Algebra Cumulative Exam Flashcards

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?

105

63 (correct)

Which table represents a direct variation function?

Which graph could Becky have created to represent her trip?

a 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?

0.6 Signup and view all the answers

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

-100k + 3 + 101k = -245 - 181k Signup and view all the answers

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

negative Signup and view all the answers

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

c Signup and view all the answers

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

(3, 4) Signup and view all the answers

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

c Signup and view all the answers

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

12 teaspoons Signup and view all the answers

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

b = 2 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?

a Signup and view all the answers

At which job does Percy earn a greater hourly wage?

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

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

infinitely many Signup and view all the answers

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

h(t) = -5t + 500 Signup and view all the answers

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

d Signup and view all the answers

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

0.25 kWh per day Signup and view all the answers

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

20 Signup and view all the answers

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

c Signup and view all the answers

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

c Signup and view all the answers

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

The point value of a test item is more than 1.25 points and less than 1.5 points. 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?

slope: 2, y-intercept: -20 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)?

7x + 2y = 1 Signup and view all the answers

Which table represents viable solutions for y = 5x?

a Signup and view all the answers

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

2 Signup and view all the answers

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

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

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

one solution: (-0.6, 1.6) Signup and view all the answers

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

180 food tickets and 350 ride tickets Signup and view all the answers

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

F(x) > 0 over the intervals (-∞, -2.5) and (-0.75, 0.75). Signup and view all the answers

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

x > Signup and view all the answers

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

h(x) = x + 2 Signup and view all the answers

Which sequences are arithmetic? Select three options.

-8.6, -5.0, -1.4, 2.2, 5.8,... Signup and view all the answers

What equation can be used to determine unknown concentration c?

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

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

-24 Signup and view all the answers

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

$80 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?

10 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?

9 feet Signup and view all the answers

Which best describes why the delivery fee function is nonlinear?

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

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

(-2, -1) Signup and view all the answers

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

1.5 Signup and view all the answers

What is the domain of the function on the graph?

all real numbers Signup and view all the answers

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

n = 20 Signup and view all the answers

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

a Signup and view all the answers

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

2 Signup and view all the answers

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

d Signup and view all the answers

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

a Signup and view all the answers

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

x = 5 Signup and view all the answers

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

45.36 feet per second Signup and view all the answers

What is the value of f(-1)?

c 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.

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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.