Quadratic equations Questions and Answers

Match the domain and range for the relation 5 2 3 7 8 6 0 4 3 3 6 6 1 3 The domain is Select and the range is Select

2 Find the volume of the region bounded above by the paraboloid z x y and below by the triangle enclosed by the lines y x x 0 and x y 2 in the xy pla The volume under the paraboloid is Tuno simplified fraction

If this figure is c C Draw 2c 4 and 2 c 4 Label each drawing so you can clearly see each expression

en the function t x whose graph is shown below place the black draggable dot at the point that corresponds to Provide your answer below fer 3 2 3 2 6 5 3 2 3 4 5 6 2 3 4 5 FEEDBACK MORE INSTRUCTION S

Evaluate the following expressions a log 3 b log 8 c log4 64 d log44 wwwww

Functions 11 Write the equation for each of the given graphs 2x b Sabe a 43688888 20 10 1 2 1

An equation that defines y as a function of x is given a Solve for y in terms of x and replace y with the function notation f x b Find f 3 4x 2y 1 a Solve for y in terms of x and replace y with the function notation f x f x 4x 1 2 b Find f 3 f 3 Use integers or fractions for any numbers in the expression Type an integer or a fraction

tch help video Factor completely 3 x 5x 9x 45

Question 10 Find the number of terms in 3x 8x 9y 2y 9 02 0 3 04 Points 2 05

Find Circle Center and Radius from Equation General Form Jun 05 11 12 13 PM Watch help video Find the center and radius of the circle represented by the equation below Center Radius x y 18x 2y 1 0

Decide whether each relation defines y as a function of x Give the domain and range 9 x 10 y Does this relation give a function No Yes What is the domain Type your answer in interval notation

Watch help video Subtract x 8x from 3x 3x 7

2 In 2013 the United States Postal Service charged 0 46 to mail a letter weighing up to 1 oz and 0 20 per ounce for each additional ounce Which function would determine the cost in dollars c z of mailing a letter weighing z ounces where z is an integer greater than 1 1 c z 0 46z 0 20 2 c z 0 20z 0 46 3 c z 0 46 z 1 0 20 4 c z 0 20 z 1 0 46 3 Last week a candle store received 355 60 for selling 20 candles Small candles sell for 10 98 and large candles sell for 27 98 How many large candles did the store sell 1 6 2 8

The graph depicts the growth in costs using a line segment Use the midpoint formula to approximate the cost during the year 1987 The approximate cost during the year 1987 was Average Annual Cost of Tuition and Fees At 4 Year Private Colleges During 1983 1991 Cost 10000 8000 6000 4000 2000 5047 1983 Year 10

The table lists how poverty level income cutoffs in dollars for a family of four have changed over time Use the midpoint formula to approximate the poverty level cutoff in 1987 to the nearest dollar The poverty level cutoff in 1987 was Round to the nearest dollar as needed dollars Year 1970 1980 1990 2000 2004 Income in dollars 3213 8393 13526 17076 19946

For the points P and Q do the following a Find the distance d P Q b Find the coordinates of the midpoint M of the segment PQ P 3 2 5 5 Q 2 5 a The distance d P Q is Simplify your answer Tyne an exact answer uning

A right triangle has a 30 angle The leg adjacent to the 30 angle measures 25 inches What is the length of the other leg Round to the nearest tenth O 14 4 in O 21 7 in 28 9 in O 43 3 in

The equation sin 40 20 0 the length of line segment AC A b C 20 cm can be used to determine 40 B TIME C What is the length of AC Round to the nearest tem 11 8 cm 12 9 cm 14 9 cm 15 3 cm

60 18 30 B Which trigonometric ratios are correct for triangle ABC Select three options sin C 3 cos B 2 O tan C 3 12 12 23 O tan B 2 3 sin B 4

Dot Pattern F Stage 0 Stage 1 Stage 2 Stage 3 Describe the pattern s growth rate and determine which function family the pattern belongs to

Stage 0 Stage 1 Define a function to describe the pattern Stage 2 Stage 3

Stage Dot Pattern D Stage 1 Stage 2 Stage 3 Do you agree with either justification Explain your reasoning Stage 0 Dot Pattern E Stage 1 Diego says Both dot patterns D and E are linear because the number of dots increases for each stage Elena says Dot Pattern D is linear and Dot Pattern E is exponential because the growth rates are different Stage 2 Stage

Stage 0 Stage 1 Stage 2 Complete the table Find the number of dots in stage 4 of Pattern F Stage Number x Number of Dots 0 Stage 3 3

9 log 2 x log 7 2 11 log x 3 logg x 4 1 13 logg 5x 10 logg 6 2 2 5XH 6 5 30x 60 64 60 60 60600 36x 42 30 2 301 X 2 15 15 log 9 log 4x log 75 10 log 4 x 12 log x 1 log x 2 2 14 log 3x 9 log 5 log 60 16 log 10 log4 4x 2 log 4 80

Solve each equation 1 log4 6 log 4 x 3 6 43 64x 6 2 x 3 32 64 2 3 log69 log x 8 2 5 log6 7 log x log6 65 og x 6 log x 4 log 67 2 log 7 log x 2 2 4 logg 9 logg x logg 34 a 34 34x 9 3 34 x 9 34 6 log 10 log 2x 7 1 8 log 4 2 log 4 5x 1 log 25

