Sequences & Series Questions and Answers

Simplify the expression This type of expression arises in calculus when using the quotient rule 1 2 1 2 6 8 x x 8 x 8 X

Rationalize the denominator 1 9 7

Rationalize the denominator y 2 y

1 The two triangles in the figure below are similar NKLAJ K L In these similar triangles j 6 k 15 1 18 and k 25 where all lengths are given in inches What is the value of j K k A 10 B 15 C 25 D 30 E 35 L j K l j J k L

3 y 3 x 4 6 64 2 6 5 68 x 4 32 2 4 y x 4x 4 Ay 6 44 2 6

Day 1 2 3 4 Avi s Rule Dollars 0 01 0 02 0 04 0 06 Benita s Rule Dollars 100 200 300 400 The table shows how much you ll earn with each rule Complete the table for Day 4 Then predict Who do you think pays more on Day 10 Avi Benita Explain your thinking because Benita s rule will get to 100 faster than Avi s rule

000 5000 payment in dollars 4000 3000 2000 1000 T Benita 10 15 200m Day 20 X 20 GO Which rule do you think will pay more on Day 20 Use math to support your answer Use the sketch tool on the graph if that helps to illustrate your thinking Benita s Rule Avi s Rule Explain your thinking Benita s form of pay increases more than Avi s Edit my response Your classmates said SEBASTIAN HARRIS Benita s Rule Benita s rule is rising while Avi s rule is staying the same AZIZI PRESCOTT Benita s Rule Her rule is getting higher while avis is staying the same

Repair Shop payment in dollars 1200 800 400 0 8 Visualize the rules Benita Avi 0 6 12 day 8 Avi s rule is shown in RED Benita s rule is shown in BLUE Describe what you notice about the graphs In particular how are they similar How are they different Benita s graph is closer to 1200 than Avi s graph They re similar because they are both showcasing how much money is being made Your classmates said ALEXARAE SPRUELL They both end up on the same line but Benitas pay is so much higher than Avi Edit my response IMANI TOOMER I notice that Benita isn t getting money and avi is but they are both on the same day MYKAYLA KNIGHT O Jan 2

1 Evaluate the expression a 12 6 8 b 2 9 4 32 1

Simplify each expression Verify your results a 2 k 5k b 2 k 5k C 8 k 5k d 8 k 5k e 6 k k f 6 k k

Write the following expression as x to a single power

5 Find values for A and B so that A 5B 25 Type your answer for A B as in the blank

Write the following expression as x to a single power single power 2 Type a response

Find the missing side of a right triangle with one leg 8 and hypotenuse 17 If it is not a whole number leave in radical form NOTE There are no units in this question

Solve Give BOTH answers in simpliest radical form x 15 14 DECIMALS ARE NOT ALLOWED IN THIS QUESTION

For which graph is the parent function y x 5 54 3 2 1 5 4 3 2 1 T 2 3 4 5 x

Rewrite the expression in rational exponent form 23 5 5 22 bofremtop 32 2 15 15 3 Rewrite the expression in radical form 25 3 3 Rewrite the expression in radical form 3 34 83 2 18 24 13 13 36 163 4 33 37 93 2 2 7 7 26 7 1 6 7 Rewrite the expression in rational exponent form Evaluate 29 3 27 1 27 30 256 256 Rewrite the expression in radical form Evaluate 16 35 3 5 3 2 9 31 4 50 50 not possible 2 38 64 1 8 3 64

he following function on the axes for x 0 1 for provided f x 4 3 x 5 0 5

X y Directions 7 9 Complete the table for each function and make a complete graph Identify key points line of symmetry LOS and state the domain D and range R 7 y x 2x 3 y 3 4 3 y 9 12 72321 X X 2 y 3 1 9 8 y x 4x y 9 y x 4x 3 x int D D x int R y int y R y int H 3 1 Vertex LOS 1 1 2 3 Vertex LOS

Identify the constant ratio in the following exponential growth function f x 100 1 05 O 100 O 5 95 O 105

Question 1 N 1 2 3 2 1 d The exponential equation for this table can be written as 0 4 4x4 ON 0 21 1 pts

X 0 1 2 8 Z The exponential equation for this table can be written as O f x 4x O f x 4 2 x f x 2 4 1 2 2 3 4 32 128 512 O f x 2 4 x

The graph shows the net profit in thousands for Enrico s catering business for the past year 16 14 Net profit in thousands of dollars 12 10 84 et Month Use slopes to determine the month in which the net profit showed the greatest increase O January July June February O May

