Algebra I A
SUBJECT: : REPRESENTING RELATIONSHIPS
Quantitative Reasoning : Pre-test / Quiz
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.
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 feet15 feet18 feet22 feet : 18 feet
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.
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.
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
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.
How many inches are in 12 feet?1 inch24 inches120 inches144 inches : 144 inches
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 feet45 miles per hour46 miles per hour47 miles per hour48 miles per hour : 48 miles per hour
Which expression can be used to convert 80 US dollars (USD) to Australian dollars (AUD)?1 USD = 1.0343 AUD1 AUD = 0.9668 USD : D
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 dollars44.70 US dollars73.06 US dollars136.87 US dollars140.41 US dollars : 44.70 US dollars
How many square inches are in 60 square feet?5 square inches72 square inches720 square inches8,640 square inches : 8,640 square inches
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 dollar213 euros2,557 euros30,685 euros57,487 euros : 213 euros
Three ounces of cinnamon cost $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound? : $12.80
What is the most accurate representation of the area of a plot measuring 11.7 cm by 15.4 cm? : 180.2 cm2
What is the value of y in the equation 6.4x + 2.8y = 44.4, when x = 3?y = 5y = 6y = 8y = 9 : y = 9
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.
What is the value of x in the equation 8x - 2y = 48, when y = 4?671448 : 7
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 = 100What 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.
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=54.617.4+b=54.626.1+b=54.634.8+b=54.6 : 34.8+b=54.6
Writing and Graphing Equations in Two Variables : Pre-test / Quiz
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? : B
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+xy = x − 4y = 4 · xy = x ÷ 4 : y=4+x
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)
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 billsthe total number of puzzle pieces, y, in a brand new 50-piece puzzle, and x brand-new 100-piece puzzlesthe total weight of the barbell, y, where the bar weighs 50 pounds and x 100-pound weights are added to itthe 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
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
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.
Introduction to Functions : Pre-test / Quiz
What is the lowest value of the range of the function shown on the graph?--203 : -2
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 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}
How many points need to be removed from this graph so that it will be a function?1 point2 points3 points4 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.
Which graph shows a set of ordered pairs that represent a function? : SEE IMAGE
Which set of ordered pairs represents a function? : {(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}
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)=1f(2)=-10f(0)=6f(1)=-10 : f(0)=6
Consider the function represented by the table.For which x is f(x)=-3?-7-445 : -7
Consider the function represented by 9x+3y=12 with x as the independent variable. How can this function be written using function notation? : B
Which is true regarding the graphed function f(x)?f(0)=3f(5)=-1f(3)=2f(2)=-2 : f(5)=-1
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) = 8f(3) = 5f(8) = 0f(-6) = 10 : f(-6) = 10
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 releasedthe initial height of the rocketthe initial velocity of the rocketthe height of the rocket after t seconds : the number of seconds after the rocket is released
The table represents the function f(x).What is f(3)?-9-119 : 9
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)
If f(x) = 6x - 4, what is f(x) when x = 8?2164452 : 44
If f(x) = 5x + 40, what is f(x) when x = -5?-9-8715 : 15
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)
Analyzing Graphs : Pre-test / Quiz
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.
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 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.
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 zeroAs 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.
A sequence is defined recursively using the equation . If f(1)=100, what is f(6)?52606892 : 60
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?-7-117 : -1
A sequence is defined by the formula f(n+1)=f(n)−3. If f(4)=22, what is f(1)?10133134 : 31
What is the common ratio between successive terms in the sequence?27, 9, 3, 1, , , , ...-3-1/31/33 : 1/3
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) + 20f(n + 1) = f(n) + 110f(n + 1) = f(n + 1) + 20f(n + 1) = f(n + 1) + 110 : f(n + 1) = f(n) + 20
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)?−15−7.57.515 : 7.5
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 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
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)
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.
Representing Relationships, Unit Test : 100%
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? : D
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 inverse of the function f(x) = 1/4x - 12?h(x) = 48x - 4h(x) = 48x + 4h(x) = 4x - 48h(x) = 4x + 48 : h(x) = 4x + 48
The graph of the function f(x) is shown below.What is x when f(x)=0?-1.8-1.205 : -1.8
If f(x) = 2x2 + 1, what is f(x) when x = 3?171319 : 19
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?zeroconstantdecreasingincreasing : decreasing
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)}
The function f(x) is shown on the graph.What is f(0)?12 only2 and 3 only-2, -1, 1, and 2 only-2, -1, 1, 2 and 12 : 12 only
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%
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 faceperimeter of 1 face and area of 1 facesurface area and volumearea of 1 face and surface areaside length and volume : side length and perimeter of 1 facearea of 1 face and surface area
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.
