Algebra I A

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What is the value of x in the equation x - y = 30, when y = 15? 4 8 80 200

200

Which function shows a fabric with a price of $1.25 per square yard?

Which recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n > 1? 9.6, -4.8, 2.4, -1.2, 0.6, ... f(n + 1) = (-0.5)f(n) f(n + 1) = (0.5)f(n) f(n + 1) = f(0.5n) f(n + 1) = f(-0.5n)

f(n + 1) = (-0.5)f(n)

SUBJECT:

LINEAR FUNCTIONS

What value of x is in the solution set of -5x - 15 > 10 + 20x? -2 -1 0 1

-2

What is the common ratio between successive terms in the sequence? 2, -4, 8, -16, 32, -64, ... -2 -6 6 2

-2

The function f(x) is given by the set of ordered pairs. {(1,0), (-10,2), (0,6), (3,17), (-2,-1)} Which equation is true? f(-0)=1 f(2)=-10 f(0)=6 f(1)=-10

f(0)=6

Which linear inequality is represented by the graph? y ≤ x - 1.3 y ≤ x - y ≥ x - y ≥ x - 1.3

y ≤ 1/3x - 1.3

Which graphs show functions with direct variation? Select three options.

B C E

Which inequality pairs with y≤−2x−1 to complete the system of linear inequalities represented by the graph? y<−2x+2 y>−2x+2 y<2x−2 y>2x−2

y>−2x+2

Solve for x. 6(x - 1) = 9(x + 2) x = -8 x = -3 x = 3 x = 8

x = -8

Solve the equation for a. K = 4a + 9ab

Which expression can be used to convert 80 US dollars (USD) to Australian dollars (AUD)? 1 USD = 1.0343 AUD1 AUD = 0.9668 USD

Kathleen and Arnob both run from the park entrance along a loop. Kathleen starts walking from the park entrance and gets a 5-mile head start on Arnob. The graph shows how far they have both traveled. How many minutes does it take Arnob to catch up to Kathleen? 9.8 10 73.5 75

What is the solution to the system of equations? y = -5x + 3 y = 1 (0.4, 1) (0.8, 1) (1, 0.4) (1, 0.8)

(0.4, 1)

Which ordered pair makes both inequalities true? y > -3x + 3 y > 2x - 2 (1,0) (-1,1) (2,2) (0,3)

(2,2)

Consider the equation 5/3v + 4 + 1/3v = 8. What is the resulting equation after the first step in the solution? 5/3v +4 = 8 - 1/3v 4/3v +4 = 8 4 + v = 8 - 5/3v 2v + 4 = 8

2v + 4 = 8

Which is the graph of the linear inequality y < 3x + 1?

Function Notation

Pre-test / Quiz

The graph of a linear function is shown. Which word describes the slope of the line? positive negative zero undefined

positive

Which graph represents the compound inequality? n < -2 or n ≥ 4

Which graph shows a set of ordered pairs that represent a function?

Which linear function represents the line given by the point-slope equation y + 7 = -2/3(x + 6)? f(x) = -2/3x - 11 f(x) = -2/3x - 1 f(x) = -2/3x + 3 f(x) = -2/3x + 13

f(x) = -2/3x - 11

Which equations and/or functions represent the graphed line? Select three options. f(x) = 1/5x - 4 f(x) = 1/2x + 2 f(x) = 1/2x + 1 y - 3 = 1/2(x - 2) y - 1 = 1/2(x+ 2)

f(x) = 1/2x + 2 y - 3 = 1/2(x - 2) y - 1 = 1/2(x+ 2)

Which ordered pair could be removed so that the set of ordered pairs is a function? (4, -2) (-3, 2) (3, 4) (1, 1)

(-3, 2)

Linear Functions Unit Test Review

100%

Which graph represents a function?

Solving Systems of Linear Equations: Linear Combinations

Pre-test / Quiz

Rahul solved the equation 2(x - ) - x = . In which step did he use the addition property of equality? Step 1 Step 2 Step 3 Step 4

Step 3

What is the inverse of the function f(x) = x +3? h(x) = 1/3x + 3 h(x) = 1/3x - 3 h(x) = x - 3 h(x) = x + 3

h(x) = x - 3

The equation f = v + at represents the final velocity of an object, f, with an initial velocity, v, and an acceleration rate, a, over time, t. Which is an equivalent equation solved for t? t = f-v/a t = f-a/v t = a(f - v) t = v(f - a)

t = f-v/a

Step 1: -10 + 8x < 6x - 4Step 2: -10 < -2x - 4Step 3: -6 < -2xStep 4: ________ What is the final step in solving the inequality -2(5 - 4x) < 6x - 4? x < -3 x > -3 x < 3 x > 3

x < 3

What is the common difference between successive terms in the sequence? 0.36, 0.26, 0.16, 0.06, -0.04, -0.14, ... -0.1 -0.01 0.01 0.1

-0.1

Cumulative Exam Review

100%

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? 40 - h 50 - h 5(45) - h 5(45 - h)

5(45 - h)

Karl rides his bicycle 120 feet in 10 seconds. How many feet does he ride in 1 minute? 2 feet 12 feet 720 feet 7,200 feet

720 feet

Which statement is true about the end behavior of the graphed function? As the x-values go to positive infinity, the function's values go to positive infinity. As the x-values go to zero, the function's values go to positive infinity. As the x-values go to negative infinity, the function's values are equal to zero. As the x-values go to negative infinity, the function's values go to negative infinity.

As the x-values go to positive infinity, the function's values go to positive infinity.

SUBJECT:

SYSTEMS OF EQUATIONS AND INEQUALITIES

What is the solution to the linear equation? 6k + 10.5 = 3k + 12 k = 0.5 k = 2 k = 7.3 k = 9

k = 0.5

Which number line represents the solutions to |x + 4| = 2?

Which input value produces the same output value for the two functions on the graph? x = −1 x = 0 x = 3 x = 4

x = 4

How many square inches are in 60 square feet? 5 square inches 72 square inches 720 square inches 8,640 square inches

8,640 square inches

Which graph represents a line with a slope of -2/3and a y-intercept equal to that of the line y = 2/3x - 2?

What is the value of n in the equation 1/2(n-4)-3=3-(2n+3)? n = 0 n = 2 n = 4 n = 6

n = 2

The graph of a linear function is shown. Which word describes the slope of the line? positive negative zero undefined

zero

What is the domain of the function shown in the mapping? {x | x = -5, -3, 1, 2, 6} {y | y = -9, -6, 0, 2, 4} {x | x = -9, -6, -5, -3, 0, 1, 2, 4, 6} {y | y = -9, -6, -5, -3, 0, 1, 2, 4, 6}

{x | x = -5, -3, 1, 2, 6}

Solving Mixture Problems

Pre-test / Quiz

Solving One-Variable Inequalities

Pre-test / Quiz

Solving Systems of Linear Equations: Graphing

Pre-test / Quiz

Solving Systems of Linear Equations: Substitution

Pre-test / Quiz

Solving Systems of Linear Inequalities

Pre-test / Quiz

The table shows the number of cups of water required when cooking different amounts of rice. Which statements apply to the ratio of rice and water? Choose two options. The amount of rice is the dependent value. The amount of water is the dependent value. The amount of rice is the independent value. The amount of water is the independent value. The values cannot be labeled as dependent or independent without a given equation.

The amount of water is the dependent value. The amount of rice is the independent value.

What is the value of a in the equation 3a+b=54, when b=9 ? 15 18 21 27

The point (-3, -5) is on the graph of a function. Which equation must be true regarding the function? f(-3) = -5 f(-3, -5) = -8 f(-5) = -3 f(-5, -3) = -2

f(-3) = -5

y=5x - 1-15x - 3y=3 How many solutions does this linear system have? one solution: (0, -1) one solution: (1, 4) no solution infinite number of solutions

one solution: (0, -1)

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? 85 < p < 125 85 ≤ p ≤ 125 p < 85 or p > 125 p ≤ 85 or p ≥ 125

p ≤ 85 or p ≥ 125

Which is a y-intercept of the graphed function? (-9, 0) (-3, 0) (0, -9) (0, -3)

(0, -9)

Evaluating Functions

Pre-Test

Special Linear Relationships

Pre-test / Quiz

Writing Linear Equations

Pre-test / Quiz

Solve the equation. −10x + 1 + 7x = 37 x = −15 x = −12 x = 12 x = 15

x = −12

Line GH passes through points (2, 5) and (6, 9). Which equation represents line GH? y = x + 3 y = x - 3 y = 3x + 3 y = 3x - 3

y = x + 3

Line AB contains points A(4, 5) and B(9, 7). What is the slope of ? -5/2 -2/5 2/5 5/2

2/5

Which graph matches the equation y + 6 = 3/4(x + 4)?

The function v(r)=4/3nr3 can be used to find the volume of air inside a basketball given its radius. What does V(r) represent? the radius of the basketball when the volume is V the volume of the basketball when the radius is r the volume of the basketball when the radius is V the radius of the basketball when the volume is r

the volume of the basketball when the radius is r

Which graph shows the solution to the system of linear inequalities? x - 4y < 4 y < x + 1

Which graph shows the equation V = 4 + 2t, where V is the total volume of water in a bucket and t is the elapsed time in minutes?

The graph of a relation is shown. Which of these values could be the slope of the line? Select two options. -2 -8/5 0 7/4 3

D, E

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 miles he runs. months he runs. miles he ran the first day. calories he burns.

months he runs.

Solve for n. n + 1 = 4(n - 8) n = 1 n = 8 n = 11 n = 16

n = 11

If a bus driver leaves her first stop by 7:00 a.m., her route will take less than 37 minutes. If she leaves after 7:00 a.m., she estimates that the same route will take no less than 42 minutes. Which inequality represents the time it takes to drive the route, r? r < 37 or r ≥ 42 r < 37 or r > 42 37 < r ≥ 42 37 > r ≥ 42

r < 37 or r ≥ 42

The formula for the circumference of a circle is C = 2r, where r is the radius and C is the circumference. The equation solved for r is r = . Find the radius of a circle that has a circumference of 16. r = 4 r = 8 r = 12 r = 16

r = 8

Solve the equation. -3x + 1 + 10x = x + 4 x = 1/2 x = 5/6 x = 12 x = 18

x = 1/2

Which linear inequality is represented by the graph? y > 2x + 2 y ≥ 1/2x + 1 y > 2x + 1 y ≥ 1/2x + 2

y > 2x + 1

How many solutions exist for the given equation? 3x + 13 = 3(x + 6) + 1 zero one two infinitely many

zero

Three ounces of cinnamon cost $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?

$12.80

The table represents a linear function. What is the slope of the function? -6 -4 4 6

-6

Which is a correct first step in solving 5 - 2x < 8x - 3? 5 < 6x - 3 3x < 8x - 3 5 < 10x - 3 2 - 2x < 8x

5 < 10x - 3

Three points of a function are graphed. Which statement describes the function through the points? The function is a direct variation function with a constant of variation of 1.5. The function is a direct variation function with a constant of variation of 1.8. The function is linear but is not a direct variation function. The function is not a linear function.

The function is linear but is not a direct variation function.

The table represents the function f(x). When f(x) = -3, what is x? -29 -10 -3 -1

-1

If f(x) = 6x - 4, what is f(x) when x = 8? 2 16 44 52

Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b. What is an equivalent equation solved for h? h = (- b)÷ r h = - b ÷ r h = ÷ r - b h = ÷ r

Which table represents a linear function?

The table represents the amount of storage space, in megabytes, used by music files on Zayd's computer. Which statement best describes the relationship between storage space and number of music files? As the number of files remains constant, the storage space used decreases. As the number of files remains constant, the storage space used increases. As the number of files increases, the storage space used decreases. As the number of files increases, the storage space used increases.

As the number of files increases, the storage space used increases.

A car increases, then decreases, its speed. Which table could represent the speed of the car?

What is the solution to the system of equations? y = 2/3x + 3 x = -2 (-2, -15/2) (-2, 5/13) (-2, 11/6) (-2, 13/3)

(-2, 5/13)

Which points are solutions to the linear inequality y < 0.5x + 2? Select three options. (-3, -2) (-2, 1) (-1, -2) (-1, 2) (1, -2)

(-3, -2) (-1, -2) (1, -2)

Vera wants to graph a line that passes through (0, 2) and has a slope of . Which points could Vera use to graph the line? Select three options. (-3, 0) (-2, -3) (2, 5) (3, 4) (6, 6)

(-3, 0) (3, 4) (6, 6)

What are the x-intercepts of the graphed function? (-3, 0) and (0, 1.5) (-3, 0) and (1,0) (-1, 2) and (1, 0) (0, 1.5) and (1, 0)

(-3, 0) and (1,0)

Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces. Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces? (-3, -18) (-0.5, -3) (0, 0) (0.5, 3)

(0, 0)

What is the solution to the system of linear equations? (-3, 0) (-3, 3) (0, 2) (3, 1)

(0, 2)

Which lists all of the x-intercepts of the graphed function? (0, 6) (1, 0) and (2, 0) (1, 0), (2, 0), and (-3, 0) (1, 0), (2, 0), (-3, 0), and (0, 6)

(1, 0), (2, 0), and (-3, 0)

Which ordered pairs make both inequalities true? Select two options. y < 5x + 2 y > x + 1 (-1, 3) (0, 2) (1, 2) (2, -1) (2, 2)

(1, 2) (2, 2)

Which ordered pair can be removed so that the resulting graph represents a function? (-2, 2) (1, 3) (5, -4) (-4, -4)

(1, 3)

y = 5x + 23x = -y + 10 What is the solution to the system of equations? (-4, -18) (-18, -4) (7, 1) (1, 7)

(1, 7)

Which is the best approximate solution of the system of linear equations y = 1.5x - 1 and y = 1? (0.33, 1) (1.33, 1) (1.83, 1) (2.33, 1)

(1.33, 1)

A metalsmith is mixing two molten metals, each containing different percentages of silver. The table shows the amount of each molten metal used. Which two expressions are both equivalent to t, the total number of grams of silver in the mixture? (15)(0.75) and 0.7(15 - x) + 0.9x (15)(0.75) and 0.7(15 - x)(0.9x) 15 + 0.75 and 0.7(15 - x) + 0.9x 15 + 0.75 and 0.7(15 - x)(0.9x)

(15)(0.75) and 0.7(15 - x) + 0.9x

The solutions to the inequality y > −3x + 2 are shaded on the graph. Which point is a solution? (0, 2) (2, 0) (1, −2) (−2, 1)

(2, 0)

What is the y-value of the solution to the system of equations? 3x + 5y = 1 7x + 4y = −13 −3 −1 2 5

Shawn and Dorian rented bikes from two different rental shops. The prices in dollars, y, of renting bikes from the two different shops for x hours is shown. Shop Shawn used: y = 10 + 3.5xShop Dorian used: y = 6x If Shawn and Dorian each rented bikes for the same number of hours and each paid the same price, how much did each pay for the rental?

The graph below represents the speeds of Kael and Lynn as they run around a track. For how many minutes did Lynn run at a greater speed than Kael? 12 17 23 28

A sequence is defined by the formula f(n+1)=f(n)−3. If f(4)=22, what is f(1)? 10 13 31 34

Line AB passes through points A(−6, 6) and B(12, 3). If the equation of the line is written in slope-intercept form, y=mx+b, then m=. What is the value of b? −6 −5 5 6

What value of b will cause the system to have an infinite number of solutions? y = 6x - b -3x + 1/2y = -3 b = 2 4 6 8

What is the value of x in the equation 8x - 2y = 48, when y = 4? 6 7 14 48

Which graph represents a function with direct variation?

Writing and Solving Equations in Two Variables

Pre-test / Quiz

Which step could be used to help isolate the variable in the following equation? 5.6j - 0.12 = 4 + 1.1j Subtract 0.12 from both sides. Subtract 5.6 from both sides. Subtract 4j from both sides. Subtract 1.1j from both sides.

Subtract 1.1j from both sides.

Which best describes the relationship between the successive terms in the sequence shown? 9, -1, -11, -21, ... The common difference is -10. The common difference is 10. The common ratio is -9. The common ratio is 9.

The common difference is -10.

The depth of snow after n hours of a snowstorm is represented by the function f(n + 1) = f(n) + 0.8 where f(0) = 2.5. Which statement describes the sequence of numbers generated by the function? The depth of snow was 0.8 inches when the storm began, and 2.5 inches after the first hour of the storm. The depth of snow was 1.7 inches when the storm began, and 0.8 inches of snow fell each hour. The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour. The depth of snow was 3.3 inches when the storm began, and 2.5 inches of snow fell in 1 hour.

