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Algebra I
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Terms in this set (705)
What is the rate of change for the function on the table?
A.
15 grapes eaten per minute
When compared with the independent variable, how many of the remaining three columns represent a linear relationship?
C.
2
The final cost of a sale item is determined by multiplying the price on the tag by 75%. Which best describes the function that represents the situation?
A.
It is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant.
In order for the data in the table to represent a linear function with a rate of change of +5, what must be the value of m?
C.
m = 18
Which table represents a linear function?
C.
1 / -3
2 / -5
3 / -7
4 / -9
A data set contains an independent and dependent variable. Which must be true of the data set if a linear function can be used to represent the data?
A.
The set must have a constant additive rate of change.
Ellen makes and sells bookmarks. She graphs the number of bookmarks sold compared to the total money earned. What is the rate of change for the function graphed to the left?
D.
5/2
What is the change in the y-values and x-values on the graph?
A.
The change in the y-values is 40 and the change in the x-values is 1.
Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the size of the lawn in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points?
B.
Aaron's rate for mowing lawns is 0.5 acres per hour.
At work, Brett must check and record the internal temperature of the freezer on an hourly basis. When working properly, the temperature should remain constant over time. What word describes the slope of a line showing the temperature of the freezer as a function of time in hours when the freezer is working properly?
The slope of the line will be (ZERO).
The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool?
A.
The height of the water increases 2 inches per minute.
What is the y-intercept of the function f(x)=4 - 5x?
C.
4
Which equation represents the shipping cost as a function of x, the weight in pounds?
A.
f(x) = 2.25x + 5
Which function of t has the same slope and y-intercept as f(x)?
A.
f(t) =2/3 t + 4
Which equation represents y, the profit earned by the concession stand for x hot dogs sold?
C.
y = 2x - 48
What is the slope of the line represented by the equation y =4/5 x - 3?
C.
4/5
A leaf hangs from a branch 12 feet in the air. It falls to the ground at a rate of 0.25 feet per second. Which graph could represent the leaf's height in feet as a function of time, in seconds, after leaving the branch?
D.
Which equation represents the graphed function?
A.
y = -2x + 3
What are the slope and y-intercept of the linear function graphed to the left?
B.
slope: -1/2; y-intercept: 1
Which equation represents the graphed function?
C.
3/2x - 3 = y
What is the slope of the line?
5/2
Chin was shown the graph of a line that contained point (1, 7). He wrote f(x) = 4x + 3 to correctly represent the line. Which of these equations could represent the same line?
C.
y - 7 = 4(x - 1)
Which equation represents a line that passes through (-2, 4) and has a slope of 2/5?
A.
y - 4 = 2/5(x + 2)
What number will complete the point-slope equation that models this scenario?
-3,000
Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3?
B.
y - 2 =1/3 (x - 3)
Which equation represents a line that passes through (-9, -3) and has a slope of -6?
D.
y + 3 = -6(x + 9)
Which equation represents a line that passes through (5, 1) and has a slope of 1/2?
C.
y - 1 = 1/2(x -5)
Line GH passes through points (2, 5) and (6, 9). Which equation represents line GH?
A.
y = x + 3
Julissa is running a 10-kilometer race at a constant pace. After running for 18 minutes, she completes 2 kilometers. After running for 54 minutes, she completes 6 kilometers. Her trainer writes an equation letting t, the time in minutes, represent the independent variable and k, the number of kilometers, represent the dependent variable.
A.
k - 2 = 1/9(t - 18)
Which equation represents the line that passes through (-6, 7) and (-3, 6)?
B.
y = -1/3x + 5
The point-slope form of the equation of the line that passes through (-4, -3) and (12, 1) is y - 1 = (x - 12). What is the standard form of the equation for this line?
A.
x - 4y = 8
The ice skating rink charges an hourly fee for skating and $3 to rent skates for the day. Gillian rented skates and skated for 3 hours and was charged $21. Which equation represents the cost, c(x), of ice skating as a function of x, the number of hours of skating?
B.
c(x) = 6x + 3
Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?
C.
y = x + 2
The slope-intercept form of the equation of a line that passes through point (-3, 8) is y = -2/3x + 6. What is the point-slope form of the equation for this line?
D.
y - 8 = -2/3(x + 3)
Which statement is true about the graphs of the two lines y=-8x - 5/4 and y= 1/8x + 4/5?
The lines are perpendicular to each other because -8 and 1/8 are opposite reciprocals of each other.
Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. Which best describes this function?
D.
It is nonlinear because linear functions increase or decrease at the same rate.
The table shows the number of grapes eaten over several minutes.
What is the rate of change for the function on the table?
A.
15 grapes eaten per minute
When compared with the independent variable, how many of the remaining three columns represent a linear relationship?
C.
2
The final cost of a sale item is determined by multiplying the price on the tag by 75%. Which best describes the function that represents the situation?
A.
It is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant.
In order for the data in the table to represent a linear function with a rate of change of +5, what must be the value of m?
