Algebra Questions

c d 3 2x50 1 2 28 2

2 1 x sy b 3 y 1 4 x 1 lo

Which of the following is equivalent to Select the correct answer below cos acot 3 sin a cos acot sin a tan acos sin Cosa sin atan B cos a sin atan cos a b cos B for all values of a and B for which cos a cos B is defined

a TA

What is the range for the quadratic 2 function y x 2x 3 Answer x 3 O y 2 O y 1 all real numbers

Rewrite the quadratic function 2 y x 2x 3 in vertex form Answer y x 2 x 3 y x 2 3 Oy x 1 2 x 2x 3 0 O y

What is the axis of symmetry for the quadratic function y x 2x 3 2 Answer Additional Solution No Solution

What is the domain for the quadratic 2 function y x 2x 3 Answer x 3 Y 2 x 1 all real numbers Submit

What is the y intercept quadratic function y Answer 0 2 2 0 3 0 0 3 for the 2 x 2x 3

What is the vertex for the quadratic 2 function y x 2x 3 Answer 2 3 O 1 2 3 2 2 1

Factor completely 46x yz 29z

Factor Answer x 11x 24 2

Factor the expression completely 4 x y xy

Factor the expression completely 5x Answer X

Factor the expression completely 60x 54x Answer

Solve the following quadratic equation for all values of x in simplest form 4 x 9 20 Answer Additional Solution 4 No Solution

Solve for all values of x by factoring Answer x 6x 10 Additional Solution X No Solution

Write the quadratic equation in standard form 2x 9 4x Answer 2x 1

58 Find an eigenpair for the matrix 2 3 5 4 2

3 1 3 4 Factor each completely 1 8x 28x 3 Simplify each expression 2x x 3 A B C D 5 i 2x x 2 5x2 5x 6 2x x 3 4x 10x x 3 x 2 6x 3x x 1 2x 1 2x 3x 2 61 6 7 2 4 2 6x 4x 4 3x S A B C 7 D 2 4x 6 6x 5x 4 2 2x 3 6x 7x 1 2 2x 3 6x 9x 2 2 2x 3 3x 3 8 S P 500 trending up

11 A 34 22 C 36 02 Find each quotient 11 z I WIN Al A 1 C 38 B B 29 72 D 39 52 D l c w 8

What does this puzzle represent 1

Given the angle 3 4 To which quadrant does belong Write your answer as a numerical value 2 T Find the reference angle for IN RADIANS 4 Find the point where intersects the unit circle

r is the growth or decay rate It is positive for growth and negative for decay Growth and decay problems can deal with money interest compounded continuously bacteria growth radioactive decay population growth etc So A t can represent any of these depending on the problem Practice The growth of a certain bacteria population can be modeled by the function A t 350e0 0796t where A t is the number of bacteria and t represents the time in minutes a What is the initial number of bacteria 350 round to the nearest whole number of bacteria b What is the number of bacteria after 20 minutes 1720 round to the nearest whole number of bacteria c How long will it take for the number of bacteria to double least 3 decimal places your answer must be accurate to at

Find RS S R 21 RS 7 9 T Write your answer as an integer or as a decimal rounded to the nearest tenth

Graph the image of kite KLMN 1 after a dilation with a scale factor of 5 centered at the origin 104Y N 6 4 2 8 6 4 2 2 4 6 8 1 0 2 M 4 6 8 K L X 10 ES

Graph the image of ABCD after a dilation with a scale factor of 4 centered at the origin 6 4 D 2 B 1 0 8 6 4 2 2 4 6 8 Y N 2 C 4 6 00 8

Graph the image of trapezoid CDEF after a dilation with a scale factor of centered at the origin 1 4 F 1 0 8 6 4 C 2 10 8 6 4 2 2 4 6 8 1 0 y 2 E 4 6

Find SU T 41 SU 9 2 U S Write your answer as an integer or as a decimal rounded to the nearest tenth

Find RS 49 R RS 8 S Write your answer as an integer or as a decimal rounded to the nearest tenth

