# Algebra Questions

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Algebra

Complex numbersDecide whether the relation defines y as a function of x Give the domain and range y x7 Does the relation define a function Yes O No What is the domain Type your answer in interval notation

Algebra

Complex numbersThe following table shows the number of endangered and threatened species in the US from 2003 to 2013 Use DESMOS to detemine if th model is a quadratic or linaer model for the data Describe the data 2003 813 2004 2005 2006 2007 2008 941 962 1053 1132 1194 The data does not fit a quadratic model it is a linear model O The data does not fit a linear model it is a quadratic model O There is no way to determine what the model is to be There is no correct answer given 2009 2010 1205 1244 2011 1254 2012 1262

Algebra

Complex numbersDecide whether the relation defined by the graph to the right defines a function and give the domain and range Does the graphed relation define a function No O Yes What is the domain of the graphed relation Type your answer in interval notation 10 8 8 4 10 TO AY di 2 4 6 do 10 2

Algebra

Quadratic equations2 In 2013 the United States Postal Service charged 0 46 to mail a letter weighing up to 1 oz and 0 20 per ounce for each additional ounce Which function would determine the cost in dollars c z of mailing a letter weighing z ounces where z is an integer greater than 1 1 c z 0 46z 0 20 2 c z 0 20z 0 46 3 c z 0 46 z 1 0 20 4 c z 0 20 z 1 0 46 3 Last week a candle store received 355 60 for selling 20 candles Small candles sell for 10 98 and large candles sell for 27 98 How many large candles did the store sell 1 6 2 8

Algebra

Quadratic equationsThe graph depicts the growth in costs using a line segment Use the midpoint formula to approximate the cost during the year 1987 The approximate cost during the year 1987 was Average Annual Cost of Tuition and Fees At 4 Year Private Colleges During 1983 1991 Cost 10000 8000 6000 4000 2000 5047 1983 Year 10

Algebra

Quadratic equationsThe table lists how poverty level income cutoffs in dollars for a family of four have changed over time Use the midpoint formula to approximate the poverty level cutoff in 1987 to the nearest dollar The poverty level cutoff in 1987 was Round to the nearest dollar as needed dollars Year 1970 1980 1990 2000 2004 Income in dollars 3213 8393 13526 17076 19946

Algebra

Complex numbersIs the triangle with the vertices A 7 3 B 0 7 and C 8 7 a right triangle Is the triangle a right triangle O Yes O No

Algebra

Permutations and CombinationsDetermine whether the three points are collinear 0 4 3 9 2 0 Are the three points collinear O Yes No

Algebra

Quadratic equationsFor the points P and Q do the following a Find the distance d P Q b Find the coordinates of the midpoint M of the segment PQ P 3 2 5 5 Q 2 5 a The distance d P Q is Simplify your answer Tyne an exact answer uning

Algebra

Permutations and CombinationsFor the point P 13 9 and Q 8 6 find the distance d P Q and the coordinates of the midpoint M of the segment PQ What is the distance Simplify your answer Type an exact answer using radicals as need

Algebra

Complex numbersConsider the graph of y 2x 4x 1 The x intercepts are located at No solution Enter the coordinates of ALL the x intercepts or if no x intercepts exist select that ch Question Help Video Written Example

Algebra

Quadratic equationsSolve by the quadratic formula List the solutions separated by commas 6x x 13x 5

Algebra

Quadratic equationsUse the like bases property and exponents to solve the equation 4 5 2500 x

Algebra

Complex numbersDraw the graph of f x 4 7 6 5 4 3 2 Clear All Draw 7 6 5 4 32 H 2 23 4 5 6 7 1 2 3 4 5 6 7

Algebra

Complex numbersSolve 2 U 15 5 2 0 Express your answer in radical form If no real solution exists enter DNE Question Help Video Written Example

Algebra

Complex numbersFind the last term to make the trinomial into a perfect square x 8x Write the trinomial as a binomial squared

Algebra

Matrices & DeterminantsLet A 2 3 7 5 and u 7 Define a transformation T R R by T x Ax Find T u the image of u under the transformation T

Algebra

Matrices & DeterminantsQuestion 11 wo Find the standard matrix of the linear transformation T T R R rotates points about the origin through angle T 4 radians with counterclockwise rotation for a positive

Algebra

Quadratic equationsDetermine whether the given binomial is a factor of the polynomial p x If it is find the remaining factors of p x 6 5p x 2x 5x x 6 x 2 Do thi L2 2 5 1 6 2 1 x 2 2x 1x 3

Algebra

Quadratic equationsA right triangle has a 30 angle The leg adjacent to the 30 angle measures 25 inches What is the length of the other leg Round to the nearest tenth O 14 4 in O 21 7 in 28 9 in O 43 3 in

Algebra

Permutations and CombinationsWhat is the length of AC Round to the nearest tenth 10 5 m O 12 3 m 18 3 m 21 4 m

Algebra

Quadratic equationsThe equation sin 40 20 0 the length of line segment AC A b C 20 cm can be used to determine 40 B TIME C What is the length of AC Round to the nearest tem 11 8 cm 12 9 cm 14 9 cm 15 3 cm

Algebra

Complex numbersFind the length of AC Use that length to find the length of CD B 10 cm 30 A C 25 D What is the length of CD Round t 2 3 cm 4 0 cm 10 7 cm 18 6 cm

Algebra

Sequences & SeriesWhat is the approximate value of x Round to the nearest tenth X O 3 1 cm 3 9 cm 4 6 cm 5 4 cm 6 cm y 50 D

