Algebra Questions

5 3 Simplify the expression x 4 2x 3 10

d 2 Simplify the expression 4 2x 4 2 x 5

3 A sum of 5000 is invested at 8 p a compounded annually a Determine the amount of the investment after 3 years n b Determine the time for the investment to amount to 6211 48 at the same rate p

1 Let A 0 0 Select all of the statements that are true B 0 and C 0 4 OA The matrix Cis a diagonal matrix B The matrix product AB is defined OC The matrix sum A C is defined OD The matrix Cis a square matrix OE The determinant det A is defined OF The scalar multiple B is defined OG The matrix B is an identity matrix OH The matrix power C is defined OI The matrix product AC is defined 0 83 3 0

11 5x3 24x 61x 30 5x 4 6 A x 4x 9 B x 4x 9 C x 4x 9 D x 4x 7 5x 4 8 51 4 1 5x 4 5 5x 4

Divide 1 a 11a 13a 27 a 10 6 a 10 7 A a a 3 B a a 3 C a a D a a 10 5 a 10 a 3 3 a 10 3 b 3b 32b 28 b 7 A b 4b 3 B b 4b 1 C b 4b 4 D b 4b 4 2 b 7 4 b 7 4 2 2 x 14x 56x 59 x 8 6 A x 6x 9 x 8 8 B x 6x 9 C x 6x 6 D x 6x 8 A k 3k 4 B k 3k 3 C k 3k 5 x 8 1 4 k 13k 33k 30 k 10 1 k 10 D k 3k 6 x 8 5 x 8 5 k 10

10 224x49x 90 14x 14x 7 8 14x 7 1 2x 1 4 A x 4x 14 B x 4x 15 C x 4x 11 D x 4x 13 14x 7 10 14x 7

12 16r 92r 178r 116 8r 10 11 A 2r 10r 12 8r 10 3 B 2r 9r 11 4r 5 C 2r 10r 8 D 2r 9r 13 7 8r 10 11 8r 10

8 12v 153v 48v 45 12v 9 4 3 4v 3 2 3 4v 3 1 4v 3 A v 12v 8 B v 12v 4 C v 12v 7 D v 12v 5 X

7 99x 119x 76x 96 11x 2 A 9x x 6 11x 12 3 11x 12 B 9x x 8 C 9x x 8 D 9x x 7 2 11x 12

9 21 154p 104p 172p 2 14 A 11p 9p 12 B 11p 7p 10 C 11p 6p 8 D 11p 9p 11 2 1 7p 5 2 14p 1 2 14p 1 2 14p

Long Division Divide 1 a 11a 13a 27 a 10 6 a 10 7 A a a 3 B a a 3 C a a a 10 5 a 10 3 a 10 D a a 3 3 b 3b 32b 28 b 7 A b 4b 3 B b 4b 1 C b 4b 4 D b 4b 4 2 b 7 4 b 7 5 n 4n 128n 143 n 13 A n 9n 11 B n 9n 8 C n 9n 10 D n 9n 8 1 n 13 3 n 13 1 n 13

Long Division Divide 1 a 11a 13a 27 a 10 6 a 10 7 A a a 3 B a a 3 C a a a 10 5 a 10 D a a 3 3 a 10 3 b 3b 32b 28 b 7 A b 4b 3 B b 4b 1 C b 4b 4 D b 4b 4 2 b 7 4 b 7 5 n 4n 128n 143 n 13 A n 9n 11 1 n 13 3 B n 2 9n 8 C n 9n 10 D n 9n 8 n 13 1 n 13 4 2 6 2 x 14x 56x 59 x 8 6 A x 6x 9 x 8 8 B x 6x 9 C x 6x 6 D x 6x 8 A k 3k 4 B k 3k 3 C k 3k 5 x 8 1 4 k 13k 33k 30 k 10 1 k 10 D k 3k 6 x 8 5 x 8 5 k 10 6 k k 130k 24 k 12 A k 11k 2 B k 11k 5 k 12 5 k 12 C k 11k 4 D k 11k 4

Divide 1 a 11a 13a 27 a 10 6 a 10 7 A a a 3 B a a 3 C a a a 10 5 a 10 3 a 10 D a a 3 3 b 3b 32b 28 b 7 2 b 7 A b 4b 3 B b 4b 1 C b 4b 4 D b 4b 4 4 b 7

