Quadratic equations Questions and Answers

Use a graphing calculator to approximate the real zeros Give each zero as a decimal to the nearest tenth f x 3x x2 15x 5 OA 0 3 2 2 2 2 OB 3 2 3 2 3 OC 0 3 2 2 2 2 OD 3 5 5

Determine whether fog x x and whether gof x x f x g x x X OA fog x x gof x x OB fog x gof x x OC fog x x gof x x OD fog x x gof x x

A triangular shaped lake front lot has a perimeter of 1100 ft One side is 200 ft longer than the shortest side while the third side is 300 ft longer than the shortest side Find the lengths of all three sides OA 100 ft 300 ft 300 ft OB 300 ft 300 ft 300 ft OC 300 ft 500 ft 600 ft OD 200 ft 400 ft 500 ft

The graph of a linear function f is shown below Write the equation that defines f Write the equation in slope intercept form Ld Ay 8 6 4 di 2 9 O A y 5x 6 OB y 5x 6 OC y 5x 6 OD y 5x 6

Give the domain and range of the relation Year 1993 1994 1995 1996 1997 Number of Companies 52 102 187 170 218 OA The domain is 1993 1994 1995 1996 1997 The range is 52 102 170 187 212 OB The domain is Year The range is Number of Companies OC The domain is 52 102 170 187 218 The range is 1993 1994 1995 1996 1997 OD None of these

Find the values of a b and c for which the quadratic equation ax bx c 0 has the given numbers as solutions Then use the values to write a quadratic equation 3 6 OA x 3x 18 0 OB x2 18x 3 0 O c x 3x 18 0 D x 18x 3 0

Solve the following equation for t t S 1 1191 Potions

Solve the equation by the square root property x 20 OA 20 OB 10 OC 2 5 O D 400

7x 4 6 x 1 2x 3 OA OB O C equation O D 13 1 7 9 13 15

Solve the equation 4 0 5x x x 5 3

How much should you invest into an account with 3 2 interest compounded quarterly if you want to receive a payment of 1000 each quarter for the next 5 years

f x x 5 5 6 41 9 X 8 subtract 5 then take square root subtract 5 then take square root Draw a machine diagram for the function f x subtract 5 then take square root subtract 8 take reciprocal multiply by 7 subtract 8 take reciprocal multiply by 7

6 Scientists use the following formula when examining skeletal remains H 66 4 2 26 H represents a person s height and f is the length of the person s femur bone length The equation has a margin of error of 3 42 centimeters All changes sa a You are on an archeological dig and need to calculate the height of some of the remains You have found several femur bones In order to determine the heights we need to first solve the given formula for H b The femur bones measure 40 6 cm 39 cm and 48 2 cm Find the height of each person c Find the height of each person in feet note 2 54 cm 1 inch d Using the margin of error create an absolute value inequality to represent the range of the height for each individual

According to one source the world population can be modeled using the function P t 6 17e0 012t where P t is the world population in billions of people and t is the number of years after January 1st 2000 a Predict the year during which the world population is expected to reach 10 3 billion people year 2043 Not equivalent b Predict the world population on January 1st 2060 Round to the nearest person population 13000000000 I Preview 2043 people Preview 13 000 000 000 people

Under ideal conditions a certain bacteria population is known to double every 4 hours Suppose there are initially 800 bacteria a Find the number of bacteria after 12 hours bacteria b Find the function P t which gives the number of bacteria after t hours P t bacteria c Estimate the number of bacteria after 17 hours Round your answer to the nearest whole number bacteria

According to one source the world population can be modeled using the function P t 6 17e0 012 where P t is the world population in billions of people and t is the number of years after January 1st 2000 a Predict the year during which the world population is expected to reach 10 3 billion people b Predict the world population on January 1st 2060 Round to the nearest person population people

Force X has a magnitude of 1250 pounds and Force Y has a magnitude of 1470 pounds They act on a single point at n angle of 75 to each other Find the magnitude of the equilibrant and the angle between the equilibrant and the 250 pound force What is the magnitude of the equilibrant Round to the nearest tenth pounds

Laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours Find the probability that a randomly selected light bulb will last between 600 and 750 hours 21

Find a basis for S for the subspace S 1 1 5 S span 11

Roger has found a home to be purchase for 112 057 and has agreed to pay 10 down Find the amount of Roger s down payment Find the amount of money that Roger would need to borrow through a mortgage in order to purchase the home If Roger found a 30 year mortgage with a 5 6 APR What would Roger s monthly payment be Round your answer to the nearest cent