The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour.

Timmy writes the equation f(x) = x - 1. He then doubles both of the terms on the right side to create the equation g(x) = x - 2. How does the graph of g(x) compare to the graph of f(x)? The line of g(x) is steeper and has a higher y-intercept. The line of g(x) is less steep and has a lower y-intercept. The line of g(x) is steeper and has a lower y-intercept. The line of g(x) is less steep and has a higher y-intercept.

The line of g(x) is steeper and has a lower y-intercept.

Which ordered pair is in the solution set of the system of linear inequalities? y > 3/2x - 1 y < 3/2x - 1 (-5, 2) (2, 2) (5, 2) no solution

no solution

How many solutions exist for the given equation? 0.75(x + 40) = 0.35(x + 20) + 0.35(x + 20) zero one two infinitely many

one

Nolan plots the y-intercept of a line at (0, 3) on the y-axis. He uses a slope of 2 to graph another point. He draws a line through the two points. Which equation represents Nolan's line? y = 2x + 1 y = 2x + 3 y = 3x + 2 y = 3x + 5

y = 2x + 3

The graph represents revenue in dollars as a function of greeting cards sold. Which equation represents the function shown on the graph? y = 1/4x y = 1/2x y = 2x y = 4x

y = 4x

A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function? y = x/14 y = x/7 y = 7x y = 14x

y = 7x

The slope, m, of a linear equation can be found using the formula m = , where the x- and y-values come from two ordered pairs, and (x1, y1) and (x2, y2). What is an equivalent equation solved for y2? y2 = mx2 - x1 + y1 y2 = mx2 - x1 - y1 y2 = m(x2 - x1) + y1 y2 = m(x2 - x1) - y1

y2 = m(x2 - x1) + y1

Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let x represent the length of each of the equal pieces of yarn that Julie decides to cut. What is the equation that can be used to determine the total length of all of the yarn that she ends up cutting, y? Is the graph of the equation continuous or discrete? y=7.75x+4; discrete y=7.75x+4; continuous y=4x+7.75; discrete y=4x+7.75; continuous

y=4x+7.75; continuous

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? 3n - 15 + n = 101 3n + 15 + n = 101 3n - 15 - n = 101 3n + 15 - n = 101

3n - 15 + n = 101

Debi walks laps around the mall for exercise during the winter months. The table represents the number of steps recorded on her pedometer as she walks laps around the mall one day. Which statement is true about the graph of the line representing Debi's data? Debi walks 1,875 steps per lap around the mall. One lap around the mall is equal to 2,425 steps. One lap around the mall is equal to 4,300 steps. Debi walks 6,175 steps per lap around the mall.

One lap around the mall is equal to 2,425 steps.

Literal Equations

Pre-test / Quiz

Solving Linear Equations: Variables on Both Sides

Pre-test / Quiz

Alejandra correctly wrote the equation y - 3 = 1/5(x - 10) to represent a line that her teacher sketched. The teacher then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line? y - 6 = 2(x - 10) y - 2 = (x - 10) y - 3 = (x - 2) y - 3 = 2(x - 10)

y - 3 = 2(x - 10)

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? y - 3 = -2/3(x + 8) y + 3 = -2/3(x - 8) y + 8 = -2/3(x - 3) y - 8 = -2/3(x + 3)

y - 8 = -2/3(x + 3)

Which linear inequality is represented by the graph? y > 2x + 3 y < 2x + 3 y > −2x + 3 y < −2x + 3

y < −2x + 3

Which equation represents the graphed function? y = -3x + 3 y = 3x - 3 y = 3x -1/3 y = -1/3x + 3

y = -1/3x + 3

Which description is represented by a discrete graph? Kiley bought a platter for $19 and several matching bowls that were $8 each. What is the total cost before tax? The temperature at 9 a.m. was 83° F and is heating up at an average rate of 6°F per hour. What is the temperature x hours later? Juan ate an egg with 78 calories and some cereal with 110 calories per serving for breakfast. What is the total amount of calories he consumed? A bottle contained 2,000 mL of liquid and is being poured out at an average rate of 300 mL per second. How much liquid is left in the bottle after x seconds?

Kiley bought a platter for $19 and several matching bowls that were $8 each. What is the total cost before tax?

The graph below represents a library fine, in dollars, for a book returned late after a number of days overdue. Christen returned an overdue book to the library. Her fine was the same as the fine for returning the book yesterday. Which could be the number of days overdue?

A text font fits 12 characters per inch. Using the same font, how many characters can be expected per yard of text? There are 12 inches in a foot, and 3 feet in a yard. 36 characters 144 characters 360 characters 432 characters

432 characters

What is the common difference between successive terms in the sequence? 2, 8, 14, 20, 26, ... -6 -4 4 6

What is the value of y in the equation 5x + 2y = 20, when x = 0.3? 2.5 2.8 9.25 10.75

9.25

Which equation represents the graphed function? -3x + 2 = y -x + 2 = y x - 3 = y 2x - 3 = y

Which expression converts 100 inches per minute to feet per minute?

Which number line represents the solution set for the inequality -1/2x ≥ 4?

Which ordered pairs are in the solution set of the system of linear inequalities? y > 1/2x y < 1/2x + 1 (5, -2), (3, 1), (-4, 2) (5, -2), (3, -1), (4, -3) (5, -2), (3, 1), (4, 2) (5, -2), (-3, 1), (4, 2)

(5, -2), (3, 1), (4, 2)

The function f(x) is shown on the graph. If f(x) = 0, what is x? 0 only -6 only -2, 1, or 3 only -6, -2, 1, or 3 only

-2, 1, or 3 only

Alex has 84 quarters and nickels worth a total of $17.80. Which equation can be used to find q, the number of quarters Alex has? 0.25q + 0.05(q - 84) = 17.80 0.05q + 0.25(84 - q) = 17.80 0.25(q - 84) + 0.05q = 17.80 0.05(84 - q) + 0.25q = 17.80

0.05(84 - q) + 0.25q = 17.80

The table represents a linear function.What is the slope of the function? -3 -2 3 4

The perimeter of the scalene triangle is 54.6 cm. Which equation can be used to find the value of b if side a measures 8.7 cm? 8.7+b=54.6 17.4+b=54.6 26.1+b=54.6 34.8+b=54.6

34.8+b=54.6

What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)? 3 4 5 9

Which relationship has a zero slope?

Which is the graph of the equation y-1=2/3(x-3)?

Dimensional Analysis

Pre-test / Quiz

Which set of ordered pairs represents a function?

{(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}

Which point is a solution to the linear inequality y < -1/2x + 2? (2, 3) (2, 1) (3, -2) (-1, 3)

(3, -2)

Solve for a. 7a - 2b = 5a + b a = 2b a = 3b a = 3/2b a = 2/3b

a = 3/2b

Solve for n. 11(n - 1) + 35 = 3n n = -6 n = -3 n = 3 n = 6

n = -3

What is the domain of the given function? {x | x = -6, -1, 0, 3} {y | y = -7, -2, 1, 9} {x | x = -7, -6, -2, -1, 0, 1, 3, 9} {y | y = -7, -6, -2, -1, 0, 1, 3, 9}

{x | x = -6, -1, 0, 3}

What is the y-intercept of the function f(x) = -2/9x + 1/3? -2/9 -1/3 1/3 2/9

1/3

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? 1/5 cup 1/4 cup 3/4 cup 4/5 cup

1/4 cup

Consider the function represented by the equation y-6x-9=0. Which answer shows the equation written in function notation with x as the independent variable?

Which shows the correct solution of the equation 1/2a+2/3b=50, when b=30?

Which table represents a linear function?

Which is the graph of the linear inequality y ≥ −x − 3?

Two functions are defined as shown. f(x) = -1/2x - 2 g(x) = -1 Which graph shows the input value for which f(x) = g(x)?

The graph of a linear function is shown. Which word describes the slope of the line? positive negative zero undefined

negative

Which statement describes the relationship between x and y?

As x increases, y decreases and then increases.

Which equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same number and four"? (1 - n) - 3 = 1/2(4 - 3n) 3 - (1 - n) = 1/2(4 - 3n) (n - 1) - 3 = 1/2(3n - 4) 3 - (n - 1) = 1/2(3n - 4)

3 - (n - 1) = 1/2(3n - 4)

Which value, when placed in the box, would result in a system of equations with infinitely many solutions? y = 2x - 5 2y - 4x = □ -10 -5 5 10

-10

Jose asks his friends to guess the higher of two grades he received on his math tests. He gives them two hints. The difference of the two grades is 16. The sum of one-eighth of the higher grade and one-half of the lower grade is 52. The system that represents his scores is below. x - y = 16 1/8x + 1/2y = 52 What is the higher grade of Jose's two tests? 48 52 80 96

A store sells notebooks for $3 each and does not charge sales tax. If x represents the number of notebooks Adele buys and y represents the total cost of the notebooks she buys, which best describes the values of x and y?

The value of x can be any integer greater than or equal to 0, and y will be an integer greater than or equal to 0.

What are the intercepts of the graphed function? x-intercept = (-1, 0)y-intercept = (-3, 0) x-intercept = (0, -1)y-intercept = (0, -3) x-intercept = (0, -1)y-intercept = (-3, 0) x-intercept = (-1, 0)y-intercept = (0, -3)

x-intercept = (-1, 0)y-intercept = (0, -3)

A sequence is defined by the recursive formula f(n + 1) = 1.5f(n). Which sequence could be generated using the formula? -12, -18, -27, ... -20, 30, -45, ... -18, -16.5, -15, ... -16, -17.5, -19, ...

-12, -18, -27, ...

The table represents a function. Which value is an output of the function? -6 -2 4 7

-2

Consider the function represented by the table. For which x is f(x)=-3? -7 -4 4 5

-7

The table represents a function. What is f(5)? -8 -1 1 8

-8

The graph represents the direct variation function between earnings in dollars and hours worked. Which equation can be used to describe the direct variation function between E, the total earnings in dollars, and h, the number of hours worked? E = 1.5h E = 7.5h E = 13h E = 15h

E = 7.5h

The profit earned by a hot dog stand is a linear function of the number of hot dogs sold. It costs the owner $48 dollars each morning for the day's supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold. Which equation represents y, the profit earned by the hot dog stand for x hot dogs sold? y=48x−2 y=48x+2 y=2x−48 y=2x+48

y=2x−48

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? |x - 645| = 20; maximum guess: 635 beans |x - 645| = 20; maximum guess: 665 beans |x - 20| = 645; maximum guess: 635 beans |x - 20| = 645; maximum guess: 665 beans

|x - 645| = 20; maximum guess: 665 beans

The table shows the number of songs that were downloaded and the total cost for buying the songs. What is the rate of change for the function in the table? 2 songs for $1 $2 per song 4 songs for $1 $4 per song

$2 per song

Which ordered pair makes both inequalities true? y < 3x - 1 y > -x + 4 (4,0) (1,2) (0,4) (2,1)

(4,0)

What is the most accurate representation of the area of a plot measuring 11.7 cm by 15.4 cm?

180.2 cm2

Anya graphed the line (y−2)=3(x−1) on the coordinate grid. What is the slope of Anya's line? −3 −1 1 3

What is the slope of the line represented by the equation y = 4/5x - 3? -3 -4/5 4/5 3

4/5

Which graph represents viable values for y = 2x, where x is the number of pounds of rice scooped and purchased from a bulk bin at the grocery store and y is the total cost of the rice?

SUBJECT:

LINEAR EQUATIONS AND INEQUALITIES

Marta is solving the equation S = 2πrh + 2πr2 for h. Which should be the result? S/2πr - r = h S-r/2πr = h S - r/2π = h S - 2π/r = h

S/2πr - r = h

A chemist mixes 4 liters of one acid solution with 10 liters of a 40% solution, resulting in a 30% acid solution. The table shows the amount of each solution used. What is the value of x, the acid concentration of the first solution? 0.05 0.10 0.15 0.20

0.05

A sequence is defined by the recursive function f(n + 1) = -10f(n). If f(1) = 1, what is f(3)? 3 -30 100 -1,000

100

A sequence is defined recursively using the equation . If f(1)=100, what is f(6)? 52 60 68 92

Which value of m will create a system of parallel lines with no solution? y=mx-6 8x-4y=12 -2 -1/2 1/2 2

What is the solution to the system of equations? y = 1.5x - 4 y = -x (-1.6, 1.6) (-1.5, 1.5) (1.5, -1.5) (1.6, -1.6)

(1.6, -1.6)

The circumference of a circle can be found using the formula C = 2πr. Which is an equivalent equation solved for r? r = Cπ r = C(2π) r = C/2π r = 2π/C

r = C/2π

Solve for x. 9(x + 1) = 25 + x x = 2 x = 3 x = 4 x = 5

x = 2

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) 1/7r 7r 7(3)

1/7(3)

Solve the equation. -9x + 1 = -x + 17 x = -8 x = -2 x = 2 x = 8

x = -2

An expression to convert 50 miles per hour to miles per minute is shown. What value can be entered in the box to correctly make this conversion? 6 60 360 3,600

Which interval for the graphed function has a local minimum of 0? [-3, -2] [-2, 0] [1, 2] [2, 4]

[2, 4]

Which linear function is represented by the graph? f(x) = -2x + 1 f(x) = -1/2x + 1 f(x) = 1/2x + 1 f(x) = 2x + 1

f(x) = -1/2x + 1

What is the justification for the step taken from line 2 to line 3? the subtraction property of equality the multiplication property of equality combining like terms on one side of the equation the distributive property

the subtraction property of equality

What is the solution to this system of linear equations? y − x = 6 y + x = −10 (−2, −8) (−8, −2) (6, −10) (−10, 6)

(−8, −2)

Working together, Shawn and Hector can install a tile floor in 6 hours. It would take Shawn 9 hours to do the job alone. What is the value of r, Hector's rate of work in parts per hour? 1/18 1/91/3 2/3

1/18

The table shows the number of grapes eaten over several minutes. What is the rate of change for the function on the table? 15 grapes eaten per minute 15 minutes to eat each grape 60 grapes eaten per minute 60 minutes to eat each grape

15 grapes eaten per minute

The isosceles triangle has a perimeter of 7.5 m. Which equation can be used to find the value of x if the shortest side, y, measures 2.1 m?

2.1+2x=7.5

Which function is positive for the entire interval [-3, -2]?

Blueberries are $0.80 per pound less expensive at the farmer's market.

Which statements are true about the graph of the system of linear inequalities? Select two options. y > 3x - 4 y < 1/2x + 1 The graph of y > 3x − 4 has shading above a dashed line. The graph of y < 1/2x + 1 has shading below a dashed line. The graphs of the inequalities will intersect. There are no solutions to the system. The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).

The graph of y > 3x − 4 has shading above a dashed line. The graphs of the inequalities will intersect.