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?12141519 : 12
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 song4 songs for $1$4 per song : $2 per song
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
The graph of a linear function is shown.Which word describes the slope of the line?positivenegativezeroundefined : positive
Which graph has a slope of 4/5? : B
The table represents a linear function.What is the slope of the function?-6-446 : -6
Which relationship has a zero slope? : A
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.
The graph represents revenue in dollars as a function of greeting cards sold.Which equation represents the function shown on the graph?y = 1/4xy = 1/2xy = 2xy = 4x : y = 4x
What is the slope of the line represented by the equation y = 4/5x - 3?-3-4/54/53 : 4/5
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−2y=48x+2y=2x−48y=2x+48 : y=2x−48
What is the slope of the line represented by the equation y = -2/3 - 5x?-5-2/32/35 : -5
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.
What is the slope of the line represented by the equation y = -1/2x + 1/4 ?-1/2-1/41/41/2 : -1/2
Which linear function represents the line given by the point-slope equation y + 1 = -3(x - 5)?f(x) = -3x - 6f(x) = -3x - 4f(x) = -3x + 16f(x) = -3x + 14 : f(x) = -3x + 14
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.
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 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)
Which graph matches the equation y+3=2(x+3)? : A
Writing Linear Equations : Pre-test / Quiz
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)
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)
Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?y = 2x - 2y = 2x + 2y = x + 2y = x - 2 : y = x + 2
Which equation represents the line that passes through and (-8.11) and (4,7/2)?y = -5/8x + 6y = -5/8x + 16y = -15/2x - 49y = -15/2x + 71 : y = -5/8x + 6
Special Linear Relationships : Pre-test / Quiz
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.
Which graph represents a function with direct variation? : D
Which graph represents a function with direct variation? : C
A direct variation function contains the points (-8, -6) and (12, 9). Which equation represents the function?y = -4/3xy = -3/4xy = 3/4xy = 4/3x : y = 3/4x
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 linear function is represented by the graph?f(x) = -2x + 1f(x) = -1/2x + 1f(x) = 1/2x + 1f(x) = 2x + 1 : f(x) = -1/2x + 1
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 represents the graphed function?y = 4x - 2y = -4x - 2y = 1/4x - 2y = - 1/4x - 2 : y = 1/4x - 2
Line QR goes through points Q(0, 1) and R(2, 7). Which equation represents line QR?y - 1 = 6xy - 1 = 3xy - 7 = 2x - 6y - 7 = x - 2 : y - 1 = 3x
Which equation represents the graphed function?-3x + 2 = y-x + 2 = yx - 3 = y2x - 3 = y : C
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 dollar2/5 hours per dollar3 dollars per hour13 dollars per hour : 13 dollars per hour
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.
The graph of a relation is shown.Which of these values could be the slope of the line? Select two options.-2-8/507/43 : D, E
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.
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 = -ab - a = 0b(-a) = 0 : -b = -a
What is the y-intercept of the function f(x)=4 - 5x?-5-445 : 4
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 + 2y = 1/2 x - 4y = 1/2 x + 5/2y = 1/2 x - 7/2 : y = 1/2 x + 5/2
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)
SUBJECT: : LINEAR EQUATIONS AND INEQUALITIES
Solve the equation.5x + 8 − 3x = −10x = −9x = −1x = 1x = 9 : x = −9
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 ofmiles he runs.months he runs.miles he ran the first day.calories he burns. : months he runs.
Which input value produces the same output value for the two functions on the graph?x = −1x = 0x = 1x = 2 : x = 1
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.
Solve the equation.−10x + 1 + 7x = 37x = −15x = −12x = 12x = 15 : x = −12
Solving Linear Equations: Variables on Both Sides : Pre-test / Quiz
What is the solution to the linear equation?2.8y + 6 + 0.2y = 5y - 14y = -10y = -1y = 1y = 10 : y = 10
What is the solution to the linear equation?2/3x - 1/2 = 1/3 + 5/6xx = -5x = -1/6x =1/6x = 5 : x = -5
Solve the equation.-3x + 1 + 10x = x + 4x = 1/2x = 5/6x = 12x = 18 : x = 1/2
Which step could be used to help isolate the variable in the following equation?5.6j - 0.12 = 4 + 1.1jSubtract 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.
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.
