algebra 2b - unit 1: lost in translation lessons 1-5
use substitution to solve the system of equations {4^2x=4^2y-12... the system has exactly one solution. what is the solution to the system?
(-1, 5)
the system of equations {4^4x = 4^16y+8 , 4y+5/x+3 = 2x/y-17 what is the solution?
(-10, -3)
the system of equations {1+y/2y - 3x+1/y = 0 , 2y+8/12x+10 + 4x/y+7 = 3 has one solution. what is the solution?
(-2, -11)
the system of equations {z-2x-2y=-7 , 2y+8x-z=-11 , 3y+9z+2x=3 has exactly one solution. what is the solution?
(-3, 6, -1)
the system of equations {3x + 9y^3 = −21 , 13y^3 + 4x = −1 has exactly one solution. what is the solution?
(-88, 3)
consider the inequality x^3 + 4x^2 − 5x < 0 select all intervals for which the statement is true. select all correct answers.
(-infinity, -5) (0, 1)
use the inequality (x + 1)(x - 3)(x - 7)(x + 6) > 0 to answer the following question. what is the solution set for this inequality?
(-infinity, -6) U (-1, 3), U (7, infinity)
use substitution to solve the system of equations {4x/4x+4 - 2y/x+1=0....... the system has exactly one solution. what is the solution to the system?
(2, 1)
the system {a^2 + b^2 - c^2 = 0, 5a - b = c, a + b + c = 30} has exactly one solution. fnd the solution by using substitution.
(5, 12, 13)
which sets represent the solutions to the compound inequality x > −8 and x ≤ 5? select all that apply.
(−8, 5] (−∞, 5]∩(−8, ∞)
what is the solution set for the inequalities x^3 < 0 or 4x^4 > x^2?
(−∞, 0) ∪ (12, ∞)
what is the solution set for the inequalities x-1/2 <= 2 and 2x+3/3 <=7?
(−∞, 5]
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 −3x^2 + 1 ≤ −107?
(−∞,−6] ∪ [6,∞)
match each operation to the word or phrase that tells you to complete that operation.
+ : sum - : difference x : for each ÷ : shared equally
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?
.... she concludes that sin x >= 0 on [0, pi]
use substitution to solve the system of equations {-3a^4....... which statements correctly describe the system? select all correct answers.
0.17 of 1 the system has exactly one solution. the point (1, 1) is a solution of the system.
use the inequality 10 cos x ≥ 0 10 with a period [−2π,0] to answer the following questions. part a: which answer correctly explains the solution process of the inequality? part b: what does the period represent in this problem?
0.25 of 1 a: [-2pi, -3pi/2] U [-pi/2, 0] b: it represents the range of the inequality.
brynn and castor are counting their pocket change. brynn's change is worth more than castor's. castor has q quarters and pp 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 + 0.01p < 0.25q + 0.1d + 0.05n
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+x/5+x < 0.35
part a: which answer choice shows the correct analysis of milan's work? part b: what is the domain of the inequality? part c: what is the solution set for the inequality?
0.5 of 1 a: milan is correct. she correctly identified the interval for cos(2x) < 0 b: [0, 5pi/4) c: (pi/4, 3pi/4)
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 tt is the time in seconds since she threw the plane. after approximately how many seconds does the plane reach its maximum height?
0.5 seconds
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?
1/x + 1/y = x + y/xy
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?
10 + y/34 + x = 20/35 + x
a wildfire is spreading at an alarming rate. the wildfire begins at a size of 8 square feet. it then doubles its width every x hours, and doubles its length every y hours. after a period of time, the wildfire covers 14,000 square feet. which equation correctly represents the area of the wildfire in terms of x and y?
14,000 = 8 * 2^x+y
momoko owns a small business complex that consists of two square buildings that are attached on one side, as shown here. 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 = 4√10y + 2√5x
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 = 3x^2 - 24x + 36
the following graph shows the height, h, of a model rocket as time, t, passes in seconds. 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
a car dealership can maximize its daily profit from sales, p, according to the function p(s) = −150s^2 + 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.
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) = sint, where t is time in seconds. for what value of t in the domain 0 ≤ t ≤ 2π is the signal the weakest?
3π/2
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 xx and yy?
4500 = 3x^3 - 15x^2 + 4y^3 - 80y^2 + 400y
which trigonometric equation correctly models the distance the swimmer swam toward the buoy in terms of x and y?
