Untitled Quiz

Questions and Answers

Evaluate the expression: k + 9 when k = 7.

Evaluate the expression: $\frac{1}{3}(7 - 5.5)^2$.

0.75

Translate into expression: ¾ of a number m.

¾m

Translate into expression: 6 more than 3 times a number n.

6 + 3n Signup and view all the answers

Solve: d - 13 = 25.

d = 38 Signup and view all the answers

Evaluate: -√36.

-6 Signup and view all the answers

What is $\sqrt{250}$?

15.8 Signup and view all the answers

Solve: 8 = m - 13.

m = 21 Signup and view all the answers

Solve: 12w - 5 - 3w = 40.

w = 5 Signup and view all the answers

Rewrite in y-intercept form: 10x − y = 20.

y = 10x - 20 Signup and view all the answers

Solve: y − 2 > 3.

y > 5 Signup and view all the answers

Solve: $\frac{5}{6}(12p - 24) > \frac{2}{5}(25p - 25)$.

no solution Signup and view all the answers

|m - 6| = 5.

m = 11, 1 Signup and view all the answers

What's the solution for the system of equations y = x - 2 and y = x + 5?

no solution Signup and view all the answers

Use substitution: y = 2x + 6; y = -x + 5.

x = -1/3; y = 16/3 Signup and view all the answers

Use elimination: 3x - 4y = -16 and x - 4y = -40.

y = 13, x = 12 Signup and view all the answers

Simplify: $(-4s^2)^3(2s^3)^6$.

-4096s^24 Signup and view all the answers

Evaluate: $\frac{1}{2^{-5}}$.

32 Signup and view all the answers

Simplify: $10b^{-3}c^5$.

$\frac{10c^5}{b^3}$ Signup and view all the answers

Subtract: $(2t^3 - 3t^2 + 5t) - (6t^3 + 3t^2 - 5t)$.

-4t^3 - 6t^2 + 10t Signup and view all the answers

Add: $(8y^2 - 3y - 10) + (-11y^2 + 2y - 7)$.

19y^2 - y - 17 Signup and view all the answers

Find the product: $(x + 10)^2$.

x^2 + 20x + 100 Signup and view all the answers

Solve: $(m + 8)(m - 2) = 0$.

m = -8, 2 Signup and view all the answers

Factor: $q^2 + 3q - 40$.

(q + 8)(q - 5) Signup and view all the answers

Factor: $m^2 - 29m + 100$.

(m - 4)(m - 25) Signup and view all the answers

What is different when you graph y = x² and y = 1/2x²?

They both start at points (0,0), but y = 1/2x² is wider. Signup and view all the answers

A community hospital conducts a survey to determine patient satisfaction. Identify the population and the sampling method.

Population: Patients; Sample: Convenience Sample Signup and view all the answers

Find the range and mean of absolute deviation for the numbers: 13, 21, 17, 8, 19, 18.

Range: 13; Mean Absolute D: 3.67 Signup and view all the answers

Find the mean, median, and mode for the numbers: 4, 12, 19, 26, 19, 15, 32, 7.

Mean: 134; Mode: 19; Median: 17 Signup and view all the answers

Calculate the Mean Absolute Deviation: 1, 2, 3.5, 4, 6, 6, 9, 11, 13, 15, 15, 25.7.

Mean Absolute D: 5.56117 Signup and view all the answers

What will happen to the graph of y = 3x - 1 if the value of the y-intercept decreases by 2 units?

The graph will be translated 2 units downward. Signup and view all the answers

What does increasing the constant c by 6 units in an equation of the form y = x² + c do to its graph?

The graph is translated 6 units upward. Signup and view all the answers

Solve by factoring: y = 26x² − 64 when y = 0.

-8/5 and 8/5 Signup and view all the answers

Divide: $\frac{16x^6 - 12x^4 + 4x^2}{4x^2}$.

4x^4 - 3x^2 + 1 Signup and view all the answers

Evaluate $x^2$ for $x = \sqrt{7}$.

7 Signup and view all the answers

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?

