The formula for the surface area of a right rectangular prism is A = 2lw + 2hw + 2lh, where l, w, and h represent the length, width, and height, respectively. Which term of this formula is not dependent on the height?
To watch a varsity basketball game, spectators must buy a ticket at the door. The cost of an adult ticket is $3.00 and the cost of a student ticket is $1.50. If the number of adult tickets sold is represented by a and student tickets sold by s, which expression represents the amount of money collected at the door from the ticket sales?
Andy has $310 in his account. Each week, w, he withdraws $30 for his expenses. Which expression could be used if he wanted to find out how much money he had left after 8 weeks?
Bryan's hockey team is purchasing jerseys. The company charges $250 for a one-time setup fee and $23 for each printed jersey. Which expression represents the total cost of x number of jerseys for the team?
Konnor wants to burn 250 Calories while exercising for 45 minutes at the gym. On the treadmill, he can burn 6 Cal/min. On the stationary bike, he can burn 5 Cal/min. If t represents the number of minutes on the treadmill and b represents the number of minutes on the stationary bike, which expression represents the number of Calories that Konnor can burn on the stationary bike?
What is the constant term of the polynomial 4d + 6 + 3d^2?
When 3x^2 + 7x - 6 + 2x^3 is written in standard form, the leading coefficient is
An expression of the fifth degree is written with a leading coefficient of seven and a constant of six. Which expression is correctly written for these conditions?
When (x)(x - 5)(2x + 3) is expressed as a polynomial in standard form, which statement about the resulting polynomial is true?
Which polynomial has a leading coefficient of 4 and a degree of 3?
Students were asked to write an expression which had a leading coefficient of 3 and a constant term of -4. Which response is correct?
An example of a sixth-degree polynomial with a leading coefficient of seven and a constant term of four is:
Mrs. Allard asked her students to identify which of the polynomials below are in standard form and explain why. Which student's response is correct?
Students were asked to write 6x^5 + 8x - 3x^3 + 7x^7 in standard form. Shown below are four student responses. Which student is correct?
Which student’s response is correct?
Do you agree with Pat's answer? Explain your reasoning.
The property Kate used when solving p^2 + 5 = 8p - 7 is:
Which property justifies Emily's first step?
Which property justifies Jennifer's first step?
Which property justifies Evan's step?
Which two properties did Britney use to get to step 1?
In the process of solving the equation 10x^2 - 12x - 16x = 6, George wrote 2(5x^2 - 14x) = 2(3), followed by 5x^2 - 14x = 3. Which properties justify George's process?
A student is in the process of solving an equation. The original equation and the first step are shown below: Original: 3a + 6 = 2 - 5a + 7, Step one: 3a + 6 = 2 + 7 - 5a. Which property did the student use for the first step? Explain why this property is correct.
John was given the equation 4(2a + 3) = -3(a - 1) + 31 - 11a to solve. Some of the steps and their reasons have already been completed. State a property of numbers for each missing reason. Given: 4(2a + 3) = -3(a - 1) + 31 - 11a, 8a + 12 = -3a + 3 + 31 - 11a [____________________], 8a + 12 = 34 - 14a [Combining like terms], 22a + 12 = 34 [____________________]
Which value of x satisfies the equation (7/3)x + (9/28) = 20?
What is the value of x in the equation (x - 2)/3 + 1/6 = 5/6?
An equation is given below: 4(x - 7) = 0.3(x + 2) + 2.11. The solution to the equation is:
Which value of x satisfies the equation (5/6) * (3/8) - x = 16?
The value of x which makes (2x/3 - 1/4) = (1/5)x - 4/3 true is:
The solution to -2(1 - 4x) = 3x + 8 is:
What is the solution to the equation (3/5)x + 4/3 = 1.04?
The value of x that satisfies the equation 4/3 = x + 10/15 is:
Which value of x makes (x - 3/4 + 2/3) = 17/12 true?
The solution to 3(x - 8) + 4x = 8x + 4 is:
Which of the equations below have the same solution?
What is the solution to 2 + 3(2a + 1) = 3(a + 2)?
Solve the equation algebraically for the exact value of x: 6 - 2/3(x + 5) = 4x
Solve algebraically for x: -2/3(x + 12) + 2/3x = -5/4x + 2
A parking garage charges a base rate of $3.50 up to 2 hours, and an hourly rate for each additional hour. The sign below gives the prices for up to 5 hours of parking: 2 hours - $3.50, 3 hours - $9.00, 4 hours - $14.50, 5 hours - $20.00. Which linear equation can be used to find x, the additional hourly parking rate?