5 = 400/tanx - 400/tany
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
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. what was the approximate minimum ph recorded during the test?
6.2
donovan is painting a large wall orange. yesterday, he painted a square-shaped area that was 7x square feet. today, he extended one side of the orange area by 3 feet and the other consecutive side by 4 feet. which inequality correctly compares the size of donovan's painted area over the last two days?
7x < 7x + 7√7x + 12
the inequality x^2 - 8/x + 6 <= 0 part a: what are the zeros of the inequality to the nearest hundredth? part b: what is the solution set for the inequality?
XXX a: x = 2.83, x = 1.11 b: (-infinity, 1.11)
hugo is viewing a summary of his electricity usage over the last month. he finds that he used between 10 and 15 kilowatts every day in october. hugo can approximate his daily energy usage, e, using the function e(d) = cos(d − 3.31) + 12.42, where d is the day of the month. 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?
XXXXX a: the independent variable is Hugo's daily energy usage. b: the dependent variable is the day of the month. c: https://cdstools.flipswitch.com/asset/media/678209
the following graph shows the inequality 7 ≤ x + 4. what is the solution of the inequality shown in interval notation?
[3, ∞)
which description describes the potential graph of a system of linear equations with no solution?
a graph of two parallel lines that never intersect.
the number of car accidents that occur per week in foggy city, maine can be approximated by the function a(v), where v is the visibility index score and a is the number of accidents recorded that week. the function a(v) is graphed here. part a: what is the domain of v(a)? part b: what does the domain describe in this context?
a: (0, ∞) b: the domain describes all possible values of the visibility index.
gregor is using 35 feet of spare fencing to build a triangular play pen for his dog. part a: to the nearest degree, what is the angle between the side that is 12 feet long and the side that is 17 feet long? part b: what is the length of the second side? part c: will gregor have enough fencing to complete the triangular pen? why or why not?
a: 45 b: 12 feet c: no, gregor will not have enough fencing to complete the triangular pen. he has 35 feet of fencing, but he needs 41 feet.
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. 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?
a: [0, 10] b: the maximum of the function
the cost to construct a home can be modeled by the function c(f), where c is the total cost of the project and f is the total square footage of the home. part a: what is the domain of the function? part b: what does the domain describe in this context?
a: [0, ∞) b: the domain describes all possible values for the total square footage of a home.
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. part a: what is the fluctuation of interference, in decibel levels, throughout the morning? part b: what does part a describe regarding the function?
a: [1.2, 7.2] b: the range of the function
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?
a: devan should bake 2 batches of brownies and 5 batches of cupcakes. b: 84 servings
four friends are working to solve the system of inequalities y > 5x and x ≥ 9. part a: whose argument is correct? part b: what is the correct solution?
a: ellis argues that because a solution must satisfy both equations, izabella's conclusion is incorrect. for example, if x = 9, y must be greater than 5x, or 45. thus, y ≥ 45 cannot be the solution. b: y > 45
the trajectory of an object is represented by the equation f(x) = −x^2 + 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?
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.
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?
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: $1,500.42
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) = 15√t 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. c: https://cdstools.flipswitch.com/asset/media/687970
use the system {-9x^5-5xy^3=27 , -2y^4+7x^2=3 and its graph to answer the questions. 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?
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.
use the system {-8^xy+7^3x-2=35..... and its following graph to answer the questions. part a: what is (are) the solution(s) of the system? part b: which statement(s) about the system is (are) true? 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.
part a: which system has a solution of the empty set? part b: which statements regarding the "empty set" are true?
a: x + 1 < y and x >= y b: the empty set has no elements. b: the empty set can result from the intersection of two sets that have no common elements.
use the inequality 5 cos(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?
a: x = 1/4pi a: x = 3/4pi a: x = -3/4pi a: x = -1/4pi b: [-3/4pi, -1/4pi] U [1/4pi, 3/4pi]
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) = 22t^2 − 115t + 200, where h is alexi's height, in feet, above the water, and tt 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.
a: yes, alexi will bounce back at a height of 49.7 feet from the water. b: y-coordinate of the minimum
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) = −3x^2 + 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?