15 pts Q6 Find the smallest positive integer s such that s a mod 19 where a 1 1 35 35 Hint Multiply the equation by 351 use modular arithmetic and Wilson s Theorem

Long Division Divide 1 a 11a 13a 27 a 10 6 A a a 3 a 10 7 B a a 3 C a a a 10 5 a 10 3 a 10 D a a 3 2 2 x 14x 56x 59 x 8 6 A x 6x 9 x 8 8 B x 6x 9 C x 6x 6 x 8 1 x 8 5 x 8 D x 6x 8

Long Division Divide 1 a 11a 13a 27 a 10 6 a 10 7 A a a 3 B a a 3 C a a a 10 5 a 10 D a a 3 3 a 10 3 b 3b 32b 28 b 7 A b 4b 3 B b 4b 1 C b 4b 4 D b 4b 4 2 b 7 4 b 7 5 n 4n 128n 143 n 13 A n 9n 11 1 n 13 3 B n 2 9n 8 C n 9n 10 D n 9n 8 n 13 1 n 13 4 2 6 2 x 14x 56x 59 x 8 6 A x 6x 9 x 8 8 B x 6x 9 C x 6x 6 D x 6x 8 A k 3k 4 B k 3k 3 C k 3k 5 x 8 1 4 k 13k 33k 30 k 10 1 k 10 D k 3k 6 x 8 5 x 8 5 k 10 6 k k 130k 24 k 12 A k 11k 2 B k 11k 5 k 12 5 k 12 C k 11k 4 D k 11k 4

7 99x 119x 76x 96 11x 12 8 8 12v 153v 48v 45 12v 9 4 A 9x x 6 3 4v 3 2 3 4v 3 1 4v 3 B 9x x 8 C 9x x 8 D 9x x 7 2 11x 12 3 11x 12 9 21 154p 104p 172p 2 14p 2 A 11p 9p 12 1 7p 5 B 11p 7p 10 C 11p 6p 8 2 11x 12 B x 4x 9 D 11p 9p 11 C x 4x 9 D x 4x 7 2 14p 1 2 14p 1 2 14p 11 5x 24x 61x A x 4x 9 30 5x 4 6 5x4 8 5x 4 1 5x 4 5 5x 4 10 12 A v 12v 8 B v 12v 4 C v 12v 7 D v 12v 5 10 224x49x 90 8 A x 4x 14 14x 7 1 B x 4x 15 C x 4x 11 D x 4x 13 2x 1 4 14x 7 10 14x 14x 7 B 2r 9r 11 12 16r 92r 178r 116 8r 10 11 A 2r 10r 12 C 2r 10r 8 D 2r 9r 13 14x 7 8r 10 3 4r 5 7 8r 10 11 8r 10

b 2 3x y 81y6x4 6

Find the rectangular coordinates for the point whose polar coordinates are given 3 5

Forces of 15 pounds and 7 pounds act on each other with an angle of 105 Round the magnitude to 4 decimal places and the angles to one decimal place The magnitude of the resultant force pounds The resultant force has an angle of force with the 15 pound The resultant force has an angle of with the 7 pound force Be careful on this one One of the angles could be obtuse Also it is best to calculate each angle separately and

36 The certificates of deposit pay 2 annually and the municipal bonds pay 4 annually Over a five year period the investor expects the blue chip stocks to return 10 annually and the growth stocks to return 14 annually The investor wants a combined annual return of 6 and also wants to have only one fourth of the portfolio invested in stocks

The selling price for a classic car is 14 000 which is 1000 more than two times its original price What was the original price of the car Answer

On average the number of electronic keyboards sold in Florida each year is equivalent to seven times the average number sold yearly in Alaska It on average there are 98 854 electronic keyboards sold each year in Florida how many are sold in Alaska Answer Keypad Keyboard Shortcuts

The sum of two consecutive odd integers is 180 Find the two integers Answer

The total cost of a pair of pants and a jacket was 59 01 If the price of the pair of pants was 1 49 less than the jacket what was the price of the pair of pants Express your answer as a simplified fraction or a decimal rounded to two places

The sum of two consecutive integers is 1 Find the two integers Answer

If 1 4 plus 7 1 times a number equals the sum of the number and 30 7 what is the number Express your answer as a simplified fraction or a decimal rounded to two places

