Quadratic equations Questions and Answers

Use the Gauss Jordan method to solve the following system of equations 6x 7y 5 24x28y 20 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution is Type an ordered pair Simplify your answer B There are infinitely many solutions The solution is y where y is any real number Simplify your answer Use integers or fractions for any numbers in the expression AC There is no solution

What does correlation coefficient of linear fit represent O The linear relationship between two variables O The linear relationship between two coefficients The linear relationship between two constants

Use the information listed below to solve parts a through h demanded in hundreds p D q 16 1 25q Find the price at each level of demand Answer parts a through d a Find the price when the demand is 0 watches The price when the demand is 0 watches is b Find the price when the demand is 400 watches The price when the demand is 400 watches is c Find the quantity demanded for the watch when the price is 6 At a price of 6 the demand is for watches

Topics In Alg Domain and Range 1 The graph of y g x is given 9 1 2 a Find g 1 b Find g 1 9 1 1 c Find g 4 9 4 1 d For what value s of x is g x 3 9 2 3 e For what value s of x is g x 0 9 0 5 0 f Write the domain of g 3x 4 g Write the range of g 3 4 3 UN 3 2 2 3 y g x 2345

For credit click Add Work and show all your work to demonstrate your competence in using the quadratic formula a x h formula b C An object is thrown upward at a speed of 99 feet per second by a machine from a height of 4 feet off the ground The height h of the object after t seconds can be found using the equation 16t 99t 4 b b 4ac 2a When will the height be 48 feet Select an answer When will the object reach the ground Select an answer

Which one of the following is correct for a weak and negative correlation O r 0 98 O r 0 099 O r 0 009

Given f x O f g x x x 12 z2 15 54 Select the correct answer below O f g x O f g x O f g x O f g x x 4 x 9 O f g x x 4 x 9 x 4 x 9 H I and g x x 4 x 9 I I where a 6 9 3 where 6 9 3 x 3 find f g x and determine any domain restrictions z 6 where x 6 9 3 4 9 where x 6 9 3 4 where x 6 9 3 where 6 9 3 9

5 Suppose f x 4x 2 Determine such that X a f x 18 b f x 0

5 The total sum of complementary angles is 6 The total sum of supplementary angles is 7 Angle B and Angle C are complementary If Angle B is 43 what is Angl

Assuming all denominators are nonzero simplify the expression below a 3a 18 a a 12 a 9 a 2a 8 a 2a

If f x x 3x 28 x 4x 21 Select the correct answer below O f g x O f g x O f g x O f g x O f g x O f g x x 4 x 2 and g x 2 find f g x and any domain restrictions for f g x x 4 x 2 x 4 x 2 x 4 x 2 x where a 7 3 2 X where 7 3 2 4 2 where x 7 3 2 x 4 x 2 where x 7 3 2 where x 7 3 2 where x 7 3 2

Which of the following graphs correctly represents the system of inequalities below y 2x y2 x 1 2 Select the correct answer below 1111 7 6 5 4 3 2 1 1 2 3 4 5 6 7

A military drone can fly at 7 miles per hour in calm conditions For one fight the drone flew 54 miles with the wind and 30 miles against the wind in the same amount of time What was the wind speed for the fight Do not include the units in your response

Which one of the following is correct if the correlation coefficient is r 0 99 O Strong and negative O Weak and negative O No relationship

28 City officials conclude they should budget s million dollars for a new library building if the population increases by p thousand people in a ten year census The formula s 2 p 1 expresses the relationship between population 1 3 and library budget for the city How much can the population increase without the city going over budget if they have 5 million for a new library building

The sum of the reciprocals of two consecutive positive even integers is Select the correct answer below 4 2 O 4 6 6 8 no solutions Find all pairs of integers that satisfy this condition

1 Let g x 5x 2 Evaluate each of the follow a g 1 b g 2

Given f x O f g x Select the correct answer below O f g x r 5r 6 r 72 18 O f g x O f g x x 1 x 2 O f g x O f g x x x 2 1 x 1 I 2 and g x find f g x and determine any domain restrictions x 6 x 9 where a 9 2 6 x 1 I I x 2 where x 9 2 6 x 1 x 2 where a 9 2 6 where x 9 2 6 1 2 where x 9 2 6 where x 9 2 6

Solve for y Do not include y in your answer a Y a b a

Find the vertex algebraically For credit click Add Work and show work to demonstrate you can compute the vertex algebraically a b b b 2 2a 2a Given the function f x 4x 48x 44 The vertex is a O maximum point O minumum point Find the vertex algebraically What is the axis of symmetry

Let f x 2x 2 Evaluate each of the following a f 3 b f 6

A positive integer is 7 less than another If 6 times the reciprocal of the smaller integer is subtracted from the reciprocal of the larger integer then the result is 12 Find all pairs of integers that satisfy this condition 13 Select the correct answer below O 13 20 13 6 O 20 27

2y22 2y 5 5 2y 5y Simplify the expression above by writing it as a single simplified rational expression Sorry that s incorrect Try again

