Algebra Questions

1 Find all solutions of the following equation in the interval 0 27 4tan x 4 3 0

An element decays at the rate of S t se 0 062t where s is the initial amount in grams and t is the time in years since this initial amount was present If you have a 45 gram piece of this element how many grams will you have 4 years from now Round your answer to the nearest tenth of a gram

2 Evaluate the following expression x 7 10 n where n is a whole number 5 cos 5x 5 cos 5x 1 tan 5x

10 Verify that each equation is an identity algebraically Remember your answer is not a yes or no answer Verify means Prove and this whole proof needs to be part of your answer sec tan cos B 1 sin

9 Verify that each equation is an identity algebraically Remember your answer is not a yes or no answer Verify means Prove and this whole proof needs to be part of your answer csc s sin s cos s cot s

6 Graph the expression on each side of the equals symbol to determine whether the equation might be an identity 4 7tan x sin x 4csc x 7sec x Not an Identity Identity

8 Perform the indicated operations and simplify the result sin e cos e 1 cot 0 cos e sin e sin 0 tan 0 O 2 tan e sec 8 csc 0

7 Use the fundamental identities to simplify the expression tan 0 csc 0 cos 0 tan e Osec 0

1 Evaluate the following expression x 8 n where n is a whole number 3 tan 4x 3 cot 4x O 3 tan 4x cot 4x O4 tan 4x cot 4x O 3 tan 4x cot 4x O tan 4x cot 4x tan 4x cot 4x

5 Graph the expression on each side of the equals symbol to determine whether the equation might be an identity csc 0 cot 0 1 cos 0 sin 0 Identity Not an Identity

4 Decide whether the expression is or is not an identity sec x tan x O Identity Not an identity 0

3 Evaluate the following expression 4 O 0 4 3 sec y 3 cot 7 y 2 3 3

5 Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of 0 where cos 0 3 3 81 9x x 3 cos 0 1 0 1 Then find sin an 2

10 Use fundamental identities to write a simpler version of the expression sin a csc a sin a and explain your process Be sure to tell which fundamental identity you used

Use the trigonometric substitution x 2 tan to rewrite the algebraic expression 4 x as a trigonometric function of 0 where Explain all of your steps and how you solved it 2 x

6 Which of the following is equivalent to the given expression cos x 1 sinx

8 If x 5 sin 0 use trigonometric substitution to write 25 x as a trigonometric function of 0 where 1 0 1 2 5 cos 0 5 sec 0 5 csc 0 5 tan 0 5 sin 0

7 If x 6 sin 0 use trigonometric substitution to write 36 x as a trigonometric function of 0 where 0 0 2

An arctic village maintains a circular cross country ski trail that has a radius of 2 2 kilometers A skier started skiing from the position 1 989 0 94 measured in kilometers and skied counter clockwise for 3 3 kilometers where he paused for a brief rest Consider the circle to be centered at the origin Determine the ordered pair in both kilometers and radii on the coordinate axes that identifies the location where the skier rested Hint Start by drawing a diagram to represent this situation x y 2 199246115 0 05758928628 radii kilometers

Find the eigenvalues of the symmetric matrix Enter your answers as a comma separated list Enter your answers from smallest to largest 044 404 444 A1 For each eigenvalue find the dimension of the corresponding eigenspace Enter your answers as a comma separated list dim x

Find Gl H 5 69 Write your answer as an integer or as a decimal rounded to the nearest tenth GI Submit

Let f x 3x 4 What is the domain of f x What is the range of f x Determine f x f x What is the domain of f x What is the range of f x

Simplify the following rational expression x 6x 8 x 1 X 4 x 1 State the restrictions on the variable Express your answers as integers or fractions in lowest terms Seperate multiple answers with a comma x

Find the measure of angles x and y 62 x 30 1

Try It How does an SAT score of 1120 compare to an ACT score of 23

The population of a town is increasing by 601 people per year State whether this growth is linear or exponential If the population is 1800 today what will the population be in five years Is the population growth linear or exponential O linear O exponential What will the population be in five years

The numbers of words defined on randomly selected pages from a dictionary are shown below Find the mean median and mode of the listed numbers 56 59 47 43 61 77 78 30 69 50 What is the mean Select the correct choice below and if necessary fill in the answer box within your choice OA The mean is OD Round to one decimal place as needed B There is no mean What is the median Select the correct choice below and if necessary fill in the answer box within your choice OA The median is Round to one decimal place as needed OB There is no median What is are the mode s Select the correct choice below and if necessary fill in the answer box within your choice OA The mode s is are Round to one decimal place as needed Use a comma to separate answers as needed B There is no mode