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.
use the following system of equations to fill in the blanks. {2^a + 5^b = -b {2^a+1 + 2 * 5^b = -2b the system potentially has _blank 1_ solution(s) because _blank 2_.
blank 1: at least one blank 2: there are the same amount of equations as unknowns
consider the system of inequalities y^3 < x and x < −27. using the substitution method, the solution set found is the set of all _blank 1_ where x is in _blank 2_ and y is in _blank 3_. this may or may not be the complete set, and this can be verified using a graph.
blank 1: ordered pairs blank 2: (−∞, −27) blank 3: (−∞, −3)
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.
eliza is at least twice as old as her friend's younger sister, wendy. which inequality correctly represents eliza's age, ee, compared with wendy's age, ww?
e ≥ 2w
rory is about to begin solving the system of inequalities y ≤ x + 1 and x < 0. which answer choice describes how he would arrive at the correct solution?
first, rory looks at x < 0. this inequality is fully simplified, so there is no work to do here. next, he considers y ≤ x + 1. given that x < 0, rory decides to substitute 0 for x and solve. he concludes that y < 1. this means the set of all ordered pairs whose x-coordinate is in the interval (−∞, 0) and whose y-coordinate is in (−∞, 1) is a possible solution set for the system.
which graph shows the solution to the inequality y > √5x?
https://cdstools.flipswitch.com/asset/media/679037
wvhich graph shows the solution to the inequality y < 2x+1/x?
https://cdstools.flipswitch.com/asset/media/689019
which graph shows the solution to the system of inequalities {2y >= -3x + 6, 4y < x - 7?
https://cdstools.flipswitch.com/asset/media/689025
f(x) = -2x^3 + 5x^2 + 1 what are the approximate zeros to the nearest tenth? select all correct answers.
i think -2.58, 1.7, -0.2
the __[_blank_]__ of two sets a and b is the set of elements that are present in both a and b.
intersection
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
which statements about linear programming are true? 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.
robin, magdalena, selina, and alex each analyze the system. 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.
lesson 2
multivariable equations and inequalities
lesson 3
multivariable systems of equations
lesson 4
multivariable systems of inequalities
given that n: {1 ,2, 3, 5, 8, 13} and m: {−9, −8, −6, −4, −2, 4}, which statements about n and m are true? select all correct answers.
n∩ m = ∅ the intersection of n and m is ϕ. the intersection of n and m contains only those elements that are in both n and m
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
lesson 5
optimization and linear programming
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. part a: which equation represents the amount of money rada is spending on candy? part b: which equation represents the total weight of candy that rada is buying?
part a: 4.99x + 5.99y = 39.43 part b: x + y = 7.3
part a: watch each system of inequalities with its solution set. {y>5x^2,....} part b: which ordered pair is a member of the solution set to the system?
part a: https://cdstools.flipswitch.com/asset/media/679053 part b: (0.1, 0.25)
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
lesson 1
single-variable equations and inequalities
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
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
the following graph shows the system {y > 2 + x, x < -2} , whose solution is the area of overlap of the shaded regions.. which statement about the area of overlap is correct?
the area of overlap can be described as the set of all ordered pairs that are solutions of the system.
a system of equations may have at least one solution if _[blank]_.
the equations intersect there are more equations than unknowns/variables
use substitution to solve the system of equations {2^5y = 2^10x+5 , 3^x+y = 3 which statements correctly describe the system? select all correct answers.
the graphs of the equations intersect once the ordered pair (0, 1) is a solution of the system.
siree wants to go surfing for one hour tomorrow. when will the waves be at least 8 feet in the next 12 hours?
the height of the waves are at least 8 feet between at 12:00 a.m. and 8:00 a.m.
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.
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
lance is going out for a long bike ride. for every 15 miles he rides, he drinks 1 bottle of water. which quantity represents the independent variable in this context?
the number of miles lance will travel.
joni builds furniture for a living. today she's building stools that she will sell for $75 apiece. each stool requires 18 screws for assembly. joni wants to build as many stools as possible. which quantity represents the dependent variable in this context?
the number of stools joni can assemble.
use the system {2x^4-3y^3=10 , -4x^3-5xy^3=-7 and its graph to answer the questions. 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.
