math stuff
Which inequality is equivalent to 3+4/x≥ x+2/x
A.
What is the range of the function y=3^√x+8
A. -00<y<00
For the inverse variation equation xy = k, what is the constant of variation, k, when x = -2 and y = 5?
A. -10
Tim throws a stick straight up in the air from the ground. The function h = -16t2 + 48t models the height, h, in feet, of the stick above the ground after t seconds. Which inequality can be used to find the interval of time in which the stick reaches a height of more than 8 feet?
A. -16t2 + 48t > 8
Which expression is equivalent to (4 + 6i)2?
A. -20 + 48i
Which complex number has an absolute value of 5?
A. -3 + 4i
The inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y. y=3x10^8/x
A. 1 × 10-10 m
A 22,800-gallon swimming pool is being filled by four hoses. Water flows through each hose at a rate of 300 gallons per hour. How many hours will it take to fill the pool?
A. 19 hours
If the complex number x = 3 + bi and |x|2 = 13, which is a possible value of b?
A. 2
Evaluate (2 - 5i)(p + q)i when p = 2 and q = 5i
A. 29i
Randy and Trey take turns cleaning offices on the weekends. It takes Randy at most 4 hours to clean the offices. It takes Trey at most 6 hours to clean the offices. What is the greatest amount of time it would take them to clean the offices together?
A.2.4 hours
A certain company has a fixed cost of $200 per day. It costs the company $3.10 per unit to make its products. The company is tracking its average cost to make x units using mc026-1.jpg. Which statement is true?
A.The horizontal asymptote of y = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.
Where is the hole for the following function located? f(x)=x+3/(x-4)(x+3)
A.x = -3
The graph of the function f(x)=3/x+5 is shown below.
A.x = -5
What is the solution of x^2+x-6/x-7≤ 0
A.x mc015-2.jpg -3 or 2 mc015-3.jpg x mc015-4.jpg 7
What is the horizontal asymptote of the function f(x)=(x-2)/(x-3)^2
A.y = 0
For several years, Graham has gathered data on students who own a computer and on their performance on a typing-speed test. He creates the linear model y = 3.8x + 17.4 where y represents the typing speed, in words per minute, of a student and x represents the number of years the student has owned a computer. According to Graham's model, what is the approximate speed of a student who has owned a computer for three years?
B, 29 words/min
A basketball player's free-throw percentage is the ratio of the number of successful shots made to the number of shots attempted. A basketball player has made 13 of the first 20 free throws she has attempted this season. Which rational expression can be used to find the free throw percentage for the season if she successfully makes her next x free-throw attempts?
B.
Frank joined a fitness club. He paid a $50 registration fee, and dues are $12 per month. Which expression can be used to find the average monthly cost of an x-month membership at the club?
B.
which graph represents y=√x-4
B.
Mark and Nora both work at the same pet store. The inequality mc017-1.jpg relates x, the number of hours Mark works each week, and y, the number of hours that Nora works. Which ordered pair must be included in the solution set of the inequality when interpreted in the context of the problem?
B. (0,0)
Which equation is an example of the commutative property of multiplication?
B. (4 + 2i)(3 - 5i) = (3 - 5i)(4 + 2i)
What is the additive inverse of the complex number 9 - 4i?
B. -9 + 4i
What is the value of i 97 - i?
B. 0
A graph of a quadratic function y = f(x) is shown below. What is the solution set of the quadratic inequality f(x) ≤ 0?
B. 0/
Which statement decribes the behavior of the function f(x)=2x/1-x2
B.The graph approaches 0 as x approaches infinity.
A chemist has 500 ml of a 30% acid solution. She adds x milliliters of a 10% acid solution. Which statement is true about the graph of the function that represents the concentration of the final solution?
B.The horizontal asymptote y = 10 means that the final concentration will always be greater than 10%.
How does the range of g(x)=6/x compare with the range of the parent function f(x)=1/x?