The expenses and income of an individual are given in table form to the right Find the net monthly cash flow it may be negative or positive Assume that amounts shown for salaries and wages are after taxes and that 1 month 4 weeks Income Part time job 1100 month Student loans 8400 year Scholarship 6500 year The net monthly cash flow is Round to the nearest dollar as needed Rent 550 month Expenses Groceries 50 week Tuition and fees 6500 year Health insurance 25 month Entertainment 100 month Phone 65 month

Write a short statement that expresses a possible relationship between the variables travel time from Denver to Chicago average speed of a car Choose the correct answer below OA As the time to drive from Denver to Chicago increases the average speed of a car decreases OB As the average speed of a car increases the time to drive from Denver to Chicago decreases OC As the time to drive from Denver to Chicago increases the average speed of a car increases O D As the average speed of a car increases the time to drive from Denver to Chicago increases

During the worst periods of hyperinflation in a certain country the price of food increased at a rate of 15 per month State whether this increase was linear or exponential If your food bill was 160 in one month during this period what was it three months later Was the growth in inflation linear or exponential Olinear exponential What was the monthly food bill after three months Round to the nearest dollar as needed

Radioactive uranium 235 has a half life of about 700 million years Suppose you find a rock 1 16 and chemical analysis tells you that only of the rock s original uranium 235 remains How old is the rock Select the correct answer below OA 350 million years old OB 1 4 billion years old OC 3 5 billion years old OD 175 million years old OE 2 1 billion years old OF 2 8 billion years old

The following data give the margin of victory for a football championship over 15 years 13 8 3 11 12 33 4 26 8 4 3 3 6 14 3 a Find the mean and median margin of victory b Identify the outlier in the data set If the outlier is eliminated what are the new mean and median a Find the mean and median of the weights The mean is Round to the nearest tenth as needed The median is Type an integer or a decimal b Which if any of the margins of victory would be considered the outlier Select the correct choice below and if necessary fill in the answer box to complete your choice OA The outlier is Type an integer or a decimal OB None of the margins would be considered an outlier Find the mean with the outlier excluded Select the correct choice below and if necessary fill in the answer box to complete your choice OA The mean without the outlier is Round to the nearest tenth as needed OB None of the weights would be considered an outlier Find the median with the outlier excluded Select the correct choice below and if necessary fill in the answer box to complete your choice OA The median without the outlier is Type an integer or a decimal OB None of the weights would be considered an outlier

16 14 The solution is 7

professor records the following final grades in one course Construct a frequency table for he grades A C ABCDF A C Total A C A C B C B C 1 100 BC Complete the table Type an integer or decimal rounded to the nearest tenth as needed Grade Frequency Relative frequency Cumulative frequency B D BD B D B F CO F

What are the three basic ways to represent a function Choose the correct answer below OD OA The three basic ways to represent a function are a table a graph and an expression OB The three basic ways to represent a function are an ordered pair a graph and an expression OC The three basic ways to represent a function are a table an ordered pair and an equation OD The three basic ways to represent a function are a table a graph and an equation

is the dependent variable decide which variable is the independent variable and whic Choose the correct answer below OA Mathematical models are based on relationships between quantities that can change These relationships are described by mathematical tools called functions The quantities related by a function are called variables because they change A function describes how a dependent variable changes with respect to an independent variable The values of dependent variables depends on the values of independent variables OB Mathematical models are based on relationships between quantities that cannot change These relationships are described by mathematical tools called functions A function describes how a dependent variable changes with respect to an independent variable The values of independent variables depends on the values of dependent variables OC Mathematical models are based on relationships between quantities that can change These relationships are described by mathematical tools called functions The quantities related by a function are called variables because they change A function describes how a dependent variable changes with respect to an independent variable The values of independent variables depends on the values of dependent variables O D Mathematical models are based on relationships between quantities that cannot change These relationships are described by mathematical tools called functions A function describes how a dependent variable changes with respect to an independent variable The values of dependent variables depends on the values of independent variables

Use the theoretical method to determine the probability of the following outcome and event State any assumptions made Tossing two coins and getting either one head or two heads Choose the correct answer below O A O B O C Assuming that each coin is fair and is equally likely to land heads or tails the 4 O D probability is Assuming that each coin is fair and is equally likely to land heads or tails the 1 probability is 3 probability is 2 Assuming that each coin is fair and is equally likely to land heads or tails the 3 4 Assuming that each coin is fair and is equally likely to land heads or tails the probability is 2 x 2

