Algebra Questions

Determine the equation of the graph and select the correct answer below 10 4 1 Courtesy of Texas Instruments Oy x 4 1 Oy x 4 1 Oy x 4 1 Oy x 4 1 15 Y 1 5 4606

Which of the following is a solution of x 8x 27 O 4 i 11 O4 11 O 4 i 44 O 04 1 44

Factor completely 25x 36 O 5x 6 5x 6 O 5x 6 5x 6 O 6x 5 6x 5 O 6x 5 6x 5

Of the following which is the solution to 2x 5x 8 O 5 ti 39 4 5 39 4 5 i 39 2 5 ti 192

Which is a factor of 15xy 45x 6y 18 Oy 2 O 5x 3 O 5x 2 Oy 6

Factor completely 5x2 50x 120 O5 x 3 x 8 O 5x 15 x 8 O x 4 5x 30 05 x 4 x 6

Determine whether or not the sentence is a statement Jonathan will meet Dana at 8 00 Is the given sentence a statement O O O No because it is a command It cannot be determined with further information No because it could be labeled as true or false Yes because it could be labeled as true or false quest estion

Find the mA ENTER A NUMBER ONLY A 2x 135 2x 5

The circumference of a circle is 13 inches Find the radius Step 2 of 3 Without substitution solve the formula chosen in the previous step for the unknown variable in terms of the known variable s

e number N of cars produced at a certain factory in 1 day after t hours of operation is given by N t 600t 10t t 10 If the cost C in dollars of producing N cars is C N 15 000 3000N find the cost C as a function of the e of operation of the factory hat is the cost C as a function of the time t of operation of the factory

Cos 0 sin for the scalar variable 0 Find the characteristic polynomial ercise 12 3 4 Consider the matrix Re sin 0 Cos v choose 3 and solve for the the eigenvalues and try to solve for eigenvectors

Exercise 12 3 5 Let A V V be a linear map with eigen pair x A EV x R Prove the following A is an eigenvalue of A A 1 is an eigenvalue of A I where I V V is the identity map If A is invertible then X is an eigenvalue for A

9 If g x 8x and f x log 2x then f g x 1 4log x 1 3 2 3log x 1 2 3 log x 2 4 6log x 4

10 5 2 Compute the characteristic polynomial and solve for th 17 18 4 genvalues For each eigenvalue find a basis for the eigenspace xercise 12 3 3 Consider the matrix A 8 2

Find functions f and g so that fog H H x 4x 6 Choose the correct pair of functions O A f x x g x x 6 4 B f x 6 g x x 4 OC f x x g x 4x 6 O D f x 4x 6 g x x

xercise 12 3 2 Consider the matrix A 2 or each eigenvalue find a basis for the eigenspace 4 Compute the characteristic polynomial and solve for the eigenvalues

Exercise 12 3 1 Consider the matrix A x1 1 0 0 1 2 1 1 R R Verify the the following are eigenvectors and find their corresponding eigenvalues 0 0 x2 x3 2 1

if x 5 3a Three times the sum of 8 and x 3b Evaluate if x 3 3c Evaluate if x 10

10 Evaluate if x 10 1C Evaluate if x 2 acredion 1d Evaluate if x equals one half

5 points If f z 22 1 and g z z 1 then the product f g 22 2 z 1 True False and its domain is all real numbers

2a Twelve less than the quotient of x and 10 X 12 10 2b Evaluate if x 20

Evaluate each of the following a 97 i

Let g x f 2x 1 1 Find the domain And range of g x 3 2 1 f x a 4 points Compute f f f 4 0 2 1 2 b 5 points Find the domain and range of f x 3 I c 5 points Let g x f 2x 1 1 Find the domain and range of g

The speeds of cars on a road are approximately normally distributed with a mean a What is the probability that a randomly selected car is going between 61 and 66 km hr Round your answer to four decimal places P eTextbook and Media 58 km hr and standard deviation 6 4 km hr b What fraction of all cars are going slower than 51 km hr Dound your answer to three decimal places

2b Evaluate if x 20

2a Twelve less than the quotient of x and 10

6 5 3 2 1 Amplitude Period Based on the graph above determine the amplitude midline and period of the function Midline y 2 2 4 3 4 5

evaluaas ever coich 1d Evaluate if x equals one half

3c Evaluate if x 10

3b Evaluate if x 3

3a Three times the sum of 8 and x

The diagram shows a platform The platform has supports that are fixed to both a wall and the ground Q1 Calculate the angle 0 Platform 1 1 29 27 0 6 2 2 A 0 B Ground level

1 c Evaluate if x 2

16 Evaluate if x 10

Solve the following quadratic function to find the x intercepts f x x 12x 27 Ox 12 and 27 O x 4 and 3 x 9 and 3 x 4 and 3

Solve the following logarithmic equation log x 3 0 027 004 0 013 001

Simplify the following logarithmic expression using the Laws of Logarithms log 6x log 2x log3 log4x O log4 log12x

Solve the following exponential equation 5 20 3 4 093 1 07 1 86

What is the horizontal asymptote of the following rational function x 8 2x 10 y O y 1 2 y 2 3 O y 0 There is no horizontal asymptote

What are the vertical asymptotes of the following rational function x 3 y 2 9 x 3 x 9 x 3 Ox 3 and x 3

4 If four less than the product of 4 and x is added to the difference of x and 5 what is the value if x 2 a 3 b 1 c 7 d 12

Describe the end behavior of the right side of the function f x x 2x 7 y approaches infinity as x approaches infinity y approaches infinity as x approaches negative infinity y approaches negative infinity as x approaches negative infinity y approaches negative infinity as x approaches infinity

Use long division or synthetic division to divide the following polynomials 2x x 2x 1 x 2

Use long division or synthetic division to divide the following polynomials x 2x2 x 5 x 1

3 What is the value of twice x increased by three times y if x 3 and y 4 a 15 b 17 c 18

Find the zeros of the following function f x x 7x 12x

Solve the following quadratic function to find the x intercepts f x x 6x 9 x 5 and 1 Ox 3 and 3 x 3 x 9 and 6

2 What is the value of 2x 4y if x 2 and y 3 a 16 b 8 c 8 d 16

What is the vertex of the following function f x x 4x 3 2 1 4 3 1 4 4 3

ms 1 Write an expression for the sum of 3x and 6 then evaluate if x 4