Questions and Answers
What is the closest approximate solution to the system of equations? 7x - 4y = -8, y = x - 3
If Sonji has 21 dimes, how many nickels does she have?
Which table represents a direct variation function?
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Which graph could Becky have created to represent her trip?
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When two garbage trucks work together, what part of all the garbage bins will the first garbage truck empty?
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Which equation is equivalent to -k + 0.03 + 1.01k = -2.45 - 1.81k?
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Which word describes the slope of the line representing the data in the table of discount cards sold?
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Which equation should Lupe use to determine k for potential energy P in a spring?
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What is the solution (a, c) to the system of linear equations? 2a - 3c = -6, a + 2c = 11
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Which graph could represent the level of the water in the jug during and after practice?
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How many teaspoons of broth should Tabitha use from a cup of broth?
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What is the solution to the linear equation -12 + 3b - 1 = -5 - b?
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Which table could be used to determine correctly how long Elias and Niko would take to polish the silver together?
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At which job does Percy earn a greater hourly wage?
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How many intersections are there of the graphs of the equations x + 5y = 6 and 3x + 30y = 36?
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Which equation represents the height, h(t), of an elevator as a function of time t?
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Which table shows only viable solutions for the total number of pages Selma has read?
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What is a reasonable estimate of the constant of variation for electricity usage in kilowatts per hour?
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What is the missing value for the inverse of the function f(x) = 4?
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Which graph represents the number of minutes to install the ceiling fan?
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Which graph represents the function y = 2x - 4?
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Which scenario can be represented using the inequalities 1.25 < x < 1.5?
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What are the slope and y-intercept of the line represented by the points in Gerri's coupon book?
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What is the equation of line JK in standard form, passing through points J(-3, 11) and K(1, -3)?
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Which table represents viable solutions for y = 5x?
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What is the other solution for the equation 6 - 4|2x - 8| = -10?
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What is true about the end behavior of the graphed function?
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How many solutions does the linear system y = x + 2 and 6x - 4y = -10 have?
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How many tickets were sold at the carnival for food and rides?
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What is true about the graphed function f(x)?
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What is the solution to -2(8x - 4) < 2x + 5?
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What is the inverse of the function f(x) = 4x + 8?
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Which sequences are arithmetic? Select three options.
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What equation can be used to determine unknown concentration c?
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What is the value of x in the equation (x + 12) = (x + 14) - 3?
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What amount of money, P, will generate $40 in interest at a 10% interest rate over 5 years?
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How many classes would Gina need to take for the total cost to be the same at both Dance World and Toe Tappers?
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If Manny makes the garden 15 feet long, how wide should the garden be given he has 48 feet of wood?
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Which best describes why the delivery fee function is nonlinear?
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Which ordered pair needs to be removed for the mapping to represent a function?
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What is the slope of the line through data points recorded by Wren?
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What is the domain of the function on the graph?
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When a number is added to itself, the result is 24. What is the value of n?
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Which is the graph of linear inequality x - 2y ≥ -12?
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When f(x) = 4, what is the value of x?
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Which system of linear inequalities has the point (2, 1) in its solution set?
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Which is the graph of linear inequality 6x + 2y > -10?
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What is the solution to 4|0.5x - 2.5| = 0?
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What is the most accurate determination for the number of feet per second Tyrone traveled?
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What is the value of f(-1)?
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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.
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