Quadratic equations Questions and Answers

A bag contains 20 marbles of which 3 are blue and 7 are green One marble is drawn from the bag What is the probability that the marble drawn is not blue

Solve the following problem by first assigning variables and setting up a system of equations A cashier has a total denomination of 30 bills made up of ones fives and twenties The number of twenties is 9 more than the number of ones The total value of the money is 351 How many of each denomination of bill are there Answer Number of ones is Number of fives is

Instruction Do not write answers only For each problem show step by step the work leading to your final answer to receive credit Your completed work must be submitted by the due date Late submission will not be accepted Question 1 6 points Solve the system of equations by elimination Show work x 6 5 2y x 10 Read the detailed requirements for presenting and submitting class Activities from the Tentative Course Schedule posted on Canvas x 2 3y 2 5 1 3 Answer

In circle L with m KLM 30 find the m KNM M K L

Graph the function f x x 1 2 7 by starting with the graph of y x 2 and using transformations shifting stretching compressing and or reflecting Use the graphing tool to graph the function Click to enlarge graph RIES EXCE 10 6

In the expansion of a b c find the coefficient of the term containing a b The coefficient is Simplify

The volume of a rectangular prism is given by 6023 432 19x 3 The height of the prism is given by 4x 1 Find an expression for the area of the base of the prism Provide your answer below

snowflake gets blown sideways 2 ft for every 4 ft it falls downward In one such movement what is the total distance the snowflake travels and in what direction O 3 46 ft at 28 6 from straight downwards O 4 49 ft at 28 6 from straight downwards O 4 47 ft at 26 6 from straight downwards 3 46 ft at 36 6 from straight downwards

Rewrite without parentheses 3bc 8b 6b c 76 Simplify your answer as much as possible

6 Added 7 You can add unlike square roots You can multiply or divide like square roots 9 You can multiply or divide unlike square roots 10 The Greek letter 7 is pronounced like pie 11 Another way of saying that monomials can be added or subtracted is to say they can be combined You can add like square roots 8 12 The Subtraction Property of Regrouping is useful when dividing monomials 13 When adding monomials both the coefficients and exponents are added 14 If no number is indicated as a coefficient or exponent to a variable the number 1 is understood to be there 15 When multiplying two different variables both the coefficient and exponent are multiplied Exercise 4 Fill in the blanks with the correct word Choices are listed below and some will be used more han once Subtracted Multiplied When adding like monomials the coefficients are Divided

mtegration limits M rks will be deduct i units are in degrees Units need to be in radians 1 Fun Village has North America s largest Ferris wheel The Ferris wheel has a diameter of 56 m and one revolution took 2 5 min to complete Riders would start at the bottom which is 0 5 m above the ground and could see Niagara Falls if they were higher than 50 m above the ground a Create an equation that represents the height of a rider above the ground as a function of time 4 b Using the equation above determine the time s at which the rider reaches a height of 5 m during the second revolution 4

The population of fish in a pond can be modeled by f x 10000 fish x months after a new pond was stocked What is the carrying capacity upper limit of the number of fish that can be sustained by the pond A 1 199 10000 O 200 O 199 50

Consider the following Cube roots of 1 3i 729 2 a Use the formula z rcos co Zo Z Z Z 0 2 k n 2 i sin 0 2 k n b Write each of the roots in standard form Round all numerical values to four decimal places Zo to find the indicated roots of the complex number Enter your answers in trigonometric form Let 0 0 2

For log 6 a Estimate the value of the logarithm between two consecutive integers For example log 7 is between 2 and 3 because 2 7 2 b Use the change of base formula and a calculator to approximate the logarithm to 4 decimal places c Check the result by using the related exponential form Part 0 3 Part 1 of 3 a Estimate the value of the logarithm between two consecutive integers

Jse log 2 0 376 log 3 0 621 and log 5 0 778 to approximate the value of the given logarithm to 3 decimal places Assume that b 0 and b

Evaluate L 1 where f t sin 3r L f 1 F s f 0

Determine the quadratic regression for the data set below 1 95 2 100 3 105 4 110 5 105 6 100 Round to the nearest hundredth if needed

An exponential function in the form y 6859 b contains the point 3 1 What is the value of b Provide your answer below b 0

What value of a makes the equation 5e 34 true Round your answer to the nearest tenth Provide your answer below

Given the following functions find and simplify f g 8 5 Provide your answer below f g 8 5 f x 2 1 g x 82 4

Use the power rule to simplify log 58 Provide your answer below

Describe the end behavior of the function f x 8 z 6 z 4 5x 3 Provide your answer below As x goes to co f x goes to As x goes to 00 f x goes to

Part 1 of 2 Points 0 of 1 Save A jogger ran 6 miles decreased her speed by 1 mile per hour and then ran another 7 miles If her total jogging time was 3 5 6 hours find her speed for each part of her run

et P f x a x a x ao and g x b x b x bo We then define Addition f x a b x a b x a b Scalar multiplication rf x ra x ra x rao Show that P is a vector space

A farmer is building a triangular shaped pig pen where the third side runs the length of the barn If the barn has a length of 20 meters and he has fencing already up for one side that runs 28 meters long with an angle between these two measuring 50 find the length of the other side of his pig pen that still needs fencing Also find the area of the pig pen Round each answer to two decimal places

At Timmy s cafe to buy one sandwich two cups of coffee and three doughnuts costs 8 50 One sandwich one cup of coffee and one doughnut costs 6 00 How much does it cost to buy three sandwiches two cups of coffee and one doughnut

Use the graph of y f x to graph the function g x 2f x 4 3 86 y f x Ay ob 8 6 4 75 4 66 ext S do X Q

