Algebra Questions

10 10x 19x 6

3 f x x 4x 4

7 8x 10x 3

2 100x

2 y x 16

8 9x 49

6 36x2 25

4 6x 17x

3 n 4 2 n 1 n n 3 2n

B 5 9 Solving Rational Expressions Solve each equation Remember to check for extraneous solutions 1 5 1 5 a 3a n 4 2 n 7 1 1 6 3 6 P P a 5 3a 1 n 3 n 2n 1 x 4 2 x 4 n 6 8 2 2 2 4 8 10 2 V 1 36 b 2r 1 2b 8b 1 v 5 1 1 2 2b 6 V 1 b 2 b 4 3r 3 10r n 5 n 4 b 5 b 4b

2 r 7r 8

8 56 13b 28

7 2n 7n 5

6 Sp 18p 8

5 3b 25b 50

4 x 49

2 1 m 17m 72

2 3a2 24a 45

3 m 7m 6

7 y 3x 24x 27

4 14y2 7y 21

10 Find the vertex of y x 16x S

3 3x 31x 36

9 Find the product x 2 2x

9 Find the product x 2 2x 7

8 y 4x 20x 24 1

7 y 3x 24x 27

5 2m 16m 32

6 2x 8

1 5t 5t

10 1 2 3 14 15 14 B 13 C 14 A 12 The right 3 D 15 answer is E 16

1 1 2 4 23

12 x y EN 60 x y 52 A 120 min x y B 136 C 142 D 156 E 172 The right right answer

Find all integer a such that 2 37 mod 7 20 pts

2 Each day a local dog shelter spends an average of 2 40 on food per dog The manager estimates the shelter s daily expenses assuming there is at least one dog in the shelter using the function E x 30 2 40x Which statements regarding the function E x are correct I x represents the number of dogs at the shelter per day II x represents the number of volunteers at the shelter per day III 30 represents the shelter s total expenses per day IV 30 represents the shelter s nonfood expenses per day 1 I and III 2 I and IV 3 II and III 4 II and IV

4 When written in standard form the product of 3 x and 2x 5 is 2 2x 11x 15 4 6x 15 2x 5x 1 3x 2 3 2x x 15

5 David wanted to go on an amusement park ride A sign posted at the entrance read You must be greater than 42 inches tall and no more than 57 inches tall for this ride Which inequality would model the height x required for this amusement park ride 1 42 x 57 2 42 x 57 3 42 x or x 57 4 42 x or x 57

6 The table below shows the height in feet h t of a hot air balloon and the number of minutes t the balloon is in the air Time min Height ft 2 5 7 10 12 64 168 222 318 369 The function h t 30 5t 8 7 can be used to model this data table Explain the meaning of the slope in the context of the problem Explain the meaning of the y intercept in the context of the problem

8 Determine if the point 0 4 is a solution to the system of inequalities below Justify your answer 101 10 yz 2x 4

7 Solve algebraically for x 3600 1 02x 2000 1 04x

2 3 If y 3x x 5 and z 5 and z 4x 34 3 6x 4x 22 1 6x 4x 2 x 12 which polynomial is equivalent to 2 y z 2 6x 3x 17 4 6x 2x 17

13 pq Given 3 r express p in terms of q and r 9 Diberi P 3 r ungkapkan p dalam sebutan q dan r Answer Jawapan 14 Solve each of the following linear equations Selesaikan tiap tiap persamaan linear berikut a 2k 6

10 2 2 2 2 2 marks True or false If true prove it and if false give a counter example i The vector n 2 3 is perpendicular to the line 2x 3y 7 ii The set W A E Man det A 0 is a subspace of the vector space Mnn the set of all n x n matrices with the usual addition and scalar multiplication iii If E and E2 are elementary matrices then the product E E2 is an elementary matrix iy If A is an invertible symmetric matrix then adj A is also a symmetric matrix v The zero vector of any vector space is unique

18 points Let be the vector space of polynomials of degree 2 or less Consider the following two ordered bases of 2 x x 2 2x x 1 x 2 x x 2 x 5 x 2x id a Find the change of basis matrix from the basis to the basis id b Find the change of basis matrix from the basis to the basis

Let W be the set of all vectors 8 x y x y with x and y real Find a basis of W

1 2 l 1 3 3 1 3 marks Consider the system of equations k x y z w 2x 3y 4z w 10 3x 4y 5z 2w 14 2x 5y lw For which values of k and I does the system have i no solution ii a unique solution iii exactly two solutions iv infinitely many solutions K 10 14 3 2R Rz 3R R3 2 R R4 09 D 1 03 I N N H 3 2 www 3 2 1 fund e 2 10 2k 14 3k 3 2 k

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Show that In x x 1 for all x 1

A financial analyst constructs a statistical model to represent the market shares of several similar companies She then collects data over the next month to evaluate her model At the end of the month she finds that for one of the companies the difference between her model and the data is 5 She decides to collect data for an additional two months If her model is valid what could she expect from the total data collected after three months OA The difference between the data and the model will get smaller OB The difference between the data and the model will get larger OC The difference between the data and the model will stay the same O D It is impossible to predict how the difference between the data and the model change

Drag the appropriate factor to the missing box to factor each trinomial completely 6x 8x8 x 5x 1 5x 19x 12 5x 5x 18x 9 5x 4x 15x25 x