Complex numbers Questions and Answers

K Find the vertical and horizontal asymptotes of f and the graph of f that includes the asymptotes 8x x 25 Choose the correct asymptotes OA x 5 x 5 OC x 5 x 5 y 0 OB x8 x 8 OD x 8 x 8 y 0

K Drag each of the statements given below into the appropriate concept on the right Statements Concepts Rational function If x k is a zero of the denominator but not of the numerator a C is equivalent to ad bc b provided b and d are nonzero Continuous except at x values where the denominator equals zero p x f x where p x and q x are q x polynomials with q x 0 Occurs when the degree of the numerator is less than or equal to the degree of the denominator Vertical asymptote Horizontal asymptote Graph of a rational function Basic rational equation

y 9 6y x

For f x 1 xand g x 2x x 2 find the following functions a fog x b go f x c fog 3 d gof 3

the following Regression line Revenue and cost are the same Slope Scatter Plot Data presented in a visual form as a set of points The line that best fits the data points 3 Rate of Change 1 2 4 Breaking even

Listen Determine whether 0 2 is a solution of the system 2x 3y 6 4x 5y 10 Yes No

Listen Find the slope of the line that goes through the points 4 7 and 2 11 O 2 04 02 0 2 Pag

4 2 points The functions below are common streamfunctions for fluid flow which means that the level curves show trajectories of the fluid The first partial derivatives are related to the velocity components of the fluid in particular v 3 of For each streamfunction sketch several level curves enough to clearly see the shape and find the associated velocity vector v of the fluid for each pair x y a f x y 2xy b f x y x y

Divide 37i 2 12i 37i 2 12i Simplify your answer Type your answer in the form a bi Use integers or fractions for any numbers in t

26 14i 2i 26 14i 2i Simplify your answer Type your answer in the form a bi Use integers or fractions for any numbers in the

68 1 4i 68 1 4i Simplify your onewer Tyng your cou Em

a Find the conjugate of the complex number b Multiply the complex number by its conjugate 7 6i a The conjugate of the complex number is Type your answer in the form a bi

Write a ratio to show the relationship between the number of cups of flour and the number of pancakes made 2 10

Write in standard form 20 32 8 20 32 8 Simplify your answer Type your answer in the form a bi Type an exact answer using radicals as integers or fractions for any numbers in the expression

Multiply 25 9 COORD 25 9 Simplify your answer Type your answer in the form a biType an exact answer using radicals

2 i 8i 2 i 8i

8i 5 7i 8i 5 7i Type your answer in the form a billse integers or fractions for any numbers in the

Subtract 2 9 7 16 2 9 7 16 Type your answer in the form a bi Use integers or fractions for any numbers in the expres

erform the indicated subtraction in the expression below Express your answer in standard form 7 9i 5 9i 7 91 5 9 Simplify your answer

Write the following expression in standard form 9 8 9 Simplify your answer

75 4 3i 75 4 3i Simplify your answer Type your answer in the form

Multiply 4 3i 4 3i 4 3i 4 3i Type your answer in the form a bi

Find the complex conjugate of 4 9i The complex conjugate of 4 9i is Type your answer in the form a bi

4 8 5 32 4 8 5 32 Simplify your answer Type your answer in the form a biType an exact answer using radicals

25 36 25 36 Simplify your answer Type your answer in the form a biType an exact answer using radica

Perform the indicated subtraction in the expression below 2 7i 4 6i 2 7i 4 6i 0 Simplify

Add 6 i 3 6i 6 1 3 6i Simplify your answer Type your answer in the form a

Express the number in terms of i 3 16 3 16 Simplify your answer

State whether the following statement is true or false All real numbers are complex numbers Choose the correct answer below A True because the real number system is a subset of the complex number system OB False because the complex number system is a subset of the real number syster OC False because there are some real numbers that cannot be written in the form a O D True because the real number system and the complex number system are the s

Express in terms of i 25 25 Simplify your answer Type your answer in the form a bi

Write the number as a product of a real number and i Simplify all radical expressions 7 7 Simplify your answer Type your answer in the form a bi Type an exact answer using radicals as need

Sketch the graph of the function Include two full periods Use a graphing utility to verify your result y 2 sec 4x 2 O n 10000 Need Help th Read It 2 1

ow much money should be deposited today in an account that earns 5 compounded semiannually so that it will accumulate to Click the icon to view some finance formulas me amount of money that should be deposited is Cound up to the nearest cent Formulas In the provided formulas A is the balance in the account after t years P is the principal investment r is the annual interest rate in decimal form n is the number of compounding periods per year and Y is the investment s effective annual yield in decimal form A P 1 1 nt COOEE P A nt 1 A Pert Y 1 5 1 X

Question 8 y Write an equation for a line parallel to y 3x 1 and passing through the point 1 1 Check Answer

rk 8 3 a The amount of interest is Round to the nearest cent as needed Part 1 of 2 In order to start a small business a student takes out a simple interest loan for 3000 for 3 months at a rate of 6 75 a How much interest must the student pay b Find the future value of the loan O

Determine the present value P that must be invested to have the future value A at simple interest rate r after time t A 5000 r 1 55 t 3 months The present value P that must be invested is Round up to the nearest cent as needed

Simplify by factoring 40 40 Type an exact answer using

plify by factoring 3 63 Type an exact answer using radicall

The equation of the line with slope 5 and y intercept 3 can be written in the form y mx b where the number m is the number b is 3

Question 8 Write an equation for a line parallel to y 3x 5 and passing through the point 1 8 y

Select the correct response from the dropdown menu 5 4 3 2 1 5 4 3 2 1 e 32 6 This function belongs to the quadratic linear absolute value square root function family

3 A parking meter charges 2 50 per hour How much would it cost to park for three and a half hours a 71 b 7 50 c 7 80 d 8 75 4 In 4 of an hour Becca completes 1 5 5 complete the project a 4 hours 25 b 1 hour of a project How many hours will it take her to c 4 hours d 4 2 25 hours

A sofa regularly sells for 760 The sale price is 600 40 Find the percent decrease of the sale price from the regular price

Express the given fraction as a percent 35 80 Type an integer or a decimal

Express the given percent as a decimal 10 10

Express the given decimal as a percent 0 99

Express the given decimal as a percent 0 2871

olve the inequality Write the solution in interval notation and graph it 3 48 C Choose the correct solution in interval notation O A 5 00 O C 0 5 Choose the correct graph of the solution O A O B O C D 4 3 O B 5 00 O D 0 5

x 4 Choose the correct graph O A O B O C O D 10 10 10 10 The inequality can be written as O A 4 00 10 10 10 10

Find the quotient 58 6 0 79 58 6 0 79 Round to the nearest tenth as needed