Algebra Questions

The graph of a polynomial function is given to the right On the basis of the graph answer the following questions a Find as many factors of the polynomial as possible b Construct a polynomial function with the zeros shown in the graph c Is it possible to find any other polynomial functions with the given zeros d Is it possible to find any other polynomial functions with the given zeros and the same graph a The factor s is are Simplify your answer Use a comma to separate answers as needed b P x Type your answer in factored form c Is it possible to find any other polynomial functions with the given zeros Yes 400 400

a The graph of y f x is shown Draw the graph of y f x H X S

K Certain positive angles are marked in the given figure Find the corresponding radian or degrees measures 30 radians 6 T Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression 60 T 4 radians 45 Simplify your answer Do not include the degree symbol in your answer 2 T 3 radians Simplify your answer Type an exact answer using a as needed Use integers or fractions for any numbers in the expression radians 120 O 3 Simplify your answer Do not include the degree symbol in your answer 3 radians 4 Simplify your answer Do not include the degree symbol in your answer 3x 4 2k 3 radians 150 radians 180 210 225 4x 3 radians 3x 2 KIN 90 2 radians 60 x 4 radians 270 5x 3 radians 30 10 330 315 X 0 radians radians Q Q

b The graph of y g x is shown Draw the graph of y 2g x KH 8 6 4 2 19 2 T 6 8 2 6 8 x X

A member of your research team wants to compare the prevalence of liver cancer in Japan to the prevalence of liver cancer in the Philippines The only information you have with you is Surveillance data for the year 2015 shows there were 7 734 existing cases of liver cancer in the Philippines Among those cases 1 432 were new cases of liver cancer In the same year there were 36 147 existing cases of liver cancer in Japan During this time Japan s population was 127 600 000 people and 96 710 000 people were living in the Philippines What do you tell your team Which country has higher prevalence 4 points for calculating prevalence in each country 2 points for explaining your response

For certain decisions the time it takes to respond is a logarithmic function of the number of choices faced C R 0 17 0 44 log N where R is the reaction time in seconds and N is the number of choices Find a formula that gives the numb can be faced in terms of the reaction time Express numbers in exact form Use symbolic notation and fractions where needed eachillan Learning

From the function s graph identify and interpret its maximum O The function s maximum is 2 385 000 at x 5 This implies the company s maximum annual revenues from selling the cookers will be 2 300 000 This happens if the company raises the unit price by 5 00 five times O The function s maximum is 2 250 000 at x 5 This implies the company s maximum annual revenues from selling the cookers will be 2 250 000 This happens if the company raises the unit price by 5 00 making the unit price 55 dollars O The function s maximum is 2 250 000 at x 5 This implies the company s maximum annual revenues from selling the cookers will be 2 250 000 This happens if the company raises the unit price by 5 00 five times making the unit price 50 25 75 dollars The function s maximum is 2 250 000 at x 5 This implies the company s maximum annual revenues from selling the cookers will be 2 250 000 This happens if the company makes the unit price 5 00 Harry runs a firework business and needs to calculate how high fireworks fly He fires a firework into the air on a hill 100 feet ab level The height of the firework s trajectory can be modeled by the polynomial function in the following graph 160 140 120 100 80 60 40 201 y g 0 2 0 4 0 6 0 8 10 12 14 16 18 20 22 24 2 6 2 8 3 0 32 34 3 6 3 8 4 0 4 2 4 4 4 6 4 8 mat

1 f x x36x 9x 40 0 0 PILLE DURATION CENTEN VE 1700 a State the domain in interval notation MIREZION 128 b State the range in interval notation c State the end behavior d State the local maxima e State the local minima f State the x intercepts g State the y intercepts h State the intervals where the graph is increasing

Use the unit circle along with the definitions of the circular functions to find the exact values for 3 2 the given functions when s Select the correct choice below and fill in any answer boxes in your choice A O A sin Part 2 of 3 3 1 2 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression B The solution is undefined Select the correct choice below and fill in any answer boxes in your choice COS sin O 32 3r 1 32 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OB The solution is undefined Points 0 of 1 COS 3r 2 n tan 3x 2

Locate and interpret the function s maximum O The function s maximum is 2 2 at x 6 2 It implies the stock s price hit the maximum of 2 20 at 2 12 p m O The function s maximum is 8 at x 7 1 It implies the stock s price hit the maximum of 8 00 at 3 06 p m O The function s maximum is 7 2 at x 8 It implies the stock s price hit the maximum of 7 20 at 4 00 p m O The function s maximum is 6 2 at x 2 2 It implies the stock s price hit the maximum of 6 20 at 10 12 a m Johan is observing some suspicious activities on a web server The following graph shows the web server s CPU usage in the past 10 minutes TCPU Usage in Percent

