Complex numbers Questions and Answers

3 The repeating decimal 5 868686 may be expressed in a fraction as

4 Express the following decimal as a fraction 0 378378 in simplest form O O O 378 1000 378 999 42 111

thinking Here is the question you will answer on this discussion board Situation 1 Origami paper is always in the shape of a square If you take the top corner of either side of a 9 x 11 inch piece of paper and fold it to the lower opposite side and trim off the excess paper this creates the square that we need Then fold the top corner to the opposite comer to create a diagonal which is a typical first step to most origami designs 1 Refer to situation 1 What are the dimensions of your square What is the length of the

base of the doghouse will be needed Determine the length and width of your doghouse The roof of the house is a triangle with two sides that are the same length Decide the height of the roof Refer to situation 3 Find the slant height of the roof using the dimensions you chose If you are hoping to put shingles on the roof you need to know what the square footage of the roof will

Consider a triangle ABC like the one below Suppose that A 96 B 36 and a 24 The figure is not drawn to scale Solve the triangle Round your answers to the nearest tenth If there is more than one solution use the button labeled or a B A c b c 0 or X No solution

12 Find the inverse of the function Mark all correct answers f x 15x 1 0 4 0 4

7 Factor 49x2 16 to its simplest factors O 7x 4 7x 4 O 7 7x 2 O 7x 4 7x 4 O4 4

3 How do the factors of a polynomial function relate to the graph of the func

11 Find the inverse of the function f x x 10 x 10 x 10 2 10 O x 10 x 10

9 Find the inverse of the function f x 7x 7 x x

1 Graph the function and its inverse f x x 2

Find an equation for the line below H F

11 You want to rent a back hoe for some excavation The rental company employee says it s a flat fee of 312 to rent the back hoe and an additional 25 per hour used Write a function that describes the cost of renting the back hoe Use a to represent the hours x answer y

Find the present value of 7000 payable at the end of 2 years if money may be invested at 7 with interest compounded continuously The present value of 7000 is Round to the nearest cent as needed

11 Write an equation expressing the volume of a box made from a paper x x 28 from which a square with side length 1 is cut from each corner and the sides of the box are folded as shown V cubic units

an important package you ll need a box Graph the following equation 6 2x 20 2x x which represents of the volume of a box made from a rectangular cardboard sheet 6 inches wide and 20 inches long from which a square is cut from each corner and the sides of the box are folded as shown The value a represents the side length of the square cutout What is the length x of a side of the square cut from each corner of the paper used to find the maximum volume for V 6 2x 20 2x x Round your answer to the nearest hundredth value for at maximum volume

9 You want to rent a drill for some home repair The rental company employee says it s a flat fee of 34 to rent the drill and an additional 11 per hour used Also you may only keep the drill for a maximum of 38 hours How much will it cost for you to rent drill for the maximum time total cost

water balloons at each other s targets The balloon launchers are math based so you must enter quadratic functions to aim your launcher Your teammate has determined the following equation will launch a balloon at the other team s target h 16t 93t 5 where t represents the time in seconds after the balloon s release and h represents the height of the balloon The height versus time graph for the equation looks like this h How much time in seconds will it take before the balloon s height reaches 24 feet on the way back down Hint Set 24 equal to 16t2 93t 5 and solve for t using the quadratic formula Check your answer on a graphing calculator

7 You ve been asked to build a machine for a TV commercial that launches shampoo bottles from ground level over the heads of models with their unruly hair stacked high You estimate the shampoo needs to clear at least 9 feet in order to sail over their heads The equation that represents the height of the bottle as a function of time t in seconds is h 16t 35 2t How many times does the shampoo cross the 9 foot threshold shampoo reaches 9 feet times

5 You ve been asked to design a fountain that shoots water jets over a walkway in an amusement park without soaking the patrons You estimate the water needs to clear at least 7 feet in order to sail over the patrons The equation that represents the height of the fountain as a function of time t in seconds is h 16t2 32t How many seconds does it take for the water to reach 7 feet More than one answer may be correct select all that apply t 0 31 t 0 25 t 0 38 Ot 1 88 Ot 1 81 Ot 1 75

6 Graph the following using a graphing calculator Identify all of the roots of the equation 2x 3x 32x 48 More than one answer may be correct select all correct answers 8 4 x 1 5 x 4 4 0 1 5 6 4 3 4 el roots

