Algebra Questions

Exercise 1 24 a Given n E N let Yn be the set of all binary sequences of length n so for example Y1 0 1 and Y2 00 01 10 11 Find and prove a formula for the number of elements in Yn b Let Y be the set of all finite binary sequences that is Y n 1 UYn Decide whether Y is countable or uncountable and prove

Tree height feet Tree Growth y 2 4 0 2 6 4 Age years X Use the graph to write an equation of the line

Solve 5x 4 3x 8 a Model b Perform the step to have variables circles on only one side c Write the resulting step

Note that this function does not have any vertical asymptotes because the denominator cannot equal zero In the graph below drag the green intercepts to the correct positions Drag the orange horizontal asymptote to the correct position Drag the blue y intercept to the correct position When finished click CHECK 10 5 0 10 6 0 1 0 5 0 10

x 4 In the graph below drag the green x intercept s to the correct position s Drag the red vertical asymptote s to the correct position s Drag the orange horizontal asymptote to the correct position hese Determine several points of the function and drag the blue point to one locations Choose a point that is not an x intercept and for which the y coordinate is a multiple of 0 1 Otherwise you won t be able to drag the blue poin to the exact location When finished click CHECK 10 6 2 5 10 5 5 5 10

confirm your work In the graph below drag the green x intercept s to the correct position s Drag the red vertical asymptote s to the correct position s Drag the orange horizontal asymptote to the correct position Determine several points of the function and drag the blue point to one of these locations Choose a point that is not an x intercept and for which the y 10 f x coordinate is a multiple of 0 1 Otherwise you won t be able to drag the blue point to the exact location When finished click CHECK 6 2 2x 12x 18 x 2x 8 5 10 5 0 5 10

Consider the rational function below x 3 x 1 x 4 x 4 x 5 x 4 Give the domain of f by listing all a values that are restricted domain restrictions List the x coordinates of the x intercept s Separate multiple answers with a commas x intercepts at List the locations of the vertical asymptote s Separate multiple answers with commas vertical asymptotes List the x value s for which f has a missing point removable discontinuity Separat multiple answers with commas missing points at

Graph the rational function below on paper by hand Then do the steps that follow to confirm your work In the graph below drag the green x intercept s to the correct position s Drag the red vertical asymptote s to the correct position s Drag the orange horizontal asymptote to the correct position Determine several points of the function and drag the blue point to one of these locations Choose a point that is not an x intercept and for which the y 10 f x coordinate is a multiple of 0 1 Otherwise you won t be able to drag the blue point to the exact location When finished click CHECK 6 2 5 x 5 x 4 10 5 5 10

f x x 16 Note that this graph should have only one x intercept and one vertical asymptote In the graph below drag the green x intercept to the correct position Drag the red vertical asymptote to the correct position Drag the orange horizontal asymptote to the correct position Determine several points of the function and drag the blue point to one of these locations Choose a point that is not an x intercept and for which the y coordinate is a multiple of 0 1 Otherwise you won t be able to drag the blue point to the exact location 10 5 10 5 0 0 1 5 6 5 1 10

Simplify each of the following numbers to the to the polar re i theta form Ther plot the number in the complex plane Thank you a z b C 1 z 1 1 z 1 Z

Fill in the blank to make equivalent rational expressions w 9 7 2w 8w 28

partial graph of f x 1 67 92 54 is given below Use the graph of f to solve the following equation 1 6x 91 54 0 6 5 4 3 2 1 0

The graph of f x 30x 27x 9x 6 is given below Use the graph of f to solve the following equation 301 271 9x 6 0 2 VA 0 1

Use synthetic division to verify that 3 and 1 are roots of f x 90x 366x 1008r 264 288 Use the results of synthetic division to find all solutions to 4 90x 366x 1008x 264x 288 0

4 4x 2x 7

Solve the following polynomial equation given 96x 104x 160x 150 0 5 3 is a root of f x 96r 104r 160 150 4

Solve the following polynomial equation given 1 is a root of f x 302 24 30z 24 30r 24z 30z 24 0

s x 2 x 3 x 7 x 8 Use the Leading Coefficient Test to determine the end behavior of the graph of 8 Determine the I intercepts of 8 and the multiplicity of each intercept Also describe the behavior of the graph at each z intercept If a third x intercept does not exist enter DNE when appropriate According to the Leading Coeffiecient Test the graph of s O falls to the left and falls to the right falls to the left and rises to the right Orises to the left and rises to the right O rises to the left and falls to the right Determine the x intercepts of s Enter solutions using a comma separated list The multiplicity of the least x intercept x The multiplicity of the greatest intercept a The multiplicity of the other intercept x At the least x intercept I is is is the graph of s Select an answer

3 A Contractor is making a different tile patteren using blue and Green tiles In this file Pattern there are blue Filed for every 4 green tiled IF The contractor used ne use 22 5 blue tied how many total thief will he use

