p - 25)$.
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|m - 6| = 5.
|m - 6| = 5.
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What's the solution for the system of equations y = x - 2 and y = x + 5?
What's the solution for the system of equations y = x - 2 and y = x + 5?
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Use substitution: y = 2x + 6; y = -x + 5.
Use substitution: y = 2x + 6; y = -x + 5.
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Use elimination: 3x - 4y = -16 and x - 4y = -40.
Use elimination: 3x - 4y = -16 and x - 4y = -40.
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Simplify: $(-4s^2)^3(2s^3)^6$.
Simplify: $(-4s^2)^3(2s^3)^6$.
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Evaluate: $\frac{1}{2^{-5}}$.
Evaluate: $\frac{1}{2^{-5}}$.
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Simplify: $10b^{-3}c^5$.
Simplify: $10b^{-3}c^5$.
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Subtract: $(2t^3 - 3t^2 + 5t) - (6t^3 + 3t^2 - 5t)$.
Subtract: $(2t^3 - 3t^2 + 5t) - (6t^3 + 3t^2 - 5t)$.
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Add: $(8y^2 - 3y - 10) + (-11y^2 + 2y - 7)$.
Add: $(8y^2 - 3y - 10) + (-11y^2 + 2y - 7)$.
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Find the product: $(x + 10)^2$.
Find the product: $(x + 10)^2$.
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Solve: $(m + 8)(m - 2) = 0$.
Solve: $(m + 8)(m - 2) = 0$.
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Factor: $q^2 + 3q - 40$.
Factor: $q^2 + 3q - 40$.
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Factor: $m^2 - 29m + 100$.
Factor: $m^2 - 29m + 100$.
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What is different when you graph y = x² and y = 1/2x²?
What is different when you graph y = x² and y = 1/2x²?
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A community hospital conducts a survey to determine patient satisfaction. Identify the population and the sampling method.
A community hospital conducts a survey to determine patient satisfaction. Identify the population and the sampling method.
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Find the range and mean of absolute deviation for the numbers: 13, 21, 17, 8, 19, 18.
Find the range and mean of absolute deviation for the numbers: 13, 21, 17, 8, 19, 18.
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Find the mean, median, and mode for the numbers: 4, 12, 19, 26, 19, 15, 32, 7.
Find the mean, median, and mode for the numbers: 4, 12, 19, 26, 19, 15, 32, 7.
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Calculate the Mean Absolute Deviation: 1, 2, 3.5, 4, 6, 6, 9, 11, 13, 15, 15, 25.7.
Calculate the Mean Absolute Deviation: 1, 2, 3.5, 4, 6, 6, 9, 11, 13, 15, 15, 25.7.
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What will happen to the graph of y = 3x - 1 if the value of the y-intercept decreases by 2 units?
What will happen to the graph of y = 3x - 1 if the value of the y-intercept decreases by 2 units?
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What does increasing the constant c by 6 units in an equation of the form y = x² + c do to its graph?
What does increasing the constant c by 6 units in an equation of the form y = x² + c do to its graph?
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Solve by factoring: y = 26x² − 64 when y = 0.
Solve by factoring: y = 26x² − 64 when y = 0.
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Divide: $\frac{16x^6 - 12x^4 + 4x^2}{4x^2}$.
Divide: $\frac{16x^6 - 12x^4 + 4x^2}{4x^2}$.
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Evaluate $x^2$ for $x = \sqrt{7}$.
Evaluate $x^2$ for $x = \sqrt{7}$.
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Cory makes badges and sells them for $0.75 each. If he sells 30 more badges today than he did yesterday, how much more money will he make today?
Cory makes badges and sells them for $0.75 each. If he sells 30 more badges today than he did yesterday, how much more money will he make today?
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Which is a solution of this system of equations: x + y = 3 and x − 3y = 3?
Which is a solution of this system of equations: x + y = 3 and x − 3y = 3?
