Quadratic equations Questions and Answers

A triangle lies between two parallel lines m2A 43 m2B 32 m2 1 B 2

Use a calculator spreadsheet or another tool to solve for the unknown sides of the given right triangle The length of the hypotenuse is 13 a is the length of the side opposite the 10 angle and b is the length of the side opposite angle B a a Round your answers to four decimal places Number B 13 b 10

17 1 4 1 3 2 10 2 Write an equation for the proportional relationship shown below 2 2 1 8 3 3 2 9 3 3 Write an equation for the proportional relationship shown below 15 4 3 2 12 9 6 6 18 4 4 Write an equation for the proportional relationship shown below 20 10 4 5 16 12 10 8 30 5 Write an equation for the proportional relationship shown below 10 50 12 6 21 14 5 20 15 45 12 60 20 10 30 20

Question 9 2 2 19 Part 2 of 6 Find the exact values of the six trigonometic functions for the following angle 45 sin 45 2 2 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationaliz cos 45 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationali

total cost in dollars 60 50 40 10 70 30 20 Part 2 A 10 20 30 40 50 square feet of carpet 60 70 1 Create a table of the values shown in the graph at left 2 What is the cost per square foot of carpet 3 Write an equation for the cost y of x square feet of carpet 4 If an apartment is 800 square feet how much would it cost to put in carpet 5 If a roll of carpet costs 600 how many square feet is it 6 An apartment has 3 rectangular rooms The living room measures 20 feet by 30 feet the bedroom measures 15 feet by 20 feet and the kitchen measures 10 feet by 40 feet If the owner wanted to put carpet in the living room and bedroom how much would it cost

Water used gal 50 40 30 20 10 O 2 Water Use refer 6 8 10 Partner Practice 1 Construct a table for the relationship between time and water used X y 2 How much water is used each minute Time min 3 Write an equation for the relationship between the time and water used 4 How much water would be used in 30 minutes 5 If 300 gallons of water were used how much time would it take 6 How many gallons of water would be used in 2 and a half hours

4 Given the four different brands of dish soap below which brand costs the least per ounce Dish Soap Prices Brand Lots of Suds Bright Wash Spotless Soap Lemon Bright Price 0 98 for 8 ounces 1 29 for 12 ounces 3 14 for 30 ounces 3 45 for 32 ounces 0 122 0 10

4 Equation X y 2 4 6 6 8

Scenario 2 The number of hours that it takes Angie to read a book is directly proportional to the number of pages of the book It takes Angie x hours to read y pages The equation that represents the relationship is y 30x 1 How long would it take Angie to read a book that contains 360 pages l hars 2 How many pages could Angie read in 10 hours 300 Pages 3 If Angie has 4 books with an average of 175 pages each how long would it take her to read

Part 2 Using Unit Rate to Make Comparisons 1 Jean sells M Ms to friends at 4 for 5 cents The machine at the store sells 9 for 25 cents Which is the better deal 2 The hardware store sells 4th of July sparklers for 19 cents each The fireworks stand charges 85 cents for four Where would you purchase sparklers The 3 Frosted Flakes has 11 grams sugar per ounce and Raisin Bran 13 grams per 1 4 ounces Which cereal has more sugar per ounce

Fill in the blanks so the resulting statement is true A measure that is used to describe the strength and direction of a relationship between variables whose data points lie on or near a line is called the r COL A measure that is used to describe the strength and direction of a relationship between variables whose data points lie on or near a line is called the to r ranging from r ranging from r causation coefficient regression line correlation coefficient regression coefficient to

7B HW Decide whether the given ordered pair is a solution of the given system 1 4 3x 5y 23 4x 2y 12 Question 8 4 1 15 Is the ordered pair a solution to the equation Yes O No

Solve the equation and check the proposed solution 497 20 z The solution set is Simplify your answer

a b c x KEZ 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 which is given by x t lim x 1 1E1 b t b Thus x 1 lim xo f f s X s ds x 1 EB xo b for each 1 to b t b MKk k 1 x 1 x 1 1 2 Finally the validity of this integral equation has the following two implications X x f s x s ds x 0 x 1 to b t b k20 x lim ff s x s ds x lim f s x s ds x f f s lim x s ds x f f s x s ds Thus the function tx 1 satisfying the integral equation x 1 x f f s x s ds for all r te b t b dx dt 0 df f s x s ds f t X t This now proves that the curve X 1 8 4 89 thus obtained is a solution of the initial value problem

