Algebra Questions

Solve the inequality and graph the solution set on real umber line Express the solution set in interval notati 5 5 x 5 x 6 The solution set is Type your answer in interval notation Use integers or fractions for any numbers in the expression Choose the correct graph below O A O C 8 8 6 6 2 2 0 2 6 8 OB D 8 8 6 6 2 2 0 2 2 7 4

Graph f x 4 and g x log ax in the same rectangular coordinate system O Q CXS

y varies jointly as x and z y 56 when x 2 and z 7 Find y when x 6 and z 6 V

6 State whether the product of 3 and 9 is rational or irrational Explain your answer

Britney is solving a quadratic equation Her first step is shown below 2 Problem 3x 1 2 Step One 3x 8 10x 3 2x 3 10x 8 6x 9 Which two properties did Britney use to get to step 1 addition property of equality I II commutative property of addition III multiplication property of equality IV distributive property of multiplication over addition 1 I and III 3 II and III 2 I and IV 4 II and IV

3 A dolphin jumps out of the water and then back into the water His jump could be graphed on a set of axes where x represents time and y represents distance above or below sea level The domain for this graph is best represented using a set of 1 Integers 3 Positive Integers

8 Solve algebraically for x 2 3 2 x 12 x x 2 5 3 4

4 The solution to 3 x 8 4x 8x 4 is 1 12 2 28 3 12 4 28

2 Nicci s sister is 7 years less than twice Nicci s age a The sum of Nicci s age and her sister s age is 41 Which equation represents this relationship 1 a 7 2a 41 3 a 2a 7 41 2 2a 7 41 4 a 2a 7

Without using a calculator find the exact value of the following expression log 39 log 1 log 18 log 0 0001 3 2 log 39 log 1 10 Jeg 0 0001 Simplify your answer

Name the parent function describe the transformations 1 x 3 4 3 2 x 2 7 2 2 x 1 5

Sketch a 45 45 90 triangle with a hypotenuse of 7 Label the other side lengths

1 2 3 4 X Need Help Read It Additional Materials 1 6 9 12 Submit Answer Tech Guide Excel Tech Guide TI 83 84 Tech Guide TI Nspire

Determine the surface area of the solid obtained by rotating the following parametric curve about the x axis x cos 0 y sin 0 0 0

A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight She currently weighs 105 pounds She hopes each week to multiply her weight by 1 08 each week a Find a formula for an exponential function that gives the woman s weight w in pounds after t weeks on the regimen

3 a 2 C 4 2 2 4 6 8 10 1 3 Is the degree of the polynomial odd or even Explain how you know odd The degree is 3 b Is the sign of the leading term of the polynomial positive or negative X What is the constant term of the polynomial

8 Huy borrowed 4500 from a bank at a rate of 5 per year compound interest He paid back the money and interest at the end of 2 years How much interest did he pay

Write a polar equation for an ellipse which a has a focus at the pole vertex at 28 0 and e 7 ep Write a polar equation using the standard form r 1 e cos 0 r Simplify your answer

Eliminate the parameter t Then use the rectangular equation to sketch the plane curve represented by the given parametric equations Use arrows to show the orientation of the curve corresponding to increasing values of t x 4 cost y 3 sint 0st 2t The rectangular equation is with

C 5b T2 The Lush Landscaping Company is involved in a project for the city They will be enlarging the garden in front of City Hall The current dimensions of the garden are 24 feet long by 16 feet wide The company plans to make the garden area larger by planting a border of white flowers all the way around the existing garden The border will have the same width x around the entire garden d Let x represent the width of the white flower border Complete the expressions for the length and the width of the new garden space after the border has been added in terms of x length 24 width 16 24 feet b Write an expression representing the rectangular area of the new garden space after the border has been added as a product of the length and width in terms of x 16 fee Using your expression from part b write a trinomial expression that represents the rectangular area of the new garden space after the border has been added Using your expression from part c write a polynomial expression that represents the area of the border of the landscape company plans to add

x 4 1 3x 6 7 from f x

100 The matrix P 0 3 8 is the transition matrix from what 0 1 1 basis B v1 v2 v3 to the basis 1 1 1 1 1 0 1 0 0 for R v 1 1 1 V2 27

