Quadratic equations Questions and Answers

Graph the solution set of the system of inequalities x 3y 6 y x 4 Use the graphing tool to graph the system Click to enlarge graph

Solve the system of equations by the addition method 15x 3y 75 3x 5y 43 Select the correct choice below and fill in any answer boxes present in your choice OA The solution set is OB There are infinitely many solutions Oc There is no solution Simplify your answer Type an ordered pair

The graph of a one to one function f is given Choose the graph of the inverse function F 3 4 2 2 4 2 Ay 4 2 2 0 1 1 0 2 2 2 Q OU Choose the correct graph of the inverse function f A C Ay OB O D Ay Q

Solve the system by the addition method 4x 3y 5 20x 15y 25 Select the correct choice below and if necessary fill in the answer box within your choice OA There is exactly one solution The solution set is Simplify your answer Type an ordered pair OB There are infinitely many solutions The solution set is x y 14x 3y 5 or x y 20x 15y OC The solution set is

Find the inverse function of the given one to one function f x x 4 5 f x Simplify your answer

The graph of an exponential function is given Find the correct function of the graph Find the function represented by the graph Choose the correct answer below OA f x 4 1 OC f x 4 OE f x 4x 4 O G f x 4 OB f x 4 OD f x 4x 1 OF f x 4 4 OH f x 4 Oo Time Remaining 01 43 42

Approximate each number using a calculator a 62 4 b 62 44 c 62 449 a 62 4 b 62 44 c 62 449 d 62 4494 e 6 5 d 62 4494 Round to three decimal places as needed Round to three decimal places as needed Round to three decimal places as needed Round to three decimal places as needed Round to three decimal places as needed e 6 6

Determine if the function is one to one 0 4 1 3 2 2 1 4 2 3 Is the function one to one No Yes

For the given functions f x x and g x x 5 find a fog x b gof x c fof x d gog x a fog x b gof x c fof x d gog x Simplify your answer Do not factor Simplify your answer Do not factor Simplify your answer Do not factor Simplify your answer Do not factor

10 8 6 4 a Je 25 b 20 15 10 S 10 15 20 25 Identify a and b for the hyperbola with equation y X 4 6 8 10 x a y 82

Solve the equations below State which method you used to solve taking square roots zero product property completing the square or quadratic formula State whether the solution s are rational irrational or non real complex Answers should be left in exact radical form simplified and approximate decimal form rounded to the nearest tenth You must use each method at least once a 4x 6 406 b x 13x 40 0 c x 4x 52 0 d 6x x 3 0

For each of the following f x and d x use long division to find q x and r x a f x 2x 9x 7x 8x 10 d x 2x 3 b f x 5x4 3x 8x 9 d x x 2 c f x 6x4 2x 5x 9x12 d f x 3x5 4x3 9x 1 d x x 2x d x x x 3

Figure is not drawn to scale 13 cm 2 cm 2 cm What is the surface area of the pyrmid cm

Products of Rational and Irrational Numbers The product of two rational number is The product of a rational and irrational number is The product of two irrational numbers is The following are NYS Regents Exam Questions Example 12 Determine if the product of 3 2 and 8 18 is rational or irrational Explain your answer Example 13 Ms Fox asked her class Is the sum of 4 2 and 2 rational or irrational Patrick answered the sum would be irrational State whether Patrick is correct or incorrect Justify your reasoning Aud and Example 14 Which statement is not always true The product of two jerational numbers is irrational 1 The product of two rational numbers is rational The sum oftvo rational numbers is rational The sum of a rational number and an irrational number is irrational 2 3 4 Example 15 For which value of P and Wis P W a rational number 1 2 3 4 and W P and W P and W P 25 and W 2 P Example 16 Given the following expressions I II 2 III 5 5 IV 3 49 to Which expression s result in an irrational number 1 II only 2 III only 3 I III IV 4 II III IV

5 Cost The cost c of a house in Du Quoin Illinois is a function of the number of square feet s of the house The cost of the house can be approximated by c s 0 01s 78s 22 000 1300 s 3900 i Estimate the cost of a 1600 square foot house ii How large a house can Sharon purchase if she wishes to spend 160 000 on a house

3 Solve by the method of your choice 3r r 2

2 Solve by the quadratic formula x 6x 16 0

4 Write an equation that has x intercepts 4 N 2 5

Use synthetic division x3 7x 14x 8 x 4 Ox 13x 66 272 x 4 Ox 3x 2 x 4 Ox 3x 2 O 4x 3x 2

The graph of a polynomial p x is shown below Which x value could represent a zero with multiplicity 2 AY X 10 0 2 4 6 8 10 O 6 0 2 0

A polynomial f and one zero of fare given Find the other zeros of f Select all that apply f x x 4x x 4 1 1 0 1

Shown below is the graph of a function Assume all critical points are AY 2 8 6 8 21 28618 00 64 40 32 40 64 XA O The equation has a negative leading coefficient There is a zero of 6 with a multiplicity 2 O The graph could represent a O There is a zero at x 1 4th degree equation

Which statement is NOT true regarding the graph 104 8 N496 to p 84 10 X O As x f x O It has a y intercept of 0 2 O It has zero at x 1 O It decreases on the interval 1 5 0

Describe the end behavior of the graph of the function f x x 4x 4 As x f x As X f x

