Algebra Questions

x 5x 24 x 0x 0x 8

Find all real zeros of f x 3x4 5x 10x 2x 4 as we have done in c Give exact answers for the zeros i e no decimal approximations

2m n 2m n 2mm A 16m n 9 4n B D 14 512m 6 120 10 10 A C 2a 2a 2a b 46 2 B 16ba D 4a17

1 3 Exponents Rules Simplify Your answer should contain only positive exponents 1 xy 2x y A x y C 3 2xy 2a a b 2ab A C 1663 a 1664 B D 1 B b 2a D I 2 4 2 a b 2ab 266 A C 2a b 2 m C A 4m n m m 11 mn 4 4n B D ab 2 8a b B n m D m 8

5 5 21 2 uv A C 7 2uv 4u A mn m n 2m n 2m n B 32mn D 8 20 m 8n D m n B 13 6 8 6 A 2yyx 2 C A 9 32 16x 2m n 2nm 2m n 0 m 722 211 7 B D D 16y12 p 6 B 8m n 32m n 12 13 ZO

After declining between 1940 and 1980 the number of multigenerational households has been increasing since 1980 The function h x 0 012x 0 573x 35 726 can b used to estimate the number of multigenerational households in country A in millions x years after 1940 In what year were there 40 million multigenerational households There were 40 million multigenerational households in Round down to the nearest whole number

Use the quadratic formula to find exact solutions 8x 4x 5 X Simplify your answer Type your answer in the form a bi Use a comma to separate answers as needed Use integers or fractions for any numbers in t

ve for x X 1 0 The solution is x 0 Simplify your answer Type an exact answer using ra Express complex numbers in terms of i Use a comma as needed

Factor the following polynomial using the difference of squares 422 81

Exercise 5 Let z z E C Prove 1 Rez 2 2 2 Imz z 7 3 z 2 zz 4 z 7 ZER 5 12 2 z 2 6 2z 2 2 7 2 2 z z z z 8 121 12 1 1 2 1 1 1

Factor the following polynomial using the sum of cubes 8x 125

3 Find the Fourier transform of f x xe if x 0 and f x 0 if x 0

Cool Down Find Some Find all points of intersection between the graphs of the functions f x x 5 x and g x x 5

Use a calculator to write the following expression as a decimal rounded to two decimal places 23

Evaluate the radical 3 1 343 Select the correct choice below and fill in any answer boxes in you O A 1 343 Type an integer or a simplified fraction 3 OB The root is not a real number

Click here to watch the video Simplify the given expression 3 3 Vy

Simplify the radical 3 5x 1

Simplify the given expression 3 3 ly 3 3

Simplify the radical 4 7 4 4

Let the function P be defined by P x x 10x 23x 132 where x 11 is a factor To rewrite the function as the product of two factors long division was used but an error was made 1 Identify the error x 21x 208 x 11 x 10x 23x 132 x 11x 2 Redo the long division correctly 21x 23x 21x 231x 208x132 208x 2288 2156

P is a polynomial defined by P x 4x 11x 6x 9 Two factors are x 1 Rewrite the expression for P as the product of linear factors Here is a blank diagram to use to organize your thinking if needed

Use the information provided to sketch a possible graph for described on the provided axis Degree 4 Zeros 3 4 6 End behavior As x gets larger and larger in either the positive or the negative direction y gets larger and larger in the negative direction YA H 10 8 6 4 2 2 11 8 4 6 X

The equation A t 8000e0 06t gives the balance after t years of an initial investment of 8000 dollars which pays 6 00 compounded continuously dA a Find a formula for dt b Find and interpret A 6 Include appropriate units c Compare the approximation of 688 to the actual change Report your answer to two decimal places a dA dt b A 6 Round up to the nearest dollar Interpret A 6 688 OA The future value of a 7 year investment of 8001 will be of 8000 B The future value of a 6 year investment of 8001 will be of 8000 more than the future value of a 6 year investment more than the future value of a 6 year investment OC The future value of a 6 year investment of 8000 at 7 00 will be investment of 8000 at 6 00 OD The future value of a 7 year investment of 8000 will be more than the future value of a 6 year more than the future value of a 6 year investment

Find the amount of each payment into a sinking fund if 15000 must be accumulated Payments are made at the end of each quarter for 3 years with interest of 6 compounded quarterly Round to the nearest cent

Exercise 2 10 points Let T VV be an invertible operator and let A be eigenvalue of T 1 4 points Prove that A 0 2 6 points Prove that is an eigenvalue of T

7 m A C C 11 n 2m 3n m n 1 2m n 1 32mn A 2m n 2m n2 2m 2mn A 16m n m 4n C mon 3 m n nm 4 4 10 6 8m 16 15 B 1 2 10 n m B 8n D mm3 D B D m m 2 n n 20 m 512m 16 20 8 13 4 14 n 8 10 12 8 A 10 3 2m n 2nm A 12 C C 2m n 8 n m 2n m 40 2a 2a 4 2a b 5 466 2 aff3 A 4x8y 2 1 36 8 x6 x y 4 2 y 3 B 8m n D B 16ba 1 4a17 D 36 12 B 1 32m n 2 D 1 8ry6

Two functions g and fare defined in the figure below 5 7 g Domain of g Range of g Domain of fog 0 Range of f g O 6 8 Find the domain and range of the composition fo g Write your answers in set notatio Domain of f Range of f X

Exponents Rules Simplify Your answer should contain only positive exponents 1 A x 2y xy 2x y x 4 C 3 5 A 2a a b4 2ab 18 1 2x 0y4 A a 16613 17 16614 2u v 2u uv 1 2uv 4u vll B B B D D 1 D 1 2 1 1 V b 2a U 8 20 2 6 4 2 4 A 6 a C ab 4 Ab 2ab 266 1 2a b 3 4 2m n m n A C A 4m n m 3 4 m 11 4n 6 8 2y yx 2 4 32113 x 16x4 y D 3 412 a bo 2 B B n m n17 D 8a D m 8 28 16y 2 y8x6 4

