Complex numbers Questions and Answers

Consider the graph on the right Explain why F I H D is not a path Choose the correct choice below OA It is not a path because vertices F and I are not adjacent OB It is not a path because vertices H and D are not adjacent OC It is not a path because edge HD is used twice OD It is not a path because edge Flic wood bu B Do D E F G

Consider the graph on the right Explain why G F D E D is not a path Choose the correct choice below OA It is not a path because edge FG is used twice B It is not a path because vertex D appears more than once OC It is not a path because edge DE is used twice OP It is not a path because vertices OOC Do I H

Identify the even vertices and identify the odd vertices B Use a comma to separate answers as needed Ea Identify the even vertices Select the correct choice below and if necessary fill in the answer box to complete your choice OA The only even vertex is OB The even vertices are

In the graph to the right which vertex vertices is are adjacent to vertex G Choose the correct answer below OA A and C OC D G and I OE G and I OG C and B OI A and H CILE OB D OD F and H OF A B C and D OH E OJ C E and F

Find the degree of each vertex in the graph Complete the following table Vertex A Degree of Vertex B CDE F GHI A B C D E F

Explain why edge DF is a bridge While edge DF is included in the graph the graph is C If edge DF were removed the graph would be disconnected B C D

Using the graph shown find a Hamilton path that begins at C and ends at F One Hamilton path is C F Use a comma to separate vertices as needed E F

An investor wants to save money to purchase real estate She buys an annuity with monthly payments that earn 5 interest compounded monthly Payments will be made at the end of each month Find the total value of the annuity in 17 years if each monthly payment is 60 Do not round any intermediate computations and round your final answer to the nearest cent If necessary refer to the list of financial formulas 2 5 X Charli

Use the equation to complete the table Use the table Lo list some of the ordered pairs that satisfy the equation 2x 5y 18 Complete the table 6 3 y 4 x y X 6 3 y 4 x y

How many whole numbers between 100 and 400 contain the digit 2

Consider the following sets U a b c d e f g h i j k A a d f h i k B b d f g h j Find the following C 7 An B 8 ANB 9 An A 10 AU A

About the sequence x kezt we have the following 1 B x b for each te to b t b a MK 1 1 l b t b k20 k 1 c x kezt is uniformly Cauchy on t b t b verification of these properties is left for the reader We consider the uniform limit of the sequence x 1 8 to 8 B x b C which is given by x 1 lim x 1 1 l b to b Thus x 1 lim x f s x s ds 565 8 60 ds b Finally the validity of this integral equation has the following two implications X t x s x s ds x 0 x 1 x lim ff s x s ds x lim f s x s ds x f f s lim x s ds x ff s x s ds Thus the function x 1 satisfying the integral equation x 1 x f s x s ds for all 1 t b t b 2 dx dt d 0 ff s x s ds f 1 X t This now proves that the curve X 1 8 1 82 thus obtained is a solution of the initial value problem

If the point x y is equidistant from the points 3 3 and 5 5 show that x and y satisfy the linear equation x y 2 A

4 Find the values of y so that the distance from 0 2 to 12 y is 13 units

8 6 4 2 y 8 6 4 2 2 4 6 8 A 4 4 2 0 2 4 2 4 6 8 X

Identify the coordinates of each point labeled in the figure a A b B c C d D e E a A b B c C d D Type an ordered pair Type an ordered pair Type an ordered pair Type an ordered pair

Plot the points 0 8 and 4 16 in a rectangular coordinate system Then draw a line through the two points Find and interpret the slope of the line containing the points Click to enlarge graph A Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA The slope of the line is The value of y will increase by unit s when x increases by unit s Type integers or simplified fractions OB The slope of the line is The value of y will increase by unit s when x decreases by unit s Type integers or simplified fractions OC The slope is undefined 20 516 12 BI 41 20 16 12 8 8 12 16 20

Find the slope and y intercept of the line whose equation is y 5x 6 What is the slope Select the correct choice below and if necessary fill in the answer box to complete your choice A The slope is Type an integer or a fraction OB The slope is undefined What is the y intercept Select the correct choice below and if necessary fill in the answer box to complete your choice A The y intercept is Type an ordered pair

Plot the given points in a rectangular coordinate system Then draw a line through the two points Find and interpret the slope of the line 4 7 and 5 7 yrapi Select the correct choice below and if necessary fill in the answer box to complete your choice OA m Type an integer or a simplified fraction OB The siope m is undefined Interpret the slope of the line Choose the correct answer below OA There is no change in x The line is vertical OB There is no change in y The line is horizontal C As x increases y decreases O x increases y increases 10 B 6 A 2 10 Ay 8 6 2 2 14 6 8 40