What is the range of the functions f x x6 3 O all real numbers all real numbers less than or equal to zero O all real numbers greater than or equal to zero all real numbers greater than or equal to 3

3 Two ships are sailing from Long Beach The Nina is sailing due west and the Pinta is sailing 41 southwest After an hour the Nina travelled 75km and the Pinta travelled 86km How far apart are the two ships

Solve each triangle 1 9 in B 22 in 26 in 2C 136 b 34 mi c 50 3 mi 2 18 31 B 9m 4 mA 130 b 29 mi c 25 mi

Does x 2 9 have a real number solution Why or why not

At a certain food truck hamburgers are sold for 5 eac and hot dogs are 3 each If Martina buys one hambur and h hot dogs and spends at least 20 and no more tha 25 what is one possible value of h

20 cm A 66 14 cm B 20 0gb A C 3 Find AC B 9 3 mi 40 ft 5 Find BC A 74 17 8 mi 78 5 38 ft C C

6 c 30 cm a 17 cm b 20 cm Cos 17 20 36 2 20 30 cos 17 20 36 B

Suppose that the following table gives information about your mutual fund Year Rate of Return 2017 2018 5 5 2019 4 5 The overall rate of return between 2017 and 2019 was 5 2 If you invested 2 000 in this fund at the beginning of 2017 what would your investment be worth at the end of 2017 Round your answer to the nearest dollar

On the xy plane sketch the graph of a function that is continuous everywhere except at x 2 and x 3

Submit Assignment Test Ch 4 and 6 Question 11 of 25 Step 1 of 1 MAX CLOUTIER Answer 2 Points 00 57 06 Simplify the expression using the properties of exponents Expand any numerical portion of your answer and only include positive exponents 7 Keypad Keyboard Shortcuts

mit Assignment Question 22 Test Ch 4 and 6 of 25 Step 1 of 1 Answer 2 Points Evaluate the radical expression Express your answer as an integer simplified fraction or a decimal rounded to two decimal places If the expression does not represent a real number indicate Not a Real Number 49 00 55 25 Not a Real Number Keypad Keyboard Shortcuts Selecting a radio button will replace the entered answer value s with the radio button value If the radio button is not selected the entered answer is used

Answer the following questions using the given graph of the polynmial function Assume all critical points are within the viewing window Is the leading coefficient positive or negative What is the least degree of the polynomial function Name the zeros that have an even multiplicity Name the zeros that have an odd multiplicity What is the approximate minimum value of the function 24

4 Rafael has a business selling computers He buys computers from the manufacturer for 450 each and sells them for 800 Each month he must also pay fixed costs of 3 000 for rent and utilities for his store If he sells n computers in a month which of the following equations can be used to find his profit 3 000 a P n 800 450 b P n 800 450 c P 3 000 x n 800 450 d P n 800 450 3 000

Question 3 T of 25 Step 1 of 1 Simplify the following expression Assume that all variables are positive Answer 2 Points 27x10y6

ubmit Assignment Test Ch 4 and 6 Question 1 of 25 Step 1 of 1 Multiply the polynomials using the distributive property and combine like terms x x 3 x 5 Answer 2 Points

At which point does the graph have a local maximum 10 8 O 6 2 0 5 O 2 9 0 8 O 7 0 O 8 3 65 5 S 2 X 29 DEAR TESTO 23

A computer virus is affecting the technology center in such a way that each day a certain portion of virus free computers is infected The number of virus free computers is recorded in the table below Day 0 1 2 a How many computers are in the technology center b Uninfected Computers 27 18 12 C computers What portion of virus free computers is infected each day How many computers will remain virus free at the end of the third doy

The graph of a polynomial p x is shown below Which x value s could represents zeros with multiplicity 27 75 60 45 20 15 30 45 60 75

Describe the end behavior of the graph of the function f x x4 x 4 As X f x and as x f x 00 O As x f x and as x f x O As x f x and as x f x O As x f x and 00 as x f x

The graph of a function is shown below The least degree of the function is 0 5 0 5 4

Question 11 of 15 Step 1 of 1 10 15 Correct Given g x 2x 1 1 use interval notation to indicate the domain Round any decimal values to two decimal places Answer

8 15 Correct Given y 3x 5 1 use interval notation to indicate the domain Round any decimal values to two decimal places Question 9 of 15 Step 1 of 1 Answer

Save Exit Certify Lesson 6 2 Rational Exponents Question 16 of 16 Step 1 of 1 Simplify the following expression using rational exponents Assume all variables are positive Answer 12 16 Correct 8x y3 x y 2

Without graphing the function describe the graph of p x x x 6 2 x 5 2 Your description should include degree end behavior zeros including multiplicity and number of turns For the toolbar press ALT F10 PC or ALT FN F10 Mac

Question 6 Points 1 Questions on the back of a warranty card are an example of which of the following O Demographics information O Market surveys O Consumer quiz Consumer assoc demographics

To use the Investment and Retirement Calculator enter your current age in the first box and enter an age 10 20 30 and 40 years from now in the Age you plan to retire box Put O in the How much have you saved for retirement box fill in the monthly contribution box and then put 12 in the What do you think your annual return will be box After filling in all of the boxes click Calculate to generate the total with compound growth 6 If you were to invest 25 each week instead of buying lottery tickets how much could you invest each month use four weeks per month How much could you invest in a year 12 months using that monthly figure