John has four more nickels than dimes in his pocket, for a total of $1.25. Which equation could be used to determine the number of dimes, x, in his pocket?
Kendal bought x boxes of cookies to bring to a party. Each box contains 12 cookies. She decides to keep two boxes for herself. She brings 60 cookies to the party. Which equation can be used to find the number of boxes, x, Kendal bought?
Nicci's sister is 7 years less than twice Nicci's age, a. The sum of Nicci's age and her sister's age is 41. Which equation represents this relationship?
Joe has dimes and nickels in his piggy bank totaling $1.45. The number of nickels he has is 5 more than twice the number of dimes, d. Which equation could be used to find the number of dimes he has?
A gardener is planting two types of trees: Type A is three feet tall and grows at a rate of 15 inches per year. Type B is four feet tall and grows at a rate of 10 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
The amount of energy, Q, in joules, needed to raise the temperature of m grams of a substance is given by the formula Q = mC(T_f - T_i), where C is the specific heat capacity of the substance. If its initial temperature is T_i, an equation to find its final temperature, T_f, is:
The formula for blood flow rate is given by F = (p1 - p2)/r, where F is the flow rate, p1 is the initial pressure, p2 is the final pressure, and r is the resistance created by blood vessel size. Which formula cannot be derived from the given formula?
Students were asked to write a formula for the length of a rectangle by using the formula for its perimeter, p = 2l + 2w. Three of their responses are shown below. Which responses are correct?
The formula for the volume of a cone is V = (1/3)πr^2h. The radius, r, of the cone may be expressed as:
The equation for the volume of a cylinder is V = πr^2h. The positive value of r, in terms of h and V, is:
The distance a free falling object has traveled can be modeled by the equation d = 1/2at^2, where a is acceleration due to gravity and t is the amount of time the object has fallen. What is t in terms of a and d?
The formula for electrical power, P, is P = I^2R, where I is current and R is resistance. The formula for I in terms of P and R is:
The formula for the area of a trapezoid is A = 1/2h(b1 + b2). Express b1 in terms of A, h, and b2. The area of a trapezoid is 60 square feet, its height is 6 ft, and one base is 12 ft. Find the number of feet in the other base.
The volume of a large can of tuna fish can be calculated using the formula V = πr^2h. Write an equation to find the radius, r, in terms of V and h. Determine the diameter, to the nearest inch, of a large can of tuna fish that has a volume of 66 cubic inches and a height of 3.3 inches.
The formula for the sum of the degree measures of the interior angles of a polygon is S = 180(n - 2). Solve for n, the number of sides of the polygon, in terms of S.
Solve the equation below for x in terms of a: 4(ax + 3) - 3ax = 25 + 3a
The formula for the volume of a cone is V = 1/3πr^2h. Solve the equation for h in terms of V, r, and π.
Using the formula for the volume of a cone, express r in terms of V, h, and π.
The formula Fg = GM1M2/r^2 calculates the gravitational force between two objects where G is the gravitational constant, M1 is the mass of one object, M2 is the mass of the other object, and r is the distance between them. Solve for the positive value of r in terms of Fg, G, M1, and M2.
Bamboo plants can grow 91 centimeters per day. What is the approximate growth of the plant in inches per hour?
Sarah travels on her bicycle at a speed of 22.7 miles per hour. What is Sarah's approximate speed in kilometers per minute?
The Utica Boilermaker is a 15-kilometer road race. Sara is signed up to run this race and has done the following training runs: I. 10 miles II. 44,880 feet III. 15,560 yards. Which run(s) are at least 15 kilometers?
A typical marathon is 26.2 miles. Allan averages 12 kilometers per hour when running in marathons. Determine how long it would take Allan to complete a marathon, to the nearest tenth of an hour. Justify your answer.
A news report suggested that an adult should drink a minimum of 4 pints of water per day. Based on this report, determine the minimum amount of water an adult should drink, in fluid ounces, per week.
Patricia is trying to compare the average rainfall of New York to that of Arizona. A comparison between these two states for the months of July through September would be best measured in:
The owner of a landscaping business wants to know how much time, on average, his workers spend mowing one lawn. Which is the most appropriate rate with which to calculate an answer to his question?
A two-inch-long grasshopper can jump a horizontal distance of 40 inches. An athlete, who is five feet nine, wants to cover a distance of one mile by jumping. If this person could jump at the same ratio of body-length to jump-length as the grasshopper, determine, to the nearest jump, how many jumps it would take this athlete to jump one mile.
