Algebra Questions

An Euler circuit always starts and ends at the same vertex True False

Determine whether the graph is connected or disconnected O Connected

Use the graph below to answer the question B Identify the vertex as odd or even Vertex D O even TH O odd

Determine whether the sequence of vertices is an Euler circuit LUI E D C D E A B C Yes B O No

Use the graph below to answer the question A O no E O yes mannk H Is vertex C adjacent to vertex D F

Determine whether the given path is an Euler Path an Euler Circuit or neither C O Euler path Oneither E F G E D G B C D B A O Euler circuit B CD

Use the graph below to answer the question 20 TE TE THE RE true D GF is a bridge false E G H F

Determine whether the graph has an Euler path Euler circuit or neither If the graph has an Euler path or circuit use Fleury s algorithm to find one B A Oneither E Euler path A B C A D C E F D F E D B Euler circuit A B D F D E C D A C B A

Use Euler s theorem to determine whether the graph has an Euler path but not an Euler circuit Euler circuit or neither The graph has 60 even vertices and no odd vertices Oneither Euler path Euler circuit

Determine how many vertices and how many edges the graph has 0 B OD 8 vertices 9 edges 9 vertices 8 edges O 9 vertices 9 edges O 9 vertices 7 edges F G H 1

Find the equation of the line with the slope 7 and the y intercept 0 C The equation of the line is Type an equation Type your answer in slope intercept form

Find the equation of the line with the slope 5 and the y intercept 0 8 8 The equation of the line is Type an equation Type your answer in slope intercept form Use integers or fractions for any numbers in the equatic

A connected graph has 30 even vertices and two odd vertices Determine whether the graph has an Euler path but not an Euler circuit an Euler circuit or neither an Euler path nor an Euler circuit and explain why The described graph has O neither an Euler path nor an Euler circuit an Euler circuit an Euler path but not an Euler circuit By Euler s theorem this is because the graph has O more even vertices than odd vertices more than two even vertices O exactly two odd vertices

Find all vectors in R perpendicular to v Draw a sketch of you answer in part 1 Include v in your ske 3

Linda wants to buy a townhouse that costs 75 000 The bank requires a 20 down payment The rest is financed with a 15 year fixed rate mortgage at 8 5 annual interest with monthly payments Complete the parts below Do not round any intermediate computations Round your final answers to the nearest cent if necessary If necessary refer to the list of financial formulas a Find the required down payment 0 b Find the amount of the mortgage c Find the monthly payment 0 X

Bonus 2 Find the circle passing through the three points 0 4 2 2 and 2 2

Problem 11 Describe all functions f x ax bx c such that f 1 f 6 3

W Bonus 2 Find the circle passing through the three points 0 4 2 2 and 2 2

Find the x and y intercepts of the function graphed below 10 10 OF 10 4

2 ABCD is a parallelogram m DAB x and m ABC z Find the values of w x y and z 2w W x 11 12 34 23 12

Use the slope and y intercept to graph the line whose equation is y x 1 Use the graphing tool to graph the line Use the slope and y intercept when drawing the line Click to enlarge graph F16 112 E4 Z 20 16 12 8 8 12 16

Use the given graph to evaluate the following expressions a f g 2 b f g 1 c fg 0 d a f g 2 y t x Q

sume that an economy is based on two industrial sectors agriculture A and energy E The technology matrix Mi A E 1 A E 0 6 0 1 0 2 0 4 M ow much input from A and E are required to produce a dollar s worth of output for A he input from A required to produce a dollar s worth of output for A is he input from E required to produce a dollar s worth of output for A is

2 If m VST 5x 23 and m VUT 8x 49 find mZSVT S WI Binbaup rope 200 000 U

X T 3x 7 8x Y Show Transcribed Text W what is the length of each segment in trapezoid TUVW UV

Math 178 Exam 1 Form A Fall 2023 Please show all your work and clearly box the final answer for each problem 1 Use the following graph of f x to find each limit 8 pts 44 Name 5 Find lim f x x 2 c Find lim f x d Find f 2 a b C d lim f x lim f x lim f x X S 2 Graph the following function to find the indicated limits and function values 13 pts a Find lim f x 24 2 lim f x 2 f x 5x 3 for x 2 x 1 for x 2 7 6 5 4 3 2 7 6 5 4 3 2 1 2 3 4 5 6 1234567 e Is the function continuous or discontinuous at x 2 Explain your answer using the definition of a continuous function Hint Verify the three conditions we discussed in class 4 pts 3 Use limit properties algebraic simplification tables of values and or graphs to find each limit if it exists If you are using table of values or graphing make sure you give me the table of values or the graph If the limit does not exist explain why and be descriptive as possible 6 pts each 4 x nt x a lim x 4 x 2 x 2x 8 b lim c lim x 25 x 5 x 5 d lim x 3 X 8 x 2 4 Find the equation of the tangent line to the curve g x x 2x 1 at 2 5 7 pts