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+41/2x + 4 = -1/2x + 4When she subtracts 4 from both sides, 1/2x = -1/2x results. What is the value of ?-1-1/201/2 : 0
What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)?3459 : 4
Solve for x.6(x - 1) = 9(x + 2)x = -8x = -3x = 3x = 8 : x = -8
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) + 34 + 6(2 + x) = 2(3x + 8) : 5 + 2(3 + 2x) = x + 3(x + 1)
Solve for x.5(x - 10) = 30 - 15xx = 1x = 4x = 5x = 8 : x = 4
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
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)
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 = 10.750.25d + 22 - d = 10.750.25(22 - d) + d = 10.75d + 0.25(d - 22) = 10.75 : 0.25(22 - d) + d = 10.75
Dr. Bhatia mixes 2 liters of a 5% saline solution with x liters of a 9% saline solution. The table shows the amount of each solution used.What is the value of x?3456 : 6
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?0.050.100.150.20 : 0.05
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?0.020.040.050.08 : 0.04
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 hour0.4 of an hour0.6 of an hour0.7 of an hour : 0.7 of an hour
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 - xx + (0.7 - x) = 14x + 5(0.7 - x) = 14x + 5(0.7 - x) = 3 : 4x + 5(0.7 - x) = 3
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?4r4/66r6/4 : 4/6
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 - 1.251.25 - t40(1.25 - t)40(t - 1.25) : 40(1.25 - t)
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 PaintedDistance (meters) : Rate (part/hour)
Literal Equations : Pre-test / Quiz
Solve for k.8k + 2m = 3m + kk = 70mk = 7mk = 7/mk = m/7 : k = m/7
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 isC = K - 273.15C = 273.15 - KC = K + 273.15C = 273.15K : C = K - 273.15
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 = 4r = 8r = 12r = 16 : r = 8
Solve for w.5w + 9z = 2z + 3ww=-7/2zw = -2/7zw = -2zw = -7z : w=-7/2z
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
Which equation has no solution?|-x - 3| = 5|2x - 1| = 0|5 - 3x| = -8|-x + 9| = 0 : |5 - 3x| = -8
Which equation has no solution?|4x - 2| = -6|-2 - x| = 9|3x + 6| = 6|-2x + 8| = 0 : |4x - 2| = -6
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.
Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)? : B
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.
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.
What value of x is in the solution set of 8x - 6 > 12 + 2x?-1035 : 5
Which is a correct first step in solving 5 - 2x < 8x - 3?5 < 6x - 33x < 8x - 35 < 10x - 32 - 2x < 8x : 5 < 10x - 3
Introduction to Compound Inequalities : Pre-test / Quiz
Which compound inequality is represented by the graph?-3 ≤ x < 1-3 < x ≤ 1x ≤ -3 or x > 1x < -3 or x ≥ 1 : -3 ≤ x < 1
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 ≥ 42r < 37 or r > 4237 < r ≥ 4237 > r ≥ 42 : r < 37 or r ≥ 42
Linear Equations and Inequalities, Unit Test Review : 100%
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 = -0.83 = 3-3 = -3 : -0.8 = -0.8
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) = 17.800.05q + 0.25(84 - q) = 17.800.25(q - 84) + 0.05q = 17.800.05(84 - q) + 0.25q = 17.80 : 0.05(84 - q) + 0.25q = 17.80
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?0.0750.1250.3750.625 : 0.075
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 - 42.3p - 10.1 = 6.49p - 4230p - 1010 = 650p - 400 - p23p - 101 = 65p - 40 - p2.3p - 14.1 = 6.4p - 4 : 2.3p - 10.1 = 6.49p - 4230p - 1010 = 650p - 400 - p
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%
Kate begins solving the equation (6x - 3) = (6x - 4). Her work is correct and is shown below.(6x - 3) = (6x - 4)4x - 2 = 3x - 2When 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.
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 · πxy = a + (πx)y = a - πxy = a ÷ (πx) : y = a ÷ (πx)
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) = 1.5t3t = 1.5(2 - t)3t + 1.5(2 - t) = 53(2 - t) + 1.5t = 5 : 3(2 - t) + 1.5t = 5
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)÷ rh = - b ÷ rh = ÷ r - bh = ÷ r : A
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) = 13.300.1n + 0.05(175 - n) = 13.300.1(n - 175) + 0.05 = 13.300.1(175 - n) + 0.05n = 13.30 : 0.1(175 - n) + 0.05n = 13.30
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 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.