C.
m = 18
What is the ratio of the change in y-values to the change in x-values?
D.
1,200:1
Line AB contains points A(4, 5) and B(9, 7). What is the slope of AB?
C.
2/5
Which word describes the slope of the line?
C.
zero
Which of these values could be the slope of the line? Check all that apply.
3
7/4
A balloon artist creates balloon hats for children at a store's grand opening. The graph shows the number of balloons the artist has remaining, y, after creating x hats.
What phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created? Check all that apply.
negative slope
constant slope
decreasing function
A line contains points M(1, 3) and N(5, 0). What is the slope of MN?
-3/4
The graph represents the balance on Harrison's car loan in the months since purchasing the car.
Which statement describes the slope of the line?
B.
Harrison makes a monthly payment of $250.
What is the y-intercept of the function f(x)=4 - 5x?
C.
4
A store offers packing and mailing services to customers. This table is given to customers to help them estimate the cost of shipping a box based on its weight in pounds, and a flat rate of $5 for packing.
Which equation represents the shipping cost as a function of x, the weight in pounds?
A.
f(x) = 2.25x + 5
The table represents the function f(x).
Which function of t has the same slope and y-intercept as f(x)?
A.
f(t) = 2/3t + 4
Four lines are drawn on a coordinate plane to form trapezoid WXYZ.
Which statements are true about the lines? Select all that apply.
Line WZ has the same slope as line XY.
Line XW has a lesser slope than line YZ.
Line ZW has the same y-intercept as line WZ.
Line XY has a greater y-intercept than line XW.
The table represents the profit earned by a concession stand for each hot dog sold.
Which equation represents y, the profit earned by the concession stand for x hot dogs sold?
C.
y = 2x - 48
What is the slope of the line represented by the equation y =4/5 x - 3?
C.
4/5
A leaf hangs from a branch 12 feet in the air. It falls to the ground at a rate of 0.25 feet per second. Which graph could represent the leaf's height in feet as a function of time, in seconds, after leaving the branch?
D.
Which equation represents the graphed function?
A.
y = -2x + 3
What are the slope and y-intercept of the linear function graphed to the left?
B.
slope:-1/2 ; y-intercept: 1
Which equation represents the graphed function?
C.
3/2x - 3 = y
Which equation represents a line that passes through (-2, 4) and has a slope of 2/5?
A.
y - 4 =2/5 (x + 2)
The equation of a linear function in point-slope form is y - y1 = m(x - x1). Harold correctly wrote the equation y = 3(x - 7) using a point and the slope. Which point did Harold use?
C.
When Harold wrote his equation, the point he used was (7, 0).
Which equation represents a line that passes through (-9, -3) and has a slope of -6?
D.
y + 3 = -6(x + 9)
Which steps should be used to graph the equation y - 4 =1/3 (x + 2)?
C.
1. Plot the point (-2,4).
2. From that point, count left 3 units and down 1 unit and plot a second point.
3. Draw a line through the two points.
Which equation represents a line that passes through (4, 1/3) and has a slope of 3/4?
B.
y - 1/3 = 3/4(x - 4)
Which equation represents a line that passes through (2, -1/2) and has a slope of 3?
C.
y +1/2 = 3(x - 2)
Which equation represents a line that passes through (5, 1) and has a slope of 1/2?
C.
y - 1 =1/2 (x -5)
Line CD passes through points C(3, -5) and D(6, 0). What is the equation of line CD in standard form?
B.
5x - 3y = 30
What is the slope of a line that is perpendicular to the line y = 8x + 5?
B.
-1/8
Which statement is true about the graphs of the two lines y=-8x - 5/4 and y=1/8 + 4/5?
A.
The lines are perpendicular to each other because -8 and 1/8 are opposite reciprocals of each other.
What is the slope-intercept form of the equation of the line that passes through the point (-6, 1) and is perpendicular to the graph of 2x + 3y = -5?
D.
y = 3/2x + 10
What is the slope of a line that is perpendicular to the line y = 1?
D.
undefined
What is the slope of a line that is parallel to the line y = -1/5?
B.
0
Which statement is true about the graphs of the two lines y = -6 and x = 1/6?`
D.
The lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope of 0, and the graph of x = 1/6 is a vertical line with a slope that is undefined.
Which statement is true about the graphs of the two lines y = -4/5 x + 2 and y = -4/5 x -1/2 ?
C.
The lines are neither parallel nor perpendicular to each other because -4/5 and -5/4 are not opposite reciprocals of each other.
Triangle ABC has vertices at A(-2, 3), B(-3, -6), and C(2, -1). Is triangle ABC a right triangle? If so, which angle is the right angle?
D.
Yes, the right angle is angle C.
What is the slope of a line that is perpendicular to the line y = -1/2x + 5?
D.
2
The equation 9(u - 2) + 1.5u = 8.25 models the total miles Michael traveled one afternoon while sledding, where u equals the number of hours walking up a hill and (u - 2) equals the number of hours sledding down the hill. Which is the value of u?