$22.50 Signup and view all the answers

Which is a solution of this system of equations: x + y = 3 and x − 3y = 3?

(3, 0) Signup and view all the answers

Divide: $\frac{12x^3 + 4x^2 - 8}{4x}$.

3x^2 + x - \frac{2}{x} Signup and view all the answers

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?

{all real numbers from 0 to 2} Signup and view all the answers

Simplify $\frac{\sqrt{48}}{\sqrt{147}}$.

$\frac{\sqrt{48}}{\sqrt{147}}$ Signup and view all the answers

Solve: $x^2 - 7x - 8 = 0$.

x = -1 or x = 8 Signup and view all the answers

Factor $x^2 - 11$.

cannot be factored Signup and view all the answers

Factor $x^2 - 6x - 16$.

(x + 2)(x - 8) Signup and view all the answers

What is the range of set B: 20, 25, 78, 84, 10, 30?

Range = 22 Signup and view all the answers

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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Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Untitled Quiz

Questions and Answers

Evaluate the expression: k + 9 when k = 7.

Evaluate the expression: $\frac{1}{3}(7 - 5.5)^2$.

Translate into expression: ¾ of a number m.

Translate into expression: 6 more than 3 times a number n.

Solve: d - 13 = 25.

Evaluate: -√36.

What is $\sqrt{250}$?

Solve: 8 = m - 13.

Solve: 12w - 5 - 3w = 40.

Rewrite in y-intercept form: 10x − y = 20.

Solve: y − 2 > 3.

Solve: $\frac{5}{6}(12p - 24) > \frac{2}{5}(25p - 25)$.

|m - 6| = 5.

What's the solution for the system of equations y = x - 2 and y = x + 5?

Use substitution: y = 2x + 6; y = -x + 5.

Use elimination: 3x - 4y = -16 and x - 4y = -40.

Simplify: $(-4s^2)^3(2s^3)^6$.

Evaluate: $\frac{1}{2^{-5}}$.

Simplify: $10b^{-3}c^5$.

Subtract: $(2t^3 - 3t^2 + 5t) - (6t^3 + 3t^2 - 5t)$.

Add: $(8y^2 - 3y - 10) + (-11y^2 + 2y - 7)$.

Find the product: $(x + 10)^2$.

Solve: $(m + 8)(m - 2) = 0$.

Factor: $q^2 + 3q - 40$.

Factor: $m^2 - 29m + 100$.

What is different when you graph y = x² and y = 1/2x²?

A community hospital conducts a survey to determine patient satisfaction. Identify the population and the sampling method.

Find the range and mean of absolute deviation for the numbers: 13, 21, 17, 8, 19, 18.

Find the mean, median, and mode for the numbers: 4, 12, 19, 26, 19, 15, 32, 7.

Calculate the Mean Absolute Deviation: 1, 2, 3.5, 4, 6, 6, 9, 11, 13, 15, 15, 25.7.

What will happen to the graph of y = 3x - 1 if the value of the y-intercept decreases by 2 units?

What does increasing the constant c by 6 units in an equation of the form y = x² + c do to its graph?

Solve by factoring: y = 26x² − 64 when y = 0.

Divide: $\frac{16x^6 - 12x^4 + 4x^2}{4x^2}$.

Evaluate $x^2$ for $x = \sqrt{7}$.

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?

Which is a solution of this system of equations: x + y = 3 and x − 3y = 3?

Divide: $\frac{12x^3 + 4x^2 - 8}{4x}$.

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?

Simplify $\frac{\sqrt{48}}{\sqrt{147}}$.

Solve: $x^2 - 7x - 8 = 0$.

Factor $x^2 - 11$.

Factor $x^2 - 6x - 16$.

What is the range of set B: 20, 25, 78, 84, 10, 30?

Study Notes

Algebraic Expressions and Evaluation

Translating Expressions

Solving Linear Equations

Square Roots and Exponents

Polynomial Operations

Factoring and Simplifying

Graphing and Transformations

Statistics: Mean, Median, Range

Inequalities and No Solutions

Notable Problem Examples

Evaluating Expressions and Results

Graphing Outcomes

Studying That Suits You

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