Podcast
Questions and Answers
Which expression is equivalent to $(2m^4)(5m^8)$? (Select one)
Which expression is equivalent to $(2m^4)(5m^8)$? (Select one)
The function $f(x) = x$ was transformed to form $g(x) = f(x) - 23$. Which statement is true about the graphs of f and g? (Select one)
The function $f(x) = x$ was transformed to form $g(x) = f(x) - 23$. Which statement is true about the graphs of f and g? (Select one)
What are the x-intercepts of the function?
What are the x-intercepts of the function?
(-1, 0) and (3, 0)
An artist bought a set of 10 paintbrushes that contained $x$ small paintbrushes and $y$ large paintbrushes. The number of small paintbrushes in the set was 4 times the number of large paintbrushes. Which system of equations can be used to find the numbers of small paintbrushes and large paintbrushes in the set? (Select one)
An artist bought a set of 10 paintbrushes that contained $x$ small paintbrushes and $y$ large paintbrushes. The number of small paintbrushes in the set was 4 times the number of large paintbrushes. Which system of equations can be used to find the numbers of small paintbrushes and large paintbrushes in the set? (Select one)
Signup and view all the answers
Which function could represent $f$ given $f(x) = 0$ has solutions $x = 5$ and $x = -2$? (Select one)
Which function could represent $f$ given $f(x) = 0$ has solutions $x = 5$ and $x = -2$? (Select one)
Signup and view all the answers
Which expression is equivalent to $
abla 75$? (Select one)
Which expression is equivalent to $ abla 75$? (Select one)
Signup and view all the answers
What is the solution set for $12 - 4w > 2(w - 18)$? (Select one)
What is the solution set for $12 - 4w > 2(w - 18)$? (Select one)
Signup and view all the answers
What are the factors of $2x^2 + x - 15$? Select TWO correct answers.
What are the factors of $2x^2 + x - 15$? Select TWO correct answers.
Signup and view all the answers
Which value represents the rate of change of $y$ with respect to $x$ for this function: $2/5x - 4/7y = 3/2$? (Select one)
Which value represents the rate of change of $y$ with respect to $x$ for this function: $2/5x - 4/7y = 3/2$? (Select one)
Signup and view all the answers
A shipping company started with 40 employees. The number of employees at the shipping company increases at a rate of 7.5% each year. Which function can be used to model the number of employees $f(x)$ at the shipping company after $x$ years? (Select one)
A shipping company started with 40 employees. The number of employees at the shipping company increases at a rate of 7.5% each year. Which function can be used to model the number of employees $f(x)$ at the shipping company after $x$ years? (Select one)
Signup and view all the answers
Which expression is a factor of $−6x^2 − 19x + 20$? (Select one)
Which expression is a factor of $−6x^2 − 19x + 20$? (Select one)
Signup and view all the answers
Which statement about $f(x) = 12x^2 - 36x + 27$ is true? (Select one)
Which statement about $f(x) = 12x^2 - 36x + 27$ is true? (Select one)
Signup and view all the answers
Which expression is equivalent to $(z + 5)(z^2 - 4z + 6)$? (Select one)
Which expression is equivalent to $(z + 5)(z^2 - 4z + 6)$? (Select one)
Signup and view all the answers
Which expression is equivalent to $x^{-6} y^{4}/(x^{3} y)$? (Select one)
Which expression is equivalent to $x^{-6} y^{4}/(x^{3} y)$? (Select one)
Signup and view all the answers
What is the solution to $10 - 3(m - 5) = 2(5 - m)$?
What is the solution to $10 - 3(m - 5) = 2(5 - m)$?
Signup and view all the answers
What is the slope of the line that passes through the points $(10, 18)$ and $(-5, -12)$? (Select one)
What is the slope of the line that passes through the points $(10, 18)$ and $(-5, -12)$? (Select one)
Signup and view all the answers
What are the solutions to the equation $x^2 - 2 = -3x$? (Select one)
What are the solutions to the equation $x^2 - 2 = -3x$? (Select one)
Signup and view all the answers
What is the simplest form of the expression $(2x^8)(3x^{-1})^2$?
What is the simplest form of the expression $(2x^8)(3x^{-1})^2$?
Signup and view all the answers
Quadratic function $f$ has vertex (4, 15) and passes through the point (1, 20). Which equation represents $f$? (Select one)
Quadratic function $f$ has vertex (4, 15) and passes through the point (1, 20). Which equation represents $f$? (Select one)
Signup and view all the answers
Which statement about the graph of the function $f(x) = 35(1.4)^x$ is true? (Select one)
Which statement about the graph of the function $f(x) = 35(1.4)^x$ is true? (Select one)
Signup and view all the answers
Which expression is equivalent to $k^2 - 5k - 6$? (Select one)
Which expression is equivalent to $k^2 - 5k - 6$? (Select one)
Signup and view all the answers
Study Notes
Algebraic Expressions and Functions
- The expression (2m^4)(5m^8) simplifies to 10m^12.
- For the transformation of functions, g(x) = f(x) - 23 translates f(x) down by 23 units, confirming that f and g are parallel.
- The x-intercepts of a graph indicate points where it crosses the x-axis, specifically at (-1, 0) and (3, 0).
Systems of Equations
- A set of paintbrushes combining small (x) and large (y) brushes must satisfy both x + y = 10 and x = 4y.
Quadratic Functions
- The quadratic f(x) = x^2 with zeroes at 5 and -2 correlates to the function f(x) = 15x^2 - 11x - 14.
- Solutions to the equation f(x) = 0 can also reflect in the factorization with roots leading to expressions like (x + 3) and (2x - 5).
Inequalities and Solutions
- To solve 12 - 4w > 2(w - 18), the solution set is w < 8.
- The equation (x + 13)(x - 6) = 0 results in solutions x = -13 and x = 6.
Functions, Transformations, and Modeling
- A function representing employee growth at a shipping company can be modeled as f(x) = 40(1.075)^x due to yearly 7.5% increases.
- When analyzing a quadratic function, transformations such as shifting right by 2 units and up by 5 units are key.
Slope and Line Equations
- The slope of the line between points (10, 18) and (-5, -12) is determined as 2.
- Parallel lines maintain consistent slopes, as seen with the transformation of y = -x + 17 for line n.
Exponential Decay
- A substance's decay can be modeled by the function y = 963(0.73)^x after an initial mass of 963 grams reducing at a 27% rate per hour.
Key Points in Graph Behavior
- The function f(x) = 35(1.4)^x shows a y-intercept at (0, 35) and approaches an asymptote of y = 0 as it increases.
Evaluation of Expressions
- Simplifying expressions, e.g., ( (2x^8)(3x^{-1})^2 ), results in 18x^6 when written in the form ax^b.
- The quadratic expression k^2 - 5k - 6 factors as (k - 6)(k + 1).
Application of Functions
- The cost comparison of dance lessons at two studios leads to an equal cost solution after 5 months, illustrating practical use of linear functions.
- The vertex form of a quadratic function can help identify characteristics of its graph, such as maximum or minimum values.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of math concepts with these STAAR-style flashcards. Each card presents a question about expressions or functions, accompanied by the correct answer. Great for review and preparation for standardized tests.