What is the inverse of the function f(x) = 2x + 1? h(x) = x - h(x) = x + h(x) = x - 2 h(x) = x + 2

h(x) = 1/2x - 1/2

What is the solution to 3|-3x + 9| = -18? x = -5 x = 5 or x = 1 x = -5 or x = 1 no solution

no solution

What is the range of the given function? {(-2, 0), (-4, -3), (2, -9), (0, 5), (-5, 7)} {x | x = -5, -4, -2, 0, 2} {y | y = -9, -3, 0, 5, 7} {x | x = -9, -5, -4, -3, -2, 0, 2, 5, 7} {y | y = -9, -5, -4, -3, -2, 0, 2, 5, 7}

{y | y = -9, -3, 0, 5, 7}

For water to be a liquid, its temperature must be within 50 Kelvin of 323 Kelvin. Which equation can be used to determine the minimum and maximum temperatures between which water is a liquid? |323 - 50| = x |323 + 50| = x |x - 323| = 50 |x + 323| = 50

|x - 323| = 50

The newspaper in Haventown had a circulation of 80,000 papers in the year 2000. In 2010, the circulation was 50,000. With x=0 representing the year 2000, the graph below models this scenario. What number will complete the point-slope equation that models this scenario? y−50,000=[_______](x−10) −3,000 −2,000 2,000 3,000

−3,000

A soccer team ordered 12 jerseys and 12 pairs of shorts, for a total of $156. Later, they had to order 4 more jerseys and 6 more pairs of shorts, for a total of $62. The system of equations that can be used to find x, the cost of each jersey, and y, the cost of each pair of shorts is shown. 12x + 12y=1564x + 6y=62 What is the cost of each jersey? $5 $8 $12 $13

What is the solution to this system of linear equations? 2x + y = 1 3x - y = -6 (-1, 3) (1, -1) (2, 3) (5, 0)

(-1, 3)

The tables represent two linear functions in a system. What is the solution to this system? (- 13/3, -25) (- 14/3, -54) (-13, -50) (-14, -54)

(-14, -54)

Which ordered pair makes both inequalities true? y > -2x + 3 y < x - 2 (0,0) (0,-1) (1,1) (3,0)

(3,0)

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? 470 kilometers 880 kilometers 940 kilometers 1,000 kilometers

1,000 kilometers

Last week, Lindsay earned $10 per hour plus a $60 bonus for good job performance. She spends 1/15 of her paycheck on dinner with friends. If she had not earned the bonus, the amount she spent on dinner would have been 1/10 of her paycheck. Which equation can be used to find h, the number of hours Lindsay worked last week? 1/15 (10h + 60) = 1/10 (10h) 1/15 (10h + 60h) = 1/10 (10h) 1/15 h(10 + 60) = 1/10h(10) 1/15 (10 + 60h) = 1/10 (10h)

1/15 (10h + 60) = 1/10 (10h)

Systems of Equations and Inequalities, Unit Test

100%

Elena agrees to finish a knitting project for a friend. The graph shows the number of rows Elena completes compared to the amount of time spent knitting. Assuming she worked at a constant rate, how many rows had been completed before Elena started working? 12 14 15 19

If f(x) = 5x + 40, what is f(x) when x = -5? -9 -8 7 15

The graph shows the relationship between the volume of a rectangular prism and the volume of a square pyramid with an identical base and height.What is the slope of the line? −3 -1/3 1/3 3

Line CD passes through points C(1, 3) and D(4, -3). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b? -5 -2 1 5

What value of x is in the solution set of 8x - 6 > 12 + 2x? -1 0 3 5

Line CD passes through points C(3, -5) and D(6, 0). What is the equation of line CD in standard form? 5x + 3y = 18 5x - 3y = 30 5x - y = 30 5x + y = 18

5x - 3y = 30

The function g(x) is graphed. Which statements about the function are true? Choose three options. g(1)=-1 g(0)=0 g(4)=-2 g(1)=1 g(-1)=1

g(0)=0 g(1)=1 g(-1)=1

How many solutions exist for the given equation? 3(x + 10) + 6 = 3(x + 12) zero one two infinitely many

infinitely many

Solve the inequality. 2(4+2x)≥5x+5 x≤−2 x≥−2 x≤3 x≥3

x≤3

A system of equations has no solution. If y = 8x + 7 is one of the equations, which could be the other equation? 2y = 16x +14 y = 8x - 7 y = -8x + 7 2y = −16x − 14

y = 8x - 7

Which ordered pair could be removed from the graph to create a set of ordered pairs that represents a function?

(1, 3)

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? (4 - g) 1.5 (4 - g) + 1.5 4g - g(1.5) (4 - g)g

(4 - g) 1.5

What is the solution to this system of linear equations? x + y = 4 x − y = 6 (4, 6) (6, 4) (5, −1) (−1, 5)

(5, −1)

A snack cart sells lemonade for $2 and hot dogs for $5. The vendor sold 86 items today for a total of $330. Which equation is true? (86 - h)(h) = 86 (86 - h) + h = 86 (86 - h) + h = 2 + 5 [2(86 - h)](5h) = 330

(86 - h) + h = 86

Line JK passes through points J(-4, -5) and K(-6, 3). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b? -21 -4 11 27

-21

Line GH contains points G(-2, 6) and H(5, -3). What is the slope of ? -7/3 -9/7 -7/9 -3/7

-9/7

Karissa begins to solve the equation 1/2 (x - 14) + 11 = 1/2x - (x - 4). Her work is correct and is shown below. 1/2 (x - 14) + 11 = 1/2x - (x - 4) 1/2x - 7 + 11 = 1/2x - x+4 1/2x + 4 = -1/2x + 4 When she subtracts 4 from both sides, 1/2x = -1/2x results. What is the value of ? -1 -1/2 0 1/2

The system of equations below has no solution. Which equation could represent a linear combination of the system? 4/3x = 42 0 = -78 15/2y = 33 0 = 0

0 = -78

Jonas jogged up the hill at an average rate of of a mile per minute and then walked down the hill at an average rate of of a mile per minute. The round trip took him 42 minutes. What is the missing value in the table that represents the distance of the trip down the hill? 1/16x 42/16- x 42 - 1/16x 1/16 (42 - x)

1/16 (42 - x)

Systems of Equations and Inequalities, Unit Test Review

100%

A collection of 108 coins containing only quarters and nickels is worth $21. Which value could replace q on the chart? 21 108 21 - n 108 - n

108 - n

Two runners are saving money to attend a marathon. The first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. The second runner has $50 in savings and will save $60 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? 112 - 25m + 45 = 50 - 60m 112 + 25 + 45m = 50m + 60 112 + 25 - 45m = -50m + 60 112 + 25m + 45 = 50 + 60m

112 + 25m + 45 = 50 + 60m

If f(x) = + 8, what is f(x) when x = 10? 4 9 13 36

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? 2/5 5/4 5/3 5/2

5/2

Step 1: Subtract 3 from both sides of the inequality.Step 2: __________Step 3: Divide both sides of the inequality by the coefficient of x. What is the missing step in solving the inequality 5 - 8x < 2x + 3? Add 2x to both sides of the inequality. Subtract 8x from both sides of the inequality. Subtract 2x from both sides of the inequality. Add 8x to both sides of the inequality.

Add 8x to both sides of the inequality.

The graph represents a mechanic's labor costs for a given number of hours of car repair. Which statement describes the relationship between labor cost and time for a car repair? All repairs requiring 1 hour or less have the same labor cost. Labor costs the same no matter how many hours are used for a repair. Labor costs for a repair are more expensive as the number of hours increases. There is no cost of labor for a repair requiring less than 1 hour.

All repairs requiring 1 hour or less have the same labor cost.

Which graph represents viable values for y = 5.5x, where x is the number of cans of tomato paste and y is the total weight of the sealed cans in ounces?

Which graph shows the equation c = 10+ 3t, where c is the total cost of going to the carnival and t is the number of $3 tickets purchased?

Which graph shows the solution to the system of linear inequalities? y < 2x - 5 y > -3x + 1

Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?

Which system of linear inequalities has the point (3, -2) in its solution set?

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? One gym charges $75 per month. Each gym charges $75 per month. Both gyms charge the same monthly rate and the same membership fee. Both gyms charge the same monthly rate, but not the same membership fee.

Both gyms charge the same monthly rate and the same membership fee.

Which is the graph of the linear inequality 2x - 3y < 12?

Which number line represents the solution set for the inequality 2x - 6 ≥ 6(x - 2) + 8?

Which number line represents the solution set for the inequality 3x < -9?

Which number line represents the solutions to |-2x| = 4?

Chin canned a number of quart jars and a number of pint jars of tomatoes from his garden. A pint is 16 ounces and a quart is 32 ounces. The number of pints he canned is represented by p, and the number of quarts he canned is represented by q. Which equation models the scenario if Chin canned a total of 1,280 ounces?

What are the possible steps involved in solving the equation shown? Select three options. 3.5 + 1.2(6.3 - 7x) = 9.38 Add 3.5 and 1.2. Distribute 1.2 to 6.3 and -7x . Combine 6.3 and -7x . Combine 3.5 and 7.56. Subtract 11.06 from both sides.

Distribute 1.2 to 6.3 and -7x . Combine 3.5 and 7.56. Subtract 11.06 from both sides.

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? The equation has one solution: x = 0. The equation has one solution: x = 1. The equation has no solution. The equation has infinite solutions.

The equation has infinite solutions.

A store offers packing and mailing services to customers. The cost of shipping a box is a combination of a flat packing fee of $5 and an amount based on the weight in pounds of the box, $2.25 per pound. Which equation represents the shipping cost as a function of x, the weight in pounds? f(x) = 2.25x + 5 f(x) = 5x + 2.25 f(x) = 2.25x − 5 f(x) = 5x − 2.25

f(x) = 2.25x + 5

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? x > 64 and x < 68 x > 64 or x < 68 x < 64 and x < 68 x < 64 or x < 68

x > 64 and x < 68

A direct variation function contains the points (-8, -6) and (12, 9). Which equation represents the function? y = -4/3x y = -3/4x y = 3/4x y = 4/3x

y = 3/4x

A circle representing a pool is graphed with a center at the origin. Grant enters the pool at point A and swims over to a friend who is located at point B. Which equation represents Grant's path? y = 2 - 4x y = 4 - x/2 y = 6 - x/4 y = 8 - 2x

y = 4 - x/2

Which linear inequality is represented by the graph? y ≥ 1/3x - 4 y ≤ 1/3x - 4 y ≤ 1/3x + 4 y ≥ 1/3x + 4

y ≤ 1/3x - 4

Which linear inequality is represented by the graph? y > 2/3x -1/2 y ≥ 3/2x + 1/5 y ≤ 2/3x + 1/5 y < 3/2x -1/5

y ≤ 2/3x + 1/5

Which linear inequality is represented by the graph? y ≤ 1/3x − 1 y ≥ 1/3x − 1 y < 3x − 1 y > 3x − 1

y ≥ 1/3x − 1

Which linear function represents the line given by the point-slope equation y - 8 = 1/2(x - 4)? f(x) = 1/2x + 4 f(x) = 1/2x + 6 f(x) = 1/2x - 10 f(x) = 1/2x - 12

f(x) = 1/2x + 6

The height of a rocket a given number of seconds after it is released is modeled by h(t)=-16r2+32t+10. What does t represent? the number of seconds after the rocket is released the initial height of the rocket the initial velocity of the rocket the height of the rocket after t seconds

the number of seconds after the rocket is released

What is the solution to the linear equation? 2/3x - 1/2 = 1/3 + 5/6x x = -5 x = -1/6 x =1/6 x = 5

x = -5

Which input value produces the same output value for the two functions on the graph? x = -3 x = -1 x = 1 x = 3

x = 3

Which equation represents the line that passes through and (-8.11) and (4,7/2)? y = -5/8x + 6 y = -5/8x + 16 y = -15/2x - 49 y = -15/2x + 71

y = -5/8x + 6

Which statement is true regarding the functions on the graph? f(-3) = g(-4) f(-4) = g(-3) f(-3) = g(-3) f(-4) = g(-4)

f(-3) = g(-3)

Which is an x-intercept of the graphed function? (0, 4) (-1, 0) (4, 0) (0, -1)

(-1, 0)

The graph of the function f(x) is shown below. What is x when f(x)=0? -1.8 -1.2 0 5

-1.8

On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with the number a. For example b = 2 3/4 when a = -2 3/4. Which equation represents this direct variation between a and b? b = -a -b = -a b - a = 0 b(-a) = 0

-b = -a

The table represents a function. What is f(-2)? -3 -1 1 3

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 0.01 0.1 10 100

100

The graph represents the heights of two climbers on a climbing wall over a 12-minute time period. How high did Abby climb above their original starting position? 8 feet 15 feet 18 feet 22 feet

18 feet

What is the value of y in the solution to the system of equations? 1/3x + 1/4y = 1 2x - 3y = -30 -8 -3 3 8

Craig ran the first part of a race with an average speed of 8 miles per hour and biked the second part of a race with an average speed of 20 miles per hour. The entire two-part, 15-mile race took him 1.125 hours to complete. Which table correctly represents his rates, times, and distances for each part of the race?

The points (3, 24) and (7, 56) represent points of a function where y, the number of photographs, varies directly with x, the number of pages in an album. Which statement describes another point on the graph of this function? A 50-page photo album holds 400 photographs. An 80-page photo album holds 560 photographs. A 100-page photo album holds 8,000 photographs. A 900-page photo album holds 8,400 photographs.

A 50-page photo album holds 400 photographs.

Which is true about the solution to the system of inequalities shown? y < 1/3x - 1 y < 1/3x - 3 All values that satisfy y < 1/3x - 1 are solutions. All values that satisfy y < 1/3x - 3 are solutions. All values that satisfy either y < 1/3x - 1 or y < 1/3x - 3 are solutions. There are no solutions.

All values that satisfy y < 1/3x - 3 are solutions.

The weight of a box of cereal can vary by 1/4 of an ounce and still be sold as a full box. Each box is supposed to contain 18 ounces of cereal. Which graph represents the possible weights of boxes that are overfilled or underfilled and cannot be sold as full boxes?

Which equation represents the line that passes through (-6, 7) and (-3, 6)? y = -x + 9 y = -x + 5 y = -3x - 11y y = -3x + 25

Which graph has a slope of 4/5?

Which graph could represent a constant balance in a bank account over time?

Which graph represents a function with direct variation?

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 C = K - 273.15 C = 273.15 - K C = K + 273.15 C = 273.15K

C = K - 273.15

Fiona is serving iced tea and lemonade at a picnic. She has only 44 glasses in which to serve the drinks. If x represents the number of glasses of iced tea and y represents the number of glasses of lemonade, which equation represents the number of glasses of ice tea she can serve?

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? The loan balance decreases $500 per month. Harrison makes a monthly payment of $250. The loan balance increases $250 per month. Harrison increases his monthly payment by $500 each month.

Harrison makes a monthly payment of $250.

Graphing Two-Variable Linear Inequalities

Pre-test / Quiz

Slope-Intercept Form of a Line

Pre-test / Quiz

Solving Absolute Value Equations

Pre-test / Quiz

Solving Linear Equations: Distributive Property

Pre-test / Quiz

Solving Linear Equations: Variable on One Side

Pre-test / Quiz

Solving Rate Problems

Pre-test / Quiz

Solving Systems: Introduction to Linear Combinations

Pre-test / Quiz

Writing and Graphing Equations in Two Variables

Pre-test / Quiz

At a glance, Kendra believes that the function represented on the graph is linear. How can Kendra determine if the function is actually linear? She can check to see if the rate of vertical increase equals the rate of horizontal increase between each pair of points. She can check to see if the sum of each y-value and x-value in every ordered pair is the same. She can check to see if the quotient of each y-value and x-value in every ordered pair is the same. She can check to see if the rate of change between the first two ordered pairs is the same as the rate of change between the first and last ordered pairs.

She can check to see if the rate of change between the first two ordered pairs is the same as the rate of change between the first and last ordered pairs.

Fiona solved the equation shown. - (6x - 3) = - What is the missing step of her solution? Simplify by combining like terms. Simplify by using addition property of equality. Simplify by using the multiplication property of equality. Simplify by using the division property of equality.

Simplify by combining like terms.

Talia wants to write the equation of the graphed line in point-slope form. These are the steps she plans to use: Step 1: Choose a point on the line, such as (2, 5).Step 2: Choose another point on the line, such as (1, 3).Step 3: Count units to determine the slope ratio. The line runs 1 unit to the right and rises 2 units up, so the slope is . Step 4: Substitute those values into the point-slope form. y - y1 = m(x - x1) y - 3 = (x - 1) Which of Talia's steps is incorrect? Step 1 is incorrect because it uses a point that is not on the line. Step 2 is incorrect because it uses a point that is not on the line. Step 3 is incorrect because it shows an incorrect ratio for the slope. Step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point-slope form.

Step 3 is incorrect because it shows an incorrect ratio for the slope.

The pattern of numbers below is an arithmetic sequence: 14, 24, 34, 44, 54, ... Which statement describes the recursive function used to generate the sequence? The common difference is 1, so the function is f(n + 1) = f(n) + 1 where f(1) = 14. The common difference is 4, so the function is f(n + 1) = f(n) + 4 where f(1) = 10. The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14. The common difference is 14, so the function is f(n + 1) = f(n) + 14 where f(1) = 10.

The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14.

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 = 141.61300x + 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? The cost of natural gas is $0.17 per unit. The cost of natural gas is $0.20 per unit. The cost of natural gas is $0.72 per unit. The cost of natural gas is $0.83 per unit.

The cost of natural gas is $0.83 per unit.

Which statement is true? The equation -3|2x + 1.2| = -1 has no solution. The equation 3.5|6x - 2| = 3.5 has one solution. The equation 5|-3.1x + 6.9| = -3.5 has two solutions. The equation -0.3|3 + 8x| = 0.9 has no solution.

The equation -0.3|3 + 8x| = 0.9 has no solution.