31 7 2k 8 10 8k 4 32 3 8r 6 7 r

buy a total of 50 turkey burgers and veggie burgers You spend 90 total paying 2 per veggie burger and 1 50 per turkey burger ermine the number of veggie burgers x and turkey burgers y that were purchased You MUST 1 Write a system of equations 2 Show your work to solve the system if you use DESMOS remember to use the buttons in the top right to zoom out until you see the equations then label the solution before you take a screenshot 3 Explain your answer in the context of the problem Answer the question how many veggie burgers and how many turkey burgers did you buy in a complete sentence 15

an agreement should get the same answer If you alsa A travel company uses a quadratic function to model the profit in dollars that it expects to earn from selling tickets to a river cruise at x dollars per person Determine the average rate of change for the interval 20 x 60 Partner A 1800 1700 1600 1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 Profit 100 200 Partner A Number of Widgets 0 20 40 20 60 40 80 Cost 800 Cost of Ticket Together What does the average rate of change from 20 x 60 represent 700 800 60 1100 20 1600 100 Partner B Partner B The table and graph shown below model the daily production costs in y dollars of x widgets Determine the average rate of change for the interval 20 80 from the given representation Cost 2000 1800 1600 1400 1200 1000 800 600 400 200 Cost per ticket 20 10 20 30 Together What does the average rate of change from 1 3 represent 40 50 60 40 60 Number of Widgets Profit 80 0 700 1200 1500 1600 1500 100

Let g x 2 3x 4 x 1 x 3 be a polynomial function 1 Sketch a graph of the polynomial HTT X

Let f cos x and g sin x Which of the following lie in the space spanned by fand g a cos 2x b 3 x c 1 d sin x e 0 O a c e O a b c d e O a d O a c d O d

der ideal conditions a certain bacteria population is known to double every 3 hours Suppose there are initially 200 bacteria a Find the number of bacteria after 9 hours 1599 29 Not equivalent P t b Find the function P t which gives the number of bacteria after t hours 200e 0 231t That s not it A bacterial 16112 bacteria Preview 1599 29 bacteria bacteria P t 200e0 231t c Estimate the number of bacteria after 19 hours Round your answer to the nearest whole number Preview bacteria Preview 16 112 bacteria

A newly discovered isotope has a half life of 7 5 days Initially there are 10 grams of the isotope a Find the function P t which gives the number of grams of the isotope after t days P t grams b Estimate the number of grams of the isotope after 11 days Round to two decimal places grams c Estimate the number of days it will take for the isotope to reach 4 grams Round to two decimal places

Under ideal conditions a certain bacteria population is known to double every 3 hours Suppose there are initially 200 bacteria a Find the number of bacteria after 9 hours bacteria b Find the function P t which gives the number of bacteria after t hours P t bacteria c Estimate the number of bacteria after 19 hours Round your answer to the nearest whole number

Use n 2 partitions to find an upper sum for the region under the graph of y 4x 6 above the x axis and between x 9 and x 15 The upper sum for this region is

On day one the population of gray wolves in Montana was 2100 wolves and 7 years later the population was 3000 wolves a Find the function P t which gives the population of wolves t years after day one P t wolves b Estimate the number of wolves 14 years after day one Round your answer to the nearest wolf wolves c Estimate the number of years it will take to reach a population of 4300 wolves Round to two decimal places

18 k 9 k 5

The following graph depicts the area between the x axis and a functions curve You can zoom in and out using the scroll on the mouse You can move the graph by clicking in an empty space and dragging n 6 12 Show Right Endpt Sum Show LeftEndpt Sum Show Actual Area 2 19 O A 2 C 6 8 10 What is the smallest value of n 1 for which the left endpoint sum differs from the exact area by at most 0 2

17 2 v 5 10v 18 k 9 k

Find the distance between u MAN 0 H 3 The distance between u and z is 6 and z 5 1 7

b x 4 10 2x 10 x 3

4x3 8x2 4x 42 x 3

4x3 8x2 4x 42 x 3

1 3 2x 4 2 8 2x

Write your solutions on a separate sheet of paper Estimate 250 as an integral power of 10 no calculator

9 10 1 6n 11 10 1 4v 13 4 8 3 10n 15 9 2 9 8n 10 5 6k 6 12 10 5k 6 14 9 5 3 6x 16 8 9 8n 10

a Solve 42x 1 8x 3 b Solve e e e e

P The following hyperbolic sine and cosine functions are defined below cosh x e e 2 Show that cosh x sinh x 1 sinh x e e 2

Solve 9 4 3 3 0

Suppose f x 1 b show that 1 f x 1 f x L 1

1 For each function a Sketch the graph b Describe the domain and range c State and show the x intercept and y intercept if any d State and show any asymptote e Determine over what interval the function is increasing or decreasing i f x 2x f x 2x Domain Range x intercept y intercept Horizontal Asymptote Asymptote Increasing Decreasing 40 Blank 10 UN HUMEN Wireles 10 0 Domain Range x intercept lpl y intercept Horizontal Increasing Decreasing

2 Find the value s of x a 4x 2 9 2 0 b x 4 10 x 3 2x 10 Home

4 The number of chinch bugs in a lawn doubles every month If there are about 300 bugs now how long will it take for their numbers to grow to 19000 I 300 A 19000 6 2 T n 30 days 1 month 800 19000 2 I 63 3 19000 800 2 800 19 I T 2 30

Find the value of a and b in the function f x ab if f 1 15 and f 2 5 9

Let f x 2 2 2 and g x 2 2 2 Compute f g ERSIER FORMA AIL CRVENON

4 3 6a 1 8 A 3 6a 3 24 B 12 96a 3 24 C 12 96a 12 96a 3 24 D 12 96a 3 24