Algebra II B

Use the invertible function f(x)=x+3−2 to answer the questions. Part A: What is f−1(x)? Part B: What is the domain of f−1? Select one answer for Part A and one answer for Part B.

A: f−1(x)=x2+4x+1, B: −2≤x<∞

What is the principal amount invested, P, in the compound interest equation B(t)=117(1+0.032512)12t? Enter your answer as a dollar amount, like this: $42.00.

$117.00

Consider the inequality x3+4x2−5x<0. Select all intervals for which the statement is true.

(0,1), (−∞,−5)

Which expressions are equivalent to x7? There may be more than one correct answer. Select all that apply.

(x21)1/3, x3⋅x4, x15x8

Consider the function f(x)=tan⁡⁡x with a domain of 0<x<π2, where x is in radians. What is the range of f−1(x)?

0<f−1(x)<π2

Which of the following expressions is/are equivalent to 3⋅36x? There may be more than one correct answer. Select all that apply.

12x⋅3x+1, 22x⋅32x+1, 3⋅62x

Consider the function f(x)=x3+12, and its inverse, f−1(x)=2x−13. Use f−1(x) to solve the equation 4.5=x3+12. What is the correct solution?

2

Which of the following expressions is/are equivalent to 5⋅45t? There may be more than one correct answer. Select all that apply.

5t+1⋅32t, 5t⋅(3t)2⋅5, 5t+1⋅9t

Which expression(s) is (are) equivalent to 7⋅54t? There may be more than one correct answer. Select all that apply.

7⋅6t⋅32t, 7⋅6t⋅9t, 7⋅(2⋅33)t, 7⋅2t⋅33t

Tadashi is a landscape architect, and he is designing a pool for a client's backyard. The pool will be twice as long as it is wide, and it will have a 3-foot walkway surrounding it on all sides. Which equation represents the total area that the pool surface and walkway will take up in the backyard?

A(w)=(w+6)(2w+6)

Consider the function f(x)=−x+2+5 for −2≤x<∞. The inverse of this function is f−1(x)=x2−10x+27. A: What is the domain of f−1? B: Why must the domain of f−1 be restricted? Select one answer for Part A, and select all correct answers for Part B.

B: Both functions f(x) and f−1(x) must be one-to-one, and f−1(x) is not one-to-one unless the domain is restricted., A: −∞<x≤5, B: The domain of f−1(x) must be restricted so that it matches the range of f(x).

Use the invertible function f(x)=7−x5+3 to answer the question. Which option shows the correct steps to find f−1?

Step 1 f(x)=7−x5+3 Step 2 y=7−x5+3 Step 3 x=7−y5+3 Step 4 x−3=7−y5 Step 5 (x−3)5=7−y Step 6 y=7−(x−3)5 Step 7 f−1(x)=7−(x−3)5

Use a graphing calculator, or another piece of technology, to graph the equations of the system {x+1y−4−9xy−1=410x+3y=1 Which statements correctly describe the system? There is more than one correct answer. Select all correct answers.

The system consists of equations whose graphs never intersect., The system has no real solutions.

Perry has a piggy bank with q quarters, n nickels, d dimes, and p pennies. Which equation for t correctly represents the total value of the change in Perry's piggy bank?

t=0.25q+.05n+.10d+.01p

Use the function f(x)=4x2−3x+1 to answer the question. Which option(s) represent a restricted domain that makes f invertible? There may be more than one correct answer. Select all that apply.

−∞<x≤−38, 38≤x<∞, −∞<x<0, −38<x<38, 38<x<∞

Four friends are analyzing the system of equations {4x+5y=20−2x−52y=−10 Tyler, Jordan, Margot, and Naomi each reach a different conclusion about the system of equations. Which student's conclusion is correct?

Jordan notices that the first equation is equal to the second equation multiplied by −2, and he concludes that the system has infinitely many solutions.

Which statements about linear programming are true? There is more than one correct answer. Select all correct answers.

Linear programming is a special type of optimization., Linear programming is a method to achieve the best outcome of a situation., Constraints are a component of linear programming problems.

Use the following system of equations to answer the question. {2a+1a+3b−2=52a−42−7bb−5=6 Which observation about the system of equations is accurate?

The system is potentially solvable because there is an equal number of equations and unknowns.

If you graph the equations you chose in the previous question, what would the x- and y-axes represent?

The x-axis would represent the number of pounds of chocolate candy, while the y-axis would represent the number of pounds of fruit-flavored candy.