B.The range of both f(x) and g(x) is all nonzero real numbers
What are the vertical and horizontal asymptotes of f(x)=2x/x-1
B.horizontal asymptote at y = 2, vertical asymptote at x = 1
What are the vertical and horizontal asymptotes for the function f(x)x^2+x-6/x^3-1
B.vertical asymptote: x = 1 horizontal asymptote: y = 0
What are the removable discontinuities of the following function? f(x)=x2-36/x3-36x
B.x = -6 and x = 6
A pharmacist has 80 milliliters of a 25% saline solution. Which expression can be used to find the percentage concentration of the final solution if she adds x milliliters of a 10% saline solution?
D.
Louis plans to buy a new washing machine. The washing machine costs $560 and has an estimated annual operating cost of $48. Which rational function models the average annual cost in dollars of owning the washing machine for x years?
D.
The teachers' edition of a statistics textbook sells for $150, and students' edition of the book sell for $50 each. Which function can be used to find the average cost per book if two teachers' editions and x students' editions are purchased?
D.
Which graph represents the function f(x)=1/x -1
D.
Which of the following is the graph of y=-4√x
D.
Which pair of complex numbers has a real-number product?
C. (1 + 3i)(1 - 3i)
For a fixed amount of gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. The function mc006-1.jpg relates the volume in cubic inches and pressure in pounds per square inch of a gas. What is the volume when the pressure is 900 pounds per square inch?
C.20 in.3
The function mc004-1.jpg yields the average cost in dollars per cup of lemonade made by Lincoln at his lemonade stand when he makes x cups of lemonade. Which statement best fits the situation modeled by the function?
C.Lincoln uses 25 cents worth of supplies per cup.
How does the graph of y=√x +2 compare to the graph of the parent square root function?
C.The graph is a vertical shift of the parent function 2 units up.
Which statement is true about the discontinuities of the function f(x)? f(x)=x^2-4/x^3-x^2-2x
C.There are asymptotes at x = 0 and x = -1 and a hole at mc012-2.jpg.
For which data set is a linear regression most reasonable?
C.a set of four data pairs with a correlation coefficient r = -0.8
What is the domain of f(x)=3x/x-1
C.all real numbers except 1
Which function has no horizontal asymptote?
C.f(x)2x^2/3x-1
The graph below shows the function f(x)=5x+10/x2+7x+10
C.x = -2
The critical points of a rational inequality are x = -4 and x = 2. Which set of points can be tested to solve the inequality?
C.x = -5, x = 0, and x = 3
Jerald jumped from a bungee tower. If the equation that models his height, in feet, is h = -16t2 + 729, where t is the time in seconds, for which interval of time is he within 104 feet above the ground?
Not C
What are the equations of the asymptotes of the graph of the function f(x)=3x2-2x-1/x2+3x-10
Not C
What are the vertical and horizontal asymptotes for the function f(x)= 3x2/x2-4
Not C
Which function is the inverse of f(x) = 2x + 3?
Not C
Which statement could be used to explain why the function h(x) = x3 has an inverse relation that is also a function?
Not C
The height of a triangle is 4 in. greater than twice its base. The area of the triangle is no more than 168 in.2. Which inequality can be used to find the possible lengths, x, of the base of the triangle?
Not C or D
Which function has the same domain as y=2√x
Not C or D
Which phrase includes "being equal to 50"?
Not C.
The school's guidance department compares the grade-point averages and standardized state test scores for 10 students in each grade. The table below shows the correlation coefficient for each data set.
Not C. 10th and 12th
Irina plotted the number of participants in a summer camp program on a coordinate plane to create the following scatterplot. Which graph shows the line of best fit for this scatterplot?
Not D
Poloma believes that the equation of the line of best fit for the following scatterplot is mc024-1.jpg. Which statement best summarizes why she must be wrong?
Not D
What are the critical points for the inequality x^2-9x/x-5<0
Not D
What is the solution of x+8/5x-1> 0
Not D
Which inequality is graphed below? X starts a 2
Not D
Which function has an inverse that is also a function?