Lily begins solving the equation 4(x - 1) - x = 3(x + 5) - 11. Her work is shown below. 4(x - 1) - x = 3(x + 5) - 11 4x - 4 - x = 3x + 15 - 113x - 4 = 3x + 4 How can her partial solution be interpreted? The equation has one solution: x = 0. The equation has one solution: x = 8. The equation has no solution. The equation has infinite solutions.

The equation has no solution.

The graph represents a person's heart rate in beats per minute during 30 minutes of exercise. Which statement best describes the relationship between heart rate and time during exercise? The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually increases for 5 minutes. The heart rate decreases for 6 minutes, remains constant for 19 minutes, and then gradually increases for 5 minutes. The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes. The heart rate remains constant for 6 minutes, increases for 19 minutes, and then gradually decreases for 5 minutes.

The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes.

Which statement describes the graph of the system of equations below? 1.5x + 0.2y = 2.68 1.6x + 0.3y = 2.98 The lines are parallel. The lines overlap at all points. The lines intersect at (1.6,1.4). The lines intersect at (3.1,0.5).

The lines intersect at (1.6,1.4).

The system of equations is solved using the linear combination method. 1/2x+4y=8 → -2(1/2x+4y=8) → x-8y=-16 3x+24y=12 → 1/3(3x+24y=12) → x+8y=4 0=-12 What does 0 = −12 mean regarding the solution to the system? There are no solutions to the system because the equations represent parallel lines. There are no solutions to the system because the equations represent the same line. There are infinitely many solutions to the system because the equations represent parallel lines. There are infinitely many solutions to the system because the equations represent the same line.

There are no solutions to the system because the equations represent parallel lines.

A particular beach is eroding at a rate of 4 centimeters per year. A realtor converts this rate to millimeters per day. Which expression, when evaluated, results in the correct units and numerical value?

How many points need to be removed from this graph so that it will be a function? 1 point 2 points 3 points 4 points

3 points

Which explains why the graph is not a function? It is not a function because the points are not connected to each other. It is not a function because the points are not related by a single equation. It is not a function because there are two different x-values for a single y-value. It is not a function because there are two different y-values for a single x-value.

It is not a function because there are two different y-values for a single x-value.

Yana is in the school computer lab writing a paper for history class. The graph represents the number of words Yana has written after a number of minutes. Which situation could describe Yana's activities in the computer lab? Yana opened her saved paper, wrote, took a break, deleted some of the words, and then began writing again. Yana began writing a new paper, deleted some of her words, took a break, and then began writing again. Yana opened her saved paper, deleted some of her words, began writing, and then took a break. Yana began writing a new paper, took a break, and then deleted some of what she had written.

Yana opened her saved paper, wrote, took a break, deleted some of the words, and then began writing again.

Chen is bringing fruit and veggies to serve at an afternoon meeting. He spends a total of $28.70 on 5 pints of cut veggies and 7 pints of cut fruit. The food cost is modeled by the equation , where v represents the cost of one pint of cut veggies and f represents the cost of one pint of cut fruit. If the cost of each pint of fruit is $2.85, what is the approximate price of a pint of veggies? (Round to the nearest cent, as needed.) $1.75 $2.06 $2.39 $3.99

$1.75

The graph below shows the amount of money left in the school's desk fund, f, after d desks have been purchased. For each new desk that is purchased, by how much does the amount of money left in the school's desk fund decrease? $110 $135 $165 $190

$110

The graph shows the relationship between the total amount of money that Carly will have left, y, if she buys x packs of baseball cards. How much money will she have if she doesn't buy any packs of baseball cards? $16 $18 $19 $20

$20

The cost in dollars, y, of a large pizza with x toppings from Pat's Pizzeria can be modeled by a linear function. A large pizza with no toppings costs $14.00. A large pizza with 2 toppings costs $17.50. What is the cost of a pizza with 5 toppings? Round to the nearest penny. $19.00 $22.75 $43.75 $70.00

$22.75

What is the slope of the line represented by the equation y = -2/3 - 5x? -5 -2/3 2/3 5

-5

Representing Relationships, Unit Test

100%

Representing Relationships, Unit Test Review

100%

Which number can each term of the equation be multiplied by to eliminate the fractions before solving? 6 - 3/4x + 1/3 = 1/2 x + 5 2 3 6 12

What is the y-intercept of the function f(x)=4 - 5x? -5 -4 4 5

What value of x is in the solution set of 2x - 3 > 11 - 5x? -3 0 2 4

The table represents the function f(x). What is f(3)? -9 -1 1 9

Quantitative Reasoning

Pre-test / Quiz

Which statements are true about the linear inequality y > 3/4x - 2? Select three options. The slope of the line is -2. The graph of y > 3/4x - 2 is a dashed line. The area below the line is shaded. One solution to the inequality is (0, 0). The graph intercepts the y-axis at (0, -2).

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).

Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Which best describes why the graph relating the total amount of gasoline in the tank, y, to the number of gallons that she added to it, x, will be continuous or discrete?

The graph will be continuous because the amount of gas that she added to the tank does not need to be an integer amount.

Tim explained a function in words and Paul wrote an equation. Tim The amount of money in a savings account increases at a rate of $225 per month. After eight months, the bank account has $4,580 in it. Paul y−1,400=56(x+26) Whose function has the smaller y-intercept? Tim's with a y-intercept of $2,700 Paul's with a y-intercept of $2,856 Paul's with a y-intercept of $2,800 Tim's with a y-intercept of $2,780

Tim's with a y-intercept of $2,780

What is the solution to the linear equation? 4b + 6 = 2 - b + 4 b = -2 b = 0 b = 4 b = 6

b = 0

The graph below represents the distance a pilot is from the home airport during a period of time. Which describes the pilot's distance in section I? zero constant decreasing increasing

decreasing

Which linear function represents the line given by the point-slope equation y + 1 = -3(x - 5)? f(x) = -3x - 6 f(x) = -3x - 4 f(x) = -3x + 16 f(x) = -3x + 14

f(x) = -3x + 14

On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be 76.1°. He plans to use the function to convert this temperature from degrees Fahrenheit to degrees Celsius. What does C(76.1) represent? the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius the temperature of 76.1 degrees Celsius converted to degrees Fahrenheit the amount of time it takes a temperature of 76.1 degrees Fahrenheit to be converted to 32 degrees Celsius the amount of time it takes a temperature of 76.1 degrees Celsius to be converted to 32 degrees Fahrenheit

the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius

Solve for x. 5(x - 10) = 30 - 15x x = 1 x = 4 x = 5 x = 8

x = 4

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? positive zero negative undefined

zero

Which set of ordered pairs represents a function? {(2, -2), (1, 5), (-2, 2), (1, -3), (8, -1)} {(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)} {(6, 8), (5, 2), (-2, -5), (1, -3), (-2, 9)} {(-3, 1), (6, 3), (-3, 2), (-3, -3), (1, -1)}

{(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}

Consider the function represented by the graph. What is the domain of this function? {x|x≥0} {x|x≤8} {x|0≤x≤8} {x|x≤0x≥8}

{x|x≥0}

Which equation has no solution? |4x - 2| = -6 |-2 - x| = 9 |3x + 6| = 6 |-2x + 8| = 0

|4x - 2| = -6

Which equation has no solution? |-x - 3| = 5 |2x - 1| = 0 |5 - 3x| = -8 |-x + 9| = 0

|5 - 3x| = -8

Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee? (-3, -0.90) (-2.5, -0.75) (4.5, 1.35) (8, 2.40)

(8, 2.40)

How many inches are in 12 feet? 1 inch 24 inches 120 inches 144 inches

144 inches

Otto used 6 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y? y=6x; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 6. y=6x; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6. y=x+6; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 6. y=x+6; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6.

y=x+6; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6.

The table shows the profit from a school book fair based on the number of books sold.What is the rate of change for the function represented in the table? $0.50 per book $0.67 per book $1.07 per book $1.50 per book

$1.50 per book

A line contains points M(1, 3) and N(5, 0). What is the slope of MN? -4/3 -3/4 3/4 4/3

-3/4

Linear Functions Unit Test

96%

What is the solution to the system of equations? (5, 0) (0, 5) (0, -5) (-5, 0)

(0, -5)

Which is the best approximation for the solution of the system of equations? y = -2/5x + 1 y = 3x - 2 (0.45, 0.88) (0.88, 0.65) (0.88, 1.1) (1.3, 0.88)

(0.88, 0.65)

What is the solution to this system of linear equations? 2x + 3y = 3 7x - 3y = 24 (2, 7) (3, -21) (3, -1) (9, 0)

(3, -1)

2x + 4y = 12 y = 1/4x - 3 What is the solution to the system of equations? (-1, 8) (8, -1) (5, 1/2) (1/2, 5)

(8, -1)

Which sequences are geometric? Select three options. -2.7, -9, -30, -100, ... -1, 2.5, -6.25, 15.625, ... 9.1, 9.2, 9.3, 9.4, ... 8, 0.8, 0.08, 0.008, ... 4, -4, -12, -20, ...

-2.7, -9, -30, -100, ... -1, 2.5, -6.25, 15.625, ... 8, 0.8, 0.08, 0.008, ...

Which compound inequality is represented by the graph? -3 ≤ x < 1 -3 < x ≤ 1 x ≤ -3 or x > 1 x < -3 or x ≥ 1

-3 ≤ x < 1

Working together, Melissa and Jing can mow a lawn in 5 hours. It would take Melissa 8 hours to do the job alone. What is the value of r, the part of the lawn that Jing could complete in 1 hour? 0.075 0.125 0.375 0.625

0.075

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? 0.1n + 0.05(n - 175) = 13.30 0.1n + 0.05(175 - n) = 13.30 0.1(n - 175) + 0.05 = 13.30 0.1(175 - n) + 0.05n = 13.30

0.1(175 - n) + 0.05n = 13.30

The table shows the distance traveled over time while traveling at a constant speed. What is the rate of change in the y-values with respect to the x-values? minutes per meter minutes per meter 900 meters per minute 1,200 meters per minute

1,200 meters per minute

What is the common ratio between successive terms in the sequence? 27, 9, 3, 1, , , , ... -3 -1/3 1/3 3

1/3

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? 8 9 12 13

The graph shows the amount of money Miguel earns after working x hours. What is the rate of change of the amount earned with respect to hours worked for this function? 1/13 hours per dollar 2/5 hours per dollar 3 dollars per hour 13 dollars per hour

13 dollars per hour

The system of equations can be solved using linear combination to eliminate one of the variables. 2x − y = −4→10x − 5y = −203x + 5y = 59→3x + 5y = 59 13x = 39 Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution? 2x - y = -4 10x - 5y = -20 7x = 39 13x = 39

13x = 39

If f(x) = 2x2 + 1, what is f(x) when x = 3? 1 7 13 19

What is the value of x in the equation ? 1/3 1/2 2 13

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? 2 loaves of bread and 4 batches of muffins 3 loaves of bread and 3 batches of muffins 4 loaves of bread and 2 batches of muffins 5 loaves of bread and 1 batch of muffins

2 loaves of bread and 4 batches of muffins

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? 1,158 1,737 2,342 2,921

2,921

Melinda and Paula 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 Paula shoveled for 25 minutes to complete 345 square feet of driveway. 30x + 30y = 45020x + 25y = 345 How much more can Paula shovel in 1 minute than Melinda? 3 square feet per minute 6 square feet per minute 9 square feet per minute 15 square feet per minute

3 square feet per minute

What is the x-value in the solution to this system of linear equations? 2x − y = 11 x + 3y = −5 −3 −1 2 4

What is the value of m in the equation , when ? 20 32 44 48

Consider the equation 3p - 7 + p = 13. What is the resulting equation after the first step in the solution? p - 7 = 13 - 3p 2p - 7 = 13 3p - 7 = 13 - p 4p - 7 = 13

4p - 7 = 13

Which equation has no solution? 4(x + 3) + 2x = 6(x + 2) 5 + 2(3 + 2x) = x + 3(x + 1) 5(x + 3) + x = 4(x + 3) + 3 4 + 6(2 + x) = 2(3x + 8)

5 + 2(3 + 2x) = x + 3(x + 1)

A restaurant freezes a cherry and lime juice mixture to create slushes. Cherry juice costs $5 per quart, and lime juice costs $3 per quart. Each day, the restaurant spends a total of $36 on 8 quarts of juice. The restaurant manager organizes the information in the table below. Which equation can be used to determine the amount of cherry juice in each mixture? 5q + 3(8 - q) = 36 5q + 3(8 - q) = 8 q + (8 - q) = 8 q + 5 = 5q

5q + 3(8 - q) = 36

A sequence is defined by the recursive function f(n + 1) = f(n) - 2. If f(1) = 10, what is f(3)? 1 6 8 30

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? 3 4 5 6

Which equation can be used to represent "six added to twice the sum of a number and four is equal to one-half of the difference of three and the number"? 6 + 2(x + 4) = 1/2(3 - x) 6 + 2(x + 4) = 1/2(x - 3) (6 + 2)(x + 4) = 1/2(3 - x) (6 + 2)(x + 4) = 1/2(x - 3)

6 + 2(x + 4) = 1/2(3 - x)

A sequence is defined recursively using the formula f(n+1)=-0.5f(n). If the first term of the sequence is 120, what is f(5)? −15 −7.5 7.5 15

7.5

To support a shelf, the diameter of a bolt can measure anywhere from 0.2 cm less than 1.5 cm to 0.2 cm greater than 1.5 cm. Which graph represents the possible measures of the diameter of the bolt?

Which graph matches the equation y+3=2(x+3)?

Which are correct representations of the inequality 6x ≥ 3 + 4(2x - 1)? Select three options. 1 ≥ 2x 6x ≥ 3 + 8x - 4

A B C

Which functions have an additive rate of change of 3? Select two options.

A E

Which scenario can be modeled using the graph below? A temperature range is within 5 degrees of 60 degrees Fahrenheit. A scientist uses more than 55 and less than 65 mL of water in an experiment. A commuter train takes less than 55 minutes or more than 65 minutes to complete one route. A worker makes greater than $55 per day but less than $65 per day.

A temperature range is within 5 degrees of 60 degrees Fahrenheit.

Which statement is true about the end behavior of the graphed function? As the x-values go to positive infinity, the function's values go to negative infinity. As the x-values go to zero, the function's values go to positive infinity. As the x-values go to negative infinity, the function's values are equal to zero. As the x-values go to positive infinity, the function's values go to positive infinity.

As the x-values go to positive infinity, the function's values go to negative infinity.

Which statement is true about the end behavior of the graphed function? As the x-values go to positive infinity, the function's values go to negative infinity. As the x-values go to zero, the function's values go to positive infinity. As the x-values go to negative infinity, the function's values are equal to zero As the x-values go to positive infinity, the function's values go to positive infinity.

As the x-values go to positive infinity, the function's values go to positive infinity.

The goals against average (A) for a professional hockey goalie is determined using the formula A = 60 (g/t). In the formula, g represents the number of goals scored against the goalie and t represents the time played, in minutes. Which is an equivalent equation solved for g? At/60 = g A/60t = g 60A/t = g 60At = g

At/60 = g

Consider the function represented by 9x+3y=12 with x as the independent variable. How can this function be written using function notation?

The amount of potential energy, P, an object has is equal to the product of its mass, m, its height off the ground, h, and the gravitational constant, g. This can be modeled by the equation P = mgh. What is the equivalent equation solved for h?

Which graph could represent y, the amount owed on a car loan, as regular payments are made each month, x?

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? One landscaper charges $20 for 5 hours of work. One landscaper's hourly rate is $15 lower than the other landscaper's. Both landscapers charge the same hourly rate and the same fee per job. Both landscapers charge the same hourly rate, but not the same fee per job.

Both landscapers charge the same hourly rate, but not the same fee per job.

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?

Eli left his house one afternoon to study at the library. The graph shows his distance, in miles, away from his house as a function of time, in minutes. What could explain what happened when the time was equal to 120 minutes? Eli arrived at the library. Eli rode his bicycle home from the library. Eli rode his bicycle to the store, getting farther away from his house. Eli continued to study at the library for 13 more minutes.

Eli rode his bicycle home from the library.

Marty and Ethan both wrote a function, but in different ways. Marty Ethan Whose function has the larger slope? Marty's with a slope of 2/3 Ethan's with a slope of 2/5 Marty's with a slope of 1/3 Ethan's with a slope of 1/5

Marty's with a slope of 1/3

Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.Whose plant grew at a faster rate, and what was the rate? Suzanne's at 2 inches per week Suzanne's at 1.5 inches per week Megan's at 3 inches per week Megan's at 2.5 inches per week

Megan's at 2.5 inches per week

Which statement is true about the local minimum of the graphed function? Over the interval [-4, -2], the local minimum is 0. Over the interval [-2, -1], the local minimum is 25. Over the interval [-1, 4], the local minimum is 0. Over the interval [4, 7], the local minimum is -7.