Use the properties of exponents to rewrite the expression x2⋅y5x−1⋅y4 in the form xa⋅yb. What are the values of a and b? Enter your answer as numbers in the order of a, b, placing a comma between the numbers, like this: 4, 2

3, 1

Is f(x)=4x2−3 a one-to-one function on the domain (−∞,∞)?

No, f(x)=4x2−3 is not a one-to-one function on (−∞,∞) because there is an output value that has more than one corresponding input value.

Examine the system of equations {x+2y+z=34x−y+9z=1−3x+5y=7 Which observation about the system of equations is accurate?

The system is potentially solvable because there is an equal number of equations and unknowns.

Which properties of exponents have been used to rewrite the expression 62t as (12t2t)2? There may be more than one correct answer. Select all that apply.

bxcx=(bc)x, (bx)y=bxy

Moira owns a small clothing store. She buys clothing items from a distributor and then sells them to her customers for a marked-up price. She determines the mark-up amount based on the distributor price. Which quantity represents the dependent variable in this context?

the mark-up amount

Consider the function f(x)=2sin⁡⁡(x2)−1 on [0,π2). Use a graphing tool to approximate the zero(s) to the nearest thousandth. Use π≅3.14 if needed.

x=13π

Examine the equation ex=(x−3)(y+4)(z−5). Which option correctly isolates y?

y=e2x(x−3)(z−5)−4

Which system of inequalities has no solution?

{y>34x+4 y<34x−5

Which description describes the potential graph of a system of linear equations with no solution?

A graph of two parallel lines that never intersect.

Use substitution to solve the system of equations {42x=42y−1253x=5y−8 The system has exactly one solution. What is the solution to the system? Enter your answer as an ordered pair, like this: (42, 53)

(-1, 5)

Which option is closest to the value of e?

2.71828

Use the exponential function f(t)=1.02t to answer the questions. A: What is the equation of the horizontal asymptote in this function? B: Does this function represent exponential growth or decay? Remember that an exponential function is growing if it is increasing, and decaying if it is decreasing. C: What is the initial value of the function, f(0)? Select one answer for question A, one answer for question B, and one answer for question C.

C: f(0)=1, B: exponential growth (increasing), A: y=0

Which sets represent the solutions to the compound inequality x>−8 and x≤5? There is more than one correct answer. Select all that apply.

(−8,5], (−∞,5]∩(−8,∞)

Which set represents the solutions to the compound inequality x<−3 or x≥7?

(−∞,−3)∪[7,∞)

Which solution set describes the solutions to the inequality −3x2+1≤−107?

(−∞,−6]∪[6,∞)

Which answer choice gives the solution set of the system of inequalities −5<x and y≥2?

The set of all ordered pairs whose x-coordinate is in the interval (−5,∞) and whose y-coordinate is in [2,∞).

Use substitution to solve the system of equations {7c=73d−322c+1=28+6d Which statements correctly describe the system? There is more than one correct answer. Select all correct answers. Note that ordered pairs are in the order (c,d).

The system has no solution., All values of c and d will result in false statements.

Robert and Natalie are raking leaves in their backyard. For every 50 pounds of leaves they rake, they create another leaf pile. What is the independent variable in this context?

the amount of leaves in pounds

Cadence is counting the number of beats in two songs, "Minuet" and "Duo." "Minuet" is w minutes long and has x beats per minute. "Duo" is y minutes long and has z beats per minute. "Duo" has at least as many beats as "Minuet." Which inequality correctly compares the total number of beats in "Minuet" to the total number of beats in "Duo"?

wx≤yz

Gil has x shirts, x pairs of pants, and x pairs of shoes. Gil then goes shopping and buys 3 shirts and 2 pairs of shoes. If an outfit consists of 1 shirt, 1 pair of pants, and 1 pair of shoes, which inequality correctly compares the number of possible outfits Gil owned before and after shopping?

x3<x3+5x2+6x

Brynn and Castor are counting their pocket change. Brynn's change is worth more than Castor's. Castor has q quarters and p pennies. Brynn has d dimes, q quarters, and n nickels. Which inequality correctly compares the value of Brynn's pocket change to the value of Castor's pocket change?

0.25q+.01p<.025q+.1d+.05n

Elaina throws a paper airplane across her bedroom. The height of the plane is modeled by the function h(t), where h is the height of the airplane in feet, and t is the time in seconds since she threw the plane. The function h(t) is shown in the graph. An even-degree polynomial whose ends are pointing downward and which passes through the points (negative 0.01, 0), (0.54, 6.93), (1.79, 1.69), (2.52, 2.95), and (2.98, 0). The x-axis is labeled as Time (in seconds), and the y-axis is labeled as Height (in feet). © 2017 FlipSwitch. Created using GeoGebra. After approximately how many seconds does the plane reach its maximum height?