Not D {(-4, 4), (-2, -1), (-1, 0), (4, 1), (11, 1)}
Jeremy works two jobs. He makes $8/hr working at a deli and $12/hr working for a landscaper. Let x represent the number of hours he works at the deli, and let y represent the number of hours he works for the landscaper. What do the solutions of the inequality mc013-1.jpg represent?
Not D.
What is the solution set of the quadratic inequality 4(x + 2)2 ≤ 0?
Not D.
what is the solution set of the quadratic inequality 6x^2+1 ≤ 0
Not D.
The relationship between voltage, E, current, I, and resistance, Z, is given by the equation E = IZ. If a circuit has a current I = 3 + 2i and a resistance Z = 2 - i, what is the voltage of the circuit?
Not D. 8 + 7i
What is the domain of the function y=2√x-6
Not b
Which graph represents the function f(x) =2/x-1 +4
Not b or c
Which statement verifies that f(x) and g(x) are inverses of each other?
d. f(g(x)) = x and g(f(x)) = x
What is the distance from the origin of point A graphed on the complex plane below?
B. √13 and a is at (-3,-2)
Which notation best represents the phrase "no more than 200"?
B. ≤200
What is the sum of √-2 and √-18?
B.4√2i
A graph of quadratic function y = f(x) is shown below. What is the solution set of the quadratic inequality f(x)≥ 0?
A. { x | xer and u graph all in top left
What is the solution of 1/x+1/3<1/5
A.-15/2<x<0
The scatterplot shows the number of minutes spent reading (x) and the number of pages read (y) by each of seven students last night. Use the labeled points to create a linear model that predicts the number of pages that a typical student reads in x minutes. Which equation represents this linear model?
A. 7/11x+29/11
A local store's clearance rack is full of DVDs selling for $8 each and CDs selling for $6 each. Let x represent the number of DVDs, and let y represent the number of CDs. Which inequality can be used to find combinations of DVDs and CDs that can be bought with a $50 gift card?
A. 8x+6y50
Donte simplified the expression below. mc024-1.jpg What mistake did Donte make?
A. He did not apply the distributive property correctly for 4(1 + 3i).
Marta believes that the equation of the line of best fit for the scatterplot below is mc026-1.jpg. Which statement best summarizes why Marta is likely incorrect?
A. Marta's equation has a positive y-intercept, but the scatterplot suggests a negative y-intercept.
The function mc003-1.jpg yields the average cost in dollars for a company to produce x calendars. Which statement best fits the situation modeled by the function?
A. The company spends $600 on a new computer and printer before beginning the project.
Which property of multiplication is shown below? If x = a + bi and y = c + di, x × y = y × x.
A. commutative property
Which graph shows a function whose inverse is also a function? two of them
A. f1(x) and f(x)
Which function is the inverse of f(x) = -5x - 4?
A. f1(x)=-1/5-4/5
The graph of f(x) is shown below.
A. line going straight up
If the function f(x) = mx + b has an inverse function, which statement must be true?
A. m=/0
A sociologist recorded the estimated life expectancies of women born in Center City. Use the data from women born in 1970 and 2000 to create a linear model that predicts the life expectancy, in years, (y) of a female born in a given year (x).
A. y = 0.213x - 352.0
The range of which function includes -4?
A. y=√x -5
Which inequality is graphed below? x starts at 4
A. y≥ -1/2x+2
If f(x)=5x-25 and g(x)=1/5x+5, which expression could be used to verify g(x) is the inverse of f(x)?
B
Which graph shows the solution set of x^2+9x+20/x^2-x-20≥ 0
B
Which of the following is equivalent to 18-√-25
B. 18 - 5i
The scatterplot shows the number of minutes Tyler played in his last eight basketball games and the points he scored in each game. Estimate the location of the line of best fit. About how many points would Tyler score if he played for 40 minutes?
B. 22 points
If f(x) and f-1(x) are inverse functions of each other and f(x)=2x+5, what is f-1(8)?