If f x x 2 and g x x 2 a f g x b g f x c Thus g x is called an function of f x

Use the table below to fill in the missing values f x 7 3 1 0 2 4 6 I 0 1 2 234 5 6 7 8 9 f 4 5 9 8 if f x 4 then 2 if f x 5 then a AMERA LE ME REQUEN THE 1 SUS PAREMIHIL

Divide 6x 18 2x 6 15x 10 3x 2 Simplify your answer as much as possible 0 P

f x x 3 5x 2 17x 21f x x and x 7x 7 is If a factor of f x f x then find all of the zeros of f x f x algebraically

1 Solve this problem X 2 Y3 When X 3 and Y 2

1 PE bo Question 18 Use the image at the top of the page to determine the correct response option from those listed below Select the response choice that replaces the questic mark If no question mark oxists you are to select the response choice that comes next in the sequence 99 po DO 0 2 D ON 00

Order Lorazepam 1mg every 6 hours Available Lorazepam 0 5mg per tablet How many tablets will the nurse administer per dose TYDO YOU

C d 4 3 i 4 3 2 14 54 5 4 3 2 1 2 1 2 LAY 3

Question Find the midpoint of the line segment with endpoints 7 12 and 5 15 Provide your answer below

hich of these situations involves a combination Determining how many different 6 letter passwords can be made using the letters in the word pencil G Determining how many different groups of 3 employees can be chosen from 10 employees H Determining how many different ways 8 runners can be assigned lanes on a track for a preliminary race Determining how many different seating charts can be made placing 7 people around a table

Find the sticker price Check your answers in the back of the book 1 River City Autos has a pickup truck for sale Its base price is 22 225 Prices for available options are 6 speed transmission 2 908 cruise control 240 trailer towing package 230 and power windows 738 Its destination charge is 900 2 Coble Downtown is selling a sport coupe hybrid at a base price of 24 990 Options are the convenience package 1 300 sunroof 850 and sunroof wind deflector 100 Destination charge is 625

Find the sticker price Base Price Options 2 400 1 260 4 865 3 861 4 19 900 5 21 540 6 32 654 7 49 842 Destination Charge 350 345 338 425 S Sticker Price

Complete the problem Check your answer in the back of the book 3 Nayan Patel purchases a compact vehicle with an MSRP of 17 980 00 including the destination charge and title fee He selects 6 way power front passenger seat which costs 10 times the amount of remote keyless entry The total cost of the compact vehicle including a 7 sales tax is 19 591 70 Find the cost of the power front passenger seat and the remote keyless entry

Find the distance between the points 2 2 and 3 3 Distance Give an exact answer Simplify any radicals

nts possi Question 13 Solve the equation for the requested variables f vp g q y Solve for f f Solve for p p entry tip if you have several parts to a numerator or denominator put them in parenthes 2x a b we type 2x a b Work

24 1252 3 26 243 2 5 28 3434 3

Equat s possible uestion 12 10 30 answ dd Work meters and the width is rectangular room is 2 times as long as it is wide and its perimeter the room The length is meters

variable needs to be eliminated to solve the system of rrect first step 5x 9y 99 6x 9y 0 Subtract to eliminate x Add to eliminate x

An element with mass 780 grams decays by 16 3 per minute How much of the element is remaining after 16 minutes to the nearest 10th of a gram

Using the graph below solve the quadratic equation 6x 36x 51 x 6x 11 5 4 3 IS X98 x9 x f 2 g x x 6x 11 3 2 11 T 2 31 41 5 Ox 3 Ox 4 or x 2 O O 2 xs 2 29 or xs 3 71 x 11 or x 51 3 4 55

Simplify the following complex number O O 1 1

Question 11 of If w the weight of a trout which algebraic expression represents the phrase below twice the weight of the trout OA 2w B W OC w 2 D w 2

Find the mean of the following set of numbers 1 2 7 2 3 9 11 1 2 4 Enter the answer

What is the range of the following function Hint The range is the y values D A B X 4 2 1 4 2 0 2 4 6 0 2 4 7 11 1 4 7 11 14 17 4 14

Question 4 20 points Rewrite the following radical in rational exponential form and simplify if possible O 5x 25x

Simplify 4x 2 x 2 3 4 3 04 2 5 3 O 4x 2 4 3 3x 2 5 3 4 5 3 O O O O

ege inctions 50 Poin ansf 9 a Write the equation of each absolute value function 3 pts each 4 3 2 3 4 3 2 6 5 2 1 0 6 5 4 3 2 1 11 3 2 1 0 01 2 3 10 The figure shows the complete graph of the function f in the xy plane The function g not shown is defined by g x f x 2 What is the y intercept of the function g 2 pts b 01 3 2 1 0 2 1 01 2 3 5