Angela owes 15 50 for text messaging in the month of July If her text messaging plan costs 11 for the first 600 messages and 30 for each additional text message how many text messages did she send that month Answer Keypad

ind the equation for the graph of the hyperbola with vertices at 0 3 and 0 3 and one focus 0 6 BANJIC24 ZAHUSANDA TURNG PANG WE SUNDAY AEROPO SETKA ZA Cu 1955

26 7 fint Z n 6 m 5 n 1

Simplify the expression Write the final form with no fractions tan x 4 tanx 4 sinx tanx 2 sinx sin cos

K Give the degree measure of 0 if it exists Do not use a calculator 1 2 0 arccos Select the correct choice below and fill in any answer boxes in your choice 4 2 Type your answer in degrees O A OB 0 arccos arccos does not exist

a Find a matrix B so that BA A for any 2 x 4 matrix A B b Find a matrix C so that AC A for any 2 x 4 matrix A C

K Find the exact value of the real number y if it exists Do not use a calculator y cos O A Select the correct answer below and if necessary fill in the answer box to complete your choice OB 2 COS y cos 2 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression 1 3 2 COLLE does not exist

Find the exact value of the real number y if it exists Do not use a calculator y tan 3 Select the correct choice and fill in any answer boxes in your choice below O A y tan 3 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the express 1 OB tan 3 does not exist

Consider the inverse cosine function defined by y cos 1 x or y arccos x Complete parts a through d a What is its domain Points 0 of 1 Type your answer in interval notation Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers

Select the correct choice that completes the sentence below The point 1 lies on the graph of y tan x Therefore the point of 4 2 2 lies on the graph of y tan

The truss is made of three A 36 steel members each having a cross sectional area of 206 mm Determine the magnitude P in kN required to displace the roller to the right 0 368 mm 0 8 m 0 8 m B P 5 kN 0 6 ms

Suppose that a matrix A satisfies the characteristic polynomial CA A A 2A 3

Al calcular 3 2 VI x 1 dx se obtiene 2 3 x 1 2 3 x x 1 2 C 2 3 x 1 2 3 C x 1 2 C

Is 33 52 a factor of 34 52 Explain why or why not Choose the correct answer below O A No because the exponents on the 5 terms are the same B Yes because 34 52 3 33 52 OC No because 33 52 cannot be written as a number times 34 5 D Yes because the two terms have the same factors P

Let A 27 3 6 Answer R Find an example of a nonzero 2 x 2 matrix B so that AB a 2 9 0 c d Hint Try finding a b c d so that A SED

DA If C M are n x n matrices then C M C 2CM M B If C is a square matrix so that C2 0 then C 0 OC If C Mare n x n matrices so that CM 0 then C 0 or M 0 OD For any n x n matrix C there exists a matrix M so that CM MC DE If C Mare nx n matrices so that CM 0 and M has an inverse then C 0 OF For any n x n matrices C M it s true that CM MC

Let A a Compute A using the formula for the inverse of a 2 x 2 matri A 11 5 b Suppose that C is a matrix so that AC 8 1 3 44 3 Use the inverse from part a to find the matrix C C 94 84

Let A 14 19 a a13 b a31 19 10 11 6 c a a22 13 3 15 Find the following matrix entri FI A

Find the following for the function f x a f 0 e f x b f 1 f f x 3 4x 5 6x 7 c f 1 g f 7x a f 0 Simplify your answer Type an integer or a simplified fraction b 1 1 Simplify your answer Type an integer or a simplified fraction c 1 1 Simplify your answer Type an integer or a simplified fraction d f x h f x h d 1 x Simplify your answer Use integers or fractions for any numbers in the expression e 1 x Simplify your answer Use integers or fractions for any numbers in the expression f 1 x 3 Simplify your answer Use integers or fractions for any numbers in the expression 0 1 7x Simplity your answer Use intogors or tractions for any numbers in the expression

Given the triangle below find the measure of angle x Round to two decimal places Note picture is NOT drawn to scale but x is obtuse 26 26 X

b 3x 2 3 1 4 6 81y x

7 Find all values of k such that the following system of equations x 2y 3z 9 2xy z 8 x 3y k 1 z k has i Unique solution ii More than one solution and find them iii No solu