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.
what solution set is found when using substitution to solve the system of inequalities 4y+2x/x-4<6 and x<1?
the set of all ordered pairs whose x-coordinate is in the interval (−∞, 1) and whose y-coordinate is in (−5, ∞).
which statement is correct about the system of inequalities x+2/y < 1 and y - 7 > 5?
the set of all ordered pairs whose x-coordinate is in the interval (−∞, 10) and whose y-coordinate is in (12, ∞) is part of the complete solution for the system.
which answer choice gives the solution set of the system of inequalities x < 4 and y ≤ 7?
the set of all ordered pairs whose x-coordinate is in the interval (−∞, 4) and whose y-coordinate is in (−∞, 7]
use substitution to solve the system of equation {-4x+y+7z=-13..... which statements correctly describe the system? select all correct answers.
the system has exactly one solution. the point (2,−5,0) is a solution of the system.
use the system of equations {x-5/x-7 + y+6/x+2 = 3 , y+8/x-2 = 6 and its following graph to answer the question. which answer provides a completely correct description of the system?
the system has no real solution because the equations do not intersect within the displayed region of the graph. furthermore, the end behavior of the equations suggests that they will not intersect at any part of the graph that is not shown. thus, the system has no real solutions.
use a graphing calculator, or another piece of technology, to graph the equations of the system {x+1/y-4 - 9x/y-1 = 4 , 10^x+3^y=1 which statements correctly describe the system? select all correct answers.
the system has no real solutions. the system consists of equations whose graphs never intersect.
use a graphing calculator, or another piece of technology, to graph the equations of the system {5x^3y-4y^3x-15y^2=16..... which statements correctly describe the system? select all correct answers.
the system has no real solutions. the system consists of equations whose graphs never intersect.
use substitution to solve the system of equations {2x+6/y - 4x+4/2y = 0 , 2x/y + 6x+5y/y+1 = 5. which statements correctly describe the system? select all correct answers.
the system has no solution. the graphs of the equations will never intersect.
use the following system of equations to answer the question. {2a+1/a + 3/b-2 = 5/2 {a-4/2 - 7b/b-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.
the following graph shows the system {f(x)=3^x+4 g(x)=1/x-4 which statement about the solution to the system is true?
there appears to be a solution near (4, 85).
the __[_blank_]__ of two sets a and b is the set of elements that are present in a, in b, or in both a and b.
union
consider the function f(x) = 2 sin(x/2) − 1 on [0, π/2). what are the zero(s) of the function on the interval [0,π/2)?
x = 1/3pi
match each system of inequalities with its solution set.
x > -5 and y > -9 : the set of all ordered pairs whose x-coordinate is in the interval (−5, ∞) and whose y-coordinate is in (−9, ∞). x < 5 and y < 9 : the set of all ordered pairs whose x-coordinate is in the interval (−∞, 5) and whose y-coordinate is in (−∞, 9). x <= 9 and y <= 5 : the set of all ordered pairs whose x-coordinate is in the interval (−∞, 9] and whose y-coordinate is in (−∞, 5]. x > 9 and y > 5 : the set of all ordered pairs whose x-coordinate is in the interval (9, ∞) and whose y-coordinate is in (5, ∞).
anona hires a decorator to redecorate her bedroom. if a layout includes a wall color, ceiling color, and flooring, which option correctly shows the comparison between the total number of unique layouts offered by the basic and gold plans?
x^3 < 4x^2 + 3x < x^3 + 13x^2 + 54x + 72
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?
x^3 < x^3 + 5x^2 + 6x
use the following graph of a system of inequalities to answer the question https://cdstools.flipswitch.com/asset/media/679032 which solution set is a partial solution for the system?
{(0, 2),(−1, 4),(−12, 3),(1, 5)}
which set of ordered pairs is a partial solution set for the system y < 0 and x ≤ y?
{(−1, −1),(−7, −6),(−8, −2),(−10, −3)}
which system of inequalities has no solution?
{y > 3/4x + 4 {y < 3/4x - 5
in which systems of inequalities is the point (2, 4) a member of the solution set of the system? select all that apply.
{y >= 3x - 5 {y < -2/3x + 6 {y >= 2x {y <= -1/2x + 5
aroldo purchases 20 feet of brick pavers to line the front edge of his lawn. he will also extend the brick pavers 2 extra feet past the end of the lawn on both sides. the area of his square lawn is 8x feet. select the inequality that models the length of aroldo's paving project and the situation in which aroldo does not have enough feet of brick pavers to complete his job.
√8x + 4 > 20