What is the value of x in the equation ?1/31/2213 : 2
A system of equations has 1 solution. If 4x - y = 5 is one of the equations, which could be the other equation?y = -4x + 5y = 4x - 52y = 8x - 10-2y = -8x - 10 : y = -4x + 5
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)
What is the solution to the system of linear equations?(-3, 0)(-3, 3)(0, 2)(3, 1) : (0, 2)
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 - 4.5y = 2/3x - 36y = 6x - 27y = 3/2x - 4.5 : y = 2/3x - 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 +14y = 8x - 7y = -8x + 72y = −16x − 14 : y = 8x - 7
What value of b will cause the system to have an infinite number of solutions?y = 6x - b-3x + 1/2y = -3b =2468 : 6
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?9.81073.575 : 75
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+0.50xHow many bars would the team need to purchase from each company in order for the total cost to be equal?683040 : 40
What is the solution to the system of equations?y = 1/3x - 102x + y = 4(-8, 6)(-6, 16)(6, -8)(16, -6) : (6, -8)
Solving Systems: Introduction to Linear Combinations : Pre-test / Quiz
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 = 25.503x + 2y = 24.00What is the price of a protein shake?$3.75$4.50$4.95$5.25 : $5.25
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 = 3,500x - y = 2,342Solve the system of equations. How many contemporary titles does Jarred have?1,1581,7372,3422,921 : 2,921
Solving Systems of Linear Equations: Linear Combinations : Pre-test / Quiz
The system of equations is solved using the linear combination method.1/2x+4y=8 → -2(1/2x+4y=8) → x-8y=-163x+24y=12 → 1/3(3x+24y=12) → x+8y=40=-12What 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.
Which statement describes the graph of the system of equations below?1.5x + 0.2y = 2.681.6x + 0.3y = 2.98The 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).
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 = 75.90Karina 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 is the graph of the linear inequality 2x - 3y < 12? : C
Which linear inequality is represented by the graph?y ≤ 1/3x − 1y ≥ 1/3x − 1y < 3x − 1y > 3x − 1 : y ≥ 1/3x − 1
Which linear inequality is represented by the graph?y ≥ 1/3x - 4y ≤ 1/3x - 4y ≤ 1/3x + 4y ≥ 1/3x + 4 : y ≤ 1/3x - 4
Which is the graph of the linear inequality y ≥ −x − 3? : A
Which graph shows the solution to the system of linear inequalities?x + 3y > 6y ≥ 2x + 4 : D
Which ordered pair makes both inequalities true?y < -x + 1y > x(-3, 5)(-2, 2)(-1, -3)(0, -1) : (-2, 2)
Which is true about the solution to the system of inequalities shown?y < 1/3x - 1y < 1/3x - 3All 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.
Which ordered pairs are in the solution set of the system of linear inequalities?y > 1/2xy < 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)
Systems of Equations and Inequalities, Unit Test Review : 100%
What is the y-value of the solution to the system of equations?3x + 5y = 17x + 4y = −13−3−125 : 2
Which is the best approximation for the solution of the system of equations?y = -2/5x + 1y = 3x - 2(0.45, 0.88)(0.88, 0.65)(0.88, 1.1)(1.3, 0.88) : (0.88, 0.65)
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 is true about the solution to the system of inequalities shown?y > 3x + 1y < 3x - 3Only 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.
Systems of Equations and Inequalities, Unit Test : 100%
What is the value of y in the solution to the system of equations?1/3x + 1/4y = 12x - 3y = -30-8-338 : 8
Which inequality pairs with y≤−2x−1 to complete the system of linear inequalities represented by the graph?y<−2x+2y>−2x+2y<2x−2y>2x−2 : y>−2x+2
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)
What is the solution to this system of linear equations?3x - 2y = 145x + y = 32(3, 5)(6, 2)(8, -1)(14, -18) : (6, 2)
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)
Which system of linear inequalities is represented by the graph?y > x - 2 and x - 2y < 4y > x + 2 and x + 2y < 4y > x - 2 and x + 2y < 4y > x - 2 and x + 2y < -4 : y > x - 2 and x + 2y < 4
y=5x - 1-15x - 3y=3How many solutions does this linear system have?one solution: (0, -1)one solution: (1, 4)no solutioninfinite number of solutions : one solution: (0, -1)
Which value of m will create a system of parallel lines with no solution?y=mx-68x-4y=12-2-1/21/22 : 2
Which number line represents the solution set for the inequality 3x < -9? : C
Which table represents a linear function? : A
Which table represents a linear function? : C
The solution to the system of equations shown is (2, 0).3x − 2y = 6x + 4y = 2When 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 = 6x + 4y = 26x − 4y = 62x + 8y = 2x + 4y = 27x = 146x − 4y = 67x = 14 : x + 4y = 27x = 14
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 ≤ 12.212 > x ≤ 12.2x > 12 or x ≤ 12.2x < 12 or x ≤ 12.2 : 12 < x ≤ 12.2
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 interval contains a local minimum for the graphed function?[-4, -2.5][-2, -1][1, 2][2.5, 4] : [2.5, 4]
What is the inverse of the function f(x) = x +3?h(x) = 1/3x + 3h(x) = 1/3x - 3h(x) = x - 3h(x) = x + 3 : h(x) = x - 3