Over the interval [4, 7], the local minimum is -7.

Introduction to Compound Inequalities

Pre-test / Quiz

Introduction to Functions

Pre-test / Quiz

Introduction to Linear Functions

Pre-test / Quiz

Heather writes the equations below to represent two lines drawn on the coordinate plane. -6x + 18y = 0 4x - 12y = 20 After applying the linear combination method, Heather arrived at the equation 0 = 60. What conclusion can be drawn about the system of equations? The equation has no solution; therefore, the system of equations has no solution. The equation has a solution at (0, 60); therefore, the system of equations has a solution at (0, 60). The equation has infinite solutions; therefore, the system of equation as infinite solutions. The equation has a solution at (0, 0); therefore, the system of equations has a solution at (0, 0).

The equation has no solution; therefore, the system of equations has no solution.

What is the slope of the line represented by the equation f(t)=2t−6? The slope is 2 and the y-intercept is −6. The slope is −6 and the y-intercept is 2. The slope is 2 and the y-intercept is 6. The slope is 6 and the y-intercept is 2.

The slope is 2 and the y-intercept is −6.

Which is true about the solution to the system of inequalities shown? y > 3x + 1 y < 3x - 3 Only values that satisfy y > 3x + 1 are solutions. Only values that satisfy y < 3x - 3 are solutions. Values that satisfy either y > 3x + 1 or y < 3x - 3 are solutions. There are no solutions.

There are no solutions.

Which interval for the graphed function contains the local maximum? [-3, -2] [-2, 0] [0, 2] [2, 4]

[0, 2]

What is the domain of the function on the graph? all real numbers all real numbers greater than or equal to 0 all real numbers greater than or equal to -2 all real numbers greater than or equal to -3

all real numbers greater than or equal to -3

Livia eats a chicken drumstick with 11 grams of protein. She also eats x cheese sticks, each with 7 grams of protein. The table shows y , the total number of grams of protein that Livia will consume if she eats x cheese sticks. What is the range of the function?

all real numbers greater than or equal to 11

What is the range of the function on the graph? all real numbers all real numbers less than or equal to -1 all real numbers less than or equal to 3 all real numbers less than or equal to 0

all real numbers less than or equal to 3

What is the range of the function on the graph? all the real numbers all the real numbers greater than or equal to 0 all the real numbers greater than or equal to 2 all the real numbers greater than or equal to -3

all the real numbers greater than or equal to -3

Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108.00. Which linear function represents c, the total cost, when x tickets are ordered? c(x) = 5.50 + 20.50x c(x) = 5.50x + 20.50 c(x) = 5.50 + 21.60x c(x) = 5.50x + 21.60

c(x) = 5.50 + 20.50x

Which statement is true regarding the graphed functions? f(4) = g(4) f(4) = g(-2) f(2) = g(-2) f(-2) = g(-2)

f(-2) = g(-2)

Which statement is true regarding the graphed functions? f(0) = g(0) f(-2) = g(-2) f(0) = g(-2) f(-2) = g(0)

f(0) = g(0)

If point (4, 5) is on the graph of a function, which equation must be true? f(5)=4 f(5,4)=9 f(4)=5 f(5,4)=1

f(4)=5

How many solutions exist for the given equation? 12x + 1 = 3(4x + 1) - 2 zero one two infinitely many

infinitely many

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. Which equation can be used to represent k, the number of kilometers Julissa runs in t minutes? k - 2 = 1/9(t - 18) k - 18 = 1/9(t - 2) k - 2 = 9(t - 18) k - 18 = 9(t - 2)

k - 2 = 1/9(t - 18)

Solve for k. 8k + 2m = 3m + k k = 70m k = 7m k = 7/m k = m/7

k = m/7

Solve for w. 5w + 9z = 2z + 3w w=-7/2z w = -2/7z w = -2z w = -7z

w=-7/2z

Solve the inequality. 2(4x - 3) ≥ -3(3x) + 5x? x ≥ 0.5 x ≥ 2 (-∞, 0.5] (-∞, 2]

x ≥ 0.5

Which linear inequality is represented by the graph? y > 2/3x - 2 y < 2/3x + 2 y > 2/3x + 1 y < 2/3x - 1

y < 2/3x - 1

Which linear inequality is represented by the graph? y < 2/3x + 3 y > 3/2x + 3 y > 2/3x + 3 y < 3/2x + 3

y > 2/3x + 3

Which system of linear inequalities is represented by the graph? y > x - 2 and y < x + 1 y < x - 2 and y > x + 1 y < x - 2 and y > x + 1 y > x - 2 and y < x + 1

y > x - 2 and y < x + 1

Which equation has only one solution? |x - 5| = -1 |-6 - 2x| = 8 |5x + 10| = 10 |-6x + 3| = 0

|-6x + 3| = 0

Kari and Samantha have determined that their water-balloon launcher works best when they launch the balloon at an angle within 3 degrees of 45 degrees. Which equation can be used to determine the minimum and maximum optimal angles of launch, and what is the minimum angle that is still optimal? |x - 3| = 45; minimum angle: 42 degrees |x - 3| = 45; minimum angle: 45 degrees |x - 45| = 3; minimum angle: 42 degrees |x - 45| = 3; minimum angle: 45 degrees

|x - 45| = 3; minimum angle: 42 degrees

Which situation could be represented by the graph? Students in the children's choir are at least 8 years old but no more than 11 years old. Babysitters earn between $8 and $11 per hour. A program at a community college can be completed in no fewer than 8 months, but must be completed in less than 11 months. The dogs at a veterinary clinic are all 8 years old or under or are older than 11 years.

A program at a community college can be completed in no fewer than 8 months, but must be completed in less than 11 months.

Fiona and her friends went to a smoothie shop. They ordered three strawberry smoothies and two protein shakes for a total of $24.00. Last week they ordered one strawberry smoothie and four protein shakes for a total of $25.50. The system that represents their purchases is below. x + 4y = 25.50 3x + 2y = 24.00 What is the price of a protein shake? $3.75 $4.50 $4.95 $5.25

$5.25

Working together, Katherine and Marina can sand a large cabinet in 2 hours. It would take Katherine 10 hours to do the job alone. What is the value of r, the part of the job that Marina can complete in 1 hour? 0.1 0.4 0.5 0.6

0.4

Which sequence is generated by the function f(n + 1) = f(n) - 2 for f(1) = 10? -10, -12, -14, -16, -18, ... -2, 8, 18, 28, 38, ... 8, 18, 28, 38, 48, ... 10, 8, 6, 4, 2, ...

10, 8, 6, 4, 2, ...

Linear Equations and Inequalities, Unit Test

100%

Bob has some 10 lb weights and some 3 lb weights. Together, all his weights add up to 50 lb. If x represents the number of 3 lb weights and y represents the number of 10 lb weights, which equation can be used to find the number of each type of weight Bob has? 3x - 10y = 50 3x = 50 - 10y 50 + 10y = 3y 50 + 3y = 10y

3x = 50 - 10y

What is the value of s in the equation , when ? 4 8 100 200

Which number can each term of the equation be multiplied by to eliminate the fractions before solving? -3/4m - 1/2 = 2 + 1/4m 2 3 4 5

What is the slope of the line whose equation is y−4=5/2(x−2)? -5/2 -2/5 2/5 5/2

5/2

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? 5/8 + 5r = 8 5/8 + 5r = 1 5(5/8) = r 5/8 = 5r

5/8 + 5r = 1

What is the local maximum over the interval [-3, 1.5] for the graphed function? 0 56 -11.4 2

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? 6 7 8 9

It takes 5 minutes to fill the sink using only the cold water. If both the hot water and the cold water are turned on, it takes 2 minutes to fill the sink. Which is the correct table that can be used to determine x, the time in minutes it takes to fill the sink using only the hot water?

Which graph shows the solution to the system of linear inequalities? x + 3y > 6 y ≥ 2x + 4

Analyzing Graphs

Pre-test / Quiz

Which graph shows a set of ordered pairs that represent a function?

SEE IMAGE

The graph shows the relationship between the total cost and the number of erasers bought at the student store. Which statement is true? Each eraser costs $1.00. Each eraser costs $1.50. Three erasers cost $6. Seven erasers cost $3.50.

Seven erasers cost $3.50.

Which best describes the relationship between the successive terms in the sequence shown? 2.4, -4.8, 9.6, -19.2 The common difference is -7.2. The common difference is -2.4. The common ratio is -2.0. The common ratio is -0.5.

The common ratio is -2.0.

What is the range of the function on the graph?

all the real numbers greater than or equal to -3

What is the solution to the linear equation? d - 10 - 2d + 7 = 8 + d - 10 - 3d d = -5 d = -1 d = 1 d = 5

d = 1

What is the inverse of the function f(x) = 1/4x - 12? h(x) = 48x - 4 h(x) = 48x + 4 h(x) = 4x - 48 h(x) = 4x + 48

h(x) = 4x + 48

Fiona wrote the linear equation y = 2/5x - 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 - y = x - y = x - y = x - y =

x - 5/2y = 25/2

Which compound inequality is represented by the graph? -2 < x ≤ 4 -2 ≤ x < 4 x < -2 or x ≥ 4 x ≤ -2 or x > 4

x < -2 or x ≥ 4

What is the value of x in the equation 2(x−3)+9=3(x+1)+x? x = −3 x = −1 x = 0 x = 3

x = 0

Solve the equation. 8 - 2x = -8x + 14 x = -1 x = -3/5 x = 3/5 x = 1

x = 1

The tables represent the functions f(x) and g(x). Which input value produces the same output value for the two functions? x = -3 x = -1 x = 0 x = 1

x = 1

Which expression can be used to convert 22 Australian dollars to US dollars? Assume 1.2 Australian dollars equals 1 US dollar. $22 AUD $22 AUD $1.20 AUD $1.20 AUD

Malik's solution to the equation , when , is shown below. What error did Malik make first when solving the equation ? Malik did not multiply correctly. Malik added 240 to each side of the equation. Malik did not multiply correctly. Malik substituted 60 for y instead of x.

Malik substituted 60 for y instead of x.

The graph will be discrete because there is no such thing as a partial person to sign up and the booth is set up once each day for sign ups.

Peaches are being sold for $2 per pound.The customer created a model to represent the total cost of peaches bought. If x represents the number of pounds of peaches bought and y represents the total cost of the peaches, which best describes the values of x and y? The values of both x and y can be any real number. The values of both x and y will be real numbers greater than or equal to 0. The value of x and y will always be zero The value of x can be any real number greater than or equal to 0, but the value of y must be an integer greater than or equal to 0.

The values of both x and y will be real numbers greater than or equal to 0.

What is the range of the function on the graph? all real numbers all real numbers greater than or equal to 0 all real numbers greater than or equal to 1 all real numbers greater than or equal to 2

all real numbers greater than or equal to 2

Raj's bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining. What is the range of this function? all real numbers such that y ≤ 40 all real numbers such that y ≥ 0 all real numbers such that 0 ≤ y ≤ 40 all real numbers such that 37.75 ≤ y ≤ 40

all real numbers such that 0 ≤ y ≤ 40

Diep bought a baguette loaf of bread 65 centimeters long. For lunch every afternoon, he cuts 15 centimeters of bread for his sandwich. Diep wants to determine the length of the loaf of bread, l, after d days. What is the equation of the scenario? Is the graph of the equation continuous or discrete?

l = 65 - 15d; discrete

What is the domain of the given function? {(3, -2), (6, 1), (-1, 4), (5, 9), (-4, 0)} {x | x = -4, -1, 3, 5, 6} {y | y = -2, 0, 1, 4, 9} {x | x = -4, -2, -1, 0, 1, 3, 4, 5, 6, 9} {y | y = -4, -2, -1, 0, 1, 3, 4, 5, 6, 9}

{x | x = -4, -1, 3, 5, 6}

The solution is n = -2 verified as a solution to the equation 1.4n + 2 = 2n + 3.2. What is the last line of the justification? 0.8 = 0.8 -0.8 = -0.8 3 = 3 -3 = -3

-0.8 = -0.8

A sequence is defined recursively by the formula f(n + 1) = f(n) + 3 . The first term of the sequence is -4. What is the next term in the sequence? -7 -1 1 7

-1

What is the slope of the line with equation y−3=-1/2(x−2)? -2 -1/2 1/2 2

-1/2

What value of x is in the solution set of 9(2x + 1) < 9x - 18? -4 -3 -2 -1

-4

What value of b will cause the system to have an infinite number of solutions? y = 6x + b -3x + 1/2y = - 3 -6 -3 3 6

-6

What is the common difference between successive terms in the sequence? 9, 2.5, -4, -10.5, -17, ... -11.5 -6.5 6.5 11.5

-6.5

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? -6x + y = 3/2 6x + y = 3/2 -6x + 2y = 3/2 6x + 2y = 3/2

-6x + 2y = 3/2

The table shows ordered pairs of the function . What is the value of y when ? -20 -8 8 48

-8

The table shows ordered pairs of the function y = 8 - 2x. When x = 8, the value of y is

-8

The graph shows the relationship between the number of minutes Maria spent jogging on a treadmill and the distance she jogged. What was her speed? 0.1 mile per minute 0.5 mile per minute 5 miles per minute 10 miles per minute

0.1 mile per minute

To fit in an existing frame, the length, x, of a piece of glass must be longer than 12 cm but not longer than 12.2 cm. Which inequality can be used to represent the lengths of the glass that will fit in the frame? 12 < x ≤ 12.2 12 > x ≤ 12.2 x > 12 or x ≤ 12.2 x < 12 or x ≤ 12.2

12 < x ≤ 12.2

The function f(x) is shown on the graph. What is f(0)? 12 only 2 and 3 only -2, -1, 1, and 2 only -2, -1, 1, 2 and 12

12 only

The formula to convert °F to °C is C = (F - 32). Convert 50°C to °F. 10°F 20°F 122°F 132°F

122°F

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? 4 5 14 15

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? 15 minutes 18 minutes 38 minutes 75 minutes

18 minutes

The volume, V, of a rectangular prism is determined using the formula V=lwh, where l is the length, w is the width, and h is the height of the prism. 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? Round to the nearest tenth. 0.2 inches 4.5 inches 46.1 inches 414.7 inches

4.5 inches

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? 4r 4/6 6r 6/4

4/6

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? 50 ≤ x ≤ 58 x ≥ 50 or x ≤ 58 x ≥ 52 or x ≤ 56 52 ≤ x ≤ 56

50 ≤ x ≤ 58

Lola needs to sign 96 invitations. Using a stopwatch that measures time to tenths of a second, it takes Lola 5.3 seconds to sign her full name. Going by the accuracy of the stopwatch, which is the most accurate determination for the number of seconds Lola needs to sign all 96 invitations? 508 seconds 510 seconds 509 seconds 508.8 seconds

508.8 seconds

The sum of the interior angles, s, in an n-sided polygon can be determined using the formula s=180(n−2), where n is the number of sides. Using this formula, how many sides does a polygon have if the sum of the interior angles is 1,260°? Round to the nearest whole number. 6 sides 7 sides 8 sides 9 sides

9 sides

The velocity of an object in meters per second varies directly with time in seconds since the object was dropped, as represented by the table.The acceleration due to gravity is the constant of variation. What is the acceleration due to gravity of a falling object? 4.9 m/s2 9.8 m/s2 10.2 m/s2 19.6 m/s2

9.8 m/s2

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 area of land mowed 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? It takes Aaron about 1 hour to mow 2 acres. Aaron's rate for mowing lawns is 0.5 acres per hour. The ratio of acres to time is 5 acres to 3 hours. The rate to mow a lawn is 0.6 hours per acre.

Aaron's rate for mowing lawns is 0.5 acres per hour.

Which graph shows the solution to the system of linear inequalities? x + 5y > 5 y < 2x + 4

The graph shows the relationship between the number of hours that Michelle has been driving and the distance that she has left to travel to get to her destination. Which statement is true? It took Michelle 6 hours to complete the trip. For each hour that Michelle drove, she traveled an additional 50 miles. In the first 6 hours, Michelle had traveled a total of 50 miles. In the first 3 hours, Michelle had traveled a total of 200 miles.

For each hour that Michelle drove, she traveled an additional 50 miles.

