Algebra Questions

6 8 1 33 2 4 2 4 1 2 316 0

Find a matrix P such that PTAP orthogonally diagonalizes A Verify that PTAP gives the proper diagonal form Enter each matrix in the form row 1 rov comma separated list A 0 10 10 0 10

A DJ is preparing a playlist of 21 songs How many different ways can the DJ arrange the first six songs on the playlist There are different ways that the DJ can arrange the first six songs on the playlist Type a whole number

The demand D for a new rollerball pen is given by D 0 007p 0 4p 120p where p is the price in dollars a Find the rate of change of quantity with respect to price dD dp b How many units will consumers want to buy when the price is 25 per unit c Find the rate of change at p 25 and interpret this result d Would you expect dD dp to be positive or negative

By recognizing each series below as a Taylor series evaluated at a particular value of x find the sum of each convergent series A 1 3 31 31 3 7 B 3 1 72 272 1 1 ng2n 1 2n 1 M

In Exercises 11 14 identify all pairs of angles of the given type See Example 3 11 corresponding 12 alternate interior 13 alternate exterior 14 consecutive interior 15 25 and 21 34 17 26 and 213 USING STRUCTURE In Exercises 15 18 classify the angle pair as corresponding alternate interior alternate exterior or consecutive interior angles 56 34 78 56 8 9 10 11 12 13 14 15 16 16 211 and 413 18 42 and 4

47 DOUGHNUTS Mi Ling is ordering doughnuts for a class party The box contains 2 dozen doughnuts some of which are plain and some of which are jelly filled The plain doughnuts each cost 0 50 and the jelly filled cost 0 60 If the total cost is 12 60 use Cramer s Rule to find how many jelly filled doughnuts Mi Ling ordered

Ise a matrix equati 28 x y 3 2x y 6

18 4x 2y 7z 26 5x 3y 5z 50 7x 8y 3z 49

Orthogonally diagonalize the matrix giving an orthogonal matrix P and a diagonal matrix D To save time the eigenvalues are 10 2 and 2 442 A 424 244 Enter the matrices P and D below Use a comma to separate answers as needed Type exact answers using radicals as needed Do not label the matrices

Suppose f x 5 Determine and graph four distinct antiderivatives of f 10 8 6 Clear All Draw 10 8 6 4 2 15 4 6 8 10 2 4 6 8 16

3 2 2 3 4 8 7 6 5 The graph of a function y f x is shown Make a sketch of the antiderivative F given that F is continuous and F 0 3 3 2 2 3 15 6 ON M 3

11 15 23 P5 Answer the following constructed response question Follow all directions to receive full points A Write two expressions that can be used to find the area of the figure below Expression 1 4x 4x 8x 1 Expression 2 B If x 3 find the area of the rectangle using one of your expressions from Part A All measurements are in feet Show all of your work

Factor the expression Use the fundamental identities to simplify if necessary There is more than one correct form of each answe sin x 6 cos x 15

d x 2i x 2 x 1 x 1 x 2 x 2 e 9 Use the definition of the logarithmic function to find x log4x 3 a x 12 b x 4 c x 81 d x 64 e none of these

1 point Find a linearly independent set of vectors that spans the same subspace of R as that spanned by the vectors A linearly independent spanning set for the subspace is 1 2 0 0

iven the functions f x and g x below find all solutions to the equation f x g x to the earest hundredth f x 0 2x x x 4 8 g x 0 3x 3 9

Challenge x 1 10 12 S 15 2

As age increases so does the likelihood of a particular disease The fraction of people x years old with the disease is modeled by 0 8 f x 1 271e 0 122x a Evaluate f 25 and f 65 Interpret the results b At what age does this likelihood equal 60 CELEB a Select the correct choice below and fill in the answer boxes within your choice OA 25 Round to three decimal places as needed and f 65 This means that among people age 25 have the disease while among people age 65 have the disease B 25 0 058 and f 65 0 729 Round to three decimal places as needed This means that among people age 25 5 8 have the disease while among people age 65 72 9 have the disease b At about yr this likelihood equals 60 Do not round until the final answer Then round to the nearest integer as needed

8 x 8 7

6 3 x 2

1 x 90

5 2 x 3 8

8 x 4 9

5 Jada measures the growth of 10 tomato plants and lists the data in a table Use the data in the table to create a line plot a Plant Growth inches A 2 8 0 B 7100 8 C 318 J D 218 1 8 E 5100 8 13234 F 13 G 00011 8 H 48 7 8 618 1 778 b What is the difference in inches between the growth of the plant with the greatest amoun of growth and the plant with the least amount of

2 2x 5 41

Given sin 0 5 and cos 0 find the exact values of the following 7 sin 20 cos 20 tan 20

f x 3 2x 3 on the interval 4 2

Find the function f t such that f t f t 40 t and f 1 7

plity each expression 1 5 8r 8 3 I 3 8 6p 8 2 5 3 1 8n 8 7 3 8 y 7 9 7 3x 2 7x C B 2 8 7 7x 1 4 6n 6 4n 2 6 7 8b 1 1 8 7 7 n 6 10 7 5 x 7 6

11 9 6 6x 13 8 7 4m 6 15 5 3 3r 9r 17 8m 6 4m 5 19 4 2r 5 4 12 2 10 5 6m 14 10k 4 10 10k 16 7x 7 x 9 18 10 4 4a 4a 20 10 6 5

Solve the equation log 4256 2x 2 Change the given logarithmic equation to exponential form 256 42x 2 Type an equation Do not simplify The solution set is Type integers or simplified fractions Use a comma to separate answers a

se the given function f to answer parts a through f below X 4 f x 4 5 Choose the correct graph of f below OA B 10 y 10 40 10 X 10

How does an SAT score of 1120 compare to an ACT score of 23

x 1 Ella and Alicia are comparing scores on their college entrance exams Ella s SAT score is 1380 Alicia s CT score is 32 The mean SAT score is 1000 with a standard deviation of 200 The mean ACT score is 21 with standard deviation of 5 Who has the better score

Use the given function f to answer parts a through f below X 4 f x 4 5 B There is no horizontal asymptote d Find f the inverse of f f x 4 log 4 x 5 Simplify your answer e Find the domain and range of f The domain of f is 1 Type your answer in interval notation

Use the given function f to answer parts a through f below f x log x 4 3 d Find f the inverse of f f x 10x 3 4 Simplify your answer e Find the domain and range of f1 The domain of f is

Multiply 4 21

Subtract 2 7 5 3i

3 5i 6 4i

1 3i 6 4i

Add 4i 2 8i

Find the complex number for the given radical expression 4 121

4 5i 6 10i

5 2i

8 3i 7 3i

2 2i 9 5i

Use the given function f to answer parts a through f below X 4 f x 4 5 112 LU 40 c From the graph determine the range and any asymptotes of f The range of fis IU N

The complex number 1 2i 3 represents which radical expression below A 1 12 B 1 12 C 1 6 D 1 6

What are the solutions for the given equations belo 15 0 5