The distance traveled is equal to the rate of speed multiplied by the time traveled. If the distance is measured in feet and the time is measured in minutes, then the rate of speed is expressed in which units? Explain how you arrived at your answer.
Determine the speed of the plane, at cruising altitude, in miles per minute.
Write an equation to represent the number of miles the plane has flown, y, during x minutes at cruising altitude, only. Assuming that the plane maintains its speed at cruising altitude, determine the total number of miles the plane has flown 2 hours into the flight.
Determine the total hours it will take them to reach their destination.
Calculate to the nearest tenth of an hour how much time the family will save if her dad drives the remainder of the trip.
Write equations to model the distances Aidan and Ella traveled. Graph these equations. How many seconds does it take Aidan to catch up to Ella? Justify your answer.
During which time interval did the cost increase at the greatest average rate?
The table below shows the year and the number of households in a building that had high-speed broadband internet access. Number of Households: 11, 16, 23, 33, 42, 47 Year: 2002, 2003, 2004, 2005, 2006, 2007 For which interval of time was the average rate of change the smallest?
The table below shows the average diameter of a pupil in a person’s eye as he or she grows older. Age (years): 20, 30, 40, 50, 60, 70, 80 Average Pupil Diameter (mm): 4.7, 4.3, 3.9, 3.5, 3.1, 2.7, 2.3 What is the average rate of change, in millimeters per year, of a person’s pupil diameter from age 20 to age 80?
Joey enlarged a 3-inch by 5-inch photograph on a copy machine. He enlarged it four times. The table below shows the area of the photograph after each enlargement. Enlargement: 0, 1, 2, 3, 4 Area (square inches): 15, 18.8, 23.4, 29.3, 36.6 What is the average rate of change of the area from the original photograph to the fourth enlargement, to the nearest tenth?
Which statement does not correctly interpret voting rates by age based on the given graph?
During which time interval did the temperature in the kiln show the greatest average rate of change?
Which statement about average resting heart rates is *not* supported by the graph?
Over which interval does the helicopter have the *slowest* average rate of change?
What is the average speed, in meters per second, of the rock between 5 and 10 seconds after it was dropped?
The average rate of change for Tony's investment was $19 per:
Determine the average rate of change between hour 2 and hour 7, including units.
Calculate the average rate of change from 3 to 9 seconds, in feet per second.
Which interval, 1 a.m. to 12 noon or 6 a.m. to 3 p.m., has the greater rate of snowfall, in inches per hour? Justify your answer.
The graph below shows the variation in the average temperature of Earth's surface from 1950-2000, according to one source. During which years did the temperature variation change the most per unit time? Explain how you determined your answer.
A manager wanted to analyze the online shoe sales for his business. He collected data for the number of pairs of shoes sold each hour over a 14-hour time period. He created a graph to model the data, as shown below. The manager believes the set of integers would be the most appropriate domain for this model. Explain why he is incorrect. State the entire interval for which the number of pairs of shoes sold is increasing. Determine the average rate of change between the sixth and fourteenth hours, and explain what it means in the context of the problem.
A population of rabbits in a lab, p(x), can be modeled by the function p(x) = 20(1.014)^x, where x represents the number of days since the population was first counted. Explain what 20 and 1.014 represent in the context of the problem. Determine, to the nearest tenth, the average rate of change from day 50 to day 100.
In 2013, the United States Postal Service charged $0.46 to mail a letter weighing up to 1 oz. and $0.20 per ounce for each additional ounce. Which function would determine the cost, in dollars, c(z), of mailing a letter weighing z ounces where z is an integer greater than 1?
Last weekend, Emma sold lemonade at a yard sale. The function P(c) = 0.50c - 9.96 represented the profit, P(c), Emma earned selling c cups of lemonade. Sales were strong, so she raised the price for this weekend by 25 cents per cup. Which function represents her profit for this weekend?
A high school club is researching a tour package offered by the Island Kayak Company. The company charges $35 per person and $245 for the tour guide. Which function represents the total cost, C(x), of this kayak tour package for x club members?
At Benny's Cafe, a mixed-greens salad costs $5.75. Additional toppings can be added for $0.75 each. Which function could be used to determine the cost, c(s), in dollars, of a salad with s additional toppings?
Alex is selling tickets to a school play. An adult ticket costs $6.50 and a student ticket costs $4.00. Alex sells x adult tickets and 12 student tickets. Write a function, f(x), to represent how much money Alex collected from selling tickets.
