Algebra Questions

Determine if the triangles in the given pair are similar Choose the correct answer below 630 90 27 63 27 O A The triangles in the given pair are similar under the Angle Angle Angle Case because all of the corresponding angles have equal measures OB The triangles in the given pair are similar under the Side Angle Side case because the lengths of the two given corresponding sides in each triangle are proportional and th angles between the corresponding sides have equal measures OC The triangles in the given pair are not similar under the Side Angle Side case because the lengths of the two given corresponding sides in each triangle are proportional bu the angles between the corresponding sides do not have equal measure OD The triangles in the given pair are not similar under the Angle Angle Angle Case because at least one pair of corresponding angles does not have equal measures

Simplify the expression 5 2 8x y 4x y 8x y 4x y Simplify your answer Use positive exponents only

lly the expression 2x 3x 9 2x 3x5 Simplify your answer Use positive exponents only

Simplify the expression 900 256 900 256 30 Simplify your answer Type an exact answer using radicals as needed

K Write the following word phrase as an algebraic expression A number x decreased by eight The algebraic expression of A number x decreased by eight is 8 C

D ferrets mice birds dogs P turtles pigs F snakes rabbits cats gerbils Last week there were several types of animals at a local animal shelter Let U be the set of the types of animals at the shelter last week During the week some of the animals were treated by the veterinarians on staff Let D be the set of animal types that were treated by Dr Dean Let F be the set of animal types that were treated by Dr Fee Let P be the set of animal types that were treated by Dr Pham Use the Venn diagram to get your answers below Consider this set which is written in descriptive form The set of animal types that were not treated by Dr Fee but were treated by Dr Dean or Dr Pham a Which of these is a correct way to write the set OF n DUP OF N DOP 5 Write the set in roster form OF U DUP OF U DNP birds 0 0 mice cats ferrets gerbils snakes dogs pigs rabbits

In an international food festival Raina can try foods from Korea and Japan She can choose to try foods from one or neither but not both of these countries In the braces below list all the possible sets of countries whose food Raina can try Write each set in your list in roster form If there is more than one set in your list separate them with commas If you need the empty set in your list use the symbol 0 Korea Japan

Serial numbers for a product are to be made using 3 letters followed by 3 digits The letters are to be taken from the first 5 letters of the alphabet with no repeats The digits are taken from the 10 digits 0 1 2 9 with no repeats How many serial numbers can be generated

The lunch special at Trey s Restaurant is a sandwich and a drink There are 4 sandwiches and 2 drinks to choose from How many lunch specials are possible 11 X

Graph each inequality on the number line and write in interval notation Enter your answer using interval notation Example 2 1 5 6172 Use U for union to combine intervals and oo for Infinity Example 00 2 U 4 00 a 1 5 z 4 5 i Graph the inequality b C 4 3 2 1 0 Clear All Draw ii Write in interval notation 5 4 x 1 i Graph the inequality 4 3 2 Clear All Draw ii Write in interval notation 3 4 5 i Graph the inequality 5 4 3 1 0 2 1 Clear All Draw ii Write in interval notation 0 1 2 3 1 1 2 3 4 O 4 2 4

Simplify the following polynomial Express your answer as a single polynomial in standard form 2x 19x 13 2x 4x 8 2x 19x 13 2x 4x 8 Simplify your answer

5 8x y 4x y 3 8x y 4x y Simplify your answer Use positive exponents only

3 Determine which of the following numbers are in the domain of the variable x for the expression shown below x 8 x 4x 32 a x 8 b x 0 a Is 8 in the domain of the variable O A c x 9 d x 4 No because the value of the denominator x 4x 32 at x 8 is O B Yes because the value of the numerator x 8 at x 8 is OC Yes because the value of the denominator x 4x 32 at x 8 is O D No because the value of the numerator x 8 at x 8 is

Write the interval 11 The interval 2 Type an inequality or a compound inequality Choose the correct graph below O A 10 8 OC 8 10 6 11 as an inequality Then graph the inequality 6 can be written as the inequality 4 4 2 2 0 0 2 2 4 4 6 8 6 8 10 10 OB O D 10 8 10 8 6 6 4 A 4 2 2 0 2 4 02 4 6 60

3 x 5 2x 10 The solution using set builder notation is x Simplify your answer Use integers or fractions for any numbers in the inequality The solution using interval notation is Simplify your answer Use integers or fractions for any numbers in the expression Graph the inequality Choose the correct answer below OA 5 OB 1 45 OC OD 5 0 val notation Graph the solution set 0 0 10 10 10

f 3x 1 2x 1 g x x 7x oldu una g re g 8 ka olabilir A 4 B 2 C 0 D 2 E

There are 4 consecutive integers with a sum of 46 What is the value of the greatest integer

Write the inequality that results from the following direction Then state which property of inequalities is being utilized Subtract 3 from each side of the inequality x 3 7 The resulting inequality is Which of the following properties is being utilized Choose the correct answer below O Addition Property of Inequalities O Multiplication Property of Inequalities