Use algebraic methods to solve the following equations for a a 4 18 x 4 5 b 15 9 2 8 45 2 c 8 96 0 89 x 38 Preview DE Preview Preview

Find the solution of the system x y 1 mod 7 x z 2 mod 7 y z 3 mod 7

principal 12 000 interest rates 14 date repaid October 07 how many days and what the simple interest and amount paid back

Practice Aniyah is working at the mall wrapping presents during the holidays She she wraps The function f x 2x represents Aniya s daily earnings for x number of presents wrapped 2 1 Are the values 2 3 10 and 0 5 possible inputs for this situation Explain why or why not No 2 2 Explain why 24 50 is an impossible daily earning amount for Aniyah concert is being held at a local venue Tickets are 25 per person The concert venue has a maximum capacity of 500 people e function f t 25t represents the amount of money raised for t tickets sold 1 Select all the possible values in the domain of f t 0 1 25 3 7 Describe the domain of f t Select all the possible values in the range of f t 25 00 25 525 860 173 12 500

The economy of a small island nation is based on two sectors coal and steel Production of a dollar s worth of coal requires an input of 0 20 from coal and 0 25 from steel Production of a dollar s worth of steel requires an input of 0 56 from coal and 0 20 from steel Find the output from each sector that is needed to satisfy a final demand of 44 million for coal and 52 million for steel The output from the coal sector is approximately Round million

The population of a town has been growing following the equation P 400t 4000 where t is years after 2010 The number of restaurants in the town has been growing according to the equation R 5t 35 Complete an equation for the number of restaurants per capita per person Restaurants per capita

uppose A is a real matrix and A 832 84 42 Please find A

Write as a single logarithm with coefficient 1 Simplify as much as possible log 3x 2 2loglx 1 loglx 2

Select all the points of intersection between the graphs of the functions f x x 5 x 2 and g x 2x 1 x 2 5 2 0 5 2 a 5 0 b 1 0 d 2 0 4 c 2 12 3 What are the solutions to the equation x 3 x 5 Rewrite the equation in standard form then factor and solve algebraically Draw a rough sketch of the graph of g x x x 2 Label key points end behavior Explain your work e 4 18 f 5 30 intersection 2 15

Unit 2 Lesson 2 Cumulative Practice Problems 3 1 Select all polynomial expressions that are equivalent to 6x 4x 7x 5x 8 Explain a 16x b 10 6x 4x 7x 5x 8x e 8 5x 7x 4x 6x d 8 5x 7x 4x 6x

rsh B s 207 15 10 D A C 10 86 4 2 YA 5 10 15 20 E F G 2 4 6 8 61 H Point A b Point B Point C a C d e f ind g Point D Point E Point F Point G h Point H 05 50 Hese of is wrong 1 bo aut ostumes ALORS blivion to and 70 eistiacering 15 2 Add one term to the polynomial expression 14x 9 9x 5 11x 5x 3 to make it into a 22nd degree polynomial

Unit 2 Lesson 5 Cumulative Practice Problems 3 1 Which polynomial function has zeros when x 2 x 1 or x 5 h a f x x 2 3x 4 x 5 b f x x 2 4x 3 x 5 f x x 2 3x 4 x 5 d f x x 2 4x 3 x 5 C

4 The graph given below models the Nemo s distance from home in miles after x hours of swimming Two coordinate points have been labeled 3 5 and 6 10 a Interpret the point 6 10 in the context of this situation in a complete sentence Distance from home b What would the units be for the average rate of change in this scenario Answer 3 5 Time 6 10 x

5 Find the singular value decomposition of A 1 1 Find the pseudo inverse A of matrix A 23 0 1 0 2 2 3

4 Show that the sequences of functions f n k 1 1 x converges k 0 R defined by f x n pointwise to f x uniform 1 1 x 1 but the convergence is not