Jackson is starting an exercise program. The first day he will spend 30 minutes on a treadmill. He will increase his time on the treadmill by 2 minutes each day. Write an equation for T(d), the time, in minutes, on the treadmill on day d. Find T(6), the minutes he will spend on the treadmill on day 6.
Jim is a furniture salesman. His weekly pay is $300 plus 3.5% of his total sales for the week. Jim sells x dollars' worth of furniture during the week. Write a function, p(x), which can be used to determine his pay for the week. Use this function to determine Jim's pay to the nearest cent for a week when his sales total is $8250.
The cost of airing a commercial on television is modeled by the function C(n) = 110n + 900, where n is the number of times the commercial is aired. Based on this model, which statement is true?
A satellite television company charges a one-time installation fee and a monthly service charge. The total cost is modeled by the function y = 40 + 90x. Which statement represents the meaning of each part of the function?
Each day, a local dog shelter spends an average of $2.40 on food per dog. The manager estimates the shelter's daily expenses, assuming there is at least one dog in the shelter, using the function E(x) = 30 + 2.40x. Which statements regarding the function E(x) are correct?
The cost of belonging to a gym can be modeled by C(m) = 50m + 79.50, where C(m) is the total cost for m months of membership. State the meaning of the slope and y-intercept of this function with respect to the costs associated with the gym membership.
A student plotted the data from a sleep study and used the equation y = -0.09x + 9.24 to model the data. What does the rate of change represent in terms of these data?
During a recent snowstorm in Red Hook, NY, Jaime noted that there were 4 inches of snow on the ground at 3:00 p.m., and there were 6 inches of snow on the ground at 7:00 p.m. If she were to graph these data, what does the slope of the line connecting these two points represent in the context of this problem?
The table below shows the height in feet, h(t), of a hot-air balloon and the number of minutes, t, the balloon is in the air:
Which function has the same y-intercept as the given graph?
On the set of axes provided, draw the graph of the equation y = -3/4x + 3. Is the point (3,2) a solution to the equation? Explain your answer based on the graph drawn.
Samantha buys a package of sugar cookies. The nutrition label states that each serving size of 3 cookies contains 160 Calories. Samantha creates the graph below showing the relationship between the number of cookies eaten and the number of Calories consumed. Explain why it is appropriate for Samantha to draw a line through the points on the graph.
On the set of axes below, graph the line whose equation is 2y = -3x - 2. This linear equation contains the point (2, k). State the value of k.
How many of the equations listed below represent the line passing through the points (2,3) and (4,-7)?
The graph of a linear equation contains the points (3,11) and (-2,1). Which point also lies on the graph?
Sue and Kathy were doing their algebra homework. They were asked to write the equation of the line that passes through the points (-3,4) and (6,1). Sue wrote y - 4 = -1/3(x + 3) and Kathy wrote y = -1/3x + 3. Justify why both students are correct.
The inequality 7 - 2/3x < x - 8 is equivalent to:
When 3x + 2 <= 5(x - 4) is solved for x, the solution is:
Which value of x is a solution to the equation 13 - 36x^2 = -12?
The solution of the equation (x + 3)^2 = 7 is:
The solutions to (x + 4)^2 - 2 = 7 are:
What are the solutions to the equation 3(x - 4)^2 = 27?
What is the solution of the equation 2(x + 2)^2 - 4 = 28?
A correct next step in the solution of the problem is:
Solve the quadratic equation 4x^2 - 5 = 75 for the exact values of x.
Solve 5x^2 = 180 algebraically.
Solve 6x^2 - 42 = 0 for the exact values of x.
How many feet did the object fall between one and two seconds after it was dropped? Determine, algebraically, how many seconds it will take for the object to reach the ground.
What is the solution set of the equation (x - 2)(x - a) = 0?
Which equation has the same solutions as 2x^2 + x - 3 = 0?
What are the solutions to the equation 3x^2 + 10x = 8?
In the equation x^2 + 10x + 24 = (x + a)(x + b), b is an integer. Find algebraically all possible values of b.
Solve x^2 - 8x - 9 = 0 algebraically. Explain the first step you used to solve the given equation.
Solve 6x^2 + 5x - 6 = 0 algebraically for the exact values of x.
Solve 8m^2 + 20m = 12 for m by factoring.
Solve the equation 4x^2 - 12x = 7 algebraically for x.
Solve the equation for y: (y - 3)^2 = 4y - 12.
Amy solved the equation 2x^2 + 5x - 42 = 0. She stated that the solutions to the equation were 7/2 and -6. Do you agree with Amy's solutions? Explain why or why not.