The graph shows the speed of Sam's car over time. Which best describes what is happening in section C? His car is stopped. His car is speeding up. His car is slowing down. His car is traveling at a constant speed.

His car is slowing down.

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? 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. It is linear because the function is continuous. It is nonlinear because the final cost is determined by multiplying each price tag by 0.75. It is nonlinear because the price tag and final cost columns do not have the same common difference.

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.

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? It is linear because the graph decreases over time. It is linear because there is both an independent and a dependent variable. It is nonlinear because linear functions are increasing functions. It is nonlinear because linear functions increase or decrease at the same rate.

It is nonlinear because linear functions increase or decrease at the same rate.

Kate begins solving the equation (6x - 3) = (6x - 4). Her work is correct and is shown below. (6x - 3) = (6x - 4)4x - 2 = 3x - 2 When she adds 2 to both sides, the equation 4x = 3x results. Which solution will best illustrate what happens to x ? The equation has infinite solutions. The equation has one solution: x = 0. The equation has one solution: x = . The equation has no solution.

The equation has one solution: x = 0.

To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? First equation: 4x − 3y = 34 Second equation: 3x + 2y = 17 The first equation should be multiplied by 2 and the second equation by 3. The first equation should be multiplied by 2 and the second equation by −3. The first equation should be multiplied by 3 and the second equation by 4. The first equation should be multiplied by 3 and the second equation by −4.

The first equation should be multiplied by 2 and the second equation by 3.

To eliminate the x terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? First equation: 6x - 5y = 17 Second equation: 7x + 3y = 11 The first equation should be multiplied by 3 and the second equation by -5. The first equation should be multiplied by 3 and the second equation by 5. The first equation should be multiplied by 7 and the second equation by -6. The first equation should be multiplied by 7 and the second equation by 6.

The first equation should be multiplied by 7 and the second equation by -6.

Karl has stamps in his desk drawer. The possible combinations of stamps are shown below. Which statement about the stamps is correct? The total number of stamps is 25. The total value of the stamps is $18.75. The total number of stamps is 35. The total value of the stamps is $19.15.

The total number of stamps is 35.

Which interval contains a local minimum for the graphed function? [-4, -2.5] [-2, -1] [1, 2] [2.5, 4]

[2.5, 4]

Mrs. Jackson gives the table below to her students. In order for the function to be linear, what must a be and why? a = 22 because the rate of change is 1. a = 20 because the rate of change is 3. a = 22 because the rate of change is -1. a = 20 because the rate of change is -3.

a = 20 because the rate of change is -3.

The formula for the area of a rhombus is A = 1/2d1d2, where d1 and d2 are the lengths of the diagonals. Which are equivalent equations? Select two correct answers. d1 = 2Ad2 d1 = 2A/d2 d2 = d1/2A d2 = 2A/d1 d2 = 2Ad1

d1 = 2A/d2 d2 = 2A/d1

An electrician earns $110 after his first hour of working for a client. His total pay based on the number of hours worked can be represented using the sequence shown. 110, 130, 150, 170, ... Which recursive formula can be used to determine the total amount of money earned for each successive hour worked based on the amount of money currently earned? f(n + 1) = f(n) + 20 f(n + 1) = f(n) + 110 f(n + 1) = f(n + 1) + 20 f(n + 1) = f(n + 1) + 110

f(n + 1) = f(n) + 20

For one month Siera calculated her home town's average high temperature in degrees Fahrenheit. She wants to convert that temperature from degrees Fahrenheit to degrees Celsius using the function . What does C(F) represent? the temperature of F degrees Fahrenheit converted to degrees Celsius the temperature of F degrees Celsius converted to degrees Fahrenheit the temperature of C degrees Fahrenheit converted to degrees Celsius the temperature of C degrees Celsius converted to degrees Fahrenheit

the temperature of F degrees Fahrenheit converted to degrees Celsius

The solution to the system of equations shown is (2, 0). 3x − 2y = 6 x + 4y = 2 When the first equation is multiplied by 2, the sum of the two equations is equivalent to 7x = 14. Which system of equations will also have a solution of (2, 0)? 6x - 4y = 6 x + 4y = 2 6x − 4y = 6 2x + 8y = 2 x + 4y = 2 7x = 14 6x − 4y = 6 7x = 14

x + 4y = 2 7x = 14

The point-slope form of the equation of the line that passes through (-4, -3) and (12, 1) is y - 1 = 1/4(x - 12). What is the standard form of the equation for this line? x - 4y = 8 x - 4y = 2 4x - y = 8 4x - y = 2

x - 4y = 8

Which equation represents the graphed function? y = -2x + 3 y = 2x + 3 y = 1/2x + 3 y = -1/2x + 3

y = -2x + 3

A system of equations has 1 solution. If 4x - y = 5 is one of the equations, which could be the other equation? y = -4x + 5 y = 4x - 5 2y = 8x - 10 -2y = -8x - 10

y = -4x + 5

A line that passes through the points (-4, 10) and (-1, 5) can be represented by the equation y = (x - 2). Which equations also represent this line? Select three options. y = -5/3x - 2 y = -5/3x + 10/3 3y = -5x + 10 3x + 15y = 30 5x + 3y = 10

y = -5/3x + 10/3 3y = -5x + 10 5x + 3y = 10

The point-slope form of the equation of the line that passes through (-9, -2) and (1, 3) is y - 3 = (x - 1). What is the slope-intercept form of the equation for this line? y = 1/2 x + 2 y = 1/2 x - 4 y = 1/2 x + 5/2 y = 1/2 x - 7/2

y = 1/2 x + 5/2

Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD? y = 2x - 2 y = 2x + 2 y = x + 2 y = x - 2

y = x + 2

A direct variation function contains the points (-9, -3) and (-12, -4). Which equation represents the function? y = -3x y = -x/3 y = x/3 y = 3x

y = x/3

The table shows the total distance that Myra runs over different time periods. Which describes Myra's distance as time increases?

increasing

Vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete. What is the equation that can be used to find the value of y, the total time that Vlad spent on his homework, and what are the constraints on the values of x and y? y=2x+20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20. y=2x+20; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20. y=20x+2; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20. y=20x +2; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.

y=2x+20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.

Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Which equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x? y=4+x y = x − 4 y = 4 · x y = x ÷ 4

y=4+x

The graph shows the relationship between the total cost and the number of gift cards that Raj bought for raffle prizes. What would be the cost for 5 of the gift cards? $80 $90 $100 $110

$100

The tables represent two linear functions in a system. What is the solution to this system? (1, 0) (1, 6) (8, 26) (8, -22)

(8, -22)

What is the slope of the line represented by the equation y = -1/2x + 1/4 ? -1/2 -1/4 1/4 1/2

-1/2

Which number completes the system of linear inequalities represented by the graph? y > 2x - 2 and x + 4y > -12 -3 4 6

-12

Two systems of equations are shown. The first equation in system B is the original equation in system A. The second equation in system B is the sum of that equation and a multiple of the second equation in system A. 1/2x + 3y = 11 → 1/2x + 3y = 11 5x - y = 17 → 15x - 3y = 51 15 1/2x = 62 B. 1/2x + 3y = 11 15 1/2x = 62 What is the solution to both systems A and B? (3, 4) (3, 5) (4, 3) (5, 3)

(4, 3)

What is the solution to the system of equations? y = 1/3x - 10 2x + y = 4 (-8, 6) (-6, 16) (6, -8) (16, -6)

(6, -8)

What is the solution to this system of linear equations? 3x - 2y = 14 5x + y = 32 (3, 5) (6, 2) (8, -1) (14, -18)

(6, 2)

Analyze the graph of the function f(x) to complete the statement. f(x)<0 over (-, -3)and what other interval? (-2.4, -1.1) (-3,-1.1) (-1.1, 2) (-1.1, 0.9)

(-1.1, 0.9)

Which ordered pair makes both inequalities true? y < -x + 1 y > x (-3, 5) (-2, 2) (-1, -3) (0, -1)

(-2, 2)

Which lists all of the y-intercepts of the graphed function? (0, -3) (-1, 0) and (3, 0) (0, -1) and (0, 3) (-1, 0), (3, 0), and (0, -3)

(0, -3)

What is the solution to this system of linear equations? 7x - 2y = -6 8x + y = 3 (-6, 3) (0, 3) (1, -5) (15, -1)

(0, 3)

Which ordered pair is a solution to the system of linear equations? 2x + 3y= 6 -3x + 5y = 10 (0,2) (2,0) (3,2) (2,3)

(0,2)

The graph represents the cost of a subscription to a newspaper.What is the constant of variation for the subscription cost based on the number of weeks? $1.50 $7.50 $15.00 $30.00

$7.50

The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options. $8 $9 $11 $13 $14

$8 $14

What value of x is in the solution set of 4x - 12 ≤ 16 + 8x? -10 -9 -8 -7

-7

Mike and Jamal are 9 miles apart, and are planning to meet up. Mike is walking at an average speed of 3 miles per hour to meet Jamal. Jamal is driving at an average speed of 25 miles per hour to meet Mike. Which equation can be used to find t, the time it takes for Mike and Jamal to meet? 25t - 3t = 0 25t - 3t = 9 25t + 3t = 1 25t + 3t = 9

25t + 3t = 9

The point-slope form of the equation of the line that passes through (-5, -1) and (10, -7) is . What is the standard form of the equation for this line? 2x - 5y = -15 2x - 5y = -17 2x + 5y = -15 2x + 5y = -17

2x + 5y = -15

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? 5t + 4t = 1 5t + 4t = 3 5t - 4t = 0 5t - 4t = 3

5t + 4t = 3

At a grocery store, blueberries come packaged in 8-ounce containers for $2.80. At a farmer's market, blueberries cost $4.20 for 14 ounces. There are 16 ounces in one pound. Which statement accurately compares the cost of blueberries? Blueberries are $0.23 per pound more expensive at the farmer's market. Blueberries are $0.50 per pound less expensive at the farmer's market. Blueberries are $0.80 per pound less expensive at the farmer's market. Blueberries are $1.40 per pound more expensive at the farmer's market.

Blueberries are $0.80 per pound less expensive at the farmer's market.

Which graph represents a function with direct variation?

Which number line represents the solutions to -2|x| = -6?

Point-Slope Form of a Line

Pre-test / Quiz

Recognizing Patterns

Pre-test / Quiz

Slope of a Line

Pre-test / Quiz

Which graph shows a set of ordered pairs that represents a function?

SEE IMAGE

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? She is correct, because both solutions satisfy the equation. She is not correct, because she made a sign error. She is not correct, because there are no solutions. She is not correct, because there is only one solution: x = 3.5.

She is not correct, because there are no solutions.

The graphs below show measurements from cubes with different side lengths. Which pairs of variables have a linear relationship? Select two options. side length and perimeter of 1 face perimeter of 1 face and area of 1 face surface area and volume area of 1 face and surface area side length and volume

side length and perimeter of 1 face area of 1 face and surface area

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? u = 0.25 u = 0.75 u = 1.1 u = 2.5

u = 2.5

What is the range of the given function? {x | x = -5, 1, 4, 6} {y | y = -7, -1, 0, 9} {x | x = -7, -5, -1, 0, 1, 4, 6, 9} {y | y = -7, -5, -1, 0, 1, 4, 6, 9}

{y | y = -7, -1, 0, 9}

What is the lowest value of the range of the function shown on the graph? - -2 0 3

-2

While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent. 1 European euro = 1.3687 US dollars 44.70 US dollars 73.06 US dollars 136.87 US dollars 140.41 US dollars

44.70 US dollars

The acceleration of an object due to gravity is 32 feet per second squared. What is acceleration due to gravity in inches per second squared?

384 inches per second squared

Jackrabbits are capable of reaching speeds up to 40 miles per hour. How fast is this in feet per second? (Round to the nearest whole number.) 5,280 feet = 1 mile 27 feet per second 59 feet per second 132 feet per second 288 feet per second

59 feet per second

Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number of bottles she needs to sell to earn $100. 1.25x + 1.49 = 100 What error did Barbara make in writing the equation? Barbara's equation did not consider the number of bottles of water. Barbara's equation did not consider the number of bottles of iced tea. Barbara's equation did not use the correct price for the bottles of iced tea. Barbara's equation did not use the correct total for sales.

Barbara's equation did not consider the number of bottles of iced tea.

Katrina drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she drinks in a week? There are 16 cups in a gallon.

Alina is able to swim at a rate of about 2.5 miles per hour. Talia is able to swim at a rate of 1.8 meters per second. Which statement comparing the two swimmers is accurate? 1 mile 1,609 meters Alina swims about 0.7 miles per hour faster than Talia. Talia swims about 0.7 miles per hour faster than Alina. Alina swims about 1.5 miles per hour faster than Talia. Talia swims about 1.5 miles per hour faster than Alina.

Talia swims about 1.5 miles per hour faster than Alina.

The graph below represents the distance of a dog from a trainer after a command is given. Which statement could describe the dog's movement 5 seconds after the command was given? The dog stopped to lie down and obey the trainer's command. The dog was running towards the trainer to receive a treat. The dog was running away from the trainer to chase a squirrel. The dog was stopped but began running towards the trainer.

The dog was running towards the trainer to receive a treat.

The table shows the height of the tree that Margo planted over an 11-month period. Which statement can be supported by the information in the table? The tree increased in height each month during the entire 11-month period. The tree decreased in height each month during the entire 11-month period. The tree increased in height each month until the time period between month 9 and month 11. The tree decreased in height each month until the time period between month 9 and month 11.

The tree increased in height each month until the time period between month 9 and month 11.

The graph below represents the distance a pilot is from the home airport during a period of time. Which describes the pilot's distance in section I?

decreasing

Which scenario is most likely the one shown on the graph? the total amount of money in the cash register, y, containing $50 in change and small bills and x $100 bills the total number of puzzle pieces, y, in a brand new 50-piece puzzle, and x brand-new 100-piece puzzles the total weight of the barbell, y, where the bar weighs 50 pounds and x 100-pound weights are added to it the total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce

the total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce

Sonji paid $25 for two scarves, which were different prices. When she got home she could not find the receipt. She remembered that one scarf cost $3 more than the other. What was the price of the more expensive scarf? $11 $12 $13 $14

$14

Raphael graphed the system of equations shown. y = - 3 y = x - 0.8 What is the best approximation for the solution to this system of equations? (-3.2, -3) (-2.9, -3) (-2.2, -3) (-1.9, -3)

(-2.2, -3)

Which is the approximate solution to the system y = 0.5x + 3.5 and y = −2/3x + 1/3 shown on the graph? (-2.7, 2.1) (-2.1, 2.7) (2.1, 2.7) (2.7, 2.1)

(-2.7, 2.1)

Which ordered pairs are in the solution set of the system of linear inequalities? y > -1/3 x + 2 y < 2x + 3 (2, 2), (3, 1), (4, 2) (2, 2), (3, -1), (4, 1) (2, 2), (1, -2), (0, 2) (2, 2), (1, 2), (2, 0)

(2, 2), (3, 1), (4, 2)

Billy graphed the system of linear equations to find an approximate solution. y = -7/4x + 5/2 y = 3/4x - 3 Which points are possible approximations for this system? Select two options. (1.9, 2.5) (2.2, -1.4) (2.2, -1.35) (1.9, 2,2) (1.9, 1.5)

(2.2, -1.4) (2.2, -1.35)

The solutions to the inequality y ≤ 2x − 4 are shaded on the graph. Which point is a solution? (−1, 1) (1, −1) (3, 2) (2, 3)

(3, 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? (7, 3) (0, 7) (7, 0) (3, 7)

(7, 0)

Two linear equations are shown. What is the solution to the system of equations? (7, 4) (7, 13/3) (8, 14/3) (9, 7)

(7, 13/3)

Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b? -15 -9 3 9

-9

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? 0.02 0.04 0.05 0.08

0.04

The levels of mercury in two different bodies of water are rising. In one body of water the initial measure of mercury is 0.05 parts per billion (ppb) and is rising at a rate of 0.1 ppb each year. In the second body of water the initial measure is 0.12 ppb and the rate of increase is 0.06 ppb each year. Which equation can be used to find y, the year in which both bodies of water have the same amount of mercury? 0.05 - 0.1y = 0.12 - 0.06y 0.05y + 0.1 = 0.12y + 0.06 0.05 + 0.1y = 0.12 + 0.06y 0.05y - 0.1 = 0.12y - 0.06

0.05 + 0.1y = 0.12 + 0.06y

Mia jogs 3 kilometers in 20 minutes. There are about 0.6 miles in a kilometer. What is Mia's approximate speed in miles per minute? 0.25 miles per minute 0.09 miles per minute 4 miles per minute 11 miles per minute

0.09 miles per minute

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? 0.15(40) + 0.6x = 0.25(40 + x) 0.15(40) + 0.6(x - 40) = 0.25(x) 0.15(40) + 0.6x = 0.25(40 - x) 0.15(40) + 0.6(x + 40) = 0.25(x)

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? d - 22 + 0.25d = 10.75 0.25d + 22 - d = 10.75 0.25(22 - d) + d = 10.75 d + 0.25(d - 22) = 10.75

0.25(22 - d) + d = 10.75

Irina rode her bike to work at an average speed of 16 miles per hour. It started to rain, so she got a ride home along the same route in her coworker's car at an average speed of 27 miles per hour. If Irina's ride home in the car took 24 minutes (0.4 of an hour), how many hours was her bike ride to work, to the nearest tenth of an hour? 0.2 of an hour 0.4 of an hour 0.6 of an hour 0.7 of an hour

0.7 of an hour

What is the common ratio between successive terms in the sequence? 1.5, 1.2, 0.96, 0.768, ... -0.8 -0.3 0.3 0.8

0.8

Brass is made from a mixture of copper and other elements. A mixture that is 80% copper is combined with a mixture that is 60% copper, resulting in 100 pounds of brass that is 65% copper. Which equation can be used to find x, the amount of 60% mixture used to create the 65% mixture? 0.8(100 - x) + 0.6x = 100(0.65) 0.6(100 - x) + 0.8x = 100(0.65) 0.8(100) + 0.6x = 0.65(100 - x) 0.6(x) + 0.8(100 + x) = 0.65

0.8(100 - x) + 0.6x = 100(0.65)

Which steps should be used to graph the equation y - 4 = (x + 2)? 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. 1. Plot the point (2, 4).2. From that point, count left 1 unit and down 3 units and plot a second point.3. Draw a line through the two points. 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. 1. Plot the point (-2,4).2. From that point, count left 1 unit and down 3 units and plot a second point.3. Draw a line through the two points.