B. 3/2
The scatterplot shows the number of home runs Mario hits during his first four seasons on the company softball team. If his output continues to follow the linear model, approximately how many home runs will Mario hit during his ninth season?
B. 35 home runs
What is the greatest possible integer value of x for which √ x-5 is an imaginary number?
B. 4
The function h(x) is given below. h(x) = {(3, -5), (5, -7), (6, -9), (10, -12), (12, -16)} Which of the following gives h-1(x)?
B. {(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}
vA grocery store sells almonds for $7/lb and peanuts for $5/lb. Let x represent the number of pounds of almonds, and let y represents the number of pounds of peanuts. Which inequality can be used to find how much of each type of nut can bought without spending more than $10?
B. 7x+5y≤10
What is the sum of 12 - 5i and -3 + 4i?
B. 9 - i
The table below shows the lengths and weights of six dolphins at an aquarium. Use the data from Pax and Snowflake to create a linear model that predicts the weight (y) of a dolphin given its length (x). Which dolphin's weight differs most from the value predicted by this model?
B. Jojo
For which scatterplot is the correlation strongest?
B. and dots make a line sort of
Which statement could be used to explain why f(x) = 2x - 3 has an inverse relation that is a function?
B. f(x) is a one-to-one function.
What is the square root of -1?
B. i
Reyna runs a textile company that manufactures T-shirts. The profit, p, made by the company is modeled by the function mc025-1.jpg, where s is the number of T-shirts sold. How many T-shirts should be sold to earn a profit of more than $2,000?
B. s > 42
At Thursday's basketball game, there were more than twice as many adult spectators as children. If x represents the number of adults and y represents the number of children, which inequality can be used to find the possible combinations of adults and children at the game?
B. x > 2y
The graph below represents the solution set of which inequality?
B. x2 + 2x - 8 < 0
What is the solution set to the inequality 5(x - 2)(x + 4) > 0?
B. {x | x<-4 or x > 2
What values make the inequality x+6/6-x<0 true?
C
Which graph shows the solution set of x-9/7x+2≤ 0
C
Which inequality is equivalent to x-6/x+5≥ x+7/x+3
C
Which property of addition is shown in the equation below? a + bi + 0 + 0i = a + bi
C, identity property
Sarah plans to sell homemade birdhouses at the local craft fair. She spent $90 on new tools and estimates that she spends $6 in materials for each birdhouse. Which rational function models the average cost per birdhouse, y, in dollars of building x birdhouses?
C.
What is the solution of 2/x-1> 7/x+1
C.
The table below shows how the number of hours needed to fill a pool depends on the flow rate of the hoses used to fill it. How long will it take to fill the pool if two hoses are used, one that fills at a rate of 40 gallons per hour and one that fills at a rate of 60 gallons per hour?
C. 180 hours
Which of the following is a complex number?
C. 4 + 9i
Melissa and Tomas are playing a game with complex numbers. If Melissa has a score of 5 - 4i and Tomas has a score of 3 + 2i, what is their total score?
C. 8 - 2i
What is the additive inverse of the complex number -8 + 3i?
C. 8 - 3i
An amusement parks sells adult tickets for $18 each and youth tickets for $12 each. Kalila is using the inequality mc014-1.jpg to find the combinations of tickets she can buy without exceeding her $250 budget. The ordered pair (4, 3) is a solution of the inequality. What does (4, 3) represent?
C. Kalila purchases 4 adult tickets and 3 youth tickets.
Which point shows the location of 5 - 2i on the complex plane below?
C. Point C
The line of best fit for the scatterplot below passes through which pair of points?
C. R and Q s and t by self
Mark and Jessica are each making a linear model to predict the population of squirrels in the town park. The are both using the same data points to find an equation of the line of best fit: the squirrel population, p, in 2002 and the squirrel population, q, in 2011. Mark is using the year as the x-value, and he represents his data as (2002, p) and (2011, q). Jessica is using the years since 2000 as her x-value, and she represents her data as (2, p) and (11, q). Which statement best describes how their prediction equations compare?