What do we mean by combinations Explain the meaning of each of the terms in the combinations formula Give an example of its use Choose the correct answer below OA The n represents the number of permutations which includes different orderings The n r xr represents the number of different orderings of n items taken r at a time Dividing n by n r xr determines the number of permutations counting each different ordering which is a combination B The n represents the number of combinations which includes different orderings The n r xr represents the number of different orderings of n items taken r at a time Dividing n by n r xr determines the number of combinations without counting each different ordering which is a permutation OC The n represents the number of permutations not counting different orderings The n r xr represents the number of different orderings of n items taken r at a time Dividing n by n r xr determines the number of permutations counting each different ordering which is a combination OD The n represents the number of permutations which includes different orderings The n r xr represents the number of different orderings of n items taken r at a time Dividing n by n r xr determines the number of permutations without counting each different ordering which is a combination Give an example of its use Select the correct answer below OA The formula can be used when deciding how many ways someone can dial a number on a telephone OB The formula can be used when deciding how many ways the first five letters of the alphabet can be arranged OC The formula can be used when deciding how many ways someone can choose two hats from 10 options D The formula can be used when deciding how many ways someone can choose a vanity license plate

probability of winning some prize on a single ficket is 1 in 100 What is your probability of having at least one winner among your 25 tickets Choose the correct answer below OA The probability is 0 2510 according to the at least once rule for independent events OB The probability is 1 0 99 25 according to the at least once rule for independent events OC The probability is 0 2510 because each ticket counts as an independent event OD The probability is 1 0 99 25 because the probability of not winning is 1 0 25 25 OE The probability is 25 in 100 because you bought 25 tickets OF The probability is 25 in 100 because the events are non overlapping

Pinocc D write your answer as an integer or as a decimal rounded to the nearest tenth mcc

Click here to watch the video 17x 9 Find the quotient 3 cis 17x 9 3 cis 9 cis 2x 9 in rectangular form using exact values 2x 9 cis 9 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bi

32 f x 18 fit x 3 Ay 8 2 6 4 2 2 8 6 8

Click here to watch the video Find the quotient 2 cis 41x 36 2 cis 18 cis 41x 36 11x 36 in rectangular form using exact values 11x 18 cis 36 Simplify your answer including any radicals Use integers or fractions for any numbers in the

36 f x 8 2 6 x 3x 4 2x 6 4 2 8 6 4 2 4 6 8 X

Multiply 78 I 5 6 7 5 8 6 Simplify your answer Type an integer or a fraction

Rangers If you would like to have exactly one player from each position in your starting 9 people in starting line up line up in how many ways could you arrange the line up Be sure to show and explain your work as well as any formulas you use 2 points Player Name John Gray Andrew Heaney Dane Dunning Nathan Eovaldi 1 2 3 4 5 Martin Perez 6 7 8 9 10 11 Brock Burke 12 Cody Bradford 13 Corey seager 14 20 21 Jose Leclerc Josh Sborz Jordan Montgomery Will Smith Max Scherzer Nathaniel Lowe Marcus Semien 15 16 Josh Jung 17 Jonah Heim 18 Sandy Leon 19 Adolis Garcia Leody Taveras Robbie Grossman Travis Jankowski Ezequiel Duran Bubba Thompson 22 23 24 25 Austin Hedges Player s Position Player s Batting Average 000 000 000 000 000 Pitcher Pitcher Pitcher Pitcher Pitcher Pitcher Pitcher Pitcher Pitcher Pitcher Pitcher Pitcher Shortstop First base Second base Third base Catcher Catcher Right Field Center field Left field Left field Shortstop Left field 000 000 000 000 000 000 000 327 262 276 266 258 146 245 266 238 263 276

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6 From a point 125 m from the foot of a building the angles of elev the building s flagpole are 40 and 38 respectively 380 409 125 m Calculate a the height of the building the Height of the building is 236 66m Tall Pe 125 38 125 x x 138 125 125 7 125 78m T H 164 88 125 78 b the length of the flagpole 230 66 104 88 O X x Tanus Tan 88 125 78 x 104 88m 125 Tan 38 buo a Tan38 125 78 Tan 40 X Tan Uc

7 From the top of a cliff 108 m high the angles of depression of two small boats on the water are 90 and 15 20 Boat A 9 15 2 Boat B Calculate the distance a from the foot of the cliff to the closer boat 108m b between the boats if they are sighted in the same direction

From the top of a fire tower the angle of depression of a cabin is observed to be 210 Find the distance from the cabin to the foot of the tower if the tower is 212 m tall