BY FComposition of the matrix ou must show the eigenvalues eigenvectors modal matrix and the diagonalization S AS Yo tailed procedure must be shown to receive any credits for the question arry out an eigen 1 1 2 A 0 3 0 Lo 1 2

3 f x x 2 2x 1 f g f g fg Domain x 1 x 1 flg x 2 2x 1 g x Domain x 2 x 1 x 2x 1 2x 1 x 1 x 2 X 2x 1 x 1 Domain x 1 x 1 x 1 Domain x 2 2x 1 x 1 2x 1 2x 1 x 2 x 1 x 2x 1 2x 1 x 1 x x 2 2x 1 x 1 X X X 1

2 f x 2 2 X 2 a f g 2 11 g x c fg 2 2 Domain 4 4 x x Domain 2 X X X N 2 b f g 2 2 2 Domain d flg 2 2 11 X X 4 2 x 11 Domain x0

For the function polynomial function x x x 1 x 2 Where does f crosses the y avis and touch th x axis Amo What is degree of AW clvl becomes larger 1 what function does

Meangru Find the following functions and state the domain of each a f g b f g c fg 1 f x x 2x 1 g x 2x 3 a f g Domain b f g x 2x 1 2x 3 x 4x 2 c fg x 2x 1 2x 3 d flg d f g Domain f x g x x 2x 1 2x 3 Domain

with the following properties 1 Degree is 6 2 The zeros of P are 0 1 and 2 3 0 is a zero of multiplicity 1 1 is a zero of multiplicity 2 and 2 is zero of multiplicity 3 4 As x the values off 0 5 P 1 4

3 f x x 2 f g f g fg Domain x x 1 2x 1 8 x f g X 2 X 2x 1 x 1 x 2 x 1 x 2x 1 2x 1 x 1 x 2 X 2x 1 x 1 Domain x 1 x 1 Domain x 2 X 2x 1 x 1 x x 2 2x 1 x 1 2x 1 Domain x 2 x 1 x 2x 1 2x 1 x 1 2x 1 X X BIOG nimmod 2 b

Suppose T is a transformation from R2 to R Find the matrix A that induces Tif T is a reflection over the line y 1 4x b rotation by 1 3 a A b A 00 00 00 00

If a person shoots a basketball overhand from a position 8 feet above the floor then the path of the basketball through the hoop can be 16x 1 15x 8 where v is the initial velocity of the ball in ft sec y is the height of the ball and x is the 0 434v modeled by the parabola y distance away from the person a If the basketball hoop is 10 ft high and located 20 ft away what initial velocity v should the basketball have b What is the maximum height of the basketball a The initial velocity of the basketball should be approximately ft per sec Round to the nearest hundredth

R x 100x R 100 100 100 R 6 6667 e What quantity x maximizes revenue R x 100x b 2a X X R x 150 103 f What is the maximum revenue R x 100x unty of bestonlumom od p x 100 0005 100 0004 16 00 d BS a s Boomed bla 0004 2005 5 x10 R 150 100 150 on A sinsven scha g What price should the company charge to maximize revenue borq inson to bloz z vitias

Write the complex number in polar form with argument 0 between 0 and 2 5

Follow the steps for graphing a rational function to graph the function R x choice x 9 x 6 3 x 6 OB R x is already in factored form What is the domain of R x Select the correct choice below and if necessary fill in the answer box to complete your choice CA R x x A R x x 3x 54 x 3x 18 OA xx2 Type an integer or a simplified fraction OB xx Type an integer or a simplified fraction C xlx 3 6 Type an integer or a simplified fraction Use a comma to separate answers as needed D The domain is the set of all real numbers Type your answer in factored form Do not simplify Write R x in lowest terms Select the correct choice below and if necessary fill in the answer box to complete your choice x 6 x 3 Simplify your answer 4

Suppose you have a function f x and all you know is that f 4 6 and the graph of its derivative is Click on the graph to see a bigger version Use linear approximation to estimate f 4 2 Is your answer a little too big or a little too small Enter TB or TS 1 0