Algebra Questions

Find mZV V mZV Submit 3 26 W 3 13 X

2 Determine if each of the following is a group a monoid that is not a group a semigroup that is not a monoid or not a semigroup Explain your answer for each one Z addition on the set of positive integers It farms bernise a group It satisfies closure associativity identity element and every element has an inverse ii Q subtraction on the set of rational numbers This is not a semigroup because the set of rational numbers under subtration isn t closed under subtraction iii C32 addition on a 32 hour clock It satisfies Closure associativity identity element and every element has an in verse It forms a group iv C15 0 multiplication on a 15 hour clock with 0 removed This doesn t form a group or monoid Not element has an inverse every v 0 0 1 0 1 U the set is P 0 1 and the operation is union a semigroup but not a monoid This is on the power set of 0 1 forms a sem igroup The set is closed under the union operation which is associative It doesn t have an identity element so it s not a mencid vi 0 1 2 where x y y for example 0 2 2

1 3 Multiply Rational Expressions Simplify each expression 35m 65n 10 28n 4n 1 A 10n n 1 3 n 3 n 1 3 C 21n 53n 8 6n 13n 8 A 2 5n 3 C70 B Sn B D 3n 50n 80 n 1 n 9 3 An n 8 20n 10n 42n 6 9 5n 9 n 2 2 4 his reserved 2 7r 70 5r 39r 54 35r 42 10r A 4 C r 1 r 8 7 6 r 3 B v 3 A 7 C v 9 v 4 6v 35v 5 63y 9v 5v 45 r 10 r 9 10r D r 5 2 3 v 9 D 7 v 6 B

9 9 6b 3b 5b 13b 6 3b 9 5b 22b 8 A B b 3 1 b b 4 7 b 8 b 3 b 9 C 18 D 186 10 10 3a 6 21a 66a 48 A C 2 5 a 8 10 a 1 9 14a 16 5a 40 3a a 8 B D a 1 27a

7 7 2n 8 42n 24n A C n 4 3n 3 4 16 16n 21n 3n 4 5 7n D 7 n 4 B 8 8 8x 28x 7x 25x 12 A C x 7 64x 3 x 2 x 5 70x 30 2x 7 B D 40x x 4 x 8 x 5 10x

5 A 3n 35n 21n 14 15n 18n 5n 6 C 7 D A 9 2n 8 42n 24n n 4 3n C n 3 561 A B 3 4 B D 4n 9 6b3b 5b 13b 6 3b 9 5b 226 8 b 9 C 18 D 186 35n 21n 14 n 4 6n 16 16n 21n 3n 4 5 7n D 7 n 4 b 3 1 b b 4 7 b 8 b 3 B 6 6 10 A 8 8 9k 36k 15k 3 15k 3k 6k C k 10 A 10 C 8x 28x 7x 25x 12 k 2 k 1 A C x 7 64x 3 x 2 x 5 B 3a 6 21a 66a 48 2 5 a 8 10 a 1 9 D 70x 30 2x 7 B D B k 7 10k k 10 3k k 4 2 D zoom 40x x 4 14a 16 5a 40 3a a 8 1 1 x 8 x 5 10 x 27a

A survey approximates the number of Americans that are age 65 and older and projects that by the year 2050 approximately 81 8 million Americans will be at least 65 The bar graph shows the estimated number of Americans with projected figures for the year 2020 and beyond A graphing calculator screen displays an exponential function that models the U S population age 65 and over y in millions x years after 1899 Use this information to solve a d below Click the icon to view the bar graph a Explain why an exponential function was used to model the population data OA An exponential function was used because exponential functions are always more accurate than linear functions OB An exponential function was used because there are too many data points to use a linear function OC An exponential function was used because population is always modeled using exponential functions OD An exponential function was used because the data in the bar graph is increasing more and more rapidly b Use the graphing calculator screen to express the model in function notation with numbers rounded to three decimal places f x c According to the model in part b how many Americans age 65 and over were there in 2010 Use a graphing calculator million Type an integer or a decimal rounded to one decimal place as needed million Does this rounded number overestimate or underestimate the 2010 population displayed by the bar graph By how much Choose the correct answer below and fill in the answer box to complete your choice Type an integer or decimal rounded to one decimal place as needed OA The rounded number overestimates the 2010 population by OB The rounded number underestimates the 2010 population by million ExpReg y a b x a 3 3354487089 b 1 023374183