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.

Consider the functions shown on the graph. What is the best approximation for the input value when f(x)=g(x)? 0.0 0.5 1.5 3.0

1.5

The Allied 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? 1.95x + 2.50 = 27.46; Isaac traveled 15.4 miles. 1.95x + 2.50 = 27.46; Isaac traveled 12.8 miles. 2.50x + 1.95 = 27.46; Isaac traveled 11.8 miles. 2.50x + 1.95 = 27.46; Isaac traveled 10.2 miles.

1.95x + 2.50 = 27.46; Isaac traveled 12.8 miles.

If Judy completes a puzzle by herself, it takes her 3 hours. Working with Sal, it only takes them 2 hours. What is the missing value from the table that represents Judy's rate? r 3 - r 1/3 3

1/3

Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework? 1/4(x + 30 + 60) = x 1/4(x) = x(30 + 60) 1/4x(30 + 60) = x 1/4(x) = (30 + 60)

1/4(x + 30 + 60) = x

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? 1 3 10 24

Linear Equations and Inequalities, Unit Test Review

100%

Gillian purchased 25 books at the library book sale. Each hardcover book cost $1.50, and each paperback book cost $0.50. Gillian spent a total of $26.50. The book costs can be represented by the system of equations below. h + p = 251.50h + 0.50p = 26.50 How many paperback books did Gillian buy? 11 12 13 14

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p - 10.1 = 6.5p - 4 - 0.01p? Select two options. 2.3p - 10.1 = 6.4p - 4 2.3p - 10.1 = 6.49p - 4 230p - 1010 = 650p - 400 - p 23p - 101 = 65p - 40 - p 2.3p - 14.1 = 6.4p - 4

2.3p - 10.1 = 6.49p - 4 230p - 1010 = 650p - 400 - p

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? 250.5 + 35m = 300 + 45.25m 250.5 - 35m = 300 - 45.25m 250.5m - 35 = 300m - 45.25 250.5m + 35 = 300m + 45.25

250.5 - 35m = 300 - 45.25m

A ramp with a constant incline is made to connect a driveway to a front door. At a point 4 feet from the driveway, the height of the ramp is 12 inches. At a point 6 feet from the driveway, the height of the ramp is 18 inches. What is the rate of change of the ramp's incline? 1/3 inch up per foot across 1/2 inch up per foot across 2 inches up per foot across 3 inches up per foot across

3 inches up per foot across

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? 3(2 - t) = 1.5t 3t = 1.5(2 - t) 3t + 1.5(2 - t) = 5 3(2 - t) + 1.5t = 5

3(2 - t) + 1.5t = 5

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=0.75xCompany 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? 6 8 30 40

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? t - 1.25 1.25 - t 40(1.25 - t) 40(t - 1.25)

40(1.25 - t)

Four milliliters of ink A is added to 10 milliliters of ink B, forming a mixture of inks. Ink A contains 10% blue pigment. Ink B contains an unknown percentage of blue pigment. The mixture of the two inks contains 35% blue pigment. What percentage of blue pigment is in ink B? 45% 49% 60% 75%

45%

The average rate of the first part of Yi's walk on a park loop was 4 miles per hour. She then met up with a friend and the two walked the rest of the way at an average rate of 5 miles per hour. The entire 3-mile walk took Yi 42 minutes (0.7 hour). Which equation can be used to solve for x, the time in hours that Yi spent walking before meeting her friend? x = 0.7 - x x + (0.7 - x) = 1 4x + 5(0.7 - x) = 1 4x + 5(0.7 - x) = 3

4x + 5(0.7 - x) = 3

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? 5n - 300 = 1,500 5n + 300 = 1,500 5n - 200 + 100n = 1,500 5n - 100 - 200n = 1,500

5n - 300 = 1,500

Two cars that are 150 miles apart start driving toward each other on parallel roads. The average speed of the first car is 60 miles per hour. The average speed of the second car is 55 miles per hour. Which equation can be used to determine t, the time it takes for the two cars to pass each other? 60t - 55t = 0 60t + 55t = 1 60t + 55t = 150 60t - 55t = 150

60t + 55t = 150

The table represents the recommended exercise intensity for an aerobic program based on the number of visits since beginning the program. The program recommends a constant intensity for 3 visits, increasing intensity over 3 visits, and then decreasing intensity for 3 visits before restarting the pattern. Which sets of values could be the intensities of Amber's exercise during the fourth, fifth, and sixth visits? Select three options. 63%, 63%, 63% 66%, 69%, 72% 66%, 62%, 58% 63%, 65%, 67% 67%, 72%, 77%

66%, 69%, 72% 63%, 65%, 67% 67%, 72%, 77%

Students are given 3 minutes to complete each multiple-choice question on a test and 8 minutes for each free-response question. There are 15 questions on the test and the students have been given 55 minutes to complete it. Which value could replace x in the table? 7 - m 23 - m 8(15 - m) 8(15) - m

8(15 - m)

Use properties to rewrite the given equation. Which equations have the same solution as the equation 3/5x + 2/3 + x = 1/2 - 1/5x Select three options. 8/5x + 2/3 = 1/2 - 1/5x 18x + 20 + 30x = 15 - 6x 18x + 20 + x = 15 - 6x 24x + 30x = -5 12x + 30x = -5

8/5x + 2/3 = 1/2 - 1/5x 18x + 20 + 30x = 15 - 6x 24x + 30x = -5

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?

Mr. Jones asks his students to generate the next two numbers in the sequence beginning -5.5, 11, .... Taquan suggests that the sequence is geometric and the next two numbers are -22 and 44. Julia suggests that the sequence is arithmetic and the next two numbers are 27.5 and 44. Which best explains which student is correct? Taquan is correct. When the signs change in a sequence, the sequence is geometric. Each successive term is generated by multiplying by -2. Julia is correct. When the numbers alternate between decimals and whole numbers, the sequence is arithmetic. Each successive term is generated by adding 16.5. Both students could be correct about the types of possible sequences. However, one student made a computational error because it is not possible to arrive at a fourth term of 44 in two different ways. Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.

Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.

Which is a correct first step in solving the inequality -4(2x - 1) > 5 - 3x? Distribute -4 to get -8x + 4 > 5 - 3x. Distribute -4 to get -8x - 1 > 5 - 3x. Subtract 2x from both sides of the inequality. Add 1 to both sides of the inequality.

Distribute -4 to get -8x + 4 > 5 - 3x.

A personal trainer designs exercise plans based on a combination of strength-training and aerobic exercise. A beginner plan has 15 minutes per session of strength-training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. An advanced plan has 20 minutes per session of strength-training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week. Which statement describes when the plans are based on the same number of aerobic exercise sessions? Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week. Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week. Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week. Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.

Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.

The force of gravity on an object varies directly with its mass. The constant of variation due to gravity is 32.2 feet per second squared. Which equation represents F, the force on an object due to gravity according to m, the object's mass?

F = 32.2m

Which statement is true about the graphed function? F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5). F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5). F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞). F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞).

F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).

Which statement is true about the graphed function? F(x) < 0 over the interval (-∞, -4) F(x) < 0 over the interval (-∞, -3) F(x) > 0 over the interval (-∞, -3) F(x) > 0 over the interval (-∞, -4)

F(x) > 0 over the interval (-∞, -4)

Four lines are drawn on a coordinate plane to form trapezoid WXYZ. Which statements are true about the lines? Select three options. Line WZ has the same slope as line XY. Line YX has a greater slope than line ZY. Line XW has a lesser slope than line YZ. Line ZW has the same y-intercept as line YZ. Line XY has a lesser y-intercept than line XW.

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 YZ.

It would take Marco 6 hours to paint a fence by himself. It would take Jaylyn 5 hours to paint the same fence by herself. Marco is creating this table to help him determine how long it would take them to paint the fence together. Which heading should be written above the first column of numbers? Rate (part/hour) Time (hours) Part of Fence Painted Distance (meters)

Rate (part/hour)

The graph shows the increase in temperature over time in an oven. What is the change in the y-values and x-values on the graph? The change in the y-values is 40 and the change in the x-values is 1. The change in the y-values is 1 and the change in the x-values is 40. The change in the y-values is 150 and the change in the x-values is 2. The change in the y-values is 190 and the change in the x-values is 3.

The change in the y-values is 40 and the change in the x-values is 1.

Which description of the graph of the linear inequality y > 3x - 8 is correct? The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded below the line. The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded above the line. The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded below the line. The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line.

The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line.

Which description of the graph of the linear inequality y ≥ 7x - 4 is correct? The graph will be a dashed line with a y-intercept of negative four and a slope of seven. The graph will be shaded below the line. The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line. The graph will be a solid line with a y-intercept of seven and a slope of negative four. The graph will be shaded below the line. The graph will be a dashed line with a y-intercept of seven and a slope of negative four. The graph will be shaded above the line.

The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.

The yearbook club has 5 members returning from last year. They set up a booth in the cafeteria to recruit more members, and an average of 3 new members sign up each day. Which best describes why the graph relating the total number of members on the yearbook club, m, and the number of days the booth is set up, d, will be continuous or discrete? The graph will be continuous because an end day for the booth being set up is not given in the description. The graph will be continuous because there can be any number of people signing up each day since we are only given the average. The graph will be discrete because some day the number of available people to sign up for the club will run out. The graph will be discrete because there is no such thing as a partial person to sign up and the booth is set up once each day for sign ups.

The graph will be discrete because there is no such thing as a partial person to sign up and the booth is set up once each day for sign ups.

The table shows the height of water in a pool as it is being filled. 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? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.

The height of the water increases 2 inches per minute.

A line is drawn through (-4, 3) and (4, 3). Which describes whether or not the line represents a direct variation? The line represents a direct variation because -4/3= 4/3. The line represents a direct variation because it is horizontal. The line does not represent a direct variation because it does not go through the origin. The line does not represent a direct variation because -4(3) ≠ 4(3).

The line does not represent a direct variation because it does not go through the origin.

Grace is comparing cell phone plans. A prepaid phone plan costs $0.20 per minute and has no monthly fee. A contracted phone plan costs $50 per month and $0.02 per minute. How will the graphs of the monthly costs of the two cell phone plans compare where x represents minutes purchased in a month? The prepaid phone plan will have a steeper line and lower y-intercept. The contracted phone plan will have the same steepness and a higher y-intercept. The prepaid phone plan will have a less steep line and the same y-intercept. The contracted phone plan will have a steeper line and same y-intercept.

The prepaid phone plan will have a steeper line and lower y-intercept.

A data set contains an independent and a dependent variable. Which must be true of the data set if a linear function can be used to represent the data? The set must have a constant additive rate of change. The set must have a constant multiplicative rate of change. The values in the set must be positive. The values in the set must be increasing.

The set must have a constant additive rate of change.

How does the slope of g(x) compare to the slope of f(x)? The slope of g(x) is the opposite of the slope of f(x). The slope of g(x) is less than the slope of f(x). The slope of g(x) is greater than the slope of f(x). The slope of g(x) is equal to the slope of f(x).

The slope of g(x) is less than the slope of f(x).

Which statement is true about the equations -3x + 4y = 12 and 1/4x - 1/3y = 1? The system of the equations has exactly one solution at (-8, 3). The system of the equations has exactly one solution at (-4, 3). The system of the equations has no solution; the two lines are parallel. The system of the equations has an infinite number of solutions represented by either equation.

The system of the equations has no solution; the two lines are parallel.

The math team wraps gifts as a way to raise money for traveling to competitions. They offer two choices: a plain wrapping or a decorative wrapping with bows. The table represents the money raised over a busy shopping weekend. Which statement describes the amounts the team charged for wrapping gifts? The team charged $1 to wrap a gift with no bow and $2 to wrap a gift with a bow. The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow. The team charged $3 to wrap a gift with no bow and $4 to wrap a gift with a bow. The team charged $4 to wrap a gift with no bow and $5 to wrap a gift with a bow.

The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.

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? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.

The test contains 10 three-point questions and 14 five-point questions.

The system of equations shown is solved using the linear combination method 6x-5y=-8 → 6x-5y=-8 → 6x5y=-8 -24x+20y=32 → 1/4(-24x+20y=32) → -6x+5y=8 0 = 0 What does 0 = 0 mean regarding the solution to the system? There are no solutions to the system because the equations represent parallel lines. There are no solutions to the system because the equations represent the same line. There are infinitely many solutions to the system because the equations represent parallel lines. There are infinitely many solutions to the system because the equations represent the same line.

There are infinitely many solutions to the system because the equations represent the same line.

The table represents a bicycle rental cost in dollars as a function of time in hours. Which explains whether or not the function represents a direct variation? This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour. This function represents a direct variation because it has a positive, constant rate of change of $10 per hour. This function does not represent a direct variation because it does not represent the cost for 1 hour. This function does not represent a direct variation because the function rule for the cost is to add $10, not multiply by a constant.

This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.

Tomas is making trail mix using granola and walnuts. He can spend a total of $12 on the ingredients. He buys 3 pounds of granola that costs $2.00 per pound. The walnuts cost $6 per pound. He uses the equation to represent the total cost, where x represents the number of pounds of granola and y represents the number of pounds of walnuts. He solves the equation for y, the number of pounds of walnuts he can buy. Which is the first error that Tomas made? Tomas substituted the 3 for x when he should have substituted 6 for x. Tomas added 6 to both sides of the equation instead of subtracting 6. Tomas should have written the equation as . Tomas substituted 3 for x when he should have substituted 3 for y.

Tomas added 6 to both sides of the equation instead of subtracting 6.

Two functions are graphed on the coordinate plane. Which represents where f(x) = g(x)? f(4) = g(4) and f(0) = g(0) f(-4) = g(-4) and f(0) = g(0) f(-4) = g(-2) and f(4) = g(4) f(0) = g(-4) and f(4) = g(-2)

f(-4) = g(-4) and f(0) = g(0)

The function f(x) is given by the set of ordered pairs. {(8, -3), (0, 4), (1, -5), (2, -1), (-6, 10)} Which is true regarding the function? f(-3) = 8 f(3) = 5 f(8) = 0 f(-6) = 10

f(-6) = 10

Which statement is true regarding the graphed functions? f(0) = 2 and g(-2) = 0 f(0) = 4 and g(-2) = 4 f(2) = 0 and g(-2) = 0 f(-2) = 0 and g(-2) = 0

f(2) = 0 and g(-2) = 0

The functions f(x) and g(x) are graphed. Which represents where f(x) = g(x)? f(2) = g(2) and f(0) = g(0) f(2) = g(0) and f(0) = g(4) f(2) = g(0) and f(4) = g(2) f(2) = g(4) and f(1) = g(1)

f(2) = g(2) and f(0) = g(0)

Which statement is true regarding the functions on the graph? f(6) = g(3) f(3) = g(3) f(3) = g(6) f(6) = g(6)

f(3) = g(3)

Which is true regarding the graphed function f(x)? f(0)=3 f(5)=-1 f(3)=2 f(2)=-2

f(5)=-1

Consider the function represented by the table. The ordered pair given in the bottom row can be written using function notation as f(9)=5. f(5)=9. f(5, 9)=14. f(9, 5)=14.

f(9)=5.