Write an equation that defines m(x) as a trinomial where m(x) = (3x - 1)(3 - x) + 4x^2 + 19. Solve for x when m(x) = 0.
Janice is asked to solve 0 = 64x^2 + 16x - 3. Use Janice's procedure to solve the equation for x. Explain the method Janice used to solve the quadratic equation.
The quadratic equation x^2 - 6x = 12 is rewritten in the form (x + p)^2 = q, where q is a constant. What is the value of p?
Which equation has the same solution as x^2 - 6x - 12 = 0?
Which equation has the same solutions as x^2 + 6x - 7 = 0?
When solving the equation x^2 - 8x - 7 = 0 by completing the square, which equation is a step in the process?
The method of completing the square was used to solve the equation 2x^2 - 12x + 6 = 0. Which equation is a correct step when using this method?
Which equation has the same solution as x^2 + 8x - 33 = 0?
When solving x^2 - 10x - 13 = 0 by completing the square, which equation is a step in the process?
When using the method of completing the square, which equation is equivalent to x^2 - 12x - 10 = 0?
What are the roots of the equation x^2 + 4x - 16 = 0?
What are the solutions to the equation x^2 - 8x = 24?
What are the solutions to the equation x^2 - 8x = 10?
When directed to solve a quadratic equation by completing the square, Sam arrived at the equation (x - 5/2)^2 = 13/4. Which equation could have been the original equation given to Sam?
Solve the equation x^2 - 6x = 15 by completing the square.
Solve the following equation by completing the square: x^2 + 4x = 2.
Use the method of completing the square to determine the exact values of x for the equation x^2 - 8x + 6 = 0.
Determine the exact values of x for x^2 - 8x - 5 = 0 by completing the square.
A student was given the equation x^2 + 6x - 13 = 0 to solve by completing the square. State the value of c that creates a perfect square trinomial. Explain how the value of c is determined.
If the quadratic formula is used to find the roots of the equation x^2 - 6x - 19 = 0, the correct roots are:
The roots of x^2 - 5x - 4 = 0 are:
Solve for x to the nearest tenth: x^2 + x - 5 = 0.
Use the quadratic formula to solve x^2 - 4x + 1 = 0 for x. Round the solutions to the nearest hundredth.
Solve 4w^2 + 12w - 44 = 0 algebraically for w, to the nearest hundredth.
Solve 3x^2 - 5x - 7 = 0 algebraically for all values of x, rounding to the nearest tenth.
Fred's teacher gave the class the quadratic function f(x) = 4x^2 + 16x + 9. a) State two different methods Fred could use to solve the equation f(x) = 0. b) Using one of the methods stated in part a, solve f(x) = 0 for x, to the nearest tenth.
How many real-number solutions does the equation 4x^2 + 2x + 5 = 0 have?
How many real solutions does the equation x^2 - 2x + 5 = 0 have? Justify your answer.
Is the solution to the quadratic equation 0 = 2x^2 + 3x - 10 rational or irrational? Justify your answer.
Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which equation could be used to find Jeremy’s age, j, if he is the younger man?
Abigail's and Gina's ages are consecutive integers. Abigail is younger than Gina and Gina's age is represented by x. If the difference of the square of Gina's age and eight times Abigail's age is 17, which equation could be used to find Gina's age?
The length of the shortest side of a right triangle is 8 inches. The lengths of the other two sides are represented by consecutive odd integers. Which equation could be used to find the lengths of the other sides of the triangle?
Joe has a rectangular patio that measures 10 feet by 12 feet. He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x. Which equation could be used to determine x?
The length of a rectangular patio is 7 feet more than its width, w. The area of the patio, A(w), can be represented by the function:
A school is building a rectangular soccer field that has an area of 6000 square yards. The soccer field must be 40 yards longer than its width. Determine algebraically the dimensions of the soccer field, in yards.
A landscaper is creating a rectangular flower bed such that the width is half of the length. The area of the flower bed is 34 square feet. Write and solve an equation to determine the width of the flower bed, to the nearest tenth of a foot.
A contractor has 48 meters of fencing to use as the perimeter of a rectangular garden. The length of one side of the garden is represented by x, and the area of the garden is 108 square meters. Determine, algebraically, the dimensions of the garden in meters.
The length of a rectangular sign is 6 inches more than half its width. The area of this sign is 432 square inches. Write an equation in one variable that could be used to find the number of inches in the dimensions of this sign. Solve this equation algebraically to determine the dimensions of this sign, in inches.
