Quadratic equations Questions and Answers

Use the graph of the rational function to complete the following statement As x1 f x As x1 f x O LV 3

Lucy earns 75 000 and is filing her taxes as a single woman What amount of taxes does she owe Type in the number and do not include commas decimals dollar sign

Find the lengths of the sides of the right triangle Show that these lengths satisfy the Pythagorean Theorem Enter your answers from smallest to larg d d ds Show Transcribed Text d 1 1 1 d d3 Z These lengths satisfy the Pythagorean Theorem because Od d d 6 2 44 5 4 0 1234 3 45 36 62 3 5 1 These lengths satisfy the Pythagorean Theorem because Od d d3 021 12

Write the equation of the ellipse that has a center at 3 4 a vertex at 3 8 and a covertex at 1 4

1855 a person sold a house to a lady for 24 If the lady had put the 24 into a bank account paying 4 interest how much would the investment have been worth in the year 2010 if interest were compounded in the following way monthly b continuously If compounded monthly the investment would be worth in 2010 Round to the nearest dollar as needed

Graph functions f and g in the same rectangular coordinate system Graph and give the equations of all asymptotes 1 f x 6 and g x 6 6 1 Graph f x 6 and g x 6 and graph any asymptotes as dashed lines Use the graphing tool to graph the functions Click to enlarge graph 10

Use transformations of the graph of f x e to graph the given function Be sure to give the equation of the asymptote Use the graph to determine the function s domain and range ex h x C Graph h x e Use the graphing tool to graph the function Click to enlarge graph 10 Ay

The perimeter of a rectangle is 50 feet Describe the possible lengths of a side if the area of the rectangle is not to exceed 144 square feet Express the possible lengths of a side Type your answer in interval notation

1 x 8 6 0 anty set Do not solve the inequality O A The solution set is x Type an inequality OB The solution set is the empty set Next question What is the solution set Select the correct choice below and if necessary fill in the answer box to complete your choice

5 Let 4 6 k 7 Find the value of k so that is orthogonal to the vector 2 4 8

A company manufactures 2 different types of garden sheds The manufacturing time required per shed is Shed A 2 hours machine time 3 hours craft time Shed B 3 hours machine time 6 hours craft time 20 hours of machine time is available per day whilst 40 hours of craft time is available The company makes R 60 00 profit on Shed A and R 80 00 on Shed B Find the objective function 60x80y P 60x 80y P 35x 40y P None of the above

st of producing the 50th product is 6 20 it cost 6 20 to incr oduction from 49 to 50 units of output Suppose the marginal in dollars to produce x thousand mp3 players is given by the nction C x x 120x 7300 2 How many players should be produced to minimize the arginal cost What is the minimum marginal cost To minimize the marginal cost e produced The minimum marginal cost is thousand mp3 players s

Therefore the coefficient of a is m n m n BE BE 1 Assuming that a occurs in the k 1 th term of the expansion 1 a we obtain m n T C 1 a m C a Comparing the indices of a in a and in Tk 1 we obtain k n Therefore the coefficient of an is m n m n n m n n n m m n m n m m n m C 2

7 Use the given information to determine the remaining five trigonometric values OR USE sin cos 0 1 to do this a sin 0 X b tan0 x viu a X X 2 a a x 2 Show Transcribed Text 2 0 G H H 1 x H

Find the middle terms in the expansions of 3 6

x 2x 1 Find the domain of the function f x x 8x 12

wheel makes 360 revolutions in one minute Through how many radians does it turn in

Use the graph to determine a the function s domain b the function s range c the x intercepts if any d the y intercept if any and e the missing function value indicated by the question mark below f 3 f 2 a The domain is OA The x intercept s is are 6 B 6 L Use a comma to separate answers as needed Type an integer 3 b The range is Use a comma to separate answers as needed c Select the correct choice below and fill in any answer boxes within your choice OA The y intercept is OB There is no y intercept e f 3 f 2 y Type an integer Use a comma to separate answers as needed OB There is no x intercept d Select the correct choice below and fill in any answer boxes within your choice G

The figure shows the cost of mailing a first class letter f x as a function of its weight x in ounces for weights not exceeding 3 5 ounces Find f 2 5 What does this mean in terms of the variables in this situation Cost dollars 0 92 0 75 0 58 0 41 2 Weight ounces 1 f 2 5 What does this mean in terms of the variables in this situation It costs to mail a ounce first class letter 3