D.
u = 2.5
What is the input value for which the statement f(x) = g(x) is true ______?
1.5
Which step has an incorrect instruction?
A.
Step 1
Sean began jogging to live a healthier lifestyle. On his first run, he ran one-half mile. He increased his workouts by adding two miles a month to his run. He wrote the equation f(x)= 0.5 + 2x to model his progress. The variable x represents the number of
B.
months he runs.
Solve the equation.
−10x + 1 + 7x = 37
B.
x = −12
Which input value produces the same output value for the two functions on the graph?
D.
x = 3
What are the possible steps involved in solving the equation shown? Check all that apply.
Distribute 1.2 to 6.3 and -7x .
Combine 3.5 and 7.56.
Subtract 11.06 from both sides.
A number, n, is added to 15 less than 3 times itself. The result is 101. Which equation can be used to find the value of n?
A.
3n - 15 + n = 101
The Apache Taxi Company charges $2.50 to pick up a passenger and then adds $1.95 per mile. Isaac was charged $27.46 to go from one city to another. If x represents the number of miles driven by the taxi, which linear equation can be used to solve this problem, and how many miles did Isaac travel, rounded to the nearest tenth?
B.
1.95x + 2.50 = 27.46; Isaac traveled 12.8 miles.
Which input value produces the same output value for the two functions on the graph?
C.
x = 1
What is the missing step of her solution?
A.
Simplify by combining like terms.
Consider the equation 3p - 7 + p = 13. What is the resulting equation after the first step in the solution?
D.
4p - 7 = 13
Mustafa's soccer team is planning a school dance as a fundraiser. The DJ charges $200 and decorations cost $100. The team decides to charge each student $5.00 to attend the dance. If n represents the number of students attending the dance, which equation can be used to find the number of students needed to make $1,500 in profit?
A.
5n - 300 = 1,500
Which input value produces the same output value for the two functions?
D.
x = 1
y + 6 = -3y + 26
C.
y = 5
Use properties to rewrite the given equation. Which equations have the same solution as 3/5x +2/3 + x = 1/2 -1/5 x? Check all that apply.
8/5x +2/3 = 1/2 - 1/5x
18x + 20 + 30x = 15 - 6x
24x + 30x = -5
2/5 + p =4/5+3/5 p
A.
p = 1
What is the justification for the step taken from line 2 to line 3?
A.
the subtraction property of equality
8 - 2x = -8x + 14
D.
x = 1
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
B.
x = -2
6k + 10.5 = 3k + 12
A.
k = 0.5
4b + 6 = 2 - b + 4
B.
b = 0
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
C.
4
y + 3 = -y + 9
B.
y = 3
The International Business Club starts the school year with $250.50 in their account. They spend $35 each month on activities. The Future Agricultural Leaders Club starts with $300 and spends $45.25 each month.
Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money?
B.
250.5 - 35m = 300 - 45.25m
Which number can each term of the equation be multiplied by to eliminate the decimals before solving?
-m + 0.02 + 2.1m = -1.45 - 4.81m
D.
100
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
D.
12
What is the solution to the linear equation?
A.
p = 1
Which number can each term of the equation be multiplied by to eliminate the decimals before solving?
5.6j - 0.12 = 4 + 1.1j
D.
100
What is the solution to the linear equation?
d - 10 - 2d + 7 = 8 + d - 10 - 3d
C.
d = 1
What is the value of n in the equation 1/2(n - 4) - 3 = 3 - (2n + 3)?
n= ?
2
What is the value of x in the equation 2(x - 3) + 9 = 3(x + 1) + x?
X=0
Jillana begins to solve a linear equation that results in a variable expression set equal to the same variable expression. Which is the best interpretation of this solution?
D.
The equation has infinite solutions.
How many solutions exist for the given equation?
3x + 13 = 3(x + 6) + 1
A.
zero
What is the value of x in the equation 2.5(6x-4)=10+4(1.5+0.5x)?
C.
2
What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)?
B.
4
When she adds 2 to both sides, the equation 4x = 3x results. Which is the best interpretation of this equation?
B.
The equation has one solution: x = 0.
6(x - 1) = 9(x + 2)
A.
x = -8
When she subtracts 4 from both sides, 1/2x = -1/2x results. What is the value of x?
C.
0
Which equation has no solution?
B.
5 + 2(3 + 2x) = x + 3(x + 1)
Fifteen percent of the pigment in paint color A is black. Sixty percent of the pigment in paint color B is black. An unknown amount of paint color B is mixed with 40 ml of paint color A, resulting in a paint that contains 25% black pigment.
Which equation can be used to solve for x, the total amount of paint in the mixture of the two colors?
B.
0.15(40) + 0.6(x - 40) = 0.25(x)
Giuliana has 22 quarters and dollar coins worth a total of $10.75.
Which equation can be used to find d, the number of dollar coins Giuliana has?
C.
0.25(22 - d) + d = 10.75
Dr. Bhatia mixes 2 liters of a 5% saline solution with x liters of a 9% saline solution. The table shows the amount of each solution used.