Consider the following function f x Step 2 of 2 Identify the shape of the more basic function found in step 1 Answer 1 x 4 2

the angle between U and V to the nearest tenth of a degree 3 3 7 Points DETAILS MCKTRIG8 7 T 029

Iven the figure below find the values of x and z 7x 42 77 X N I I

A guy wire is used to support flagpoles in windy areas These wires are anchored in the ground to provide constant stability You need to replace the guy wire on a pole that is 20 feet tall The anchor point for this flagpole s 15 feet away from the base of the pole How long is the wire you need to purchase to replace the old wire You are also helping a friend determine the length of a guy wire for a 10 foot flagpole The wire needs to be anchored 6 feet from the base of the pole You can purchase guy wires in whole foot lengths only Using your knowledge of perfect squares estimate the length of wire you would need to complete the project How much wire

What is the surface area of the solid THE The surface area is cm Round to the nearest tenth as needed 9 cm 3 cm

A 3 r r B 15 D 9 C

How much would you need to deposit in an account each month in order to have 40 000 in the account in 10 years Assume the account earns 8 interest

Sin B 1 Cos B 2 2 Express as a fraction Sin B Cos A B

find the value of f g 1 if f x 4x 3 and g x x 2 x 3

4 Identify the correct y intercept using the equation 7x 8 of a line y b

7 Mr Davis bought stock valued at 60 00 per share and sold it for 100 00 What was the percent of profit O 100 O 0 O 166 2 3

he ratio of their areas is what Mark all correct answers more than one answer may be correct 4 9 2 3 2 to 3 4 to 9 4 9 2 3 olve for x 2 12 3 x 13

32 What is the scale factor if a 10 in by 6 in photograph is enlarged to a poster that is 2 5 ft by 1 5 ft 4 01 1 20 O 1 10 O 3

31 If there are 59 people in a biology class and 19 are boys what is the probability that a person chosen at random will be a girl 40 59 about 68 O both of these

rite an equation in slope intercept form for the follow 5 2 1 TTT X

What is the y intercept of an equation for a direct variation Explain your answer using the graph of equation 5 also may be written y y I 5x and the equation itself

11 How is the equation for a vertical line expressed How did you discover that

13 Given the equation y x 8 the y intercept is

Feet Traveled in a Walk Race ace 80 70 60 50 40 30 20 10 4 30 2 3 4 SUBMIT ALL A 7 50 567 8 Time in Seconds

Which type of variation is represented by the following e M2 1 2 131 inverse direct joint none Find y when x 75 if y varies inversely as x and y 108 when x 35 50 4 55 89 53 6

5 A pumpkin is thrown upward with an initial speed of 800 feet per second It is given that h 16t 640t h is the height of the pumpkin at any given time Use your graphing calculator to find how many seconds t before the pumpkin hits the ground on its way down Or factor and solve for t algebraically seconds t

8 Factor completely 36c 60cd 25d y

6 points each Graph and state the domain and the range of each function c f x 2 x 1 3 Step 1 Basic graph Step 2 Transformations Step 3 Graph

x 1 y 2 2 x y 5i 1 i x 2y

5 Which of the following could not possibly be probabilities A 44 B 13 7 C 0 D 7 8 a A and C b A and D c A B and C d A and B e B and C

Use the factor theorem and sy x 3 6x 2 8 x 3

Tamarr needs to buy shredded wood for his children s The shredded wood costs 10 per ton and there is a deli f 20 with each order What types of numbers are possible in the domain All rational numbers greater than 10 All positive rational numbers less than 20 All positive rational numbers All rational numbers

O 11 and 1 O 11 and 1 O 11 and 1 The cost of sending a package through first class mai indicated in the table below Find the domain of this relating weight of the package to mailing cost Weight ounces Cost 0 45 0 65 0 85 1 05 less than 1 between 1 and 2 between 2 and 3 between 3 and 4 O Domain 0 45 weight 1 05 O Domain 3 weight 4 O Domain 0 weight 4

Pascal pays 31 to join the debate team He pays 15 each time he enters a tournament Write an algebraic equation for the total cost C of debating as a function of the number of tournaments x he enters C x