0.5 seconds

Momoko owns a small business complex that consists of two square buildings that are attached on one side, as shown here. Two squares located back-to-back with the area measurements described in the question. © 2017 FlipSwitch. Created using GeoGebra. The area of the larger building is 10y square feet. The area of the smaller building is 5x square feet. Momoko decides to install a path that runs a length of 140 feet along the perimeter of the complex. Which radical equation correctly describes the length of the path in terms of x and y?

140=410y+25x

Ruben wants to plant a rectangular vegetable garden. He will use a patch of land that is 3 times as long as it is wide. Ruben also decides to leave a 3-inch border along the perimeter of the garden, where nothing will be planted. This leaves Ruben with a total planting area of 180 square inches. Which equation correctly describes the available planting area for the vegetable garden?

180=3x2+24x+36

Morad and Elias are car mechanics. Morad can complete a certain task in x hours. Elias can complete the same task in y hours. Which equation correctly describes their combined hourly rate of work?

1x+1y=x+yxy

What number, rounded to the nearest hundred thousandth (five decimal places), is represented by e?

2.71828

The following graph shows the height, h, of a model rocket as time, t, passes in seconds. A graph of a parabola opening downward and passing through the points (0, 12), (1, 20.04), (2.55, 24.76), (4, 20.64), (5, 13), and (6.1, 0). © 2017 FlipSwitch. Created using GeoGebra. What is the maximum height reached by the rocket? After how many seconds does the rocket reach that height? The rocket reaches a maximum height of about _[blank 1]_ feet after _[blank 2]_ seconds.

24.76, 2.55

Which option is equivalent to 2x⋅37+y=25⋅3y?

2x−5⋅37=1

A car dealership can maximize its daily profit from sales, P, according to the function P(s)=−150s2+9000s+5000, where s is the number of salespeople working that day. How many salespeople should be kept on hand in order to maximize daily profit? The dealership should keep _[blank]_ people on hand in order to maximize daily profit. Enter your answer as the number that correctly fills in the blank in the previous sentence, like this: 42

30

Jorge is testing an antenna's signal strength as it is exposed to cycles of interference. The antenna's signal strength during the test can be modeled by the function S(t)=sin⁡⁡t, where t is time in seconds. For what value of t in the domain 0≤t≤2π is the signal the weakest?

3π/2

Rada is buying a variety of candy from the store. She fills a bag with x pounds of chocolate candy priced at $4.99 per pound. She fills another bag with y pounds of fruit-flavored candy priced at $5.99 per pound. When she checks out, she is charged $39.43 for 7.3 pounds of candy. A: Which equation represents the amount of money Rada is spending on candy? B: Which equation represents the total weight of candy that Rada is buying? Select one answer for Question A and one answer for Question B.

4.99x+5.99y=39.43, x+y=7.3

A bird watcher spots a sparrow in a tree. The sparrow sits in a nest that is 10.5 feet above the bird watcher's eye level, at a 35° angle of elevation from the birdwatcher. The bird watcher then notices a hawk in the same tree, 7.4 feet above the sparrow, at a certain angle of elevation. The bird watcher stands 15 feet from the base of the tree. What is the angle of elevation from the bird watcher to the hawk? Round your answer to the closest degree.

50°

A rescue team is deployed via helicopter to rescue a struggling swimmer. The helicopter locates the swimmer, who is several feet from a tethered buoy. The helicopter hovers 400 feet over the buoy as its team prepares to rescue the swimmer. Initially, the swimmer sees the helicopter at an angle of elevation of x degrees. The swimmer then swims 5 feet closer to the buoy, and now sees the helicopter at an angle of y degrees. Which trigonometric equation correctly models the distance the swimmer swam toward the buoy in terms of x and y?

5=400tan⁡x−400tan⁡y

The pH level in a public swimming pool must stay between 7.2 and 8 in order to be safe for swimmers. As part of a routine inspection, the pH of one city pool was monitored for three days. The results of the test are shown in the graph. An even-degree polynomial opening up and passing through the points (0.5, 11), (1.19, 6.15), (2.28, 7.6), (2.77, 7.44), and (3.5, 11). The x-axis is labeled as Time (in days) and the y-axis is labeled as pH level. © 2017 FlipSwitch. Created using GeoGebra. What was the approximate minimum pH recorded during the test?