What is the value of x?
6
A ride on the roller coaster costs 4 tickets while the boat ride only costs 3 tickets. Michael went on the two rides a total of 10 times and spent a total of 37 tickets.
Which equation is true?
D.
4r + 3(10 - r) = 37
A lotion is made from an oil blend costing $1.50 per ounce and glycerin costing $1.00 per ounce. Four ounces of lotion costs $5.50.
Which value could replace x on the table?
A.
(4 - g) 1.5
Four ounces of oregano and 2 ounces of garlic powder are mixed to create a poultry seasoning. Oregano costs $4 per ounce, and garlic powder costs $3 per ounce. The table shows the costs of the ingredients.
What is the value of y in the table?
6
Fuji apples cost $3.00 per pound, and Golden Delicious apples cost $2.00 per pound. A childcare center purchases 30 pounds of a combination of the two types of apples for a total of $80.
Which value could replace x in the table?
B.
3(30 - g)
The hardcover version of a book weighs 7 ounces while its paperback version weighs 5 ounces. Forty-five copies of the book weigh a total of 249 ounces.
Which value could replace x in the table?
D.
5(45 - h)
Shelby mixes a 25% bleach solution with 5 cups of a 10% bleach solution, resulting in a 20% bleach solution. The table shows the amount of each solution used.
What is the value of x?
C.
10
Milk and cream are mixed together for a recipe. The total volume of the mixture is 1 cup. If the milk contains 2% fat, the cream contains 18% fat, and the mixture contains 6% fat, how much cream is in the mixture?
B.
1/4 cup
Bodhi has a collection of 175 dimes and nickels. The collection is worth $13.30. Which equation can be used to find n, the number of nickels in the collection?
D.
0.1(175 - n) + 0.05n = 13.30
A collection of 108 coins containing only quarters and nickels is worth $21.
Which value could replace q on the chart?
D.
108 - n
Four cups of a salad blend containing 40% spinach is mixed with an unknown amount of a salad blend containing 55% spinach. The resulting salad contains 50% spinach.
How many cups of salad are in the resulting mixture?
C.
12
Maki uses 20 gallons of a solution with an unknown ethanol concentration and 60 gallons of a 12% ethanol solution to make 80 gallons of a 10% solution. The table shows the amount of each solution.
What is the value of x, the concentration of the unknown ethanol solution?
B.
0.04
A 4% peroxide solution is mixed with a 10% peroxide solution, resulting in 100 L of an 8% solution. The table shows the amount of each solution used in the mixture.
What is the value of z in the table?
8
It took Amir 2 hours to hike 5 miles. On the first part of the hike, Amir averaged 3 miles per hour. For the second part of the hike, the terrain was more difficult so his average speed decreased to 1.5 mile per hour.
Which equation can be used to find t, the amount of time Amir spent hiking during the second, more difficult part of the hike?
D.
3(2 - t) + 1.5t = 5
Eduardo's average speed on his commute to work was 55 miles per hour. On the way home, he hit traffic and only averaged 40 miles per hour. If the round trip took him 1.25 hours, which expression represents the distance, in miles, for his trip home that is missing from the table?
C.
40(1.25 - t)
Working together, Alex and Millie can file all the papers in the file cabinets in 4 hours. It would have taken Alex 6 hours to do the job alone. What is the missing value in the table that represents the part of the papers that Alex would file if Alex and Millie worked together?
B.
4/6
Yuto and Lian are at train stations 1,880 kilometers apart. Yuto boards a train heading east at an average speed of 220 kilometers per hour. At the same time, Lian boards a train heading west on a parallel track at an average speed of 250 kilometers per hour. How far has Lian traveled when the two trains pass each other?
D.
1,000 kilometers
It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impatient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool. Which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?
B.
5/8 + 5r = 1
If Jasper installs a floor himself, it will take him 7 hours. Working with Yolanda, it will take them 3 hours.
If they work together, what is the missing value in the table that represents the part of the floor Jasper will install?
1/7(3)
Milla and Luka are 3 kilometers apart and walking toward each other. Milla's average speed is 5 kilometers per hour and Luka's is 4 kilometers per hour.
Which equation can be used to find t, the time it takes for Milla and Luka to meet?
B.
5t + 4t = 3
Sophie and Simon are peeling a pile of potatoes for lunch in the cafeteria. Sophie can peel all the potatoes by herself in 45 minutes, while it would take Simon 30 minutes to do the job working alone. If Sophie and Simon work together to peel the potatoes, how long will it take them?
B.
18 minutes
The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15.
When solved for C, the equation is
A.
C = K - 273.15
In physics class, Carrie learns that a force, F, is equal to the mass of an object, m, times its acceleration, a. She writes the equation as F = ma, then realizes that each of her homework problems asks her to solve for acceleration. She rewrites the formula as F/M= a.
Using this formula, what is the acceleration of an object with F = 7.92 newtons and m = 3.6 kilograms? Express your answer to the nearest tenth.
