Quadratic equations Questions and Answers

the domains of the following functions using interval notation m x h x Domain of m h x Domain of h m x Domain of 1 Add file Question 8 Solve for a log x log x 1 3

Find the equation of the quadratic function y ax bx c whose graph is shown on the right Select three points whose coordinates appear to be integers y Simplify your answer Type an expression using x as the variable

I have 20 000 to invest I plan to diversify and invest in three different investments treasury bills that yield 5 simple interest treasure bonds that yield 7 simple interest and corporate bonds that yield 10 simple interest I want to earn 1390 per year in income from these investments I plan to make my investment in treasury bills to be 3 000 more than my investment in corporate bonds How much money should I place in each investment 20 points

So far this semester we have learned about quadratic equations and the various forms they can take and how we can solve them We looked at how they ca present in our everyday lives as well One example is calculating the area of a room Another example is figuring out a profit This can be from selling lemonade to big businesses figuring out th Figuring out the speed of something for example when you go on a kayaking trip Throwing a ball or a rocket also uses the quadratic equation All of these are ways we use the quadratic equation in life Task Answer the following questions in the discussion board Each question should be answered with at least 2 sentences In your answer you need to mathematical terms 1 Give an example of something you do in your life that uses the quadratic equation If you can t think of one use one of the examples above 2 Explain how the quadratic equation would be used in that situation 3 How has this semester so far helped you re imagine the way quadratics are presented and solved You need to answer each question with at least 2 sentences You are also required to provide a response to one of your classmate s posts Everyone be positive and respectful with comments that help everyone to learn and see others viewpoints For example you can respond to another post to let know that you enjoyed the example they posted and the reason why it was helpful This rubric will help guide your reflection tations Meets Expectations Exceeds Expec

What function contains the points 0 2 and 2 18 F x 2 x F x 3 x F x 2 3 x F x 2 3 x f x 3 2 x F x 3 x 3

Find the inverse of each function Then graph the function and its inverse mx bo 5 2 S x 3 5 4 3 2 1 3 f n 6 4n 3 554 4 f x 2x 1 5 5 4 3 2 beo

MAKING AN ARGUMENT Your fri measures the circumference of a fitness ball as 2 36 meters and says The volume of the ball is 0 2219652627 cubic meters Do with your friend s statement Explai GO

0 Alejandro drew two parallel lines cut by a transversal He measured two of the angles and und that both measured 86 Circle the name of any student who made a true statement abou me two angles ABIGAIL The two angles must be on opposite sides of the transversal MALIK The two angles could be corresponding angles FLETCHER The two angles could be a linear pair

2 1 Short Questions 4 Pts Each Use the given graph to answer the following questions a f 1 b List all x values such that f x 0 5 4 3 2 4 4 3 d IN X Solve the logarithmic equation Give your answer in the form of a fraction or integer log x 2 State the domain of f x 4x 1 in interval notation

Lines A and B are parallel lines cut by a transversal Use the lines and the angles formed to answer the questions below 1 Angle 3 and Angle 6 are examples of which type of angle pair A Alternate interior angles B Same side interior angles C Vertical angles D Corresponding angles 4 Which of the following angles would not be congruent to the measure of 27 A 22 B 23 C 26 D 28 7 If the m27 115 find the measure of 22 2 Angle 1 and Angle 5 are examples of which type of angle pair ABIGAIL The two angles must be on opposite sides A Same side exterior angles B Alternate interior angles C Vertical angles D Corresponding angles 5 Which of the following is an example of corresponding angles A 28 and 24 B 25 and 27 C 21 and 27 D 23 and 25 8 If the m25 is 63 find the measure of 23 3 MALIK The two angles could be corresponding 4 5 7 6 8 B 3 Angle 6 and Angle 7 are examples of which type of angle pair A Alternate exterior angles B Same side interior angles CVertical angles 27 and 28 B42 and 43 C 21 and 27 D 26 and 24 D Corresponding angles 6 Which of the following is not an example of supplementary angles 115 1170 10 Alejandro drew two parallel lines cut by a transversal He measured two of the angles and found that both measured 86 Circle the name of any student who made a true statement about the two angles 9 If the mz1 is 57 find the measure of 26 FLETCHER The two angles could be a linear pair

Use the rules and if necessary the definition for ordering e classes to arrange the following in order from lowest to highest Ign 1 0001 Ign gn 4 24n 16n 5n

Exercise 6 dual of transportation problem Quantities a am of a certain prod uct are to be shipped from each of m locations and received in amounts b bn at each of n destinations Associated with the shipping of a unit of product from origin i to destination j is a shipping cost C It is desired to determine the amounts xij to be shipped between each origin destination pair i 1 m j 1 n so as to satisfy the shipping requirements and minimize the total cost of transportation a Formulate this as a linear program in mn variables 11 mn subject to m n equality constraints with the nonnegativity conditions xij 0 b Taking the linear program you wrote in a as the primal program state the corresponding dual program

e itliklerden hangisi do A 11 3 20 34 C 1 3 2 3 3 c D 7 2 5 2

Given that a is a nonzero parameter solve the following equation for x 2ax ay 4a 2x y 6 a O 2 5a 2 5