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Divide: $\frac{12x^3 + 4x^2 - 8}{4x}$.
Divide: $\frac{12x^3 + 4x^2 - 8}{4x}$.
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A brick at the top of a 64-foot wall comes loose and falls to the ground. What is the domain of the function h = -16t² + 64?
A brick at the top of a 64-foot wall comes loose and falls to the ground. What is the domain of the function h = -16t² + 64?
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Simplify $\frac{\sqrt{48}}{\sqrt{147}}$.
Simplify $\frac{\sqrt{48}}{\sqrt{147}}$.
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Solve: $x^2 - 7x - 8 = 0$.
Solve: $x^2 - 7x - 8 = 0$.
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Factor $x^2 - 11$.
Factor $x^2 - 11$.
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Factor $x^2 - 6x - 16$.
Factor $x^2 - 6x - 16$.
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What is the range of set B: 20, 25, 78, 84, 10, 30?
What is the range of set B: 20, 25, 78, 84, 10, 30?
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Study Notes
Algebraic Expressions and Evaluation
- Evaluate expressions by substituting variables with given values; e.g., k + 9 when k = 7 results in 16.
- Use exponents: Example, evaluate ( \frac{1}{3}(7 - 5.5)^2 ) to get 0.75.
Translating Expressions
- Translate quantities into expressions: "¾ of a number m" is represented as ( \frac{3}{4}m ).
- "6 more than 3 times a number n" translates to ( 6 + 3n ).
Solving Linear Equations
- Solve for variables using basic equations, e.g., ( d - 13 = 25 ) gives ( d = 38 ).
- Solve inequalities such as ( y - 2 > 3 ), yielding ( y > 5 ).
Square Roots and Exponents
- The square root of 36 evaluates to -6 when expressed as a negative value.
- Simplifying square roots like ( \sqrt{250} ) results in approximately 15.8.
Polynomial Operations
- Identify solutions of polynomial equations: ( (m + 8)(m - 2) = 0 ) leads to ( m = -8 ) or ( m = 2 ).
- Add or subtract polynomials: "Subtract ( (2t^3 - 3t^2 + 5t) - (6t^3 + 3t^2 - 5t) )" results in ( -4t^3 - 6t^2 + 10t ).
Factoring and Simplifying
- Factor quadratics: ( q^2 + 3q - 40 ) factors to ( (q + 8)(q - 5) ).
- Simplify expressions, e.g., dividing ( (16x^6 - 12x^4 + 4x^2) ) by ( 4x^2 ) gives ( 4x^4 - 3x^2 + 1 ).
Graphing and Transformations
- Changes in linear equations affect graphs: decreasing the y-intercept shifts 2 units downward.
- Adjustments in the constant ( c ) in ( y = x^2 + c ) translate the graph vertically.
Statistics: Mean, Median, Range
- Analyze data: The range of the set {13, 21, 17, 8, 19, 18} is 13, and the mean absolute deviation is 3.67.
- Find measures of central tendency: For the set {4, 12, 19, 26, 19, 15, 32, 7}, mean = 134, mode = 19, median = 17.
Inequalities and No Solutions
- Explore systems of equations for solutions: Example, the system ( y = x - 2 ) and ( y = x + 5 ) has no solution as they are parallel lines.
Notable Problem Examples
- Profit model: Selling each badge at $0.75 leads to a profit function. Selling 30 more badges results in an additional profit of $22.50.
- Height function representation for falling bricks follows quadratic formulas, determining a contextually relevant domain.
Evaluating Expressions and Results
- Application of concepts such as mean absolute deviation, expressed as ( 5.56117 ) for a specific data set.
- Understanding algebraic identities such as ( x^2 - 11 ) which cannot be factored.
Graphing Outcomes
- Recognize changes in graph width based on coefficients—graphs of ( y = x^2 ) and ( y = \frac{1}{2}x^2 ) start at (0,0) but exhibit differing widths.
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