Martina opens a savings account with an initial deposit and makes no other deposits or withdrawals. She earns interest on her initial deposit. The total amount of money in her savings account at the end of each year is represented by the sequence shown. 100, 105, 110.25, ... Which recursive formula can be used to determine the total amount of money earned in any year based on the amount earned in the previous year? f(n + 1) = f(n) + 5 f(n + 1) = 5f(n) f(n + 1) = 1.05f(n) f(n + 1) = 0.05f(n)

f(n + 1) = 1.05f(n)

Zina spends 1.5 hours setting up her sewing machine and making one hat. The total amount of time spent making hats can be represented by the sequence below. 1.5, 2.25, 3.0, 3.75, ... Which recursive formula can be used to determine the total amount of time spent making hats based on the total amount of time spent previously? f(n + 1) = f(n) + 1.5 f(n + 1) = f(n) + 0.75 f(n + 1) = f(n) f(n + 1) = f(n)

f(n + 1) = f(n) + 0.75

Shaunta is developing a recursive formula to represent an arithmetic sequence in which 5 is added to each term to determine each successive term. Which formula could represent her sequence? f(n + 1) = f(n) + 5 f(n + 1) = f(n + 5) f(n + 1) = 5f(n) f(n + 1) = f(5n)

f(n + 1) = f(n) + 5

Which recursive formula can be used to generate the sequence shown, where f(1) = 5 and n > 1? 5,-1, -7, -13, -19, ... f(n + 1) = f(n) + 6 f(n) = f(n +1) - 6 f(n +1) = f(n) - 6 f(n +1) = -6f(n)

f(n +1) = f(n) - 6

The sequence below represents Marisa's fine at the library for each day that she has an overdue book: $0.50, $0.65, $0.80, $0.95, $1.10, ... Which equation represents Marisa's library fine as a function of a book that is n days overdue? f(n) = 0.15n f(n) = 0.50n f(n) = 0.15n + 0.35 f(n) = 0.50n + 0.15

f(n) = 0.15n + 0.35

Consider the function represented by the equation 6q = 3s - 9. Write the equation in function notation, where q is the independent variable. f(q) = 2s + 3 f(q) = 2q + 3

f(q) = 2q + 3

In order to avoid heavy traffic, Antonio can drive home after working less than 7 hours or after working more than 9 hours. How can this be written as a single compound inequality? 7 < h < 9 7 > h > 9 h < 7 or h > 9 h > 7 or h < 9

h < 7 or h > 9

What is the inverse of the function f(x) = 2x - 10? h(x) = 2x - 5 h(x) = 2x + 5 h(x) = x - 5 h(x) = x + 5

h(x) = 1/2x + 5

Which represents the inverse of the function f(x) = 4x? h(x) = x + 4 h(x) = x - 4 h(x) = x h(x) = x

h(x) = 1/4x

What is the inverse of the function f(x) = x + 2? h(x) = 18x - 2 h(x) = 9x - 18 h(x) = 9x + 18 h(x) = 18x + 2

h(x) = 9x - 18

What is the constant of variation, k, of the direct variation, y = kx, through (-3, 2)? k = -3/2 k = -2/3 k =2/3 k =3/2

k = -2/3

Which values of m and b will create a system of equations with no solution? Select two options. y = mx + b y = -2x + 3/2 m = -3 and b = m = -2 and b = m = 2 and b = m = and b = m = -2 and b =

m = -2 and b = -1/3 m = -2 and b = -2/3

Harita must memorize 90 measures of music for her cello solo at a concert. She plans on memorizing 18 new measures for every 3 days of practice. Which equation can be used to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece? m = 72 - 15d m = 90 - 6d m = 101 - 21d m = 108 - 3d

m = 90 - 6d

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? m = yx + b m = y-b/x m = y/x - b m = y - b/x

m = y-b/x

The equation d = m/V can be used to calculate the density, d, of an object with mass, m, and volume, V. Which is an equivalent equation solved for V? dm = V d/m = V m/d = V m - d = V

m/d = V

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? Select three options. positive slope negative slope constant slope increasing function decreasing function

negative slope constant slope decreasing function

What is the solution to the system of equations? 2x - y = 7 y = 2x + 3 (2, 3) (2, 7) no solution infinite number of solutions

no solution

y = -1/2x + 4 x + 2y = -8 How many solutions does this linear system have? one solution: (8, 0) one solution: (0, 8) no solution infinite number of solutions

no solution

How many solutions exist for the given equation? 1/2 (x + 12) = 4x - 1 zero one two infinitely many

one

How many solutions exist for the given equation? 3(x - 2) = 22 - x zero one two infinitely many

one

What are the slope and y-intercept of the linear function graphed to the left? slope: -2; y-intercept: 2 slope: -1/2; y-intercept: 1 slope: 1/2; y-intercept: 2 slope: 2; y-intercept: 1

slope: -1/2; y-intercept: 1

A catering company uses different functions to estimate the itemized costs for a party. The table below represents the included tip for wait staff as a function of the number of guests served. If the tip varies directly with the number of guests, which equation represents the relationship between the tip, t, and the number of guests, g? t = 1.8g t = g/18 g = 1.8t g = t/18

t = 1.8g

Which input value produces the same output value for the two functions on the graph? x = −1 x = 0 x = 1 x = 2

x = 1

Which input value produces the same output value for the two functions on the graph? x = −3 x = −2 x = −1 x = 3

x = −2

Solve the equation. 5x + 8 − 3x = −10 x = −9 x = −1 x = 1 x = 9

x = −9

Manuela solved the equation 3−2|0.5x+1.5|=2 for one solution. Her work is shown below. 3−2|0.5x+1.5|=2 −2|0.5x+1.5|=−1 |0.5x+1.5|=0.5 0.5x+1.5=0.5 0.5x=−1 x=−2 What is the other solution to the equation? x=−6 x=−4 x=2 x=4

x=−4

Which equation represents a line that passes through (2, -1/2) and has a slope of 3? y - 2 = 3(x + 1/2 ) y - 3 = 2(x + 1/2) y + 1/2 = 3(x - 2) y + 1/2 = 2(x - 3)

y + 1/2 = 3(x - 2)

The slope-intercept form of the equation of a line that passes through point (-2, -13) is y = 5x - 3. What is the point-slope form of the equation for this line? y - 13 = 5(x - 2) y + 13 = 5(x + 2) y - 2 = 5(x - 13) y + 2 = 5(x + 13)

y + 13 = 5(x + 2)

Which equation represents a line that passes through (-9, -3) and has a slope of -6? y - 9 = -6(x - 3) y + 9 = -6(x + 3) y - 3 = -6(x - 9) y + 3 = -6(x + 9)

y + 3 = -6(x + 9)

The table represents a linear equation. Which equation correctly uses point (-2, -6) to write the equation of this line in point-slope form? y - 6 = 5/2(x - 2) y - 6 = 2/5(x - 2) y + 6 = 2/5(x + 2) y + 6 = 5/2(x + 2)

y + 6 = 5/2(x + 2)

Which equation represents a line that passes through (5, 1) and has a slope of 1/2? y - 5 = 1/2(x -1) y - 1/2= 5(x -1) y - 1 = 1/2(x -5) y - 1 = 5[x-1/2]

y - 1 = 1/2(x -5)

Line QR goes through points Q(0, 1) and R(2, 7). Which equation represents line QR? y - 1 = 6x y - 1 = 3x y - 7 = 2x - 6 y - 7 = x - 2

y - 1 = 3x

Mr. Shaw graphs the function f(x) = -5x + 2 for his class. The line contains the point (-2, 12). What is the point-slope form of the equation of the line he graphed? y - 12 = -5(x + 2) y - 12 = 2(x + 2) y + 12 = 2(x - 2) y + 12 = -5(x - 2)

y - 12 = -5(x + 2)

Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3? y + 2 = 1/3 (x + 3) y - 2 = 1/3 (x - 3) y + 3 = 1/3 (x + 2) y - 3 = 1/3 (x - 2)

y - 2 = 1/3 (x - 3)

Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3? y + 2 =1/3(x + 3) y - 2 = 1/3(x - 3) y + 3 = 1/3(x + 2) y - 3 = 1/3(x - 2)

y - 2 = 1/3(x - 3)

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? y - 7 = 3(x - 1) y - 1 = 3(x - 7) y - 7 = 4(x - 1) y - 1 = 4(x - 7)

y - 7 = 4(x - 1)

The table represents a linear equation. Which equation shows how (-10, 8) can be used to write the equation of this line in point-slope form? y - 8 = -0.15(x - 10) y + 8 = -0.15(x - 10) y - 8 = -0.2(x + 10) y + 8 = -0.2(x - 10)

y - 8 = -0.2(x + 10)

Which equation represents a line that passes through (4, 1/3) and has a slope of 3/4? y -3/4 = 1/3(x - 4) y -1/3 = 3/4(x - 4) y -1/3 = 4(x -3/4 ) y - 4 = 3/4(x -1/3 )

y -1/3 = 3/4(x - 4)

Which equation represents the graphed function? y = 4x - 2 y = -4x - 2 y = 1/4x - 2 y = - 1/4x - 2

y = 1/4x - 2

What is the solution to the linear equation? 2.8y + 6 + 0.2y = 5y - 14 y = -10 y = -1 y = 1 y = 10

y = 10

The total cost for a bucket of popcorn and 4 movie tickets is $56. The total cost for the same size bucket of popcorn and 6 movie tickets is $80. The cost of a bucket of popcorn is $8. Which equation represents the relationship between y, the total cost of the popcorn and movie tickets, and x, the number of movie tickets that are purchased? y = 12x + 8 y = 12x − 8 y = 14x + 8 y = 14x − 8

y = 12x + 8

Muriel says she has written a system of two linear equations that has an infinite number of solutions. One of the equations of the system is 3y = 2x - 9. Which could be the other equation? 2y = x - 4.5 y = 2/3x - 3 6y = 6x - 27 y = 3/2x - 4.5

y = 2/3x - 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? y = a · πx y = a + (πx) y = a - πx y = a ÷ (πx)

y = a ÷ (πx)

Which system of linear inequalities is represented by the graph? y > 1/3x + 3 and 3x - y > 2 y > 1/2x + 3 and 3x - y > 2 y > 1/3x + 3 and 3x + y > 2 y > 1/3x + 3 and 2x - y > 2

y > 1/3x + 3 and 3x - y > 2

Which system of linear inequalities is represented by the graph? y > x - 2 and x - 2y < 4 y > x + 2 and x + 2y < 4 y > x - 2 and x + 2y < 4 y > x - 2 and x + 2y < -4

y > x - 2 and x + 2y < 4

SUBJECT:

REPRESENTING RELATIONSHIPS

The graph shows the speed of Jamal's car over time. Which best describes what is happening in section B?

Jamal is traveling at a constant speed.

Which table represents a function?

Hanna shops for socks that cost $2.99 for each pair and blouses that cost $12.99 each. Let x represent the number of pairs of socks purchased, and let y represent the number of blouses purchased. Which equation models the purchases she made with $43.92? x + y = 15.98 x + y = 43.92 43.92x - 2.99y = 12.99 2.99x + 12.99y = 43.92

2.99x + 12.99y = 43.92

Varia is studying abroad in Europe. She is required to pay $3,500 (in US dollars) per year to the university; however, she must pay in euros. How many euros can Varia expect to pay per month to the university? (Round to the nearest whole euro.) 0.7306euros = 1 US dollar 213 euros 2,557 euros 30,685 euros 57,487 euros

213 euros

Rory records the percentage of battery life remaining on his phone throughout a day. The graph represents the percentage of battery life remaining after a certain number of hours. Rory's battery was full at 6:00 a.m, or t = 0. Which times could Rory's phone have been plugged into the charger? Check all that apply.

3:00 p.m. 5:00 p.m. 11:00 p.m.

Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the best estimate of the speed Morris is traveling? 1 mile = 5,280 feet 45 miles per hour 46 miles per hour 47 miles per hour 48 miles per hour

48 miles per hour

66%, 69%, 72% 63%, 65%, 67% 67%, 72%, 77%

A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are approximately 2.2 pounds in 1 kilogram. Assuming the weight loss happened at a constant rate, about how many pounds did the group lose each day? 8.8 pounds 12.7 pounds 61.6 pounds 89.1 pounds

8.8 pounds

Last month Maria hiked a total of 90 miles on two trails: a 5-mile mountain trail and a 10-mile canal trail. Let x represent the number of times Maria hiked the mountain trail, and let y represent the number of times Maria hiked the canal trail. Which equation can be used to find the number of times Maria hiked each trail? x + y = 90 5x - 10y = 90 90 - 10y = 5x 90 + 10y = 5x

90 - 10y = 5x

The graph represents the heights of two climbers on a climbing wall over a 12-minute time period. Which statement is true about the climbers' heights? Brynn was resting at a constant climbing height when Abby's climbing height was decreasing. Abby's climbing height was decreasing when Brynn's climbing height was increasing. The heights of both climbers increased, then decreased, with no rest at a constant height. Both climbers rested on the wall at a constant height for 2 minutes.

Both climbers rested on the wall at a constant height for 2 minutes.

Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let y represent the length of each of the equal pieces of yarn that Julie decides to cut. What is the equation that can be used to determine the total length of all of the yarn that she ends up cutting, t? Is the graph of the equation continuous or discrete?

t=4y+7.75; continuous

To fit between two windows, the width of a bookshelf must be no greater than feet. Mrs. Aguilar purchases a bookshelf that is 77 inches wide. Which statement describes the relationship between the width of the bookshelf and the distance between the windows? The bookshelf is 12 inches too wide to fit between the windows. The bookshelf will fit between the windows with no extra room remaining. The bookshelf will fit between the windows with 1 inch remaining. The bookshelf is 5 inches too wide to fit between the windows.

The bookshelf will fit between the windows with 1 inch remaining.

Luis created the graph below to show the temperature from 8:00 a.m. (8 hours after midnight) until 8:00 p.m. On this graph, 4:00 p.m. occurs at 16 hours after midnight, and 6:00 p.m. occurs at 18 hours after midnight. Which statements are true about the temperatures Luis recorded on the graph? Select THREE answers. The temperature increased until 4:00 p.m. The temperature was not recorded between 4:00 p.m. and 6:00 p.m. The temperature decreased after 6:00 p.m. The temperature increased and then decreased before holding constant. The temperature increased more quickly between 12:00 p.m. and 4:00 p.m. than before 12:00 p.m.

The temperature increased until 4:00 p.m. The temperature decreased after 6:00 p.m. The temperature increased more quickly between 12:00 p.m. and 4:00 p.m. than before 12:00 p.m.

The graph shows the total number of hours Katrina worked over a 10-day period. During which one-day interval did she work the most hours?

from day 7 to day 8

To bill customers for water usage, one city converts the number of gallons used into units. This relationship is represented by the equation u = 748g, where g is the total number of gallons of water used and u is the number of units. Determine which statements about the relationship are true. Choose two options. g is the dependent variable. u is the dependent variable. g is the independent variable. u is the independent variable. The two variables cannot be labeled as independent or dependent without a table of values.

u is the dependent variable. g is the independent variable.

The help desk is keeping track of the number of minutes the average caller spends on hold. According to the table, during which interval did the average time spent on hold increase? week 1 to week 3 week 1 to week 4 week 4 to week 6 week 3 to week 5

week 4 to week 6

The town librarian bought a combination of new-release movies on DVD for $20 and classic movies on DVD for $8. Let x represent the number of new releases, and let y represent the number of classics. If the librarian had a budget of $500 and wanted to purchase as many DVDs as possible, which values of x and y could represent the number of new-release and classic movies bought? x = 8, y = 45 x = 10, y = 22 x = 16, y = 22 x = 18, y = 18

x = 16, y = 22

What is the value of y in the equation 6.4x + 2.8y = 44.4, when x = 3? y = 5 y = 6 y = 8 y = 9

y = 9

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