2.2 m/s2
Marta is solving the equation S = 2Πrh + 2Πr2 for h. Which should be the result?
A.
S/2pieR- r = h
The formula for the lateral area of a right cone is LA = rs, where r is the radius of the base and s is the slant height of the cone.
Which are equivalent equations? Check all that apply.
1.
3.
The area, a, of an ellipse can be determined using the formula a = πxy, where x and y are half the lengths of the largest and smallest diameters of the ellipse.
Which is an equivalent equation solved for y?
D.
y = a ÷ (πx)
The volume, V, of a rectangular prism is determined using the formula , where l is the length, w is the width, and h is the height of the prism. Carltren solves for w and writes the equivalent equation w = V/Ih.
Using this formula, what is the width of a rectangular prism that has a volume of 138.24 cubic inches, a height of 9.6 inches, and a length of 3.2 inches?
4.5 inches
Solve for w.
5w + 9z = 2z + 3w
w =-7/2z
Solve for k.
8k + 2m = 3m + k
D.
k = m/7
The slope-intercept form of a linear equation is y = mx + b, where x and y are coordinates of an ordered pair, m is the slope of the line, and b is where the line crosses the y-axis.
Which is an equivalent equation solved for the slope, m?
B.
Which number line represents the solutions to |x + 4| = 2?
A.
Misha found that the equation -|2x - 10| - 1 = 2 had two possible solutions: x = 3.5 and x = -6.5. Which explains whether or not her solutions are correct?
C.
She is not correct, because there are no solutions.
Which number line represents the solutions to -2|x| = -6?
D.
Johan found that the equation -2|8 - x| - 6 = -12 had two possible solutions: x = 5 and x = -11. Which explains whether his solutions are correct?
B.
He is not correct because he made a sign error.
Which number line represents the solutions to |-2x| = 4?
C.
Which equation has no solution?
A.
|4x - 2| = -6
Which equation has no solution?
C.
|5 - 3x| = -8
What is the solution to -4|-2x + 6| = -24?
C.
x = 0 or x = 6
A while back, either James borrowed $12 from his friend Rita or she borrowed $12 from him, but he can't quite remember which. Either way, he is planning to pay her back or ask that she pay him back this afternoon. If he has $42.80 in his wallet, which equation represents the amounts of money he may have after he sees Rita?
A.
|x - 42.80| = 12
To win a contest, the number of beans in a jar has to be guessed within 20 of the actual number. If the number of beans in the jar is 645, which equation can be used to find the minimum and maximum number of beans that will win the contest, and what is the maximum guess that could win?
B.
|x - 645| = 20; maximum guess: 665 beans
Which equation has only one solution?
D.
|-6x + 3| = 0
Manuela solved the equation 3 - 2|0.5x + 1.5| = 2 for one solution. Her work is shown below.
The other solution to the equation is
-4
Which number line represents the solutions to |x - 5| = 1?
B.
Which statement is true?
D.
The equation -0.3|3 + 8x| = 0.9 has no solution.
Sharon's turtle escaped from her backyard sometime in the last few hours. According to her calculations, the farthest the turtle could have gone is 4 blocks down the road in either direction. If Sharon lives on the 112th block of town, which equation can be used to find the block numbers that represent the farthest distance that the turtle may be?
B.
|x - 112| = 4
Morgan is walking her dog on an 8-meter-long leash. She is currently 500 meters from her house, so the maximum and minimum distances that the dog may be from the house can be found using the equation |x - 500| = 8. What are the minimum and maximum distances that Morgan's dog may be from the house?
C.
492 meters and 508 meters
Which number line represents the solution set for the inequality -1/2x ≥ 4?
B.
What value of x is in the solution set of 3(x - 4) ≥ 5x + 2?
A.
-10
Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?
B.
Which is a correct first step in solving the inequality -4(2x - 1) > 5 - 3x?
A.
Distribute -4 to get -8x + 4 > 5 - 3x.
Which is a correct first step in solving 5 - 2x < 8x - 3?
C.
5 < 10x - 3
Which number line represents the solution set for the inequality -4(x + 3) ≤ -2 - 2x?
A.
What value of x is in the solution set of 2(3x - 1) ≥ 4x - 6?
D.
-1
Solve the inequality.
2(4x - 3) ≥ -3(3x) + 5x?
A.
x ≥ 0.5
What is the missing step in solving the inequality 5 - 8x < 2x + 3?
D.
Add 8x to both sides of the inequality.
What value of x is in the solution set of 8x - 6 > 12 + 2x?
D.
5
What value of x is in the solution set of 4x - 12 ≤ 16 + 8x?
D.
-7
2(4 + 2x) ≥ 5x + 5?
x ≤ 3
Which are correct representations of the inequality -3(2x - 5) < 5(2 - x)? Check all that apply.
-6x + 15 < 10 - 5x
4th ONE
What is a correct first step in solving the inequality -4(3 - 5x)≥ -6x + 9?
D.