C. Their equations have different y-intercepts but the same slopes.
The scatterplot shows the number of athletes on the field hockey and tennis teams at Southern High School during seven different years. Which statement is best supported by the line of best fit?
C. When there are 10 field hockey players, there will be about 35 tennis players.
For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1?
C. a = -1, m = 1
For which data set is a linear regression most reasonable?
C. a set of four data pairs with a correlation coefficient r = -0.8
Which property of addition is shown below? a + bi + c + di = a + c + bi + di
C. commutative property
Which graph represents the solution set for the quadratic inequality x2 + 2x + 1 > 0?
C. dot a -1
Which graph shows a function whose inverse is also a function?
C. f1(x)
What is the solution set to the inequality (4x-3)(2x-1) ≥ 0?
C. x | x≤ 1/2 or x≥ 3/4
Which function has an inverse that is also a function?
C. {(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}
What are the solutions to the inequality (x-3)(x+5)≤ 0 ?
C. {x| -5≤ x≤ 3}
Which graph represents the function f(x)=3x-2/x-2
D
Which graph represents y=3^√x-5
D
The line of best fit for the scatterplot below passes through which pair of points?
D s and q little r by itselg
For the inverse variation equation p=8/v, what is the value of V when p = 1/4?
D. 32
If f(x) and its inverse function, f-1(x), are both plotted on the same coordinate plane, what is their point of intersection?
D. (3, 3)
An object is dropped from a small plane. As the object falls, its distance, d, above the ground after t seconds, is given by the formula d = -16t2 + 1,000. Which inequality can be used to find the interval of time taken by the object to reach the height greater than 300 feet above the ground?
D. -16t2 + 1000> 300
Given x varies inversely with y and xy = 2, what is the value of x when y = 1?
D. 2
If f(x) = x3 - 2x2, which expression is equivalent to f(i)?
D. 2 - i
Which complex number has a distance of √17 from the origin on the complex plane?
D. 4 - i
A restaurant wishes to have at least one server for every 12 tables. Each of the tables in the restaurant seats four guests. If x is the number of servers and y is the number of guests, which inequality represents the restaurant's desired relationship of the number of servers to the number of guests?
D. 48x≥ y
For the inverse variation equation xy = k, what is the constant of variation, k, when x = -3 and y = -2?
D. 6
Naomi wants to take yoga classes. She can take classes at the high school for a one-time fee of $20 plus $10 per class. She can join the local gym for $50 and take classes for $5 per class. Which statement is true about the average cost for the two options?
D. The gym option costs less per class for seven classes.
What is the value of i 20+1?
D. i
Which property of addition is shown below? If x = a + bi and y = -a - bi, x + y = 0.
D. inverse property
In which context will the inequality 4x + 5y > 80 have only integers in its solution set?
D. when x represents the number of cats and y represents the number of dogs
The graph of the function f(x)=6/x-3 is shown below.
D. x = 3
The sum of two numbers is no more than 28. Let x represent the first number, and let y represent the second number. Which inequality represents this situation?
D. x+y≤ 28
Which inequality has a solid boundary line when graphed?
D. y+x≤7
Which quadratic inequality does the graph below represent?
D. y≤ x2-3
Which notation best represents the phrase "at least 24"?
D. ≥ 24
What is the solution of x^2-1/x^2+5x+4≤ 0
D.-4 mc016-9.jpg x mc016-10.jpg 1 and x mc016-11.jpg -1
For the inverse variation equation p=8/v, what is the value of V when p = 1/2?
D.16
What is the domain of the function f(x)=x+1/x2-6x+8
D.all real numbers except 2 and 4
Which statement describes the domain of the function f(x)=3x/4x2-4
D.all real numbers except x = -1 and x = 1
Which of the following describes the graph of y= √-4x-36 compared to the parent square root function?