Fill in the blank with the correct inequality symbol State which property of inequalities is being utilized If 3x 6 then x 2 2 www If 3x 6 then x Which of the following properties is being utilized Choose the correct answer below O Addition Property O Multiplication Property

Solve the linear inequality Write the solution using set builder notation and interval notation Graph the solution set 1 5x52 The solution using set builder notation is x The solution using interval notation is Graph the inequality Choose the correct answer below OA 5 O B 5 OC 5 OI 5 H 20 20 20 20

Solve the linear inequality Express the solution set using set builder and interval notation Graph the solution set 3x 68 4x 33 The solution set expressed in set builder notation is x The solution set expressed in interval notation is Choose the correct graph of the inequality below O A O C 15 15 0 0 15 15 O B O D 15 15 0 0 15 15

Click here to watch the video Given 3 6 write the inequality obtained by adding 3 to each side of the given inequality What property of inequalities does this illustrate Add 3 to each side of the given inequality Type an inequality Simplify your answer What property of inequalities does this illustrate Choose the correct answer below O Multiplication Property O Addition Property

Write the interval as an inequality Graph the inequality 1 7 What is the inequality Type an inequality using x as the variable Choose the correct graph below O A O C 10 8 10 8 6 4 6 4 2 2 0 2 4 0 2 4 6 8 6 8 10 10 O B O D 10 8 10 8 6 6 4 4 2 2 0 2 to 0 2 4

Find all complex solutions of the equation 2 z 1 2 z 1 Which one is closest to the imaginary unit i

points Prove that for any positive integer n there is an even positive teger k so that 1 n 2 1 A k I n

Compute the dot product u v 6 15 U 5 15 O 195 30 255 225 V

onvert 80 from degrees to radians Give the answer in exact form in terms of t 80 010 J

Consider the system of linear equations x y 9 0 0 50x 0 20y 3 45 Find the values of x and y

Dalculate the mean x and standard deviation s for the data set x Sample 2 3 Value 4 029 4 017 4 025

2 If the sum of the interior angles of a polygon is 2340 how many sides does the polygon have A 11 sides B 13 sides C15 sides D 16 sides 20

Hello Evaluate the determinant 60 0 1 5 7 5 3 6 The value of the determinant is

Solve the equation for y Then find the value of y for each value of x 3x 5y 17 x 2 0 2 Solve the equation for y y

f x x 3x 3x 3 oldu una A 4 g re f B 5 99 100 f 101 100 C 8 ka t r D 10 E

2 Fortunately in a not too distant future Dorothy Gale arrives in her farmhouse and lands on the Wicked Witch and ends her reign of tyranny Munchkins from far and wide return to their homeland but are required to pursue employment in the Emerald City to pay for the damage inflicted by the Wicked Witch The population of Munchkin Land is now modelled via the equation dp dt a 2 t rp 1 rp 1 1 1 sin 172 N 2 2 Set r 0 056 N 10000 and p 0 10000 and p 0 3000 130 where 8 and 3 are the respective fifth and sixth digits of your student number i e if 8 1 and 3 then r 0 051 and p 0 3130 a Set a 200 and use ode45 to simulate the population over a period of ten years Plot and label the Munchkin population as a function of time b How large a value can a take while ensuring the population of Munchkin Land remains positive Support your answer with example simulations in ONE clearly labelled plot Use the legend command to distinguish different a cases 5 MARKS Please include the MATLAB code used in Question 2 and all labelled plots in your final

For this participation assignment please make a grouped frequency distribution polygon using the information provided in the lecture and on this page HINT When making dots in the polygon the dot should be in the middle of the interval or the middle of the next interval for the y 0 dots The raw scores are presented in the following table X 12 13 10 11 8 9 6 7 f 4 5 3 3

then that a well known result from geometry states sum of the lengths of the sides equal to the length of Proof the is greater than side or Z Z That is 1Z Z 12 1 12 1 which is known as Z and Z the third the triangle inequality