2 Sketch the graph of the function below being sure to include at least two full periods y cos x 7 y X

6 The projected monthly sales in thousands of units of lawn mowers a seasonal product are modeled by S 71 3t 40cos Tt 6 where t is the time in months with t 1 corresponding to January Select the graph of the sales function over 1 year

4 The daily consumption C in gallons of diesel fuel on a farm is modeled by C 30 1 21 6 sin 2 t 365 10 5 10 where t is the time in days with t 1 corresponding to January 1 What is the period of the model

xatol 1700 ts bios bus bybubong add you 7 The following transformations applied to the graph of the function f x ln x a shift left 2 units b reflect the result from a over x axis c shift up the result from b 3 units ne or bru Write the equation of the resulting graph and describe the end behavior of the function

a 3 points Sketch the graph of f x 2 e by transforming the graph of y e Include any relevant asymptote on your graph

5 Determine whether the function below is even odd or neither f x 3secx Odd Neither

3 Find the relationship between the graphs of fand g Consider amplitude period and shifts f x sin 9x g x 4 sin 9x g is a shift of f9 units downward Og is a shift of f4 units downward g is a shift of f4 units upward The period of g is 4 times the period of f

1 Function g is related to a parent function f x sin x g x 8 sin 8x 7 Use function notation to write g in terms of f g x 8f 8x 10 g x 7f 8x 14 g x 8f 8x 7 g x 8f 8x 12

19 Find the matrix A if 2 26 10 27 41434 if 4 e 10 26 13 5 b 7 26 3 10

16 Let V v2 3 and v3 Note that V V2 V3 is an orthonormal set Find ca so that C V1 C2V2 C3V3 a b c d c

13 Let W be the subspace of R spanned by the vectors u 0 1 1 and u 1 2 1 Use the Gram Schmidt process to find an orthonormal basis for W a 0 1 0 2 0 0 22 6 0 2 20 to to 6 e 0 2

sig mot no estoq vodotesibi ol sua stel motorun ein to ten 12 Prove the following identity tan x sin x sec x cos x sec x

11 Let W be the subspace of R spanned by the vectors v 0 1 0 1 and v 1 0 1 0 Find the orthogonal projection of b 1 2 1 1 onto W a 1 1 1 b 3 2 1 1 c 1 1 1 d 1 0 1 0 1 27

21 Suppose that A is a matrix with eigenvalues A 9 and 8 with corresponding and 5 respectively Find a22 i e find the entry in row 2 column 2 of eigenvectors the matrix A a 4 b 5 c 1 d 3 e 2

12 Let A 2 40 120 a 3 b Which of the following vectors is in the column space of A c 6 13 Let W be the subspace of R spanned by the vectors u 0 1 1 and u 1 2 1 Use the Gram Schmidt process to find an orthonormal basis for W b a 0 1 0 0 0 e 0 oto 0 to to to e 0

18 Which of the following statements are always true 1 If A is a square matrix then tr A tr A ii If A and B are matrices such that AB B then A I ii If A and B are symmetric matrices of the same size then the matrix AB is also symmetric a 1 only b all of them c i and iii only d i and ii only e ii and iii only

9 Let V be an n dimensional vector space Which of the following statements are true i Every linearly independent subset of V is a basis for V ii Every set of vectors that spans V is a basis for V iii If V span V1 V2 Vn then V V2 Vn is a basis for V a all of them b none of them c iii only d ii only e i only

14 Which of the following statements are always true i The set of nonzero rows of a matrix A is a basis for the row space of A ii If R is the reduced row echelon form of A then the columns of R with leading I s forms basis for the column space of A iii If E is an elementary matrix then the matrices A and EA have the same row space a all of them b none of them e i and ii only d iii only e i and iii only

8 Which of the following sets of vectors span R2 i 1 2 1 0 ii 1 1 2 2 iii 1 0 0 1 3 4 a i only b i and iii only c iii only d all of them e i and ii

7 Let V be the subset of P3 consisting of all polynomials of the form ao ax a x where ao a 0 and a2 a3 0 Find the dimension of V a 2 b 1 c 3 d 4 e 5