7 The number of Apple iPads sold per year in millions t years after 2010 can be approximated by N t 0 106t 1 452t3 5 659t2 1 946t 20 714 8 pts a Find the rate of change for the number of iPads sold at t 13 b Interpret your answer in part a BONUS QUESTION 5 pts Find the derivative of the following function Write the final answer in exponential notation using only positive exponents f x 3x 4

5 A rocket can rise to a height h t t 0 5t feet in t seconds Find its accelaration 5 seconds after it is launched 8 pts 6 Find the derivative of the given functions Use the method of your choice Write final answers in exponential notation using only positive exponents 28 pts total a f x 4x5 2x 5x 3 2 x3 b f x 2x 6x 5 5 C f x x 1 x 1

Find the equation of the line whose slope is 0 and y intercept is 0 12 Graph the line The equation of the line is Type an equation Type your answer in slope intercept form

Find the equation of the line whose slope is 4 and y intercept is 0 1 Graph the line The equation of the line is Type your answer in slope intercept form

Graph the line 8x 2y 4 using the slope and y intercept Step by Step Solution Step 1 Solve the equation for y to write it in slope intercept form y mx b 8x 2y 4 2y 8x 4 y V 8x 4 2 Subtract 8x from both sides Divide both sides by 2 Simplify

Graph the line y 3x 6 using the slope and y intercept Step by Step Solution Step 1 Identify the slope and y intercept of the line y 3x 6 The slope is m Type an integer or a fraction

Draw the graphs of the two lines with the given properties on the same rectangular coordinate system Both lines pass through the point 5 3 One has a 1 3 slope of 3 and the other has a slope of Use the graphing tool to graph the lines Use the given point to graph the lines Click to enlarge graph 10 B 6 4 2 Ay 10 8 co 4 2 2 14 6 8

Draw a graph of the line that contains the given point and has the given slope 0 5 m 3 Use the graphing tool to graph the line Use the given point to graph the line Click to enlarge graph C 10 8 6 2 10 8 Ay 6 4 2 2 4 6

a Plot the points 5 4 and 1 7 in a rectangular coordinate system b draw a line through the points and c find and interpret the slope of the line a b Use the graphing tool to graph the line Use the given points to graph the line Click to enlarge graph CINE 20 F16 512 16 541 12 18 k 8 124 16

Find and interpret the slope of the line containing the given points 9 4 and 2 18 Select the correct choice below and if necessary fill in the answer boxes to complete your choice unit s when x increases by OA The slope of the line is Type integers or simplified OB The slope of the line is Type integers or simplified OC The slope is undefined The value of y will increase by fractions The value of y will increase by fractions unit s when x decreases by unit s unit s

Find the exact value of cos 45 Question 5 2 1 57 cos 45 0 7071 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Rewrite sec 54 in terms of its cofunction sec 54 0 Type an exact answer Simplify your answer Type any angle measures in degrees Do not include the degree symbol in your answer

Rewrite tan 12 in terms of its cofunction O tan 12 Type an exact answer Simplify your answer Type any angle measures in degrees Do not include

a 7 b 24 Suppose ABC is a right triangle with sides a b and c and right angle at C Use the Pythagorean theorem to find the unknown side length Then find the values of the six trigonometric functions for angle B Rationalize the denominators when applicable What is the length of side c Part 1 of 7 C Dints 0 of Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Find the exact value of sin 30 sin 30 Simplify your answer including any radicals Use integers or

Find the exact value of tan 45 tan 45 Simplify your answer including any radicals Use integ

Which expression represents x 8x 16 in factored form x 4 O O x 2 x 8 O x 4 x 4 0 x 4

Find the sum and product of the complex numbers 3 2i and 3 5i

Two sides of a triangle measure 36 m and 49 m One possible dimension of the third side is

What is the missing term in the factorization 100x 36 4 5x 5x 3 Enter your answer in the box

Which expression is the completely factored form of x 8y6 o x 2y x 2xy 4y O x 2y x 2xy 4y O x 2y x 4y4 3 x 2y

Factor 2xy 5x 12y 30 Enter your answer in the box

Factor 3x y 4 2 y 4 Enter your answer in the box

Graph the linear equation by the point plotting method or by finding intercepts 8y 16 0 Use the graphing tool to graph the linear equation Click to enlarge graph C 2016 12 B 20 16 12 8 4 4 Ay 8 12 16