A population of fish in a newly dug pond grows according to the equation P Find the initial number of fish in the pond X fish What is time 9000 1 8e 0 6t where time t is given in years

a b 1 9 a b 10AM COR

Given vectors u and v find a 4u b 4u 7v c v 7u u 9 7 v 2 0 a 4u 36 28 b 4u 7v

x 3y 3z 3 2yz 0 4yz 4x 3 a Express the system in matrix form A 6 and indicate each matrix vector below A m below 18 b Use technology to find the inverse of the coefficient matrix c Solve the system by computing A 6 without technology Enter your answer as an ordered triplet

If it exists find the inverse of the matrix A If it does not exist enter DNE 1 0 4 3 4 10 0 1 5 A

1 Sketch each angle in standard position a 1350 b 210 c 30

8 points Write the equation for the function graphed below f x x 2 6x 2 754321 A y

If it exists find the inverse of the matrix A If it does not exist enter DNE 10 5 4 5 3 01 5 A

Consider the matrices below AB A BA 1 7 2 8 3 3 3 B If possible find each product below If not possible enter none 7 6 49 4 7

Calculate the determinant of the matrix below 2 det A Choose the best statement below A 4 1 2 The matrix is invertible because its determinant is non zero The matrix is invertible because its determinant is zero O The matrix is not invertible because its determinant is zero The matrix is not invertible because its determinant is non zero

If possible find and enter the missing matrix If not possible enter DNE a 10 4 8 1 C d 01 missing matrix 2 4 4

The matrix B has dimensions m x n a Identify the value of m b Identify the value of n c Identify the value of b12 B d Identify the value of B 22 13 13 1 14 13 12 16 2

Calculate each product below 7 3 4 a b 5 7 3 7 6 3 3 578 9 1 6 1 9 8

Suppose A 5 8 2 a Compute A B 6 10 5 b Compute 3A 4B and B 4 7 8 4 10 9

b Solve the equation from part a The solution set is 1 Part 2 3 Part 3 of 3 LFFEE THE c Verify that the solution checks in the original equation log 1 9 log V

Perform the indicated operations and simplify 36x 49 X 7

1 Algebra 2 Name Izzy Unit 5 Complex s Rational Exponents Period 1 Practice Lesson 3 4 3 3 2 Unit 3 Lesson 3 Cumulative Practice Problems 1 Complete the table Use powers of 64 in the top row and radicals or rational numbers in the bottom row 64 64 64 edge length ft 3 volume ft a a b C Date 2023 11 28 4 d 64 Select all the expressions equivalent to 4 0 Explain show why below 25 2 t 5 16 b 220 4 4 d 47 0 Unit 3 Lesson 4 Cumulative Practice Problems 5 Evaluate 8 without a calculator 64 85 istrative The table shows the edge length and volume of several different cubes Complete the table using exact values 100 Select all items equivalent to 24 Explain your selected answers the area of a square with side length 24 units the side length of a square with area 24 square units the positive number x where x x 24 the positive number y where y 24 24 Mathematics 125 2 Select all expressions that are equal to 64 Explain your chosen answers a 96 b 8 c 512 d 4 e 64 f 64 e 64 1 147

Simplify completely O x 23 Ox 23 Ox 8 Ox 8 x 15x 56 X 7

Simplify completely x 2 X 9 x 10X 24 x 3x 108 X 2 x 9 x 2 X 9 x 12 X 9 X 2 OX 2 x 2 x 9 X 9 y 9 y 12 and find the restrictions on the variable

Simplify completely 12 X 7 O 12 X 7 x 7 x 3 O X 3 X 7 X 7 x 3 12x 36 x 4x 21 X 7 and find the restrictions on the variable

Simplify completely OX 3 5 OX 12 5 O xX 6 5 x 18 x 15x 36 5 60

Simplify completely Ox O 3x O X 6 6 O X 18 6 3x 18 18

Multiply Simplify the Rational Expressions x 49 6x3 8x2 x 7x 2 a b ab a4b a b ab

x 4 x 4x 9x 36x 4 x 4 a 9ab 20b a 8ab 7b a 7b a 8ab 16b

x 5x 24 x 6x 9 8x 8x 12 a4 64 a a b a 2ab b 3

25 x 5x4 x 5 x4 5x 10 2b 9a 81a 2 4b 1 9a b

2x 200 4x 40x 1 7x 21 x 7x 30 6 10 3a a 60b 75b5 5a b 10a

6x5 x 11x 18 15x x 7x 18 8 a ab 12b 2a 7ab 3 16a 8b 12

Evaluate each expression using the graphs of y f x and y g x shown below a gof 1 b gof 0 c fog 1 d fog 4 a gof 1 Simplify your answer y g x 6 d 13 y f x 8 10

Which function below has an asymptote at y b f x a b c g x c b a Oh x b a c k x a c b

The function f x 2x 3 is graphed at the right Determine the y intercept for the function f x which is shown O 1 5 0 O 2 0 0 3 0 2 6 5 4 3 f x 2x 3 2 1 S 3 2 1 F 1 n 2 Asymptote y 3

Given the function f x 3 1 determine the average rate of change from x 0 to x 2 O 2 9 9 2 4 14

Consider the function w x 3x 2 As x determine w x i e As x approaches w x w x co Ow x 2 w x 3 negative infinity what does w x approach

nger 1 Should a golfer try to hit the ball long or hit it straight off the tee Recent golfers have been able to hit the ball thanks to better equipment However this extra distance can come at the price of not being as accurate as to where the ball lands Below is data for ten golfers average driving distance yards and driving accuracy Percent where driving distance impacts the driving accuracy 260 163 Driving Distance Driving Accuracy 246 82 Miles 22 Price 266 72 XMonth January Feb Precip 4 45 254 4 01 76 Missing 0 1 Grade 90 91 March 3 26 264 1 96 71 44 14 600 a Write the linear regression equation of your line b Use your equation to predict the price for a car driven 40 thousand miles a Write the linear regression equation of your line g x 0 53 210 30 x b Use your equation to predict the driving accuracy for an average driving distance of 260 yards 8 260 2 Is there an association between the price of a used car and the number of miles it has been driven The table shows the number of miles driven 1 000 s and price for a sample of Honda CR V s 40 40 43 36 38 30 18 000 16 500 15 000 14 000 2 85 p 40 3 The table shows the monthly normal precipitation P in inches for San Francisco CA April May 1 17 256 3 83 73 0 38 268 50 15 000 6 89 66 June 0 11 270 65 July 0 03 248 75 8 13 83 76 54 56 70 70 14 500 12 000 13 600 14 600 p x 85 90x 18777 98X August Sept 0 07 0 20 Oct 14 79 1 40 248 81 Let x represent the month with x 1 corresponding to January Find an appropriate quadratic regression model for the data 3 4 Do students with more missing assignments have lower grades in math Below is data for an Algebra 1 class showing how many missing assignments the student has and their grade in the class 7 18 68 64 53 246 Nov a Write the linear regression equation of your line g x b Use your equation to predict the grade for a student who has ten missing assignments g 10 77 2 49 86 11 000 Dec 2 89 20 25 25 28 32 33 55 52 46 51

13 In the from Find expansion of x a X3 constant the beginning the value of a the 7th tem term 10

3 In In the the exponsion Ax yY terms IS of x y 3 Find 1 ore of the the value of A 3 8 A 5

Find QR R Q 5 S Write your answer as an integer or as a decimal rounded to the nearest tenth QR

6 9 11 13 31 A 288 B 272 C 260 D 256 E 240

5 In the expavion Coefficient is C 1 of 2x ay 4 Find 64 sum of the the value of a a 3

Be sure to fully justify your responses when appropriate Round percentages proportions to 4 decimal places and values of confidence interval bounds to 2 decimal places Don t forget Units anytime you give a non probability number and use complete sentences when asked to interpret your confidence intervals 1 4 pts If we are given the confidence interval 36 1 39 5 estimating the average number of credits earned by students in their third term of school What are the sample mean and margin of error for this confidence interval

Let 21 O a 5 cos i sin z2 4 cos isin and w 2 22 Find Arg 3w 4T

Solve the right triangle Q R 66 Write your answers as integers or as decimals rounded to the nearest tenth PR PQ m P P O

Find mZX X Y mZX 2 3