3 Solve the following polynomial equation given 1 is a root of f x x 8x 1lz 20 z 87 11z 20 0

Use synthetic division to evaluate and write 4x 2r 7 in the form 1 41 21 7 T 41 2x 7 1 r 4x 2x 7 divisor quotient remainder

5 The amount of money that a news Poper company cand is directly Proportional to the numbers OF Popara they sell Th News Paper Company earn s 150 For every God Pafer they Jell How much money would the Company ean on a day Ipere they sell 1500 Paperd

Use synthetic division to evaluate and write 1 36x 36 in the form T T 36x 36 divisor quotient remainder h Use the above result to determine the remaining roots of x r 36x 36 List all roots using a comma separated list 1 1 36x 36 are 2 2 362 36 2 6 The roots of 2 2 36x 36 a

New Tab PRIA 131 y 131 Free Grammar Ch P vy x y x 1 y y 18 18 8 a 5 4 3 2 1 b 5 C 4 2 J t 2 3 4 1 5 5 4 3 2 5 4 3 2 1 2 4 S 5 4 2 5 3 2 2

24 Con type per hour the type O type 3 words per second how man

Jack has a huge Poper due for his literature Class at the end of the Semester If he con write a Pase every 2 of on hour how long will it take him to write his entire il Page Paper 2

20 11x36x 5x t

How many minuetes of there in 4 days

1 Find the series radius and interval of convergence for x 2 For what values of x does the serie 10 converge absolutely Conditionally 0

John rented a truck for one day There was a base fee of 19 99 and there was an additional charge of 71 cents for each mile driven John had to pay 113 when he returned the truck For how many miles did he drive the truck miles X

Use polynomial long division to evaluate and write the solution in form 6x x 7 T 6x x7 x 1 quotient remainder divisor

2 Use the Ratio Test to determine if n 1 n n 2 n 32n converges or diverge

Ive the following homogeneous system of linear equations x2 x3 3x4 9x5 x2 3x3 9x4 6x5 0 0 x3 3x4 4x5 0 he system has no solution demonstrate this by giving a row echelon form of the augmented matrix for th u can resize a matrix when appropriate by clicking and dragging the bottom right corner of the matrix me system has a unique solution he system has no solution he system has a unique solution he system has infinitely many solutions

A polynomial of degree 6 has the following characteristics a leading coefficient 1 a zero of multiplicity 3 at x 6 a zero of multiplicity 2 at x 8 a zero of multiplicity 1 at x 7 11 Determine a possible polynomial of degree 6 that satisfies the above conditions P x Par

6 cm 2 cm 3 cm 7 m 6m 4 cm Surface Area Find the Area of this Irregular Shape Aaron was plotting the shape of his garden on grid paper While it was an irregular shape it was perfect for his yard Each square on the grid represents 1 square meter What is the area of Aaron garden in square meters

Shelly is buying 13 4 pounds of chicken to use in several recipes The chicken is on sale for 1 70 per pound at the grocery store How much will it cost Shelly to purchase the chicken

Consider the polynomial function p x 9x 12x 6x 13 2x 13x 10r What is the degree of the polynomial What is the leading coefficient What is the end behavior of the polynomial 07 ORN

2x6 y 4 2 x5 y 3

2x6y 4 x5y 3

expressions Estimates are OK If you would like to enlarge the graph or make numbers and letters easier to read you may click on it to open it in a new window You may then enlarge that window with your mouse To further enlarge the image use your browser s zoom capabilities On a PC this is usually ctrl shift and zooming out is ctrl On an Apple computer this is usually apple shift and zooming out is apple 10 8 6 a H 4 7 2 104 Y 5 5 2 4 y H x 6 8 10

Add or subtract as indicated and simplify the result 5 5 21 y y 4 y 4 5 LO 5 21

Add or subtract as indicated and simplify the result X 4 X 5 2 x 13x 40 2 X 64 X 4 2 x 13x 40 10 BA X 5 2 x 64 11

Find the least common denominator p 1 3p 4 5 5p 16p 16 P 4p LGD and 4 Type your answer in factored form

Find the least common denominator m 9 3m 8 2 m 16m 63 2 m 4m 45 and

Perform the indicated operation and simplify the result 2 x 6x 1 X X 6 2 x 6x 1 X X 6 2 4x 25x 7 X 6 2 4x 25x 7 X 6 Simplify your answer

Find the least common denominator 9 7x x 8 X 5 and

Find the least common denominator x 9 2x 1 x x 72 and 2 x 14x 45

Find the least common denominator of the expressions 2n 5 n 3 n 2n 24 2 n 8n 16 and Step by Step Solution Step 1 Write each denominator as the product of prime factors Begin by factoring the denominator of the first rational expression 2n 5 2n 5 2 7 24

Find the least common denominator y 2 2y 5y 3 LCD and 3y 2 5 y 3y 4 Type your answer in factored form

Perform the indicated operations and simplify the result 36 x 19 x 19 2 x 324 x 18 x 18 36 x 19 x 19 11