Algebra Cumulative Exam Flashcards
50 Questions
100 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the closest approximate solution to the system of equations? 7x - 4y = -8, y = x - 3

  • (-5, -6.2)
  • (-5, -7.2) (correct)
  • (-5, -6.8)
  • (-5, -5.9)

    • If Sonji has 21 dimes, how many nickels does she have?

  • 35
  • 105
  • 63 (correct)
  • 42

    • Which table represents a direct variation function?

    d

    Which graph could Becky have created to represent her trip?

    <p>a</p> Signup and view all the answers

    When two garbage trucks work together, what part of all the garbage bins will the first garbage truck empty?

    <p>0.6</p> Signup and view all the answers

    Which equation is equivalent to -k + 0.03 + 1.01k = -2.45 - 1.81k?

    <p>-100k + 3 + 101k = -245 - 181k</p> Signup and view all the answers

    Which word describes the slope of the line representing the data in the table of discount cards sold?

    <p>negative</p> Signup and view all the answers

    Which equation should Lupe use to determine k for potential energy P in a spring?

    <p>c</p> Signup and view all the answers

    What is the solution (a, c) to the system of linear equations? 2a - 3c = -6, a + 2c = 11

    <p>(3, 4)</p> Signup and view all the answers

    Which graph could represent the level of the water in the jug during and after practice?

    <p>c</p> Signup and view all the answers

    How many teaspoons of broth should Tabitha use from a cup of broth?

    <p>12 teaspoons</p> Signup and view all the answers

    What is the solution to the linear equation -12 + 3b - 1 = -5 - b?

    <p>b = 2</p> Signup and view all the answers

    Which table could be used to determine correctly how long Elias and Niko would take to polish the silver together?

    <p>a</p> Signup and view all the answers

    At which job does Percy earn a greater hourly wage?

    <p>Percy earns a greater hourly wage of $7.50 at the library.</p> Signup and view all the answers

    How many intersections are there of the graphs of the equations x + 5y = 6 and 3x + 30y = 36?

    <p>infinitely many</p> Signup and view all the answers

    Which equation represents the height, h(t), of an elevator as a function of time t?

    <p>h(t) = -5t + 500</p> Signup and view all the answers

    Which table shows only viable solutions for the total number of pages Selma has read?

    <p>d</p> Signup and view all the answers

    What is a reasonable estimate of the constant of variation for electricity usage in kilowatts per hour?

    <p>0.25 kWh per day</p> Signup and view all the answers

    What is the missing value for the inverse of the function f(x) = 4?

    <p>20</p> Signup and view all the answers

    Which graph represents the number of minutes to install the ceiling fan?

    <p>c</p> Signup and view all the answers

    Which graph represents the function y = 2x - 4?

    <p>c</p> Signup and view all the answers

    Which scenario can be represented using the inequalities 1.25 < x < 1.5?

    <p>The point value of a test item is more than 1.25 points and less than 1.5 points.</p> Signup and view all the answers

    What are the slope and y-intercept of the line represented by the points in Gerri's coupon book?

    <p>slope: 2, y-intercept: -20</p> Signup and view all the answers

    What is the equation of line JK in standard form, passing through points J(-3, 11) and K(1, -3)?

    <p>7x + 2y = 1</p> Signup and view all the answers

    Which table represents viable solutions for y = 5x?

    <p>a</p> Signup and view all the answers

    What is the other solution for the equation 6 - 4|2x - 8| = -10?

    <p>2</p> Signup and view all the answers

    What is true about the end behavior of the graphed function?

    <p>As the x-values go to negative infinity, the function's values go to positive infinity.</p> Signup and view all the answers

    How many solutions does the linear system y = x + 2 and 6x - 4y = -10 have?

    <p>one solution: (-0.6, 1.6)</p> Signup and view all the answers

    How many tickets were sold at the carnival for food and rides?

    <p>180 food tickets and 350 ride tickets</p> Signup and view all the answers

    What is true about the graphed function f(x)?

    <p>F(x) &gt; 0 over the intervals (-∞, -2.5) and (-0.75, 0.75).</p> Signup and view all the answers

    What is the solution to -2(8x - 4) < 2x + 5?

    <p>x &gt;</p> Signup and view all the answers

    What is the inverse of the function f(x) = 4x + 8?

    <p>h(x) = x + 2</p> Signup and view all the answers

    Which sequences are arithmetic? Select three options.

    <p>-8.6, -5.0, -1.4, 2.2, 5.8,...</p> Signup and view all the answers

    What equation can be used to determine unknown concentration c?

    <p>30c + 10(0.2) = 40(0.32)</p> Signup and view all the answers

    What is the value of x in the equation (x + 12) = (x + 14) - 3?

    <p>-24</p> Signup and view all the answers

    What amount of money, P, will generate $40 in interest at a 10% interest rate over 5 years?

    <p>$80</p> Signup and view all the answers

    How many classes would Gina need to take for the total cost to be the same at both Dance World and Toe Tappers?

    <p>10</p> Signup and view all the answers

    If Manny makes the garden 15 feet long, how wide should the garden be given he has 48 feet of wood?

    <p>9 feet</p> Signup and view all the answers

    Which best describes why the delivery fee function is nonlinear?

    <p>The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.</p> Signup and view all the answers

    Which ordered pair needs to be removed for the mapping to represent a function?

    <p>(-2, -1)</p> Signup and view all the answers

    What is the slope of the line through data points recorded by Wren?

    <p>1.5</p> Signup and view all the answers

    What is the domain of the function on the graph?

    <p>all real numbers</p> Signup and view all the answers

    When a number is added to itself, the result is 24. What is the value of n?

    <p>n = 20</p> Signup and view all the answers

    Which is the graph of linear inequality x - 2y ≥ -12?