About the sequence keZ we have the following a x 1 B x b for each te to b t b MKk k 1 1 x 1 te t b t b k20 c x keZ is uniformly Cauchy on t b to b verification of these properties is left for the reader We consider the uniform limit of the sequence x 1 8 to 8B x b which is given by XI lim x 1 11 b to b b Thus x t lim x 1 2 x lim ff s x s ds x f S Finally the validity of this integral equation has the following two implications X 1 x f s x s ds x 0 xo dx dt f s x s ds x f f s lim x s ds x f s x s ds Thus the function tx 1 satisfying the integral equation x 1 x f s x s ds for all t 16 b 1 b aff 0 lim f s x s ds ff s x s ds f 1 X 1 This now proves that the curve X 10 8 1 82 thus obtained is a solution of the initial value problem

2 f x tek fonksiyon g x ift fonksiyon olmak zere f 2 g 2 11 f 2 g 2 3 oldu una g re f 2 ka t r A 3 B 4 C 5 D 6 E 7

Boyu 4 metre iken dikilen han meli i e i her ay 0 5 metre b y mektedir Han meli i e inin x ay sonra boyu g x fonksi yonu ile ifade edilmektedir Buna g re Yusuf Bey in dikti i han meli i e inin boyu 6 ay sonra ka metre olur A 4 B 5 C 6 D 7 E 8

ite sec 14 in terms of its cofunction 14 0 e an exact answer Simplify your answer Type any angle measures in degrees Do not include the de answer

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 a 7 b 24 What is the length of side c A c 25 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression sin B 24 25 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression cos B Simplify your answer including any radicals Use integers or fractions for any numbers in the expression b

To go on a summer trip Henry borrows 700 He makes no payments until the end of 5 years when he pays off the entire loan The lender charges simple interest at an annual rate of 3 Answer the following questions If necessary refer to the list of financial formulas a How much total interest will Henry have to pay b What will the total repayment amount be including interest X S

16 yd 4 yd 9 yd 8 yd 7 yd

basamakl rakamlar asal ve farkl olan en b y k tek tam say ile iki basamakl rakamlar asal ve farkl olan en k k ift do al say n n toplam ka t r D 681 A 889 B 785 C 730 E 655

7 10 Correct Answer HUNTER FINDLEY The distance that a free falling object falls is directly proportional to the square of the time it falls before it hits the ground If an object fell 53 ft in 10 seconds how far will it have fallen by the end of 6 seconds Round your answer to the nearest integer if necessary Keypad Keyboard Shortcuts

Correct a varies directly as b and inversely as the square of c If a 218 when b 3 and c 6 find a if b 2 and c 7 Round your answer to two decimal places if necessary Answer Keypa

Suppose that y is proportional to the cube root of x and that y 57 when x 3375 What is y when x 1728 Round your answer to two decimal places if necessary Answer y Keyboard

Problem 4 Find the matrix A in terms of B C and D if 5BA C D A B DC B SCDB C CDB D 5BDC E BDC F CDB G 5CDB H 5B Problem 4 Select v

The electric power varies directly as the square of the voltage V and inversely as the electrical resistance R If the voltage is 15 volts and the electrical resistance is 3 ohms then the electric power is 75 watts Express the electric power as a function of voltage and electrical resistance Answer P V R Keypac Keyboard Shortcu

roblem 1 Solve for the matrix A in the following equation A F AT 41 1 2 73 4 35 28 2 10 5 18 Problem 1 Select v 2 B G 39 2 3 C 5 25 6 10 12 H 20 18 2 2 10 4 21 6 D 14 2 4 25 E 10 4 2

oblem 3 Find the matrix A in terms of B and C if 34T 5CB T 5A 5B A SCTBT 5B B SBTCT 5B C SBTC 5C D SCBT 5C E SCBT F SCTBT 5B G SBCT 5B H SBTCT 5B Problem 3 Select Y

Problem 2 For which 2 values of a is the following matrix not invertible a 3 3a 9 2 a 4 Problem 2 Note If there is only one value of a then enter it twice in the answer box e g 8 8 separate your answers with a comma If there is only one value of a then enter it twice in the answer box e g 8 8

A video store manager observes that the number of videos sold seems to vary inversely as the price per video If the store sells 570 videos per week when the price per video is 17 40 how many does he expect to sell if he lowers the price to 13 10 Round your answer to the nearest integer if necessary Answer Keypad Keyboard Shortcuts

Find cos A csc B for right triangle ABC if a 3 b 2 O 2 13 b 13 1 13 2 d 2 13 13 3

Use the graph below to answer the question C D E Which of the following is NOT a path starting at vertex A and ending at vertex E O A C D E O A D G E O A B C D E O A D E

When using Fleury s algorithm to find an Euler circuit always begin with an even vertex True False

Which of the following is another way to represent the graph shown De 8 13 O E E

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

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

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

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

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

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

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

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

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