A rectangular garden measuring 12 meters by 16 meters is to have a walkway installed around it with a width of x meters. Together, the walkway and the garden have an area of 396 square meters. Write an equation that can be used to find x, the width of the walkway. Describe how your equation models the situation. Determine and state the width of the walkway, in meters.
New Clarendon Park is undergoing renovations to its gardens. One garden that was originally a square is being adjusted so that one side is doubled in length, while the other side is decreased by three meters. The new rectangular garden will have an area that is 25% more than the original square garden. Write an equation that could be used to determine the length of a side of the original square garden. Explain how your equation models the situation. Determine the area, in square meters, of the new rectangular garden.
A rectangular picture measures 6 inches by 8 inches. Simon wants to build a wooden frame for the picture so that the framed picture takes up a maximum area of 100 square inches on his wall. The pieces of wood used to build the frame all have the same width. Write an equation or inequality that could be used to determine the maximum width of the pieces of wood for the frame Simon could create. Explain how your equation or inequality models the situation. Solve the equation or inequality to determine the maximum width of the pieces of wood used for the frame to the nearest tenth of an inch.
In the function f(x) = (x - 2)^2 + 4, the minimum value occurs when x is:
If Lylah completes the square for f(x) = x^2 - 12x + 7 in order to find the minimum, she must write f(x) in the general form f(x) = (x - a)^2 + b. What is the value of a for f(x)?
Which equation is equivalent to y = x^2 + 24x - 18?
Which equation and ordered pair represent the correct vertex form and vertex for j(x) = x^2 - 12x + 7?
Which equation is equivalent to y - 34 = x(x - 12)?
The function f(x) = 3x^2 + 12x + 11 can be written in vertex form as
An equation that represents the function could be
Based on the provided data, which statement is not a valid conclusion about the rocket's flight?
For which interval is the ball's height always decreasing on the given graph?
The expression $-4.9t^2 + 50t + 2$ represents the height, in meters, of a toy rocket $t$ seconds after launch. What is the initial height of the rocket, in meters?
The height of a ball Doreen tossed into the air can be modeled by the function $h(x) = -4.9x^2 + 6x + 5$, where $x$ is the time elapsed in seconds, and $h(x)$ is the height in meters. What does the number 5 in the function represent?
A football player attempts to kick a football over a goal post. The path of the football can be modeled by the function h(x) = -1/225x^2 + 2/3x, where x is the horizontal distance from the kick, and h(x) is the height of the football above the ground, both measured in feet. On a set of axes, graph the function y = h(x) over the interval 0 ≤ x ≤ 150.
Determine the vertex of the function y = h(x).
Interpret the meaning of this vertex in the context of the problem.
The goal post is 10 feet high and 45 yards away from the kick. Will the ball be high enough to pass over the goal post? Justify your answer.
A laboratory technician used the function t(m) = 2(3)^{2m + 1} to model her research. Consider the following expressions: - I. 6(3)^{2m} - II. 6(6)^{2m} - III. 6(9)^m The function t(m) is equivalent to which of the following?
The growth of a certain organism can be modeled by C(t) = 10(1.029)^{24t}, where C(t) is the total number of cells after t hours. Which function is approximately equivalent to C(t)?
A computer application generates a sequence of musical notes using the function f(n) = 6(16)^n, where n is the number of the note in the sequence and f(n) is the note frequency in hertz. Which function will generate the same note sequence as f(n)?
The number of bacteria grown in a lab can be modeled by P(t) = 300 * 2^{4t}, where t is the number of hours. Which expression is equivalent to P(t)?
Mario's $15,000 car depreciates in value at a rate of 19% per year. The value, V, after t years can be modeled by the function V = 15,000(0.81)^t. Which function is equivalent to the original function?
Nora inherited a savings account that was started by her grandmother 25 years ago. This scenario is modeled by the function A(t) = 5000(1.013)^t + 25, where A(t) represents the value of the account, in dollars, t years after the inheritance. Which function below is equivalent to A(t)?
The population of a city can be modeled by P(t) = 3810(1.0005)^{7t}, where P(t) is the population after t years. Which function is approximately equivalent to P(t)?
Krystal was given $3000 when she turned 2 years old. Her parents invested it at a 2% interest rate compounded annually, with no deposits or withdrawals made. Which expression can be used to determine how much money Krystal had in the account when she turned 18?
The country of Benin in West Africa has a population of 9.05 million people, growing at a rate of 3.1% each year. Which function can be used to find the population 7 years from now?
Anne invested $1000 in an account with a 1.3% annual interest rate, with no deposits or withdrawals for 2 years. If interest was compounded annually, which equation represents the balance in the account after 2 years?