-12 + 20x ≥ -6x + 9
Which are correct representations of the inequality 6x ≥ 3 + 4(2x - 1)? Check all that apply.
1 ≥ 2x
6x ≥ 3 + 8x - 4
3rd ONE
What value of x is in the solution set of 2x - 3 > 11 - 5x?
D.
4
Which number line represents the solution set for the inequality 2x - 6 ≥ 6(x - 2) + 8?
C.
What value of x is in the solution set of -5x - 15 > 10 + 20x?
A.
-2
What value of x is in the solution set of 9(2x + 1) < 9x - 18?
A.
-4
Which graph represents the compound inequality?
n < -2 or n ≥ 4
C.
Which compound inequality is represented by the graph?
A.
-3 ≤ x < 1
In order to qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches. The inequality 64 < x < 68, where x represents height, can be used to represent the height range. Which is another way of writing the inequality?
A.
x > 64 and x < 68
To make a small vase, Elisa uses no more than 4.5 ounces of clay. To make a large vase, she uses at least 12 ounces of clay. Which compound inequality represents the number of ounces of clay, c, that Elisa uses to make one vase of either size?
D.
c ≤ 4.5 or c ≥ 12
In order to avoid heavy traffic, Antonio can drive home after working less than 7 hours (h < 7) or after working more than 9 hours (h >9). How can these inequalities be written as one statement?
C.
h < 7 or h > 9
For one photography session, Dexter earns no less than $50, but no more than $100. Which inequality can be used to represent his earnings, e?
D.
50 ≤ e ≤ 100
Which graph represents the compound inequality?
-3 < n < 1
D.
In order to be invited to tutoring or extension activities, a student's performance must be at least 20 points higher or lower than an average score. If the average score is 105, which inequality represents p, the scores for students who are eligible for tutoring or extension activities?
D.
p ≤ 85 or p ≥ 125
Which graph represents the compound inequality?
h ≥ -5 and h < 2
B.
Which compound inequality is represented by the graph?
C.
x < -2 or x ≥ 4
Which set of numbers is included in the solution set of the compound inequality?
A.
{-7, 5, 18, 24, 32}
A political polling agency predicts candidate A will win an election with 54% of the votes. Their poll has a margin of error of 4% both above and below the predicted percentage. Which inequality represents the predicted possible percent of votes, x, for candidate A?
A.
50 ≤ x ≤ 58
Which situation could be represented by the graph?
C.
A program at a community college can be completed in no fewer than 8 months, but must be completed in less than 11 months.
A chef knows that ground beef used for hamburger is safe to eat once it reaches 160 degrees Fahrenheit. For optimized taste and safety, he will not allow a hamburger cooked to a temperature under 160 degrees or over 170 degrees to be served. Which graph represents the conditions under which the chef will not allow the hamburger to be served?
A.
Jeremy rides a Ferris wheel. The graph shows h, Jeremy's height above the ground at any time during the ride.
Which inequality represents the heights shown on the graph?
B.
10 ≤ h ≤ 50
Tomas wrote the equation y = 3x + 3/4. When Sandra wrote her equation, they discovered that her equation had all the same solutions as Tomas's equation. Which equation could be Sandra's?
C.
-6x + 2y = 3/2
What is the solution to the system of linear equations?
C.
(0, 2)
What value of b will cause the system to have an infinite number of solutions?
y = 6x - b
-3x +1/2 y = -3
B=6
Which is the best approximate solution of the system of linear equations y = 1.5x - 1 and y = 1?
B.
(1.33, 1)
A system of equations has 1 solution. If 4x - y = 5 is one of the equations, which could be the other equation?
A.
y = -4x + 5
Fiona wrote the linear equation y = x - 5. When Henry wrote his equation, they discovered that his equation had all the same solutions as Fiona's. Which equation could be Henry's?
x - 5/4y = 25/2
Which is the approximate solution to the system y = 0.5x + 3.5 and y =3/2 −x + 1/3 shown on the graph?
A.
(-2.7, 2.1)
How many solutions does this linear system have?
y = 2x - 5
-8x - 4y = -20
B.
one solution: (2.5, 0)
What is the best approximation for the solution to this system of equations?
C.
(-2.2, -3)
A system of equations has no solution. If y = 8x + 7 is one of the equations, which could be the other equation?
B.
y = 8x - 7
Which values of m and b will create a system of equations with no solution? Check all that apply.
y = mx + b
y = -2x + 3/2
m = -2 and b = -1/3
m = -2 and b = -2/3
What is the solution to the system of equations?
2x - y = 7
y = 2x + 3
C.
no solution
y= -6x+2
-12x - 2y = -4
How many solutions does this linear system have?
D.
infinite number of solutions
Which value of m will create a system of parallel lines with no solution?
y = mx - 6
8x - 4y = 12
M=2
What is the solution to the system of equations?
y = 1/3x - 10
2x + y = 4
C.
(6, -8)
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.
x + y = 24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
B.