childish Remember it is mostly children who consume Nutrine confectionery not teenagers not adults And children love the bunny My son still remembers the advertisement we ran in the 1980s in Chandamama with bunnies holding Nutrine SuperStar Toffees The bunny is our identity We cannot change what we are Ganapathy VP Operations But things change Even customers do The question is can the bunny hop into new confectionary categories Will customers accept the bunny in the mints and gum categories Karthik VP Marketing Introduction Nutrine was developed as the umbrella brand sometimes called the parent or family brand for all confectionery products produced by the Nutrine Confectionery Company NCC All the products it launched initially carried only the name Nutrine on their wrappers To attract its target group of children between the ages of 6 and 13 years Nutrine used a bunny brand character this bunny quickly became part of Nutrine s identity Many middle aged Indian consumers still reminisce about the Nutrine Bunny of their childhood the Bunny advertisements the Bunny teeth they received when they purchased a package of confectionaries such as Kokanaka Cookies But modern kids are different more individualistic more exposed to global media and highly brand and image conscious They understand brands through visual representations Does the bunny on the wrapper still have broad appeal More important is the Background As competition intensified in the confectionery industry in the early part of the twenty first century Nutrine found itself falling behind the competition After intensive negotiations with both Cadbury and Nestl Nutrine finally sold to Godrej Beverages and Foods GBFL in June 2006 In April 2007 GBFL entered into a joint venture with Hershey s But the lack of focus in Nutrine s brand investments between 2003 and 2006 continued to affect the business and its brands The Nutrine portfolio contains products in various confectionery categories but its major brands dominate in three hard boiled candy clairs and toffee Two key brands accounted for a whopping 70 of Nutrine s revenues Nutrine MahaLacto hard boiled candy and Nutrine clairs Unfortunately both key brands were losing substantial market share MahaLacto continued to have a strong brand name independent of its association with Nutrine Despite minimal branding efforts between 2003 and 2007 MahaLacto ranked eighth in a 2007 brand equity survey conducted by the Economic Times behind the chocolate brands Dairy Milk 5 Star KitKat and Perk and heavily advertised brands such as Big Babol and Boomer The GBFL Hershey marketing team had a clear task cut out for it to define a brand roadmap that would arrest declining revenues increase the marketing focus on key brands to enhance sales and build top lines by launching innovative brand extensions into new confectionery categories A key question considered was whether to continue with Nutrine as an umbrella brand if the company chose to make forays into new categories such as mints and gum which includes both bubble gum and chewing gum The details of this case are as of June 1 2007 Appendix 2 displays key brands owned by the Nutrine Confectionary Company Appendix 3 lists all confectionery categories and the key features of each category

Add or subtract the following rational expressions as indicated and simplify your answer 2 3 6 2 5 z 3z 10 Answer z 4 Z 2 www

the properties of exponents to simplify the following expression writing your answer with only positive expone y8 y 424 2y z

If the following statement is false choose False Statement Otherwise identify the property that justifies it If one of the properties is being used to transform the equation identify the quantity that is added to or multiplied by both sides Answer 8x x z False Statement z 8x 2y 0 Selecting an option will display any text boxes needed to complete your answer O Multiplicative Cancellation Property O Additive Cancellation Property O Zero Factor Property

plify the following union and or intersection er 2 3 U 3 00

Vrite the following set as an interval using interval notation Answer x 14 x 3

ver Natural Number Integer Irrational Number 10 3 Whole Number Rational Number Real Number

dentify the property that justifies the following statement Answer 4x5 4y 4x 5 4y O Commutative Property of Multiplication O Commutative Property of Addition O Distributive Property O Multiplicative Inverse Associative Property of Multiplication O Associative Property of Addition O Multiplicative Identity Additive Inverse

d the distance between the following numbers on the real number line a 12 b 13 swer

Identify the factors in the following expression Answer 2x y

Select all the symbols from the set that can be placed in the blank to make the following a true statement Answer Less than Greater than 6 6 6 6 Less than or Equal to O2 Greater than or Equal to Keypar Keyboard Shortc

Assessment 36 A restaurant has 15 pounds of alligator meat to make tasty alligator dishes PART A PART B Each pot of alligator stew requires 23 pounds of alligator meat Which solution shows how many pots of alligator stew can be made The restaurant could make a stew that uses 13 pounds of a many more smaller pots of a made than the larger pots A 36 pots 15 1 233 pot 2 15 7 pots 15 23 6 pots 15 23

Consider this formula Z y X f z 4 0 and y 9 2 what is the value of x Express your answer to the tenths place i e one digit after the decimal poir

a 12 Determine the Net Rental Income and estimate the market value of the property using the Income Approach Assume state and adopt any variables necessary to arrive at your answer 8 Marks enable you b The Cost Method of valuation is a method of last resort Briefly comment on this statement and indicate which of the valuation methods is the most appropriate to adopt for valuation for the purpose of the sale of a commercial property assuming there is ample evidence or comparable data 12 Marks Answer on separate answer sheet B Q8 State Housing Company SHC wishes to purchase 1 5 ha of freehold land in good residential neighbourhood of Airport East in Accra at a price of GHC 4 500 000 00 Planning permission will be available to subdivide the land and erect 31 detached two storey houses on the land The estimated cost for each house excluding professional design fees is GH 1 000 000 00 The total development period from planning through construction to disposal will take four years including the construction period of 2 years Similarly properties in the neighbourhood have recently been sold for GH 2 500 000 00 each and the current going rents in the same neighbourhood averages GH 20 000 00 per month per unit SHC is happy with 16 per cent return on capital and a developer s profit of 20 per cent Making any assumptions you consider necessary Prepare a development appraisal to advice SHC to take a decision on the viability of the proposed development and express an expert opinion whether or not the houses should be let or sold outright b Assuming SHC is yet to negotiate on the price of land prepare a residual valuation to advise SHC on a reasonable price to pay for the land Assume and state any variable necessary to enable you arrive at your answer 20 Marks Answer on separate answer sheet