Algebra

Sequences & SeriesStage 0 How many dots are in stage 21 Stage 1 For which stage are there 100 dots Stage 2 Stage 3

Algebra

Complex numbersJulian describes an angle in the triangle using these statements GH is the adjacent side HK is the opposite side GK is the hypotenuse G H Which angle s is Julian describing O ZG O ZH O ZK O ZH and ZK

Algebra

Complex numbers8 TIE F 10 E Given right triangle DEF what is the value of sin E O mun m n m O O O 35

Algebra

Complex numbers40 50 M Given right triangle MNO which represents the value cos M ON MN MN MO ON JMO MN ON

Algebra

Permutations and CombinationsX 60 4 N 30 Given right triangle XYZ what is the value of tan Y 01 1 201 2 3

Algebra

Complex numbers0 30 P Given fight triangle PQR which represents the value of sin P O RP PQ PQ RQ PR

Algebra

Quadratic equations60 18 30 B Which trigonometric ratios are correct for triangle ABC Select three options sin C 3 cos B 2 O tan C 3 12 12 23 O tan B 2 3 sin B 4

Algebra

Complex numbersExplain how you know that the number of dots in Dot Pattern B will eventually exceed the number of dots in Dot Patterns A and C Pattern B will eventually exceed the number of dots in Patterns A and C because it is i Compare the growth rates of Dot Pattern A Dot Pattern B and Dot Pattern C In your comparison rank the growth rates from slowest to fastest Slowest Growth Rate Middle Growth Rate i Fastest Growth Rate i

Algebra

Sequences & SeriesSuppose the length of voicemails in seconds is normally distributed with a mean of 40 seconds and standard deviation of 10 seconds Find the probability that a given voicemail is between 20 and 50 seconds 10 20 30 99 7 95 68 40 50 60 70 P Enter

Algebra

Sequences & SeriesTests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours Find the probability that a randomly selected light bulb will last between 750 and 900 hours 99 7 95 68 525 600 675 750 825 900 975 P Enter

Algebra

Complex numbersWeekly wages at a certain factory are normally distributed with a mean of 400 and a standard deviation of 50 Find the probability that a worker selected at random makes between 400 and 550 99 7 95 68 250 300 350 400 450 500 550 P Enter

Algebra

Permutations and CombinationsSelect the correct answer The Breaker s Manufacturing Company makes 80 of a particular sensor the Cartin Company makes 15 of them and the Flutes Company makes the other 5 The sensors made by Breaker s have a 4 defect rate the Cartin sensors have a 6 defect rate and the Flutes sensors have a 9 defect rate If a sensor is randomly selected from the general population of all sensors what is the probability that it is defective given that it was made by Breaker s A B 0 04 O D 0 05 C 0 15 0 80

Algebra

Sequences & SeriesWeekly wages at a certain factory are normally distributed with a mean of 400 and a standard deviation of 50 Find the probability that a worker selected at random makes between 350 and 450 99 7 95 68 250 300 350 400 450 500 550 P Enter

Algebra

Complex numbersDot Pattern F Stage 0 x Clear Stage 1 Create a graph to represent the dot pattern using the table Undo Stage 2 Redo Stage 3

Algebra

Quadratic equationsDot Pattern F Stage 0 Stage 1 Stage 2 Stage 3 Describe the pattern s growth rate and determine which function family the pattern belongs to

Algebra

Sequences & SeriesDiego and Elena found two new dot patterns shown below Stage 0 Patterns D is Patterns E is linear Dot Pattern D Stage 1 Stage 2 because the pattern is because the pattern is quadratic exponential Stage 3 adding 3 Stage 0 subtracting 3 Dot Pattern E Stage 1 multinting by 3 Stage 2 Stage 3 dividing by 3

Algebra

Permutations and CombinationsSuppose the number of strawberries a plant produces is normally distributed with a mean of 15 and a standard deviation of 2 strawberries Find the probability a given plant produced between 15 and 19 strawberries Probability of between 15 and 17 was 34 Probability of between 17 and 19 was 13 5 9 2 35 11 13 5 34 13 15 P 34 17 13 5 19 2 35 Enter 21

Algebra

Quadratic equationsStage Dot Pattern D Stage 1 Stage 2 Stage 3 Do you agree with either justification Explain your reasoning Stage 0 Dot Pattern E Stage 1 Diego says Both dot patterns D and E are linear because the number of dots increases for each stage Elena says Dot Pattern D is linear and Dot Pattern E is exponential because the growth rates are different Stage 2 Stage

Algebra

Quadratic equationsStage 0 Stage 1 Stage 2 Complete the table Find the number of dots in stage 4 of Pattern F Stage Number x Number of Dots 0 Stage 3 3

Algebra

Quadratic equations9 log 2 x log 7 2 11 log x 3 logg x 4 1 13 logg 5x 10 logg 6 2 2 5XH 6 5 30x 60 64 60 60 60600 36x 42 30 2 301 X 2 15 15 log 9 log 4x log 75 10 log 4 x 12 log x 1 log x 2 2 14 log 3x 9 log 5 log 60 16 log 10 log4 4x 2 log 4 80

Algebra

Quadratic equationsSolve each equation 1 log4 6 log 4 x 3 6 43 64x 6 2 x 3 32 64 2 3 log69 log x 8 2 5 log6 7 log x log6 65 og x 6 log x 4 log 67 2 log 7 log x 2 2 4 logg 9 logg x logg 34 a 34 34x 9 3 34 x 9 34 6 log 10 log 2x 7 1 8 log 4 2 log 4 5x 1 log 25