6.2

Use the compound interest equation B(t)=500(1.001)12t to answer the questions. A: Which option correctly shows the equation rewritten in the form B(t)=P(1+rn)nt? B: What is the interest rate, r, written as a percentage? Select one answer for question A and one answer for question B.

A: B(t)=500(1+.01212)12t, B: 1.2%

The trajectory of an object is represented by the equation f(x)=−x2+4x+15, where x represents seconds from when it's thrown and f(x) represents the height of the object in feet. Part A: Will the object reach a height of 20 feet? Why or why not? Part B: After how many seconds will the object reach the ground? Select one answer for Part A and one answer for Part B. Make sure your selection for Part A answers both parts of the question correctly.

A: It is not possible for the object to reach 20 feet. The y-coordinate of the maximum is 19, which describes the maximum height of the object. Because 19<20, the object will not reach the height of 20 feet., B: The object will reach the ground in approximately 6.36 seconds.

Lynton runs a rental shop for dirt bikes. He currently charges $60 per bike rental, and he averages 25 rentals per day. Lynton has been experimenting with his rental price, and he knows that for every 5 dollars he raises the rental price, he loses 3 customers per day. Lynton wants to change his rental price in order to maximize his income. Lynton's profit can be estimated with the equation P(x)=(60+5x)(25−3x). Use the profit formula to answer Part A and Part B. Part A: Which answer choice correctly explains approximately how much Lynton should charge per bike rental to maximize his profit? Part B: How much will Lynton earn per day if he maximizes his profit? Select one answer for Part A and one answer for Part B.

A: Lynton should charge approximately $51 per rental. To determine this, Lynton can use P(x) to locate the x-coordinate of the maximum (max), which is −1.83. This indicates that Lynton should decrease his price by 1.83 times 5 dollars, which is about 9 dollars. Thus, Lynton should charge about $51 per rental to maximize profit., B: $1,550.42

A scientist is measuring the reactivity rate of a chemical as he increases its temperature. The scientist records R, the reaction rate per second, and t, the temperature in degrees Celsius. The scientist focuses his measurements on temperatures between −40 and 40 degrees Celsius, and he finds that the reaction rate can be determined by the function R(t)=1.01t−35.2−0.03. Part A: Which quantity is the independent variable? Part B: Which quantity is the dependent variable? Part C: Which graph is scaled appropriately for this situation? Select one answer for Part A, one answer for Part B, and one answer for Part C.

A: The independent variable is the temperature., B: The dependent variable is the reaction rate per second.

Use the following scenario to answer Part A, Part B, and Part C. Janice is keeping track of the height of a bougainvillea bush over time. She tracks its growth for 4 years, at which point the bush has grown 30 feet tall. Janice finds that the height of the bush, h, can be determined using the function h(t)=15t, where t is the time in years since the bush was planted. Part A: What is the independent variable? Part B: What is the dependent variable? Part C: Which graph is scaled appropriately for this situation?

A: The independent variable is the time in years since the bush was planted., B: The dependent variable is the height in feet of the bougainvillea bush.

Use the system {−9x5−5xy3=27−2y4+7x2=3 and its graph to answer the questions. A graph of the system given in the problem. The graph of the function negative 9 x to the 5th, minus 5x y to the third equals 27 is represented by two curves. The first goes down to negative infinity as x approaches negative infinity and goes up to infinity as x approaches zero. The second curve goes down to negative infinity as x approaches zero from the right, comes up to approximately negative two when x is 1, and goes back down to negative infinity as x approaches infinity. The other equation in the system, negative 2 y to the fourth, plus 7 x squared equals 3, is also represented by two curves that appear as parabolas flattened at the vertices. One is open to the left with a vertex at approximately (negative 0.7, 0). The other is open to the right with a vertex at approximately (0.7, 0). © 2017 FlipSwitch. Created using GeoGebra. Part A: What is (are) the solution(s) of the system? Part B: The graph of the system of equations shows only a portion of the graph of the system. Are there other real solutions for this system that are not pictured? Why or why not? Select all correct answers for Part A, and select one answer that correctly answers both questions in Part B.

A: The ordered pair (−1.43,−1.54) is an approximate solution to the system. A: The ordered pair (−1.11,1.29) is an approximate solution to the system. B: No. Due to the end behavior of each equation, it isn't likely that there are any other real solutions for the system.