    <p>a</p> Signup and view all the answers

    When f(x) = 4, what is the value of x?

    <p>2</p> Signup and view all the answers

    Which system of linear inequalities has the point (2, 1) in its solution set?

    <p>d</p> Signup and view all the answers

    Which is the graph of linear inequality 6x + 2y > -10?

    <p>a</p> Signup and view all the answers

    What is the solution to 4|0.5x - 2.5| = 0?

    <p>x = 5</p> Signup and view all the answers

    What is the most accurate determination for the number of feet per second Tyrone traveled?

    <p>45.36 feet per second</p> Signup and view all the answers

    What is the value of f(-1)?

    <p>c</p> Signup and view all the answers

    Study Notes

    System of Equations

    • Closest approximate solution for the equations 7x - 4y = -8 and y = x - 3 is (-5, -7.2).

    Coin Value Problem

    • Sonji has $5.25 in nickels and dimes with 21 dimes, leading to a total of 63 nickels.

    Direct Variation

    • Identification of tables that represent direct variation functions is essential for understanding proportional relationships.

    Graph Interpretation

    • Becky's graph depicts her distance from home as she travelled to a park and back, showing intervals of running and resting.

    Garbage Truck Problem

    • The first garbage truck empties 60% of the bins when working together with a second truck.

    Equivalent Equation Transformation

    • The equivalent form of the equation -k + 0.03 + 1.01k = -2.45 - 1.81k is -100k + 3 + 101k = -245 - 181k.

    Slope Description

    • A negative slope describes the relationship in a table showing the number of discount cards sold versus remaining funds.

    Potential Energy in Springs

    • The formula for potential energy is P = kx², and the rearrangement for k should be used effectively.

    Solution to Linear Equations

    • The solution to the system of equations 2a - 3c = -6 and a + 2c = 11 is (3, 4).

    Water Jug Scenario

    • Ray’s water jug graph represents water levels in stages: increase, decrease, and refill.

    Measurement Conversion

    • To measure ¾ of a cup of broth, Tabitha needs to use 12 teaspoons.

    Solving Linear Equations

    • The solution to the equation -12 + 3b - 1 = -5 - b is b = 2.

    Collaborative Work

    • Elias and Niko’s combined time for polishing silver can be assessed using correct data tables.

    Payment System

    • Percy’s hourly wages at the library and coffee cart can be determined as greater at $7.50 at the library.

    Intersection of Lines

    • The equations x + 5y = 6 and 3x + 30y = 36 have infinitely many solutions as they coincide.

    Elevator Height Function

    • The elevator's height over time is represented by h(t) = -5t + 500.

    Page Reading Rate

    • Selma's reading pace can be represented in a table that displays total pages read over time.

    Constant of Variation

    • The function representing electricity usage varies directly, with a reasonable estimate for the constant at 0.25 kWh per day.

    Inverse Functions

    • The missing value for the inverse of f(x) = 2x - is 20, reflecting function properties.

    Installation Time Estimate

    • Estimated installation times for a ceiling fan depend on building code compliance.

    Function Representation

    • The function y = 2x - 4 can be graphically represented with specific characteristics.

    Inequalities Interpretation

    • The inequality 1.25 < x < 1.5 reflects pricing scenarios for test item points.

    Linear Relationship Analysis

    • Gerri's coupon savings have a slope of 2 and a y-intercept of -20 in cost analysis.

    Equation of a Line

    • The standard form equation for line JK passing through points J(-3, 11) and K(1, -3) is 7x + 2y = 1.

    Arithmetic Sequences Identification

    • Examples of arithmetic sequences include -8.6, -5.0, 5, 1, -3, -7, -11.

    Acid Concentration Problem

    • An equation representing the unknown acid concentration is 30c + 10(0.2) = 40(0.32).

    Solving Basic Equations

    • The equation (x + 12) = (x + 14) - 3 results in the value x = -24.

    Simple Interest Calculation

    • A principal amount of $80 generates $40 in interest at a 10% rate over 5 years.

    Equal Cost Classes

    • Gina would need to take 10 classes for equal total costs at Dance World and Toe Tappers.

    Garden Dimensions

    • If Manny makes the garden 15 feet long, the width should be 9 feet based on perimeter calculations.

    Nonlinear Function Explanation

    • The delivery cost function is nonlinear due to differing rates of change between certain tree purchases.

    Function Mapping Identification

    • The point (-2, -1) needs to be removed to ensure the mapping represents a valid function.

    Slope Calculation

    • The temperature slope from -2°F to 4°F over 4 hours is 1.5°F per hour.

    Function Domain Understanding

    • The domain of the function on the graph includes all real numbers.

    Problem Solving with Self-Reference

    • The equation n + n = 24 leads to a solution of n = 20.

    Graph of Linear Inequality

    • Evaluating graph representations of linear inequalities is crucial for understanding their solutions.

    Mapping Evaluation

    • For the given functional mapping, when f(x) = 4, the corresponding value of x is 2.

    Linear Inequalities Solution Set

    • Identification of the correct system of inequalities that includes point (2, 1) is essential for solution accuracy.

    Inquiry into Linear Inequality Representation

    • The graph of 6x + 2y > -10 should be analyzed for its visual representation.

    Absolute Value Equation Solution

    • The solution to 4|0.5x - 2.5| = 0 results in x = 5.

    Speed Calculation from Travel Distance

    • Tyrone's speed is determined to be 45.36 feet per second using distance and time metrics.

    Studying That Suits You

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

    Quiz Team

    Description

    Test your knowledge with these algebra flashcards focusing on systems of equations and word problems. Each question challenges your understanding and application of algebraic concepts. Perfect for reviewing cumulative exam content.

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser