Algebra Questions

What is the expression in simplest radical form 432 Enter your answer in the box

What is the expression in radical form 7x y Enter your answer in simplest form in the box

Simplify 8 200 3 162 Enter your answer in simplest radical form in the b

Simplify 7 2i 8 9i Enter your answer in standard form in the

Simplify 3 6 15 O 3 2 9 5 O 3 2 3 5 O 3 7 O 2 3 3 5

Simplify 7i 75 Enter your answer in simplest radical form in

TA and sequence U 1 defined what is by unts Unt un t the fifth with 7 n term of this sequence 5

1 Complete the table below REMEMBER These problems are testing your skills and understanding of RADICALS not if you can use a calculator Each completely correct line is worth 3 points If you simplify be sure to use the rules and conventions you learned in Unit 2 Expression 5 3 8 3 5 2x 3y 2 x4y Can it be simplified OYES NO OYES NO YES NO OYES NO YES NO If NO explain why not If YES simplify completely and rewrite in the most simplified radical expression SHOW ALL WORKI

Explanations must state what you did and WHY you did it You may not need every line below Answer Steps Work 3 4i 6i 7 2 3i Explanation Given

1 Language Acquisition Almost all humans acquire at least one language before the age of five Although people gain vocabulary throughout their lifetimes even young children are able to understand and produce complex sentences with complicated meanings How do children accomplish this remarkable feat in such a short amount of time Do adults learn language differently from children Linguistic researchers have long debated the answers to these questions but most agree that both nature and nurture are involved in language acquisition They disagree however about how much linguistic knowledge children have from birth and thus whether genetics or experience is more important in language acquisition How do the second and third paragraphs work together They present a scientific debate and then discuss what all linguists agree on They present a specific theory and then propose a novel study to prove it They present a general argument and then explain a specific theory They present a general arqument and then disprove a counterargument

3 6 A MATCH THE LETTER UNER SACH SYMBOTH THE CORRECT WORDING GREATER THAN 2 3 4 5 6 D LESS THAN AT MOST AT LEAST NO MORE THAN NO LESS THAN O

12 Charlie would like to make at least 200 washing cars this summer He charges S Write an inequality to represent Charlie s goal amount use w for the number of ca washed Type a response 13 Julie is taking a taxi cab to a restaurant in the city The cab charges 3 20 plus 55 per quarter mile Julie only has 15 to spend on the cab Write an inequality to represent the how far away the restaurant can be so that Julie can afford the taxi fare Use m for the number of quarter miles Type a response

8 Translate the verbal phrase into an inequality use x as your variable Don t solve 5 more than the product of 2 and x Type a response D 9 Translate the verbal phrase into an inequality use x as your variable Don t solve The sum of x and 1 is at least 9 Type a response U

7 Translate the verbal phrase into an inequality use x as your variable Don t solve The difference of x and 7 is less than 4 Type a response it may be difficult to format the and symbols so use the following FOR TYPE or press ALT and TYPE 755 then release ALT

Charlie attempted to find the value of expression 3 4 2 8 His work is shown below e ame 3 4 2 8 12 2 8 10 8 100 8 4 108 Complete the follow ing tasks Explain the error Charlie made when evaluating the expression State what Charlie s answer should have been

Determine the vertical asymptotes of the graph of the function f x 3 x 4 x 1 What is are the equation s of the vertical asymptote s O A x 1 and x 4 OB x 0 O C x 1 and x

X is a normally distributed random variable with mean 46 and standard deviation 12 What is the probability that X is between 21 and 71 Write your answer as a decimal rounded to the nearest thousandth

st all potential rational zeros x 5 3x 2 Which of the following choices lists all the potential r OA 0 1 2 OB 1 O C 1 2 OD 2

A 5 1 Bria 56 8P 7 7 92 p 49 solve the equation p 56 for P He incorrectly divided 56 by 7 His work is shown to the left Which of the following statements best de scribes the error Chad made while solving for P HINT 1 What is the opposite inverse operation for multiplying 2 Is the opposite inverse operation done correctly He should have added to both sides of the equation

Condense into a single logarithm 10 log x 7logy 3 log z log 107 log z O log Olog log 10 210 37 2 3 10x7y 3z

Expand the logarithm a b log3 C O 12 logs ab 7 logs c 6 log a 2log b 7 log c log as log b logs c 6 log3 a 2log b 7 log3 c

Expand the logarithm gh log3 k log g log h log k log g log3 h log k Olog g log h log k log g log hlog k

1 For the function f x x 3 use the leading term test and the knowledge of y intercepts to match the function with one of the graphs below Choose the correct answer below OA Q O B Q O C Q G OD

Condense into a single logarithm log 3 log m logn log p log 3mn P O log log mn P 3 m n P

4x 3 10 4x 14 what is the value of x Justify your response by showing your work e the sketchpad below to show your work and justify your response a O PENCIL THIN BLACK 2 4x 3 10 4x 14

How long is a guy wire reaching from the top of a 14 foot pole to a point on the ground 10 feet from the pole The guy wire is exactly feet long Type an exact answer using radicals as needed The guy wire is approximately feet long Round to the nearest thousandth

Press each hotspot Label the corresponding number below with the requested value 4 7 11 5 14 9 7 12 Press to hear a reminder or hint for this problem ar C 0 00 0 05 Speed 1x Take time to review your notes on how to find each measure of central tendency Mean Median Faused

A linear function g models a relationship in which the dependent variable increases 2 units for every 1 unit the independent variable increases Graph g when g 0 4 Identify the slope y intercept and x intercept of the graph Line Move Undo 5 4 3 2 1 5 4 3 2 19 2 3 4 5 Redo 1 2 3 x Reset 4 5

IN IDEAS MATH Eten Identity the graph of g x O 41 O A Ay 9 14 O O 2 Ay 50 HE tx Jett Doucet B Assignment Player Save Exit dy dubmit Choose the description of the transformation from the graph of x x to the graph of g O The graph of g is a vertical stretch of the graph of by a factor of 3 O The graph of g is a vertical shrink of the graph off by a factor of O The graph of g is a vertical stretch of the graph of by a factor of 3 and a reflection in the x axis Choose the description of the domain and range The graph of g is a vertical shrink of the graph off by a factor of and a reflection in the x axis O The domain is all real numbers The range is y 0 O The domain is all real numbers The range is y 20 O The domain is x 20 The range is all real numbers O The domain is all real numbers The range is the all real numbers

Compound Inequalities Solve each compound inequality and graph its solution 3 2x 10 or 23 1 2 5 3 1 0 10 m 7 7v 52 65 or 3v 22 2 202 4 6 8 10 10 12 14 Name 2 1 9 x 17 12 10 8 Date and 1 4 x 8 29 and 0 2 6 r 5 12 or 0 Period 4 3 2 10 2 3 4 5 6 7 8 9 10 11 8 10b 3 37 or 3b 10 25 8 7 6 54 3 2 10 1 2 3 4 5 6 7

Listen Let f x 2x 2 Graph g x f x 3 Line Move Undo 8 Previous 6 4 2 8 6 4 29 4 6 8 1 2 Redo 4 6 8 2 3 x Reset 4 5 6 Next Choose the description of the transformation from the graph off to the graph of g The graph of g is a vertical translation 3 units up of the graph of f The graph of g is a vertical translation 3 units down of the graph of f The graph of g is a horizontal translation 3 units left of the graph of f The graph of g is a horizontal translation 3 units right of the graph of f

Estimate the intercepts of the graph of the function 4 6 4 2 y y x x 2 2 The x intercepts are about 4 x and and the y intercept is about

The graph of f x x 9 is a vertical translation 9 units down of the graph of f x x How can you obtain the graph of f x x 9 from the graph of f x x using a horizontal translation Translate the graph of f x x O Translate the graph of f x x Translate the graph of Translate the graph of f x x 9 units down f x x 9 units up 9 units left 9 units right

Nick has 50 He just got a job as a construction worker making 10 an hour He wants to earn enough money to buy himself a new cell phone val at 900 How many hours must he work to buy the phone Write an inequality x Nick must work at least hours

Identify the domain and range of y x 4 Domain Range x 0 x 0 x 4 x 4 y 0 y 0 H

e C D at in 5 t 49 y 8 u 8 9

Given the inequality 6 1 2r 26 2r 1 2x which of the following are included in the solution Select all that apply A 2 B C 4 5 D 1 G

Solve 2r 8 4r 8

Given the inequality 3r 2 r 4 23r 4x 9 state if the given graph is correct If not explain how you would change it 3 2 1 0

Given the function f x 3 x 2 5 Compared to the parent function this function has been horizontally translated by this function has been vertically translated by the function is the function is reflected over the l units to the units by a factor of

1 Describe the domain of the following functions Show all work a f x c E x e R x X g T x 1 1 2 x x 2 2t 1 et sin x b S x d C x f L x h N x 2 x x cos x log x x 2x 4 x In x 1

Simplify the complex rational expression by using either method Be sure to remove any common factors 8 p 5p 24 6 12 P 3 P 8

Simplify the complex rational expression by using the LCD Be sure to remove any common factors 2 w 7 W 8 9w w 56

Simplify the complex rational expression by writing it as division Be sure to remove any common factors 12w w 6 w9 w 36

10 If Taylor does her homework 75 of the time how many homework assignments did she complete if there were 60 assignments given one semester

12 In a semester of math class there are a total of 600 points that can be earned In order to eam a grade of 80 or higher how many points would a student need to earn

11 Deja collects baseball cards Her favorite team is the Chicago Cubs 20 of her cards are Cubs players If she has 50 baseball cards of players on the Cubs how many cards are in her collection DERUES JOGFELET

billions of dollars a Estimate the value of the country s exports in 2008 and 2022 b What is the doubling time for the value of the country s exports a The value of the country s exports in 2008 is 1 7 billion Simplify your answer Round to the nearest tenth as needed Do not include the symbol in your answer The value of the country s exports in 2022 is 3 1 billion Simplify your answer Round to the nearest tenth as needed Do not include the symbol in your answer b The doubling time is approximately years Simplify your answer Round to the nearest integer as needed be approxim

Exercise 7 3 4 Let A be an m x n matrix of rank k If B is an invertible mxm matrix try to argue why B A is also rank k Using your above logic Suppose that A VW is a matrix with rank k Suppose that B W W is A V W is rank k What does this tell us about elementary row matrices E and rank k matrices A an invertible matrix then explain why B Using your above logic that they operate on

A weight hangs from a spring If a force is applied to the weight at t 0 seconds it will start noving up and down The following equation gives the distance d in centimetres of the weigh rom its equilibrium point d 4 sin 5t 4 cos 6t At what times during the first 2 seconds is the weight at the equilibrium point Use technology and write the solutions accurate to 3 decimal places