3 Simplify Your answer should contain only positive exponents 11 a 4 12 12 4k A 16a A k 2 C 1 C A 3 15 21 4v A 4v 1 C 2v 17 1 256a4 A w www C 4m 4nm n 1 2m 1 6 4 3m n B D B 1 D 1 a B 41 D 2v B D 1 m n 4 m 14 16 18 14 4 A 4 4 C 4 16 2 x A 4x C x 18 A C 0 3 2u v 2u 1 vou 1 2v B 64k D 16k6 B D B B D 17 11 1 2u 3 x 2

3 5 Simplify Your answer should contain only positive exponents 11 a 4 12 12 4k A 16a A k 2 C 1 C 13 1 256a4 15 3 3 3 2v 4v A 4p 1 B B 1 D 3 B 4 D 2v 14 16 4 4 A 4 4 C 4 14 16 A B 64k D 16k 13 17 B B 3 x 2

3 Simplify Your answer should contain only positive exponents 11 a 12 12 4k A 16a8 A K 2 C 1 13 A 3 C 15 21 4v A 4v 1 C 2v 17 1 256a4 ww A C 4m 4nm 1 n 2m 1 6 4 3m n B D B 1 D 3 1 a B 4 D 2v B D m n 4 m 14 16 18 14 4 A 4 4 C 4 16 2x 3 A 4x C x 18 A C 2u v 2u v 1 vou 1 2v B 64k D 16k6 B D B B D 13 14 3 x 2 1 2u

3 5 Simplify Your answer should contain only positive exponents 11 a 4 12 12 4k A 16a A k 2 C 1 C 1 256a4 13 33 A 3 15 1 2v 4v A 4 1 C 2v B D D B 1 1 3 1 8 B 4 2v 14 16 4 3 4 A 4 4 C 4 14 16 X 2 x A 4x B 64k D 16k B B D 3 17 3x 2 2

3 Simplify Your answer should contain only positive exponents 12 12 4k A k 2 C 1 11 a 4 A 16a8 C 1 256a 13 3 3 4 B 9 B 1 D 3 1 1 14 4 4 A 4 4 C 4 14 B 64k D 16k6 D C IT

Simplify Your answer should contain only positive exponents 11 a 12 12 4 A 16a8 A k 2 C 1 1 256a C B D 1 12 B 64k D 16k6

Simplify 9 2p4 A p C 9p 12 B p 2 D 4p 10 10 3v 4 A 16v8 C v6 B 16 2 D 81v4

6 6 4xy 2y A 6y x6 C y x5 B 24x89 D 8 xy7

Solve the system with the addition method 2 4x 3y 20x 15y 10 Answer Enter your answers as integers or as reduced fraction s in the form A B If there is no solu type DNE in each blank If there are an infinite number of solutions specify their form in blanks in terms of x eg x 2x 3

a Find the equation of the straight line which best fits the following points 1 1 2 3 4 6 and 5 6 b Let A 11 1 14 1 5 Find P the projection matrix on C A

A brewery produces regular beer and a lower carbohydrate light beer Steady customers of the brewery buy 11 units of regular beer and 15 units of light beer monthly While setting up the brewery to produce the beers the management decides to produce extra beer beyond that needed to satisfy customers The cost per unit of regular beer is 29 000 and the cost per unit of light beer is 35 000 Every unit of regular beer brings in 100 000 in revenue while every unit of light beer brings in 400 000 in revenue The brewery needs at least 12 000 000 in revenue and has determined that the total demand will be at least 45 units of beer Complete parts a and b a How much of each type of beer should be made so as to minimize total production costs units of regular beer and minimum total cost of Type integers or decimals units of light beer should be made for a

Exercise 4 Find complex solutions of the follow ing equations Hint assume z a bi where a b R 1 z z 1 0 2 z 2iz 5 0 3 24 3iz 4 0 4 3z 5iz 2 0 5 422 9 0

Use a half angle identity to find the exact value cos 105 Which half angle formula should be used to find the exact value of cos 105 Sele Simplify your answer including any radicals Use integers or fractions for any num A cos 105 cos B cos 105 cos cos 105 cos OD cos 105 cos 210 2 2 2 2 O O 1 cos 210 2 1 cos 1 cos 1 COS 1 cos 1 cos 2 O O O O 2 3 cos 105 2 Simplify your answer including any radicals Use integers or fractions for any nur

Use a half angle identity to find the exact value cos 105 O A cos 105 cos B cos 105 cos Which half angle formula should be used to find the exact value of cos 105 Select the correct choice below and fill in the answer boxes Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OC cos 105 cos O D cos 105 cos 5 11 1 cos 2 1 cos 1 cos 1 cos 1 cos Question 5 5 6 15 Setup Solve Part 1 of 2 1 cos 2 HW Score 86 11 Points 0 67

T R2 R is a linear transformation for which T A C E and and A is the standard matrix for this transformation then

Graph f x 2 4 2 First drag the two blue points on graph to the correct points that f x passes through Then use the remaining red point to drag the horizontal asymptote to the correct line Note that all three points are adjusted in increments of 1 4 Y

Let V R Redefine addition and scalar multiplication in the following wa 0 0 0 0 0 by Is V a vector space under this new addition and scalar multiplication A Yes B No b a

392n A 8n 3 B 16 2n

Simplify 48r A 8r 3 B 6 3 C 4r 3

Simplify 245 PO

Simplify 4864 C 2 5 6 7 8

Simplify 125xy A 6y x 2x B 2x 7y C 5y 5xy