The ages of the students in a statistics class are listed below 20 18 17 17 21 21 21 22 19 21 21 19 20 18 20 19 20 18 19 22 19 19 22 18 Complete the frequency table Provide your answer below Age 17 18 19 20 21 Frequency

To study the height of all the students in his school Christopher records all of the heights of all of the students in his class Which type of sampling is used Select the correct answer below O O Stratified sampling Systematic sampling Cluster sampling Convenience sampling

QUES nickel dime quarter Given A penny nickel dime quarter dollar B C nickel dime quarter half which of the following are true There may be more than one correct answer Select all that apply Select all that apply ACB

Abby is collecting data on the heights of her classmates What type of data is this Select the correct answer below O qualitative data discrete quantitative data continuous quantitative data Onone of the above

The quadratic regression associated with the benefit of exercising f a compared to number of 30 minute exercises a performed each week is f r 0 2619 3 42r 1 2857 Using the quadratic regression estimate the success factor when someone does 75 minutes of exercise per week Round your answer to one decimal place Provide your answer below

Question Using the quadratic regression f x 12x 25x 764 estimate the value using quadratic formula when they w is 1500 Only positive a values can be used in the equation Round your answer to the nearest whole number

The quadratic regression corresponding to the number of jogging strollers sold each year from 2007 to 2012 where a 1 corresponds to year 2007 is 2 9286x 20 243x 36 4 Use the quadratic regression to project what future year the number of jogging strollers will equal 38 Round your answer to the nearest whole number Do not include a comma in your answer Provide your answer below year

Using quadratic regression we find that the height of an airplane y in hundreds of feet above sea level a hours after takeoff is most closely modeled by the equation y 8 2x 85 6x 90 3 What is the height of the airplane in feet after 7 hours Remember that the function gives values in hundreds of feet Provide your answer below

Entomologists have discovered that a linear relationship exists between the number of chirps of crickets of a certain species and the air temperature When the temperature is 70 the crickets chirp charps at the rate of 120 Find N as a function of 7 and use this formula to determine the rate at which the crickets chirp when and when the temperature is 80 they chirp at the rate of 160 the temperature is 109 F min

For the following G P find the nth term statec a 8 24 72 find T find T 5 b 30 5

The demand function Q and total cost function T g of a commodity are given by the equations P 100 4q and TC 320 4q where P and q are the price and quantity respectively Determine the quantity that must be produced and sold at breaks even O a q 4 org 20 O b q 28 O c q 4 org 20 O d q 28

The quadratic regression relating the time a in seconds versus the velocity f a in feet sec of a quarter that s dropped from a building is given by f x 16x 1000 Use the quadratic regression to estimate the time when the velocity is 3000 ft s Round your answer to two decimal places Provide your answer below

Three circles of radil 6 5 9 7 and 12 5 cm are mutually tangent Find the area bounded by the three circles area cm

In the diagram below point A is the centre of the circle and the radius r 7 8 inches w 54 and y 73 What is the arclength denoted by the central angle a W A a r Y ieter include the units in your answer Round to the nearest tenth

Solve x 2 23 Simplify your f there is mor f there is no s

At the beginning of June Bezco Toy Company budgeted 5 000 toy action figures to be manufactured in June at standard direct materials and direct labor costs as follows Direct materials Direct labor Total The standard materials price is 4 00 per pound The standard direct labor rate is 18 00 per hour At the end of June the actual direct materials and direct labor costs were as follows Actual direct materials Actual direct labor 50 000 36 000 86 000 49 600 34 020 83 620 Total There were no direct materials price or direct labor rate variances for June In addition assume no changes in the direct materials inventory balances in June Bezco Toy Company actually produced 4 850 units during June Determine the direct materials quantity and direct labor time variances Round your per unit computations to two decimal places if required Enter a favorable variance as a negative number using a minus sign and an unfavorable variance as a positive number Direct materials quantity variance Direct labor time variance 1 100 X

If Tanisha has 100 to invest at 7 per annum compounded quarterly how long will it be before she has 200 If the compounding is continuous how long will it be Compounding quarterly it will be about years before Tanisha has 200 Round to two decimal places as needed

Find the principal needed now to get the given amount that is find the present value To get 600 after 3 years at 3 compounded quarterly The present value of 600 is Round to the nearest cent as needed

Use a system of equations to solve the following problem A private jet flies the same distance in 8 hours that a commercial jet flies in 9 hours If the speed of the commercial jet was 190 mph less than 2 times the speed of the private jet find the speed of each jet Answer How to enter your answer opens in new window speed of private jet speed of commercial ier mph Imph Keypad Keyboard Shortcuts

If f x In x g x x and h x x find the following a fog x What is the domain of f o g b gof x What is the domain of g o f c fog 7 d f o h x What is the domain of f o h e foh e

Milan is saving up money for a down payment on a condominium She currently has 2525 but knows she can get a loan at a lower interest rate if she can put down 3258 If she invests the 2525 in an account that earns 5 3 annually compounded quarterly how long will it take Milan to accumulate the 3258 Round your answer to two decimal places if necessary

Does prison really deter violent crime Let x represent the percent change in the rate of violent crime and y represent the percent change in the rate of imprisonment in the general U S population In 7 recent years the following data have been obtained Use your graphing calculator to find the line of best fit for the given data Round to 3 decimal places as needed B y 5 8 6 1 6 4 6 7 7 7 3 7 6 7 9 0 42 0 42 0 38 0 25 0 21 0 23 0 4 0 42 Linear Regression Equation Use your regression equation to predict the percent change in the rate of imprisonment when the percent change in the rate of violent crime 8 11

Consider the Sturm Liouville system x y xy 2y 0 220 and y e 0 y 1 0 a 10 marks Find all eigenvalues and eigenfunctions b 2 marks Are the eigenfunctions obtained in part a orthogonal Justify your answer