For f x x and g x x 7 find the following functions a fog x b gof x c fog 2 d gof 2 a fog x Simplify your answer b gof x Simplify your answer c fog 2 Simplify your answer d gof 2 Simplify your answer

A company that sells radios has yearly fixed costs of 500 000 It costs the company 40 to produce each radio Each radio will sell for 65 The company s costs and revenue are modeled by the following functions where x re number of radios produced and sold C x 500 000 40x R x 65x Find and interpret RC 10 000 R C 20 000 and R C 30 000 R C 10 000 What is the meaning of R C 10 000 OA If the company sells 10 000 radibs in one year its net loss is 250 000 OB If the company sells 250 000 radios in one year its net loss is 10 000 OC If the company sells 250 000 radios in one year its net profit is 10 000 OD If the company sells 10 000 radios in one year its net profit is 250 000 R C 20 000 What is the meaning of R C 20 000 OA The company cannot sell more than 20 000 radios in one year OB If the company sells 20 000 radios in one year it neither makes nor loses money OC The least the company can make in one year is 20 000 O D The most the company can make in one year is 20 000 R C 30 000 What is the meaning of R C 30 000 OA If the company sells 30 000 radios in one year its net loss is 250 000 B If the company sells 30 000 radios in one year its net profit is 250 000 OC If the company sells 250 000 radios in one year its net loss is 30 000 OD If the company sells 250 000 radios in one year its net profit is 30 000

Use the graph of g to find g 2 g 2

The graph shows the percentage of a country s adults on weight loss diets L Percentage on Diets O A NON 24 20 16 12 8 4 0 8 10 10 20 Years after 1987 a Use the two points whose coordinates are shown to find the point slope form of the equation of the line that models the percentage of adults on diets y x years after 1 Simplify your answer Type your answer in point slope form Use integers or fractions for any numbers in the equation b Write the equation in part a in slope intercept form Use function notation where f x is the percentage of adults on diets x years after 1987 f x Simplify your answer Type an expression using x as the variable Use integers or fractions for any numbers in the expression c Use the linear function to predict the percentage of adults on weight loss diets in 2007 10

1 x 16 x6 Choose the correct graph below O A q Yes 10 10 2 10 10 2 Does the function have an inverse that is a function OB an inverse that is a function that is whether the function is one to one 10 10 2 10 10 2 O C 10 10 2 10 10 2 OD 10 10 2 10 10 21

3 Find the values of other five trigonometric functions if sin x x lies in second 5 quadrant

Find the solution set for the system by graphing both of the system s equations in the same rectangular coordinate system and finding all points of intersection Check all solutions in both E x y 5 x 2 y 7 8 129 The solution set is Type an ordered pair Use a comma to separate answers as needed

Rewrite the given equation in slope intercept form and then graph the line 8x y 7 0 What is the equation in slope intercept form 0 Use the slope and the y intercept to graph the line Click to enlarge graph 10 6 A b 10 8 6 2 2 4 6 48

Use the graph of y f x to graph the function g x f x y f x Ay B Choose the correct graph of g below O A O C G B O D

Give the center and radius of the circle described by the equation and graph the equation Use the graph to identify the domain and range x 1 y 25 The center is Type an ordered pair Simplify your answer The radius is Type an integer or a simplified fraction Graph the circle Click to enlarge graph Express the domain of the relation in interval notation Express the range of the relation in interval notation 0

13 Consider the real function of real variable defined by f x e 1 X 2x 1 x 1 The domain of f is a oo 0 U 0 o b R 1 0 c 1 U 1 00 for 20 for 0 x 0

If the total cost function for producing x lamps is C x 320 39x 0 2x dollars producing how many units x will result in a minimum average cost per unit units Enter an exact number Find the minimum average cost per unit LA

Use the seven step method described in the book to graph the following rational function 10 x 4 f x 1 Determine the symmetry of the function Choose the correct answer below O The graph of f has neither y axis symmetry nor origin symmetry O The graph of f is symmetric with respect to the origin O The graph of f is symmetric with respect to the y axis

a Find the slant asymptote of the graph of the rational function and b Use the slant asymptote to graph the rational function x 1 f x X a Find the slant asymptote of the graph of f Select the correct choice below and fill in any answer boxes within your choice A y B There is no slant asymptote L

The equation for f is given by the simplified expression that results after performing the indicated operation Write the equation for f and then graph the function 3x5 x 6x 9 12x6 f x 9