A positive integer is 4 less than another If the reciprocal of the smaller integer is subtracted from 2 times the reciprocal of the larger integer then the result is Find all pairs of integers that satisfy this condition Select the correct answer below O 10 14 6 10 6 2 no solutions

The graph is a transformation of y 32 Write an equation that describes the transformation 7 6 5 4 3 2 7 7 6 5 4 3 2 1 4 2 345 5 6 7 1 2 3 4 5 6 7 Pranian

Work Hours for College Faculty The average full time faculty member in a post secondary degree granting institution works an average of 55 hours per week Round intermediate calculations and final answers to two decimal places as needed Part 0 2 Part 1 of 2 a If we assume the standard deviation is 2 8 hours then no more than of faculty members work more than 63 4 hours a week

10 Solve the exponential equation 43x 5 9 Then round your answer to two decimal places

Graph the system of non linear inequalities Select all that apply y x 2 y 2 4 8 7 6 5 4 3 2 1 y 7 6 5 2 12 3 4 X

Identify the degree leading term and leading coefficient of the polynomial 2x2 x4 5x 72x2 x4 5x 7 The degree is

Given the quadratic function of the form f x ax bx c f x 10x 10x 5 a b C The point that is the vertical intercept of the graph of the function is The graph is a parabola which will select one O Open UpwardsO Open Downwar

Consider the following minimization problem over x1 x2 R minimise 2 1 subject to x x 1 1 0 1 x 0 1 constraint v Mo constraint u constraint u Based on KKT conditions the optimal solution for the primal problem is then al X2 The optimal solution for the dual problem

Calculate 9 6i Give your answer in a bi form Give the solution with smallest positive angle Round both a and b to 2 decimal places

Use the properties of exponents to simplify each expression Write with positive exponents Assume that all variables represent positive real numbers 13 0 x 7y 3 30 o x 7y 3 Simplify your answer Type exponential notation with positive exponents C

Write each of the following products in simplest form 8x 8 9x 16 12x 16 3x x 4 a c 2x 7x 4 12x 24x 8x 4x x 6x 8 b d x x 12 x 2x 15 x 8x 15 16 x x 7x 8 3x 4x 1 1 x 9x 1

98 6 F 2 C QUESTION 6 Male g 225 198 286 235 456 OF You have 5 female rats and 5 male rats Their masses are provided in the table below Female g 209 250 225 256 307 The mean mass of the females is The mean mass of the males is C

53 4 log x log x 1 2log x 1 54 logs x 1 logs x 1 55 In a b In a b 2 ln c 56 2 logs x 2 logs y 3 logs z

5 What are the solutions of the equation below x 2 x 9 0 A x 2 x 9 B x 2 x 9 C x 2 x 9 r 2 x 9

Given f x 6x and g x 9x 4 find the following expressions a fog 4 b gof 2 c ff 1 d gog 0 a fog 4 Simplify your answer b gof 2 Simplify your answer c ff 1 Simplify your answer d gog 0 Simplify your answer

Find the real numbers that satisfy the equation below Express your answer in set builder notation Find the real numbers that satisfy the equation below Express your answer in set builder notation x x

8 For the function f x x 4 find f What is the range of f

Multiply and then simplify if possible Assume that all variables represent positive real numbers x 3 9 x 3 9 Simplify your answer Type an exact answer using radicals as needed

On average Amy takes 2 more hours to build a shelf than Kathryn If working together Amy and Kathryn can build 25 shelves in a combined 60 hours how long does it take Kathryn to build a shelf Do not include the units in your answer

8 If f x 25 and g x 2 62 5 find f g x and determine any domain restrictions Select the correct answer below O f g x O f g x O f g x O f g x 6x8 x x 5 x 1 O f g x 10x 8 x x 5 x 1 O f g x 6 x x 5 x 1 6 x x 5 x 1 where x 0 5 1 where x 0 5 1 10x8 x x 5 x 1 where x 0 5 1 6x 8 x x 5 x 1 where x 0 5 1 where a 0 5 1 where x 0 5 1

Solve the following equation for x Do not include in your answer b x C a a b

Write the following as a single simplified rational expression 2p 212 p 4p 3 p 4

15 5 1 1 3 5r 2 Simplify the expression above by writing it as a single simplified rational expression Provide your answer below x

Multiply Assume that all variables represent positive real numbers 5 4 x 4x 4 4x 4 Simplify your answer Type your answer using exponential notation Use integers or fractions for any numbers

51 A clothing manufacturer uses the model a f 4 36 to estimate the amount of fabric to order from a mill In the formula a is the number of apparel items in hundreds and fis the number of units of fabric needed If 400 apparel items will be manufactured how many units of fabric should be ordered

The graph is a transformation of y 3 Write an equation that describes the transformation 7 6 5 4 3 2 7 6 5 4 3 2 1 1 T 2 3 4 5 6 7 2 3 4 5 6 7 q

The equation of the ellipse that has a center at 3 5 a focus at 7 5 and a vertex at 2 5 x C y D A B where A B C D 1