Clark is shopping for a water fountain for his garden. He wants one that won't damage a light fixture that hangs 10 feet above where he will place the fountain. The Deluxe Fountain features a spigot that shoots a stream of water several feet into the air. The path of the water can be modeled by the function f(x)=−3x2+4x+9. Part A: Will the water from the Deluxe Fountain reach the light fixture? Part B: Which option correctly describes how to find the answer for Part A? Choose one answer for Part A and one answer for Part B.

A: Yes, the water from the Deluxe Fountain will reach the light fixture., B: Find the y-value of the maximum of the path of the water. First, solve for the x-coordinate of the maximum, and then evaluate the function for that value of x. The y-coordinate of the maximum is 10.33. If the water sprays 10.33 feet in the air, it will hit the light fixture.

The equation p(t)=2et, where t is time in months, represents a rabbit population that grows continuously. A: What is the equation of the horizontal asymptote? B: What number represents the initial number of rabbits, p(0)? Select one answer for question A and one answer for question B.

A: y=0, B: 2

The equation p(t)=12et+7, where t is time in months, represents a continuously growing population of a frog species. A: What is the equation of the horizontal asymptote? B: What number represents the initial number of frogs, p(0)? C: What value of t should be used when the population is checked after 2.5 years? Select one answer for question A, one answer for question B, and one answer for question C.

A: y=7, B: 19, C: 30

Arline wants to find the solution set for the inequality sin⁡⁡x≥0 on interval [0,2π). Which answer choice correct describes the solution process and the correct solution set of the trigonometric inequality?

Arline begins determining the zeros for sin⁡⁡x at the domain from x=0 to x=2π:sin⁡x=0 at x=0, x=π, and x=2π. Then, she determines the sign of sin⁡⁡x for each interval (0,π) and (π,2π) by picking some values for x in the related intervals and finding the related y-values. She determines that sin⁡⁡x>0 from 0 to π, and sin⁡⁡x<0 from π to 2π. She concludes that sin⁡⁡x≥0 on [0,π].

Use the exponential expression 948⋅(256)t8+2 to answer the questions. A: Which option correctly shows the expression rewritten in the form A⋅Bt? B: If this equation represents population growth of a type of bacteria, where t is the number of days, how quickly does the bacteria grow? Select one answer for question A and one answer for question B.

B: The number of bacteria doubles every day. A: Step 1 948⋅(256)t8+2 Step 2 948⋅(256)t8⋅2562 Exponent property #1: bx⋅by=bx+y Step 3 965536⋅(256)t8⋅65536 Evaluate powers. Step 4 9⋅(256)18⋅t Simplify. Step 5 9⋅(25618)t Exponent property #7: (bx)y=bxy Step 6 9⋅(2)t Evaluate powers.

The surface area of a piece of precious metal is 10 square inches. The surface area of the metal over time can be modeled by the function A(e), where A is the surface area of the metal in inches, and e is the time elapsed in years. As time continues, the metal erodes and loses surface area. The graph of the function A(e) is as follows. Graph of function A of e, which starts at point (0,10) and decreases as it moves in the positive direction of the x-axis. © 2017 FlipSwitch. Created using GeoGebra. Use the graph to answer the following questions. Part A: At what point did the metal have the most surface area? Part B: What does the answer to Part A describe regarding the function?

B: the maximum of the function, A: [0,10]

The decibel level of static interference on a radio station is measured from midnight to 8 a.m. The decibel level of static, S, at any given time can be approximated by the function S(t), where t is the number of hours elapsed since midnight. The function S(t) is graphed as follows. Graph of function S of t, which is a cosine function above the x-axis and fluctuates between about 1.3 and 7.2. The x-axis is labeled © 2017 FlipSwitch. Created using GeoGebra. Use the graph to answer the following questions. Part A: What is the fluctuation of interference, in decibel levels, throughout the morning? Part B: What does Part A describe regarding the function?

B: the range of the function, A: [1.2,7.2]

Alexi enjoys extreme sports, so she decides to bungee jump off of a bridge. It's important that the length of the bungee cord is correct: if it's too long, she will plunge into the water before the cord snaps her upwards. Alexi's height from the water before and after her first bounce can be modeled by the function h(t)=22t2−115t+200, where h is Alexi's height, in feet, above the water, and t is the time, in seconds, from the moment she jumps. Part A: Is it safe for Alexi to bungee jump with this particular cord? Part B: The height Alexi reaches just as she bounces upward is the _[blank]_ of the equation. Choose one answer for Part A and one answer for Part B.