The test contains 10 three-point questions and 14 five-point questions.
y=4x - 10
y=2
What is the solution to the system of equations?
A.
(3, 2)
The soccer team is planning to sell health bars for a fundraiser. The prices of purchasing health bars from two different companies are represented by the system of equations shown, where x is the number of bars purchased and y is the total cost in dollars.
Company A: y = 0.75x
Company B: y = 10 + 0.50x
How many bars would the team need to purchase from each company in order for the total cost to be equal?
40 BARS
Casey is deciding which of two landscapers to hire. Each landscaper charges an hourly rate plus a fee for each job.
Casey correctly wrote and solved a system of linear equations by substitution. In his work, he substituted an expression for one variable and solved for the other. This resulted in the equation 5 = 20. What can Casey conclude?
D.
Both landscapers charge the same hourly rate, but not the same fee per job.
he tables represent two linear functions in a system.
What is the solution to this system?
D.
(8, -22)
Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below.
x - y = 7
3x - 2y = 8
Step 1: x = y + 7
Step 2: 3(y + 7) - 2y = 8
Step 3: 3y + 7 - 2y = 8
Step 4: y + 7 = 8
Step 5: y = 1
In which step did Ernesto make the first error?
C.
Step 3
What is the solution to the system of equations?
y = -3x - 2
5x + 2y = 15
B.
(-19, 55)
What is the solution to the system of equations?
y = 2/3x + 3
x = -2
B.
( -2, 5/3)
What is the solution to the system of equations?
y = 1.5x - 4
y = -x
D.
(1.6, -1.6)
What is the solution to the system of equations?
(7, 13/3)
What is the solution to the system of equations?
y = -5x + 3
y = 1
A.
(0.4, 1)
Lian is deciding which of two gyms to join. Each gym charges a monthly rate plus a one-time membership fee.
Lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. In her work, she substituted an expression for one variable and solved for the other. This resulted in the equation 75 = 75. What can Lian conclude?
C.
Both gyms charge the same monthly rate and the same membership fee.
Which values, when placed in the box, would result in a system of equations with no solution? Check all that apply.
y = -2x + 4
6x + 3y = ?
-12
-4
0
4
The tables represent two linear functions in a system.
What is the solution to this system?
D.
(-14, -54)
Which value, when placed in the box, would result in a system of equations with infinitely many solutions?
y = 2x - 5
2y - 4x = ?
A.
-10
What is the solution to this system of linear equations?
2x + 3y = 3
7x - 3y = 24
C.
(3, -1)
What is the solution to this system of linear equations?
2x + y = 1
3x - y = -6
A.
(-1, 3)
Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic titles. Let x represent the number of contemporary titles and y represent the number of classic titles. The system of equations models the given information for both types of DVDs.
x + y = 3,500
x - y = 2,342
Solve the system of equations. How many contemporary titles does Jarred have?
D.
2,921
What is the solution to this system of linear equations?
x + y = 4
x − y = 6
C.
(5, −1)
What is the solution to this system of linear equations?
12q + 3r = 15
-4q - 4r = -44
B.
(-2, 13)
The system of equations can be solved using linear combination to eliminate one of the variables.
2x − y = −4 → 10x − 5y = −20
3x + 5y = 59 → 3x + 5y = 59
13x = 39
Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?
D.
13x = 39
What is the solution to this system of linear equations?
x − 3y = −2
x + 3y = 16
A.
(7, 3)
Kat has 19 coins, all quarters and dimes, that are worth a total of $4. The system of equations that can be used to find the number of quarters, q, and the number of dimes, d, she has is shown.
q + d = 19
0.25q + 0.1d = 4
How many quarters does she have?
C.
14
What is the solution to this system of linear equations?
7x - 2y = -6
8x + y = 3
B.
(0, 3)
Jillian is selling boxes of cookies to raise money for her basketball team. The 10 oz. box costs $3.50, while the 16 oz. box costs $5.00. At the end of one week, she collected $97.50, selling a total of 24 boxes. The system of equations that models her sales is below.
x+ y= 24
3.50x + 5.00y = 97.50
Solve the system of equations. How many 10 oz. boxes were sold?
D.
15
To eliminate the y-terms and solve for x in the fewest steps, by which constants should the equations be multiplied?
First Equation: 5x − 4y = 28
Second equation: 3x - 9y = 30
D.
The first equation should be multiplied by 9 and the second equation by −4.
To eliminate the x-terms and solve for y in the fewest steps, by which constants should the equations be multiplied?
First equation: 6x − 5y = 17
Second equation: 7x + 3y = 11
C.
The first equation should be multiplied by 7 and the second equation by −6.
Which statement is true about the equations -3x + 4y = 12 and 1/4x -1/3 y = 1?
C.
The system of the equations has no solution; the two lines are parallel.
To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied?
First equation: 4x − 3y = 34
Second equation: 3x + 2y = 17
A.
The first equation should be multiplied by 2 and the second equation by 3.
Which statement describes the graph of the system of equations below?
1.5x + 0.2y = 2.68
1.6x + 0.3y = 2.98
C.