2 A system of equations is given as 8x x 3x3 16 x x 4x3 3 x 4x x3 9 Explain whether this system can be solved using Gauss Seidel iteration method yes solve using Gauss Seidel iteration method with the initial approximation 1 1 If no solve using Gauss elimination method

3 8 3 15 If the answer is not an integer enter it as a decimal rounded to the nearest hundredth if neede 0 861 X

Sarah has whole milk which contains 3 25 butterfat by volume and one type of low fat milk which contains 1 butterfat by volume Which of the following systems could be used to determine the amount of whole milk w in ounces and the amount of low fat milk I in ounces that Sarah should mix to obtain 32 ounces of alow fat milk with 2 butterfat by volume A 0 011 0 0325w 32 1 w 0 02 B 0 01 0 0325w 32 1 w 0 64 C 0 011 0 0325w 0 02 1 w 32 D 0 011 0 0325w 0 64 1 w 32

The pH scale for acidity is defined by pH log10 H where H is the concentration of hydrogen ions measured in moles per liter M A The pH of pure water is 7 0 Calculate the concentration of hydrogen ions in moles per liter M H B The pH of milk is 6 6 Calculate the concentration of hydrogen ions in moles per liter M txal M

A manufacturer of bicycles builds racing touring and mountain models The bicycles are made of both steel and aluminum The company has available 26 400 units steel and 19 500 units of aluminum The racing fouring and mountain models need 11 12 and 22 units of steel and 9 24 and 15 units of aluminum respectively Complete parts a through d below a How many of each type of bicycle should be made in order to maximize profit if the company makes 0 per racing bike 13 per touring bike and 24 per mountain bike Let x be the number of racing bikes set x be the number touring bikes and let x be the number of mountain bikes What is the objective function 2x Do not include the symbol in your answers

Gravel is piled in the shape of a cone The circumference of the base is 228 ft The slant height is 42 ft Find the volume of gravel in ft 803 94 ft If gravel weighs 3 200 lb yd how many 22 ton truckloads are needed to transport the gravel Use the Metric and U S Conversion table to find the conversion factor s 22 ton truckloads

The circular tank with a conical lid in the figure below is made of 12 in steel weighing 19 8 lb ft 13 0 ft 24 2 ft 4 80 ft 18 4 ft a What is the total weight of the top in lb 18900 Xlb b What is the total weight of the top sides and bottom of the tank 101010

constant term is 1 6 coefficient is The expression represents a quartic 2 7x 9x x I polynomial with the leading term is 3 x terms T and the leading

Find the maximum possible value and the minimum possible value of the objective function f 6x 2y subject to the following constraints 4x y 20 x y 8 x y 2 x20 y20 GEITE The maximum value of the objective function subject to the constraints is The minimum value of the objective function subject to the constraints is ET P 0 0 4 4 x y 5 0 XX C

Integrate the vector function F xi yj zk over the surface of the unit sphere 10

age number e points scored in those games was 226 with a sample variance of 122 5 Assuming that the underlying distribution of the data is normal and that these observations are independent and identically distributed construct a 90 confidence interval for the true mean number of points of an NBA game Lower bound 219 14 Upper bound 232 86 Lower bound 217 49 Upper bound 234 51 Lower bound 220 85 Upper bound 231 15 Lower bound 213 62

Obtain the expression for the gradient vector Vf and Hessian matrix V for the following functions of n variables 1 T a f x x Ax b x where A is symmetric

Consider the system dr dt x x 1 y dy dt where and y denote the sizes of two interacting populations 1 1 How does the species and they species respectively behave in the absence of the othe species 1 2 Describe the type of interaction between the two species e g competition predator prey etc 1 3 Draw the phase diagram note that phase diagrams drawn by an automated plotter will b awarded zero and use it to predict the outcome of the system if initially to 2 yo 2 y x 2

Consider the function f x x 7 x 1 x 8 x 121 Where is the graph of f x tangent to the z axis

A B C D Let y t be the solution of the initial value problem d y dt dy a by f t dt a 0 b 0 y 0 0 0 0 obtained by the method of Laplace transform Then at 1 y t Te 2 f t 1 dt y t f e at y t y t f re f t t dt br Tez f t 1 dt bt ez f t 1 dr a b a 4b 0

In the image below If the bearing of the traverse line FI is 60 determine the bearing of the travers ine HG Provide your answer correct to the nearest degree F Azim 60 00 52 15 52 15 72 45

Evaluate the integral 4 6 cos t i sin t j sec t k o 6 The result is i j i O j O k Type exact answers using and radicals as needed