A high school sponsored a badminton tournament. After each round, half of the players were eliminated. If there were 64 players at the start, which equation models the number of players left after 3 rounds?
Emily was given $600 for her high school graduation and invested it in an account that earns 2.4% interest per year, with no deposits or withdrawals made. Which expression can be used to determine the amount of money in the account after 4 years?
Sunny purchases a new car for $29,873. The car depreciates 20% annually. Which expression can be used to determine the value of the car after t years?
A student invests $500 for 3 years in a savings account earning 4% interest per year, with no further deposits or withdrawals. Which statement does not yield the correct balance at the end of 3 years?
Rhonda deposited $3000 in an account at Merrick National Bank, earning 4.2% interest, compounded annually, with no additional deposits or withdrawals. Write an equation to find B, her account balance after t years.
The table shows the temperature T(m) of a cup of hot chocolate chilling over several minutes m:
Jill invests $400 in a savings bond. The table shows the value V(x) of the bond, in hundreds of dollars, after x years:
Marc bought a new laptop for $1250 and tracked its value over the next three years. Which function can be used to determine the value of the laptop for *x* years after the purchase?
Write an exponential equation for the graph shown below. Explain how you determined the equation.
Mike wants to find another point on the graph of an exponential function. Is he correct in stating (5, 28.6) is a point on the function? Explain your reasoning.
The equation y = 5000(0.98)^x represents the value y of a savings account that was left inactive for a period of *x* years. What is the y-intercept of this equation, and what does it represent?
The function V(t) = 1350(1.017)^t represents the value V(t), in dollars, of a comic book *t* years after its purchase. What is the yearly rate of appreciation of the comic book?
In the equation \( A = 1300(1.02)^7 \), what does 1.02 represent?
Milton has his money invested in a stock portfolio. The value, \( v(x) = 30,000(0.78)^x \), where \( x \) is the number of years since he made his investment. Which statement describes the rate of change of the value of his portfolio?
A population of bacteria can be modeled by the function \( f(t) = 1000(0.98)^t \), where \( t \) represents the time since the population started decaying, and \( f(t) \) represents the population at time \( t \). What is the rate of decay for this population?
The equation \( V(t) = 12,000(0.75)^t \) represents the value of a motorcycle \( t \) years after it was purchased. Which statement is true?
The 2014 winner of the Boston Marathon runs as many as 120 miles per week. During the last few weeks of his training, his mileage can be modeled by \( M(w) = 120(0.90)^w - 1 \). Which statement is true about the model \( M(w) \)?
In the equation \( A = P(1 \pm r)^t \), \( A \) is the total amount, \( P \) is the principal, \( r \) is the interest rate, and \( t \) is the time in years. Which statement correctly relates to the interest rate for each given equation?
The breakdown of a sample of a chemical compound is represented by \( p(t) = 300(0.5)^t \). Explain what 0.5 and 300 represent.
The number of carbon atoms in a fossil is given by the function y = 5100(0.95)^x, where x represents the number of years since being discovered. What is the percent of change each year? Explain how you arrived at your answer.
The value, v(t), of a car depreciates according to the function v(t) = P(0.85)^t, where P is the purchase price of the car and t is the time, in years, since the car was purchased. State the percent that the value of the car decreases by each year. Justify your answer.
Graph the function f(x) = 2x - 7 on the set of axes below. If g(x) = 1.5x - 3, determine if f(x) > g(x) when x = 4. Justify your answer.
If point (K, -5) lies on the line whose equation is 3x + y = 7, then the value of K is:
The point (3, w) is on the graph of y = 2x + 7. What is the value of w?
Which ordered pair does not fall on the line formed by the other three?
Which point is not on the graph represented by y = x^2 + 3x - 6?
Which ordered pair below is not a solution to f(x) = x^2 - 3x + 4?
If C = G - 3F, find the trinomial that represents C when F = 2x^2 + 6x - 5 and G = 3x^2 + 4.
Which expression is equivalent to (x + 4)^2 (x + 4)^3?
The expression 1/3 x(6x^2 - 3x + 9) is equivalent to:
When written in standard form, the product of (3 + x) and (2x - 5) is:
The expression (m - 3)^2 is equivalent to:
Which trinomial is equivalent to 3(x - 2)^2 - 2(x - 1)?
When (2x - 3)^2 is subtracted from 5x^2, the result is:
Which expression is not equivalent to -4x^3 + x^2 - 6x + 8?
What is the product of 2x + 3 and 4x^2 - 5x + 6?