Find the surface area of the composite figure 6 cm 4 cm 7 cm 6 cm 7 cm SA 7 cm 6 cm Hint Area of a Triangle b h cm D If you d like you can use a calculator Enter

c x y a x 2 0 25 y 0 x 0 y x 2 u x use the indicated change of variable

19 What payment 5 months from now would be equivalent in value to a 4 000 payment due today and a 3000 payment due 7 months from now Money can earn 6 5 A 7 455 01 B 6 923 82 C 7 189 58 D 7 076 18 E 6 544 98

In 1995 wolves were introduced into Yellowstone Park The function w x models the number of wolves w in the years since 1995 x 5 3 5 1 By what percent does the number of wolves change each year 5 2 8 Wh w n 14 1 0 08 w n 14 1 Determine the value of w 25 H 25 14 1 08 25 95 878652 w x 14 1 08 95 8795 H 25 What does the value of w 25 say about the wolf population W 25 95 879 96 There are au Holves in 1995 25 2020 According to the model about how many years will it take for the population to reach 5 wolves Use a graphing calculator to support your thinking

3 This graph represents the first hypothetical described in the video Imagine someone invests 10 000 with 7 returns compounding each year for 30 years 70000 60000 50000 40000 30000 20000 10000 0 10 15 20 25 years a Approximately how much does their investment grow in the first 15 years b Approximately how much does their investment grow between year 15 and 30 c This investor started with 10 000 and ended up with 74 500 after 30 years just from the growth of that initial investment Now imagine they tried to use savings to reach that same 30 year goal If they start with 10 000 how much would they need to save each year to have 74 500 after 30 years Assume they don t earn interest on savings

2 x 1 1 0 lect all of the exponential functions 0 0 5 f x 18 12 8 1 3 10 8 6 2 O 8 10 1 0 1 2 f x 2 4 8 16 10 8 6 4 2 O 2 4 6 8 10 X 1 0 1 2 f x 2 5 10 17

2 The population of a city increases by 6 every year Its population today is 450 000 Which expression represents its population in 3 years A 450 000 0 06 B 450 000 1 06 C 450 000 1 0 06 D 450 000 1 06

3 2 A new refrigerator costs 1 500 The value of the refrigerator will decrease 40 each year 3 1 Write an equation to represent this relationship Use x to represent the time in years Use y to represent the value of the refrigerator Determine the value of the refrigerator after 5 years NEW MODEL 1500

What is the probability that a random point on AK will be on DF A I 10 B 2 0 2 8 6 4 H I J K P 4 6 8 10

A restaurant has a customer satisfaction survey on each table This is an example of a a simple random sample b a cluster sample c a voluntary sample d a systematic sample e none of the above Question 11 1 point An example of a variable cost associated with owning a vehicle is a a monthly car payment b insurance c license fee d fuel e all of the above Section 2 True and False 10 marks Question 12 1 point

Question 19 1 point The A represents the angle an observer must look up from the original horizontal line of sight to see an object that is higher than the observer It is sometimes referred to as the angle of inclination Question 20 1 point When a parabola opens down the quadratic relation will have a N Question 21 1 point original investment only N has the interested calculated on the

Scientific calculators are permitted Be sure to show all steps Read each question carefully before answering Section Marks Section 1 Multiple Choice 15 Section 2 True False 10 Section 3 Fill in the Blanks 10 Section 4 Full Solutions 67 TOTAL 102 Section 1 Multiple Choice 15 marks Circle the correct answer for each question Question 1 1 point In the triangle displayed below what is the value of sin B 13 cm

A triangle has a base length of 185 with side lengths of 219 and 200 From the base the height of the triangle is 186 98 What is the area of the triangle O 17 365 25 SF 19 240 00 SF

To solve the linear equation 5x 6 7x 5 9x 10 17 the first step is to multiply each side by the least common of all the fractions in the equation What is the denominator LCD

Ind the standard form of the equation of each ellipse 13 Foci 0 3 vertices 0 5

Question Find a solution to the linear equation y 12x 24

6 Use Descartes s Rule of Signs to i determine the possible numbers of positive and negative real zeros of the function x 2x 13x 21x 2x 8 ii list the possible rational zeros of the function and iii determine the zeros of the function

A car is traveling at a rate of 81 miles per hour What is the car s rate in feet per second How many feet will the car travel in 5 seconds In your computations use the fact that I mile is equal to 5280 feet Do not round your answers Rate 0 Distance traveled in 5 seconds al X 5

A computer company receives 350 applications from college graduates for a job planning a line of new web servers Suppose that 220 of these applicants majored in computer science 147 majored in business and 51 majored both in computer science and in business How many of these applicants majored neither in computer science nor in business 316 34 120 O 17

nd the slope of the line 54 3 2 1 2 Q C C C C

2a b 10ab c 2ab

Solve the inequality 11y 412 41 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is a finite set Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed OB The solution set is an infinite set Simplify your answer Type your answer in interval notation Use integers or fractions for any numbers in the expression OC The solution set is

How many quarts of pure antifreeze must be added to 4 quarts of a 20 antifreeze solution to obtain a 60 antifreeze solution quart s of pure antifreeze must be added Round to the nearest tenth as needed

John ran the 100 m dash with a time of 9 83 sec If this pace could be maintained for an entire 26 mi marathon what would his time be Notice that 1 m 3 281 ft and 1 mi 5280 ft His time would be hr min sec Round the final answer to the nearest integer Round all intermediate answers to the nearest integer as needed

Find the quotient Write the answer in standard form a bi 3 3 8