EXTRA CREDIT Geometry The perimeter of the trapezoid is 8x 18 Find the missing length of the lower base

Identify the values for the domain of the function 5 4 3 20 5 4 3 2 1 0 1 2 3 4 5 6 1 234 AY 5 6 c A 2 1 0 1 2 B 1 2 1 1 2 0 1 1 2 2 C 1 1 2 D 2 1 1 1 0 2 1 1 2 2

In rectangle ABCD E is the midpoint of AB and F is on CD so that DF 2CF As well AE AD 1 The line segments AC AF DB and DE are drawn Label the intersections of BD and AC BD and AF DE and AF and AC and DE by W X Y and Z respectively as shown Determine the area of quadrilateral WXYZ W A E X 2 B A

21 3 cos 223 i sin 223 22 6 cos 47 i sin 47 Find the product 21 22 Enter an exact answer

Consider the following 14x 16xy 9y 42 Use a graphing utility to graph the conic Determine the angle 0 0 90 through which the axes are rotated in degrees Round your answer to two decimal places

5 points When there is a 50 mile per hour wind an airplane can fly 675 miles with the wind in the sam time that it can fly 450 miles against the wind Find the speed of the plane when there is no wind

Mr Dass gives his students a multiple choice test Every correct answer is worth 5 points and every incorrect answer takes away 3 points Ray earns 63 points on this test How many questions could there be on the test if there are not more than 26 questions A 10 B 14 C 19 D 21 E 25

One pan pizza and two beef burritos provide 3950 calories Two pan pizzas and one beef burrito provide 4060 calories Find the caloric content of each item One pan pizza contains calories

A bird flies against a wind that is going 4 miles per hour and takes 2 hours to travel a certain distance When flying with th current the bird only takes 0 5 hours to travel the same distance Approximately how fast would the bird fly in miles per hour without wind current assuming it flies at a constant rate A 6 0 mph B 6 5 mph C 6 67 mph D 7 0 mph E 7 5 mph

A logistic growth model for world population f x in billions x years after 1949 is f x According to this model the world population will be 10 billion in 46 Round to the nearest whole number as needed 12 57 0 026x 1 4 11e According to this model when will the world population be 10 billion

35 Find the exact value of sin a 3 if cos a and sin B and the terminal side of a lies in quadrant IV and the terminal side of lies in quadrant III Enter your answer exactly to avoid rounding errors

In the figure below quadrilateral ABCD is inscribed in circle P The radius of circle P is 5 units 18 What is the length of BCD Either enter an exact answer in terms of or use 3 14 for and enter your answer as a decimal

rite an equation for the graphed function f x 110 1 6 6 1 0 Click on graph to enlarge

Consider the function F x 3 4x Determine the angle the graph of F r makes with the x axis A line forms an angle with the z axis whose measure is 0 62 radians If the x intercept is 2 then construct the equation of the line For cach of the above explain your method Is there anything in com mon Is there more than one possible solution

Remember even if you enter an answer rounded to a set number of decimal places if you use that number in a future calculation you should use all of the decimal places reported on your calculator Solve triangle ABC if ZA 35 9 a 186 2 and b 245 7 sin B round answer to 5 decimal places There are two possible angles B between 0 and 180 with this value for sine Find the two angles and report them so that ZB is the acute angle LB and ZB round these and all remaining answers to 1 decimal place Thus two triangles satisfy the given conditions triangle A B C and triangle A B C2 Solve the first triangle A B C LC and C Solve the second triangle A B2 C2 LC and C

Answer the following parts using the rational function r x 2x 1 x 3 x 3 x 3 PART A 1 MARK State the domain in interval notation PART B 4 MARKS Explain how to determine the intercepts and then determine them PART C 2 MARKS Explain how to determine vertical asymptotes of a rational function List any for r x If there are any hol list them PART D 2 MARKS Explain how to determine horizontal asymptotes of a rational function List any for r x PART E 2 MARKS Use Desmos to graph r x Label the intercepts and asymptotes to verify the answers you determined fo the previous parts of this question Remember that you must show the information used to produce your graph in the screensh

a bez a 19 x b x 7 ab arp m n n alabilece i en b y k de er ka t r What is the largest value stands for a b multiplication A 48 B 36 C 32 D 30 E 24 Vo KARAB K N VERS TES Y S 2020

Rewrite the following equation in terms of base e Round any natural logarithms to three decimal places y 83 7 7 Type the model in terms of base e

Begin by graphing f x In x Use transformations of this graph to graph the given function Graph and give the equation of the asymptote Use the graphs to determine the function s domain and range g x 5 Inx Graph g x 5 In x Graph the asymptote of g x as a dashed line Use the graphing tool to graph the function Click to enlarge graph X What is the equation of the vertical asymptote of g x What is the domain of g x 5 In x Simplify your answer Type your answer in interval notation What is the range of g x 5 In x Simplify your answer Type your answer in interval notation 6 12 19 6 49 Ay