Fred is given a rectangular piece of paper. If the length of Fred's piece of paper is represented by 2x - 6 and the width is represented by 3x - 5, then the paper has a total area represented by:
When written in factored form, 4w^2 - 11w - 3 is equivalent to:
Which product is equivalent to 4x^2 - 3x - 27?
The area of a rectangle is represented by 3x^2 - 10x - 8. Which expression can also be used to represent the area of the same rectangle?
The expression 4x^2 - 4x - 120 is equivalent to:
Which expression is equivalent to x^4 - 12x^2 + 36?
Factor completely: 3y^2 - 12y - 288.
Which expression is equivalent to 36x^2 - 100?
Which expression is equivalent to 16x^2 - 36?
The expression 49x^2 - 36 is equivalent to:
The expression 4x^2 - 25 is equivalent to:
The expression 16x^2 - 81 is equivalent to:
The expression 36x^2 - 9 is equivalent to:
Which expression is equivalent to 18x^2 - 50?
Which expression is equivalent to y^4 - 100?
When factored completely, the expression p^4 - 81 is equivalent to:
The expression x^4 - 16 is equivalent to:
The expression w^4 - 36 is equivalent to:
Which expression is equivalent to 16x^4 - 64?
If the area of a rectangle is expressed as x^4 - 9y^2, then the product of the length and the width of the rectangle could be expressed as:
Factor completely: 4x^3 - 49x
Factor the expression x^4 - 36x^2 completely.
Factor x^4 - 16 completely.
Factor the expression x^4 + 6x^2 - 7 completely.
The graphs below represent functions defined by polynomials. For which function are the zeros of the polynomials 2 and -3?
The graphs below represent four polynomial functions. Which of these functions has zeros of 2 and -3?
Which of these points can determine the zeros of the equation $ y = \frac{1}{2}x^2 - x - 4 $?
Which function has zeros of -4 and 2?
Keith determines the zeros of the function $ f(x) $ to be -6 and 5. What could be Keith's function?
Which polynomial function has zeros at -3, 0, and 4?
A cubic function is graphed on the set of axes below. Which function could represent this graph?
A polynomial function is graphed below. Which function could represent this graph?
Compared to the graph of f(x) = x^2, the graph of g(x) = (x - 2)^2 + 3 is the result of translating f(x):
How does the graph of f(x) = 3(x - 2)^2 + 1 compare to the graph of g(x) = x^2?
If the parent function of f(x) is p(x) = x^2, then the graph of the function f(x) = (x - k)^2 + 5, where k > 0, would be a shift of:
Caitlin graphs the function f(x) = ax^2, where a is a positive integer. If Caitlin multiplies a by -2, when compared to f(x), the new graph will become:
What would be the order of these quadratic functions when they are arranged from the narrowest graph to the widest graph?
If the original function f(x) = 2x^2 - 1 is shifted to the left 3 units to make the function g(x), which expression would represent g(x)?
Given: f(x) = (x - 2)^2 + 4, g(x) = (x - 5)^2 + 4, When compared to the graph of f(x), the graph of g(x) is:
Josh graphed the function f(x) = -3(x - 1)^2 + 2. He then graphed the function g(x) = -3(x - 1)^2 - 5 on the same coordinate plane. The vertex of g(x) is:
If x = 2, y = sqrt(2), and w = sqrt(8), which expression results in a rational number?
Given the following expressions, which expression(s) result in an irrational number?
Given: L = 2, M = 3^(3/2), N =16, P = 9, which expression results in a rational number?
Is the product of two irrational numbers always irrational? Justify your answer.
Ms. Fox asked her class, 'Is the sum of 4.2 and sqrt(2) rational or irrational?' Patrick answered that the sum would be irrational. State whether Patrick is correct or incorrect. Justify your reasoning.
Determine if the product of sqrt(3) and sqrt(8) is rational or irrational. Explain your answer.
Is the sum of sqrt(3) and sqrt(4) rational or irrational? Explain your answer.
Jakob is working on his math homework. He decides that the sum of the expression (1/3) + (6/5)sqrt(7) must be rational because it is a fraction. Is Jakob correct? Explain your reasoning.
State whether 7 - sqrt(2) is rational or irrational. Explain your answer.
Is the product of 16 and sqrt(4) rational or irrational? Explain your reasoning.
State whether the product of 3 and 9 is rational or irrational. Explain your answer.
Is the product of 1024 and -3.4 rational or irrational? Explain your reasoning.
Is the product of 8 and sqrt(98) rational or irrational? Justify your answer.