B: y-coordinate of the minimum, A: Yes, Alexi will bounce back at a height of 49.7 feet from the water.

Use the inequality 5cos⁡⁡(2x)≤0 on [−π,π] to answer the following questions. Part A: What are the zeros to the nearest hundredth? Part B: What is the solution set for the inequality? Select all correct answers for Part A, and select one answer for Part B. Use π≅3.14 if needed.

B: [−34π,−14π]∪[14π,34π], A: x=−14π, A: x=34π, A: x=−34π, A: x=14π

The system of equations {44x=416y+84y+5x+3=2xy−17 has exactly one solution. Use substitution to find the solution. What is the solution? Enter your answer as an ordered pair, like this: (42, 53)

(-10, -3)

The system of equations {z−2x−2y=−72y+8x−z=−113y+9z+2x=3 has exactly one solution. Use substitution to find the solution. What is the solution? Enter your answer as an ordered pair, like this: (42, 53)

(-3, 6, -1)

The system of equations {3x+9y3=−2113y3+4x=−1 has exactly one solution. Use substitution to find the solution. What is the solution? Enter your answer as an ordered pair, like this: (42, 53)

(-88, 3)

Glenda plans to paint her bedroom, and she is mixing paint to create the right color. She starts with a white base paint and pours in some blue paint. Right now, her mixing bucket contains 5 quarts of paint, with a concentration of 20% blue paint. Glenda wants to increase the blue paint concentration to at least 30%, but less than 35%. Which inequality should Glenda use to find the number of quarts of blue paint she should add?

0.30≤1+x5+x<0.35

Use the half-life function Q(t)=235,000⋅((18)h)(th) to answer the question. What is the half-life, h, if (18)ℎ=12? Use this tool for calculating h to find your answer. Enter your answer as a decimal rounded to the nearest hundredth, like this: 42.53

0.33

Lorena is comparing the winning percentages of two baseball teams. The Scorpions have won 20 out of 35 games. The Iguanas have won 10 out of 34 games. There are x games remaining until the playoffs. Which rational equation correctly describes the event in which the Iguanas win y of the remaining games and reach the same winning percentage as the Scorpions? Assume that the Scorpions do not win another game.

10+y34+x=2035+x

Niko is constructing two solid boxes, each of which is a rectangular prism. The first box is 3 times longer than it is wide, and its height is 5 inches shorter than its width. The second box has a width that is 10 inches narrower than its length, and its height is 4 times longer than its width. The first box can fit 1500 cubic inches of material inside of it, and twice as much material can fit in the second box. Which equation correctly describes the total amount of material that will fit inside both boxes, in terms of x and y?

4500=3x3−15x2+4y3−80y2+400y

All of the following expressions are equivalent to 5⋅15t. However, only one expression has been rewritten by using exponent property #4, (bc)x=bxcx. Which one is it?

5⋅30t2t

Use the system {−8xy+73x−2=355y3+x4=14 and its following graph to answer the questions. A graph of the system given in the problem. © 2017 FlipSwitch. Created using GeoGebra. Part A: What is (are) the solution(s) of the system? Part B: Which statement(s) about the system is (are) true? There may be more than one correct answer for both Part A and Part B. Select all correct answers for Part A and Part B.

A: The point (1.41,1.26) is an approximate solution to the system., B: The system consists of continuous equations whose graphs intersect once. , B: The end behavior of each equation suggests that the equation will not intersect outside of the displayed region of the graph.

Dr. Valenzuela wants to find the half-life of a radioactive substance. She tried to rewrite the function Q(t)=75⋅53−t in the form Q(t)=Q0(12)th, where t is measured in years, but she got stuck. Her work is shown here. Step 1 Q(t)=75⋅53−t Step 2 Q(t)=75⋅53⋅5−t Step 3 Q(t)=9375⋅(15)t Step 4 Q(t)=9375⋅(15)h(th) Step 5 Q(t)=9375⋅((15)h)(th) A: If (15)h=12, what is h to the nearest hundredth? Use this tool for calculating h to help you. B: Which option correctly shows the function rewritten in the form (t)=Q0(12)th? Select one answer for question A and one answer for question B.

A: h≈0.43, B: Q(t)=9375(12)t0.43

In a particular science experiment, the number of bacteria is represented by the function p(t)=100et+3, where t is time in days. A: What is the equation of the horizontal asymptote? B: What number represents the initial number of bacteria, p(0)? C: What value of t should be used if you check the population after 60 hours? Select one answer for question A, one answer for question B, and one answer for question C.