2 Solve the inequality 3x 2 6 2x For full credit you will need to show and explain every step An explanation should state what you re doing and WHY A statement is not an explanation You may add more lines if you need them Steps Work 3 points Explanation 3 points

x x y v Use the Pythagorean Theorem to calculate the distance between the points 1 3 and 4 6

Use distance formula to calculate the distance between the points 1 3 and 4 6

1 02 08 Solve the compound inequality 6b 42 or 4b 12 8 1 point Ob 6 or b 5 Ob 7 or b 1 Ob 7 or b 1 Ob 6 or b 5

Solve the equation for the unknown 2r 5 10

Solve the following equation 5x 2 3 x 2 X x Simplify your answer

Solve the equation for the unknown 5 a 2

Solve and check 7x 7 35

For the following problem use the formula I PRT where I is interest in dollars P is the principal or loan amount R is the interest rate and T is the time in years 1 Find the interest if principal of 2600 is invested at 11 or 0 115 for four years 1 Round to the nearest dollar as needed

2x 1 13 f x 3 x 21 FIND f 5 Type a response 3 2x 1 x 1 1 x 5 x 5

6 6 WA CHC 2 zoom in x K 6 The DOMAIN of the fu Select The RANGE of the fun Select

Write the equation of the circle centered at 4 3 with radius 11 HT

Determine if the upper bound theorem identifies 4 as an upper bound for the real zeros of f x f x 8x 8x 3x 9 Select one a No h Yes

Suppose you saw a sign at your local bank that said 4 2 rate compounded quarterly 4 9 Annual Percentage Yield APY Is there anything wrong with the sign Explain

The Vances house is worth 320 000 and their yearly property tax is 8 88 for every 1 000 of value How much will they pay in yearly property tax

Select a symbol from the dropdown menu that correctly indicates the relationship between the first and second quantity W The number of relative minimum points The number of intervals where the function is increasing he number of relative maximum points POSSIBLE POINTS 2 The number of intervals where the function is decreasing

64 zoom in X 7 Determine the DOMAIN of the given function Ox 4 O O O O O X 4 X 4 y 0 X 0 All Real numbers x 4

12 13 f x H Find f 4 Type a response f x Find f 9 1 5x6 if x 4 1 2x 7 1 5x6 1 2x 7 if 4 x 3 44 if x 3 if x 4 if 4 x 3 if x 3

3 4 Evaluate the function g n 23 1 Find g 1 Type a response Evaluate the function Round your answer to the nearest hundredth TWO DIGITS p x 1 4 x 4 4 Find p 4 8 Type a response

co Determine if the following function is ODD EVEN or NEITHER f x x 3x O ODD EVEN NEITHER

2 Evaluate the function g n 3 2n Find g 8 60 06 O 24 48 48

1 Evaluate the function g x 2x 6x Find g 6 O36 O 108 20 56 180

4 Find the outputs from the inputs of the given functions report the solution as f input output a f x 4x 3 x 2 3 10 4 2 3 1 4 3 3 15 4 10 3 43 b g x 4x 8x 4 x 1 2 3 461 8 1 4 4 8 4 4 2 218 2 4 Blattl 56 2 4 3 8 8 4 16 x 5 c h x 4x x 3 6 5 7 5 4 3 3 27 3 5 4 6 3 6 5 4 6 3 Undefined 5 5 d T t 34t 32 t 2 5 10 3412 32 104 34 572 32 818 34 1072 32 33668 e V s 6s 4s s 7 s 4 2 5 6 4 4 4 2 4 6 2 4 2 2 7 59 331 f L x 12x 5x 3 x 1 0 1 round up to 2 decimal places 12 1 2 5 1 3 4 47 Via 0 25 0 13 g Graph part f into desmos About what domain does the graph NOT EXIST

K 7 A ladder is leaning against a vertical wall The ladder is 15 feet long and the angle between the ladder and the ground is 60 degrees Find the height at which the ladder touches the wall SRCATO Sin le X

Select the ordered pair that is a solution to the equation represented by the graph 2 8 4 6 A y 2 2 01 2 4 6 8 X

The Guitar Shoppe bought 7 sets of bongo drums and 8 guitars for 2977 90 The guitars cost 292 apiece Find the cost for a set of bongo drums A set of bongo drums costs

In the following exercise a formula is given along with the values of all but one of the variables in the formula Find the value of the variable that is not given S 2LW 2WH 2LH S 148 L 6 W 5 H

Which polynomial represents the area of the rectangle O 2z 10 O 2x x 10 O 2x x 10 02 IT 10 2x 5 x 2

Which expression is equal to 3z 5 2z 7 O 6z 31z 35 O 6z 31z 12 O 62 31z 35 O 5z 21z 12

Tom makes 244 25 in 5 days How much does he make in 2 days Tom makes in 2

On a map 3 inches represent 125 miles If two cities are 4 5 inches apart on the map how far are they actually apart The distance between the cities is miles Round to the nearest mile as needed