The lines intersect at (1.6,1.4).
The linear combination method is applied to a system of equations as shown.
4(.25x + .5y = 3.75) → x + 2y = 15
1/4(4x - 8y = 12) → x - 2y = 3
2x = 18
What is the solution of the system of equations?
D.
(9,3)
What is the value of y in the solution to the system of equations?
1/3x +1/4 y = 1
2x - 3y = -30
D.
8
Which ordered pair is a solution to the system of linear equations?
2x + 3y= 6
-3x + 5y = 10
A.
(0,2)
Mr. Brown is creating examples of systems of equations. He wants to have a system of equations with infinite solutions that includes the equation 5x + 2y = 8. Which equation could Mr. Brown use to complete the system so that it has infinite solutions?
C.
1.25x +0.5y = 2
Melinda and Paul shovel driveways and sidewalks in the winter as a way to earn extra money. Together they shoveled 450 square feet of sidewalk in 30 minutes. Then Melinda shoveled for 20 minutes while Paul shoveled for 25 minutes to complete 345 square feet of driveway.
30x + 30y = 450
20x + 25y = 345
How much more can Paul shovel in 1 minute than Melinda?
A.
3 square feet per minute
A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75. If x is the cost of one apple and y is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange.
6x + 6y = 7.50
10x + 5y = 8.75
What is the cost of one apple?
0.5
The system of equations below has no solution.
Which equation could represent a linear combination of the system?
B.
0=26
Karina uses the system of equations below to compare the monthly utility costs in July and December for electricity, x, and natural gas, y.
750x + 17y = 141.61
300x + 30y = 75.90
Karina solves the system using linear combination and arrives at the equation 116y = 96.28. She then solves this equation for y. Which statement explains Karina's solution?
D.
The cost of natural gas is $0.83 per unit.
Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins. Helena has 17 cups of flour and 4.5 cups of sugar available for baking.
Which combination of loaves of bread and batches of muffins could Helena bake?
A.
2 loaves of bread and 4 batches of muffins
The system of equations is solved using the linear combination method.
What does 0 = −12 mean regarding the solution to the system?
A.
There are no solutions to the system because the equations represent parallel lines.
Which linear inequality is represented by the graph?
B.
y ≥ 1/3x − 1
Which linear inequality is represented by the graph?
B.
y ≤ 1/3x - 4
Which linear inequality is represented by the graph?
y > 2/3x + 3
Which linear inequality is represented by the graph?
y ≤ 1/2 x + 3
Which is the graph of the linear inequality 1/2 x - 2y > -6?
D.
Which linear inequality is represented by the graph?
B.
y > 3x + 2
The solutions to the inequality y ≤ −x + 1 are shaded on the graph. Which point is a solution?
B.
(3, -2)
Which linear inequality is represented by the graph?
C.
y > 2x + 1
Which is the graph of the linear inequality y < 3x + 1?
D.
Which linear inequality is represented by the graph?
y ≤ 1/2x +1/5
Which statements are true about the linear inequality y > 3/4x - 2? Check all that apply.
The graph of y > 3/4x - 2 is a dashed line.
One solution to the inequality is (0, 0).
The graph intercepts the y-axis at (0, -2).
Which points are solutions to the linear inequality y < 0.5x + 2? Check all that apply.
(-3, -2)
(-1, -2)
(1, -2)
(1, 2)
Which is the graph of the linear inequality y ≥ −x − 3?
A.
It takes Dimitri 9 minutes to make a simple bracelet and 20 minutes to make a deluxe bracelet. He has been making bracelets for longer than 120 minutes. If x represents the number of simple bracelets that he has made and y represents the number of deluxe bracelets he has made, the inequality 9x + 20y > 120 represents the scenario.
Which is a possible combination of bracelets that Dimitri may have made?
D.
7 simple bracelets and 3 deluxe bracelets
Dan bought x pounds of potatoes for $0.85 per pound and y pounds of grapes for $1.29 per pound. The total cost was less than $5. Which inequality represents his purchase?
D.
0.85x + 1.29y < 5
Jamaal spent x minutes today practicing his guitar and y minutes today on homework. If the total time he spent on both is 45 minutes or more, which inequality best represents his practice time?
D.
x + y ≥ 45
On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points. Lorenzo needs at least 50 points on the final to earn a "B" in the class. Which inequality represents x, the number of correct multiple-choice questions, and y, the number of correct word problems, he needs to earn a "B"?
D.
4x + 8y ≥ 50
Hamburgers cost $2.50 and cheeseburgers cost $3.50 at a snack bar. Ben has sold no more than $30 worth of hamburgers and cheeseburgers in the first hour of business. Let x represent the number of hamburgers and y represent the number of cheeseburgers. The inequality 2.50x + 3.50y ≤ 30 represents the food sales in the first hour.
If Ben has sold 4 cheeseburgers, what is the maximum value of hamburgers Ben could have sold?
Ben could have sold no more than __ hamburgers.
6