B: 103, C: 2.5, A: y=3

Devan is preparing baked goods for a bake sale. Each batch of brownies uses 4 eggs and 2 cups of flour. Each batch of cupcakes uses 3 eggs and 3 cups of flour. Devan has 2 dozen eggs and 20 cups of flour on hand. A single batch of brownies or cupcakes produces 12 servings. Part A: How many batches of brownies and cupcakes should Devan make in order to maximize his number of servings of baked goods? Part B: If Devan maximizes the number of servings he can bring, how many servings of baked goods will he have? Choose one answer for Part A and one answer for Part B.

B: 84 servings, A: Devan should bake 2 batches of brownies and 5 batches of cupcakes.

Dr. Norton wants to find the half-life of a medication for his patients. He tried to rewrite the function Q(t)=100⋅44−t in the form Q(t)=Q0(12)th, where t is measured in hours, but he got stuck. His work is shown here. Step 1 Q(t)=100⋅44−t Step 2 Q(t)=100⋅44⋅4−1 Step 3 Q(t)=25600⋅(14)t Step 4 Q(t)=25600⋅(14)h(th) Step 5 Q(t)=25600⋅((14)h)(th) A: If (14)h=12, what is the value of h to the nearest hundredth? Use this tool for calculating h to help you. B: Which option correctly shows Dr. Norton's function in the form Q(t)=Q0(12)th? Select one answer for question A and one answer for question B.

B: Q(t)=25600⋅(12)t0.50, A: h=0.50

Which scale would be appropriate for the x- and y-axes?

Count each axis by units of about 0.25 because they represent the weight of the candy, and the total weight is less than or equal to 7.3.

Robin, Magdalena, Selina, and Alex each analyze the system {−16(y+1)−8(5x)=308(y+1)+4(5x)=−16. Which analysis is completely correct?

Magdalena concludes that the system has no solution. First, she notices that the first equation can be simplified. She divides that equation by −2 and simplifies to 8(y+1)+4(5x)=−15. She realizes that the left sides of both equations are equivalent, but the solutions on the right sides are different. Since these are linear equations, This observation means that the equations must have nonintersecting graphs, so there is no solution.

Four friends are analyzing the system of equations {7y=15x−57=15x−7y Melinda, Vincent, Paige, and Vivica each reach a different conclusion about the system of equations. Which student's conclusion is correct?

Melinda notices that each equation has the same slope but different y-intercept, and she concludes that the system has no solution.

Use substitution to solve the system of equations {25y=210x+53x+y=3 Which statements correctly describe the system? There is more than one correct answer. Select all correct answers.-

The graphs of the equations intersect once., The ordered pair (0,1) is a solution of the system.

Refer to the previous question. How do you know, without graphing, that the system you chose in the previous question has no solution?

The inequalities represent two lines with the same slope and different y-intercepts, which means the lines do not intersect. The line with the greater y-intercept is shaded above, while the line with the lesser y-intercept is shaded below. This means the shading never overlaps, so the inequalities share no points in common.

Julie is participating in a fundraiser. For every 100 items she sells, she earns one of 10 unique prizes. Which quantity represents the independent variable in this context?

The number of items Julie sells.

Peter runs a catering company. Cheryl books his company to serve her guests at a party. Guests are sent invitations and are asked to respond if they plan to attend Cheryl's party. The number of staff Peter schedules to work the party is determined by the number of guests who reply to confirm their attendance. Which quantity represents the dependent variable in this context?

The number of staff Peter will schedule.

Use the system {2x4−3y3=10−4x3−5xy3=−7 and its graph to answer the questions. A graph of the system given in the problem. © 2017 FlipSwitch. Created using GeoGebra. What is (are) the solution(s) of the system?

The ordered pair (1.42,−0.86) is an approximate solution to the system., The ordered pair (−0.45,−1.49) is an approximate solution to the system., The ordered pair (−1.12,−1.31) is an approximate solution to the system.

Use substitution to solve the system of equations {5y−20x2=−15y2−16x4=−15 Which statements correctly describe the system? There is more than one correct answer. Select all correct answers.

The point (1,1) is a solution of the system., The point (−1,1) is a solution of the system.

