Quadratic equations Questions and Answers

If f x 4x 7x 3x 1 and g x 3 find fog x and gof x What is fog x fog x 53 What is gof x gof x

Given f x 9x and g x 9x 7 find the following expressio a fog 4 b gof 2 c fof 1 d go g 0 a fog 4 1359 Simplify your answer b gof 2 2923 Simplify your answer c fof 1 Simplify your answer

Graph f as a solid line and f1 as a dashed line in the same rectangular coordina space Use interval notation to give the domain and range of f and f f x x 1

3 Begin by graphing the standard cube root function f x x Then use transformations of this graph to graph the given function g x x 3

Find the missing length in the similar triangles 15 12 x 6 x 12 x 3 X 9 X 3 5 A

nd the values x and x2 that maximize f x x 6x 5x2 subject to the following constraints Write the exact answer Do not round If the function has no aximum value write None If infinitely many values maximize the function write Inf Answer 3 x 2x 14 2x x 10 Tables Key Keyboard Shor

11 1 Find if possible the line of intersection between the lines 3 1 2 t 1 1 1 and 8 2 0 s 3 2 7 for t SER 3 11 2 Show if possible that the lines x 1 3t y 1 z 5 2t for t R and x 2 S 5 y 3 5s z 4 2s for s R intersect and find the point s of intersection 11 3 Find the intersection between the planes x 2y z 3 and x 3y 2z 1

Find the maximum value of f x x 5x 10x2 subject to the following constraints Write the exact answer Do not round If the function has no maximum value write None Answer 5x 253 x 2x 4 Tables Keypad Keyboard Shortcuts

8 6 00 8 6 2 14 6 8 10 Show Transcribed Text 2 6 XT Decided whether the relation defined by the graph to the right defines a function and give the domain and range

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Given the functions f and g below find g f 1 Do not include g f 1 in your answer Provide your answer below f x x 4 g x x 3x 1

Given the graphs of f x and g z below find the composition of functions f g 1 Do not type f g 1 in your answer 1 5 3 2 f x 1 0 1 21 0 3 2 g x 3 4 5 6

James knows that he eventually wants to buy a motorcycle and the model he has in mind costs 5 000 He has found a bank that will let him open a saving account with 7 interest that is compounded monthly If he wants to buy his motorcycle in 5 years he s still nervous how much money should he invest in the account now Round only at the very last step of the problem Give your answer rounded to the nearest dollar Do not include in your answer choice Provide your answer below

An initial investment of 100 000 at 12 interest is compounded weekly use 52 weeks in a year What will the investment be worth in 30 years Round your answer to the nearest dollar Do not include the dollar sign in your answer Provide your answer below

Dawson is saving for a down payment to buy a house He has opened a bank account that earns 2 5 interest compounded monthly How much should Dawson invest in the account so that the account balance after 6 years is 20 000 Round your answer to the nearest dollar Sorry that s incorrect Try again

G O A can of beans has surface area 399 cm2 Its height is 20 cm What is the radius of the circular top Hint The surface area consists of the circular top and bottom and a rectangle that represents the side cut open vertically and unrolled The radius of the circular top is cm Do not round until the final answer Then round to the nearest hundredth

21 A projectile is launched from a platform 6 feet high with an initial velocity of 80 feet per second The heighth of the projectile at t seconds after launch is given by h 16t 80t 6 feet a How many seconds after launch does the projectile attain maximum height Show work b What is the maximum height Show work

11 Find a reasonable function to fit the graph below y 50 40 30 20 10 File Preview 65 4 3 2 1 0 1 1 2 3 4 5 6

Solve the system of equations for each variable by using a graphing calculator 1 7v 2 9t 1 8t 2 9v 5 Select the correct choice below and if necessary fill in the answer box within your choice O A t Round to three decimal places as needed OB There are infinitely many solutions

ne ellipsoid 3x 5y z 72 intersects the plane y 2 in an ellipse Find parametric equations for the tangent line to this ellipse at the point 4 2 2 Enter your answers as comm eparated lists of equations Use t as your parameter

DOMAIN Range Verticar or horizontal Asymptote 3 points on the graph h x 4x 2 DOMAIN Range Verticar or horizontal Asymptote 3 points on the graph h x 4x 2

Let x 2 3 4 and y 6 8 9 be vectors in R Using the contents techniques from this course find a vector z of magnitude 2 that is perpendicular to both x and y simultaneously

State the dual problem for the given problem but do not solve it Minimize w 5y 4y 2y3 subject to y y2 Y3 28 Y y 27 5y1 y2 4y32 13 Y 20 V220 y3 20 What is the dual problem Maximize 2 0 subject to 5 4 42 2

A cylinder has radius 5 and height 42 A spiral with constant slope starts at the bottom of the cylinder wraps around the cylinder exactly three times and finishes at the top of the cylinder What is the length of the spiral

For f x x17 and g x 17 x find fog x and gof x Then determine whether fog x gof x What is fog x fog x