Find an hth degree polynomial function with real coefficients satisfying the given conditions If you are using a graphing utility use it to graph the function and verify the real zeros and the given function value n 4 1 3 and 3 3i are zeros f 1 156 f x 3x 24x 81x 54x 162 Type an expression using x as the variable Simplify your answer Choose the correct graph below O A Q All graphs are 10 10 2 by 300 300 60 OB Q U O C P O D y Q

se the graph of the rational function to complete the following statement 5x co f x sx o f x Next question 10 Q O Asymptotes are shown as dashed lines The horizontal asymptote is y 2 The vertical asymptotes are x and x 3

The equation below has real roots that are rational Use the Rational Zero Theorem to list all possible rational roots Then graph the polynomial function in the given viewing rectangle to determine which possible rational roots are actual roots of the equation 4x 4x 7x x 2 0 2 2 1 by 5 5 1 List all possible rational roots 1 1 1 2 2 2 2 4 4 Type an integer or a simplified fraction Use a comma to separate answers as needed Type each answer only once Choose the correct graph below OA 1 1 1 1 All graphs are 2 2 1 by 5 5 1 List all actual rational roots B C P Type in integer or a simplified fraction Use a comma to separate answers as needed Type each answer only once C Q Q O D Q Q

Use a graphing utility to obtain a complete graph for the polynomial function Then determine the number of real zeros and the number of imaginary zeros for the function f x x 11x 20 Choose the correct graph below A Q All graphs are 10 10 2 by 40 20 10 The function has real zero s B th o OU TIS O C Q O D

The ratio of carbon 14 to carbon 12 in a piece of wood discovered in a cave is R 1 8 5 Estimate the age of the piece of wood Round your answer to the nearest whole number 55913 X years old

Find the limit lim x x 6 X 818

2 Identify the type of exponential function Malthusian basic exponential Logistic or Gompertz each graph below represents Explain how you know which is which

Find the polynomial of the specified degree whose graph is shown Degree 4 P x 4 3 y 2 1 12 10 WebAssign Plot 6 4 2 2 1 2 3 4 X

Question 6 Given the linear equation 2x 3y 8 0 write another linear equations in two variables such that the geometrical representation of the pair so formed is 1 intersecting lines ii parallel lines iii coincident lines

Half the perimeter of a rectangular garden whose length is 4 m more than its width is 36 m Find the dimensions of the garden

hot bowl of soup is served at a dinner party It starts to cool according to Newton s Law of Cooling so that its temperature at time t is given b T t 50 143e 0 05t here t is measured in minutes and T is measured in F a What is the initial temperature of the soup 193 F b What is the temperature after 10 min Round your answer to one decimal place X F c After how long will the temperature be 100 F Round your answer to the nearest whole number min

nomial function P and its graph are given P x 4x4x3 4x 1 NJ 1 0 0 5 0 5 40 1 5 X 2 X 2 0 a List all possible rational zeros of P given by the Rational Zeros Theorem Enter your answers as a comma separated list b From the graph determine which of the possible rational zeros actually turn out to be zeros Enter your answers as a cor separated list Enter all answers including repetitions

eliminate the parameter to get an equation involving just x and y t 2 y 3 4t t Be careful here Check your signs y 3 4 t 2 t 2 None of these for 2 t 2 Oy y 3 4 x 2 x 2 y 3 4 x 2 x 2 y 3 4 x 2 x 2 y 3 4 t 2 t 2 y 3 4x 2 x 2

A model of carry on luggage has a length that is 5 inches greater than its depth Airline regulations require that the sum of the length width and depth cannot exceed 49 inches These conditions with the assumption that this sum i 49 inches can be modeled by the function V x that gives the luggage s volume in cubic inches in terms of its dept x in inches If its volume is 2000 cubic inches determine two possibilities for its depth Volume depth length width 49 depth length V x x x 5 49 x x 5 V x x x 5 44 2x Two possibilities for its depth are inches Use a comma to separate answers as needed Round to the nearest tenth of an inch as needed

Prove 4x 3x x 1 1 3 cos x cos 4x 3x

The incomplete graph to the right shows the following polynomial function f x 4x 4x 55x 100 10 0 1 by 400 400 200 3 a Find all the zeros of the function The zeros are Simplify your answer Type an integer or a simplified fraction Use a comma to separate answers as needed