A magazine publisher produces magazines about different science topics. Two of the publisher's magazines are Cool Space Stuff and Mesmerizing Marine Biology. The publisher expects a monthly demand of at least 2000 copies of Cool Space Stuff and at least 1400 copies of Mesmerizing Marine Biology. The publisher is able to print no more than 2500 copies of Cool Space Stuff and 3400 copies of Mesmerizing Marine Biology monthly. However, the publisher must print at least 3800 magazines (of either title) every month to meet the terms of his printing contract. If Cool Space Stuff currently produces a $5 profit for each copy sold, and Mesmerizing Marine Biology produces a $1 loss for each copy sold, how many magazines of each title should the publisher print in order to maximize monthly profit?

The publisher should print 2500 copies of Cool Space Stuff and 1400 copies of Mesmerizing Marine Biology each month.

The following graph shows the inequality 7≤x+4. A graph of the given inequality. A closed circle is on a number line at 3. The number line is shaded to the right of the circle.

[3,∞)

Use the following system of equations to fill in the blanks. {2a+5b=−b2a+1+2∗5b=−2b The system potentially has _blank 1_ solution(s) because _blank 2_. Select the word or phrase that fills in each blank in the previous sentence to make it a true statement.

blank 1: at least one, blank 2: there are the same amount of equations as unknowns

Eliza is at least twice as old as her friend's younger sister, Wendy. Which inequality correctly represents Eliza's age, e, compared with Wendy's age, w?

e≥2w

× + − ÷

for each, sum, difference, shared equally

What does the notation f−1 mean?

f−1 is the inverse of the function f.

Use the following graph of the function f(x)=−3x2+2x+6 to fill in the blanks. The graph of the function f of x as described in the problem. It is a downward-opening parabola. © 2017 FlipSwitch. Created using GeoGebra. Using the ___[blank 1]___, you can tell that the function f(x) ___[blank 2]___ one-to-one because ___[blank 3]___ the graph of the function in ___[blank 4]___. Match each blank to the word or phrase that correctly fills in that blank in the previous sentence.

horizontal line test is not there is a horizontal line that intersects more than one place

Jimmy, Veronica, and Ella are collecting signatures for a petition. Jimmy collects j signatures per hour and Veronica collects v signatures per hour. Ella collects e signatures per hour, which is more than the hourly total for Jimmy and Veronica combined. Which inequality correctly compares the number of signatures collected by Jimmy and Veronica to the number of signatures collected by Ella after x hours?

jx+vx<ex

A local high school wants to enclose their practice field with a fence. The school has purchased 1,000 feet of fencing for the project. Determine the dimensions of the fence that will enclose the largest area. This problem is an example of a(n) _____ problem.

optimization

Minh is building a wooden box to hold all of her dinosaur figurines. She wants the base of the box to be in the shape of a square, and she has a total of 1 square meter of wood to use when making the box. What dimensions of the box will maximize the volume? This problem is an example of a(n) _____ problem. Select the word that correctly fills in the blank in the previous sentence.

optimization

Sonja's Bakery sells cookies for $0.50 each and cupcakes for $1.75 each. Which equation for r correctly describes the revenue Sonja makes if she sells x cookies and y cupcakes?

r=0.50x+1.75y

Le Fromage is an artisanal cheese shop in Paris, Arkansas. They sell Manchego for $2.12 per ounce, and Parmigiano Reggiano for $1.77 per ounce. Which equation for r correctly describes the revenue Le Fromage makes if it sells x ounces of Manchego and y ounces of Parmigiano Reggiano?

r=2.12x+1.77y

raise to the power n take sin⁡x multiply add subtract divide

raise to the power 1/n take arcsin x divide subtract add multiply

In which systems of inequalities is the point (2,4) a member of the solution set of the system? There is more than one correct answer. Select all that apply.

{y≥2xy≤−12x+5 A graph of the given system of inequalities. The inequality y is greater than or equal to 2x is shaded in red with a solid line. The inequality y is less than or equal to negative one-half x plus 5 is shaded in blue with a solid line. The area of overlap is shaded in purple. The point (2, 4) appears at the intersection of the two lines. © 2017 FlipSwitch. Created using GeoGebra. {y≥3x−5y<−23x+6 A graph of the given system of inequalities. The inequality y is greater than or equal to 3x minus 5 is shaded in red with a solid line. The inequality y is less than negative two-thirds x plus 6 is shaded in blue with a dotted line. The area of overlap is shaded in purple. The point (2, 4) appears in the area shaded purple. © 2017 FlipSwitch. Created using GeoGebra.

Consider the function f(x)=−x2+6 on the domain [0,∞). Use the range of f(x) to determine the domain of f−1(x). What is the domain of f−1(x)?

−∞<x≤6