1 Given f x 2x 1 and g x 5 x find the following expressions 2 a fog 4 b gof 2 c fof 1 c fof 1 d gog 0 a fog 4 Simplify your answer

Click here to view the transcript When writing a rational function as a power series if the numerator has degree one less than the denominator the partial fraction method will work O True False

Verify Stokes Theorem for fas F dr where F yx i xy j zk and S is the part of the sphere 2 y z 4 that lies in the upper half space z 0

Pease extend sufficient space if you wor action f x e x 3 2x 1 is one to one ative of the function

2 8 pts Graph 2 full periods for f x 2cos 3x 1 Show the following on your graph amplitude period midline Label one maximum point and one minimum point label these on your graph as ordere pairs Don t forget to show your work

1 3 8 pts Graph 2 full periods for f x 2 csc 1x a State the stretching factor period phase shift and asymptotes b Label the following on your graph asymptotes 2 reference points P Don t forget to include your work Asymptotes

The power output P as W of a certain 12 V battery is geen by P 121 40r whoce T is the current in A Find the cuneed for which the power to a me CES Find the derivative of the action to be maximized dP The power is a man when the carent is Type an integer or a decinal

Use complete sentences to explain how to convert a logarithmic equation to a exponential equation

K c What price p maximizes revenue p Simplify your answer Type an integer or a decimal d What is the maximum revenue B Ine domain is the set of all real numbers R Simplify your answer Type an integer or a decimal e How many units are sold at this price X Simplify your answer Type an integer or a decimal f Graph R Choose the correct graph below OA 6000 0 AP 60 R Q Q OB AR 6000 0 0 60 Q g What price should the company charge to earn at least 3648 in revenue company should charge a price between a minimum of and a maximum of O C AR 6000 0 0 60 OD Ap 6000 0 60

K Find the following for the function f x 4x 4x 2 c f 2 a f 0 e f x b f 2 f f x 3 g f 5x a f 0 Simplify your answer b f 2 Simplify your answer c f 2 Simplify your answer d f x Simplify your answer e f x Simplify your answer f f x 3 Simplify your answer g f 5x Simplify your answer h f x h Simplify your answer d f x h f x h

1 2 Given f x 5x 4 and g x 4 find the following expressions a fog 4 b gof 2 c fof 1 d gog 0 a fog 4 b gof 2 c fof 1 d gog 0 Simplify your answer Simplify your answer Simplify your answer Simplify your answer

Subtract the monomials Simplify your answer completely pq4 5p 8q4

Solve the system 3x 3y 3 15x 4y 42 The system has no solution O The system has one solution The solution set is O The system has infinitely many solutions The solution set is 1 is any real number

Use the graph to identify zeros and multiplicity X smallest x value X X largest x value 6 4 2 y 6 with multiplicity with multiplicity with multiplicity 4 2 2 4 2 4 6 X

A plane has an airspeed of 149 km h It is flying on a bearing of 71 while there is a 29 km h wind out of the northeast bearing 225 What are the ground speed and the bearing of the plane The ground speed is km n Round to the nearest tenth as needed The bearing is Round to the nearest tenth as needed GEO

Question 3 Essay Worth 10 points 05 02 MC Mike is working on solving the exponential equation 37 12 however he is not quite sure where to start Solve the equation and u describe the steps to solve Hint Use the change of base formula log y log y log b

On the graph of f x sin x and the domain 0 x 2 for which of the following intervals is f x strictly decreasing Choose the lower and upper bound with respect to the x value using the draggable points in the graph below Provide your answer below 3 2 1 Lower Bound TT 2 Upper Bound 3TT 2 2TT 5TT 2

Write equation using point slope form but end in slope intercept form 4 3 3 4

Which is a solution to this inequality Check all that apply y 3 y 4x 1 0 1 1 0 1 5 3 3 2 4 1 1 1 3 Alg 2A Unit 4 Retake 1

4 6 pts The line y x passes through the origin in the x y plane What is the measure of the angle that the line makes with the positive x axis

Choose the correct set of inequalities O A B C O D O E 13 2 0 1 2 3 7 y 5 MO 6 X A B C D E y x 2 3 y x 1 yz x 2 3 y x 1 yz x 2 3 y x 1 y2 x 2 3 y x 1 y x 2 3 y x 1

5 4 pts Seismic waves travel in a circular pattern when an earthquake occurs The center of the earthquake is known as the epicenter a Suppose you are located at one of the farthest points to still feel the effects of the earthquake If that location is 30 miles east and 40 miles north of the epicenter how far is the epicenter from your location b Using the information from part a write the equation of the conic in which the earthquake can be felt assuming that the epicenter is at the origin

Find the z number associated with a 98 level of confidence Round your answer to two decimal places

or each real number a 0 define the point Pa as having coordinates ogether these points form the hyperbola with equation xy 1 a a The point Qa is the reflection of the point Pa in the line with equation y the coordinates of Qa in terms of a Taken all 2x Determine b The points Qa satisfy an equation of the form 12x bxy cy d Determine the values of b c and d

Find all zeros noting multiplicities and f x x 3 2 2x 1 x 1 3