D.stretched by a factor of 2, reflected over the y-axis, and translated 9 units left
What are the critical points for the inequality x^2-4/x^2-5x+6< 0
D.x = -2, x = 2, and x = 3
If f(x) and f-1(x) are inverse functions of each other and f(x)=2x+5, what is f-1(8)?
Not C
If i=√-1, what is the value of i 3?
Not C
How does the graph of g(x)=1/x-5 +2 compare to the graph of the parent function f(x)=1/x
Not A
The school auditorium has 900 seats. The inequalitymc018-1.jpg, with x representing adults and y representing children, can be solved to find the possible combinations of adults and children attending an event. Which reason describes why the ordered pair (450, 450) must be included in the solution set of the inequality?
Not A
The speed, s, of the current in a certain whirlpool is modeled by s=300/d, where d is the distance from the center of the whirlpool. Which statement is true?
Not A
What is the range of the function y=√x+5
Not A
Which expression is equivalent to √-80
Not A
Which function has the same range as f(x)=-2√x-3 +8
Not A
Which graph represents y=3√x
Not A
Which graph shows the solution set of x^2+9x-22/x+4≥ 0
Not A
For the inverse variation equation p=8/v, what is the value of V when p = 4?
Not A or B
The function mc002-1.jpg models y, the average annual cost in dollars of owning a car for x years. Which statement best explains why the graph of mc002-2.jpg should have a vertical asymptote at x = 0?
Not A or B
What is the domain of the function y=√x
Not A or B
The critical points of a rational inequality are -1, 3, and 4. Which set of points can be tested to solve the inequality?
Not A or C
The area of the conference table in Mr. Nathan's office must be no more than 175 ft2. If the length of the table is 18 ft more than the width, x, which interval can be the possible widths?
Not A or D
Greg is in a car at the top of a roller-coaster ride. The distance, d, of the car from the ground as the car descends is determined by the equation d = 144 - 16t2, where t is the number of seconds it takes the car to travel down to each point on the ride. For which interval of time is Greg's car moving in the air?
Not A.
The graph of the function f(x)=10/x+2 is shown below.
Not A.
Which statement is true about the discontinuities of the function f(x)? f(x)=x-5/3x2-17x-28
Not A.
Which equation demonstrates the additive identity property?
Not A. 7+4i
Which function has an inverse that is a function?
Not A. b(x) = x2 + 3
If f(x) = 3x and g(x)=1/3x which expression could be used to verify that g(x) is the inverse of f(x)?
Not A. or B.
The function mc001-1.jpg relates y, the time in hours that it takes Michael to travel to his grandparents' house, to x, his average speed in miles per hour. What does the number 60 in the function represent?
Not A. or D
Which inequality has a dashed boundary line when graphed?
Not A. y≥ 3/5x+1
A small rock falling from the top of a 124-ft-tall building with an initial downward velocity of -30 ft/sec is modeled by the equation h(t) = -16t2 - 30t + 124, where t is the time in seconds. For which interval of time does the rock remain in the air?
Not B
Craig bought a treadmill for $400. He estimates that the annual costs to maintain the machine will be $36. Which rational function yields the average annual cost in dollars of owning the treadmill for x years?
Not B
If f(x) = 1 - x, which value is equivalent to |f(i)|?
Not B
If f(x) = 5x, what is f-1(x)?
Not B
What is the horizontal asymptote of f(x)=-2x/x+1
Not B
What is the value of the product (3 - 2i)(3 + 2i)?
Not B
Where are the asymptotes for the following function located? f(x)=14/(x-5)(x+3)
Not B
Which expression is equivalent to i 233?
Not B
Which phrase is equivalent to "Franco must work a minimum of 32 hours"?
Not B
Which statement decribes the behavior of the function f(x)=3x/4-x?
Not B
What is the domain of the function y=3^√x
Not B or D
Which equation shows an example of the associative property of addition?
Not B(-4 + i) + 4i = 4i + (-4i + i)
Aiko incorrectly used the identity property by combining the real number and the coefficient of the imaginary part.
Not C