In Venezuela the population on January 1 2000 was 24 8 million and the 2000 mid year population was 25 million people 125 000 deaths occurred during the year ending December 31 2000 These included 15 000 deaths from diabetes For the year 2000 80 000 new cases of diabetes were diagnosed As of the start of 2000 1 1 million residents of Venezuela had diabetes You may assume that no one immigrated into or emigrated from Venezuela in 2000 note this study would be difficult to conduct today in part because of problems counting the large number of emigrants 1 point each for the correct numerator denominator and answer 1 2 point will be deducted for missing UNITS cases deaths per population if applicable a What was the diabetes specific mortality rate in Venezuela in 2000 per 100 000 population b What was the prevalence of diabetes per 100 000 population at the end of the year on December 31 2000 assuming the population was the same as mid year

Identify the function s minimum O The function s minimum is 10 4 at x 1 4 O The function s minimum is 5 at x 4 O The function s minimum is 4 at x 5 O The function s minimum is 2 5 at x 4 The following chart recorded a company s stock price change in a certain day Stock Price in Dollars 765 N 8 3 2 1 GO AY

Find the inverse of the function on the given domain Enter the domain using interval notation f x x 6 6 0 f 1 x on domain

f 2 2 62 5 Does the parabola defined by fopen upward or downward O Downward O Upward Determine the vertex in z y form of the parabola defined by f Is the vertex the maximum or minimum value of f O Minimum O Maximum Determine the y intercept in x y form of the parabola defined by f Determine the x intercept s in x y form of the parabola defined by f If multiple x intercepts exist enter the solutions using a comma separated list If no z intercepts exist enter DNE

2 3x x 14x The solution set is Type your answer in interval notation

3 5x 17x 40x The solution set is Type your answer in interval notation

2 Use the key features of the function to sketch its graph x intercept none y intercept 0 1 Continuity continuous Increasing all values of x 0 Decreasing all values of x 0 Extrema minimum at 0 1 flv

8 Let be an angle such that sin 9 Find the exact values of tan 0 and sec 0 tan 0 sece 0 0 and cot0 0 3 16 X S

Find two numbers that a multiply to 40 and add to 6

x 12 3 The solution set is Type your answer in interval notation Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed

X b The solution set is Type your answer in interval notation Use integers or fractions for any numbers in the expression Type an exact answer using radicals as needed

11x 4 X 1 www The solution is Type your answer in interval notation Use integers or fractions for any numbers in the expression Type an exact answer

Solve x 4 x 5 2 X 5 x 7 The solution set is Type your answer in interval notation

Use long division to find the quotient Q x and the remainder R x when P x is divided by d x and express P x in the form d x Q x R x 4 2 P x x 2x 8 d x x 2

x x 8 16 Determine the vertex of the parabola in x y form Determine the y intercept of the parabola in x y form Determine the x intercept s of the parabola in x y form If mulitple intercepts points using a comma separated list If no x intercepts exist enter DNE

A ball is thrown from an initial height of 3 feet with an initial upward velocity of 33 ft s The ball s height in feet after 1 seconds is given by the following h 3 331 167 Find all values off for which the ball s height is 19 feet Round your answer s to the nearest hundredth If there is more than one answer use the or button initial height ground seconds Dor X

d the exact value COS Type an integer or a fraction Type an exact answ

Use a calculator to approximate tan 6 5711 tan 6 5711 Round to four decimal places as needed

and the exact value S T 6 COS Points 0 of 1 Type an integer or a fraction Type an ex

Use the figure of the first quadrant of the unit circle to find the exact circular function value COS 90 H6 N S 0 1 60 WIN 45 30 2 2 NO N 0 0 1 0 G COS T Simplify your answer including any radicals Use integers or fractions for any numbe the expression

The function f x x 7 10 is one to one and therefore invertible Determine f Graph both f 1 and f along with the identity function f x x f x

Find the exact value of the following expression Do not use a calculator to enter a decimal approximation sin RIN sin Type an integer or a fraction Type an exact answer using radicals as needed Rationalize all denominators

Write a polynomial f x in completely factored form with leading coefficient 1 that satisfies the conditions Then determine the graph of f x Degree 3 zeros 4 with multiplicity 2 and 3 with multiplicity 1 Type your answer in factored form Type exponential notation with positive exponents

Use a half angle or reduction formula to fill in the blanks in the identity below cos 8x cos x

Identify each of the following examples as primary secondary or tertiary prevention An anti smoking program for healthy adults i Select A program to help adults with type 2 diabete Select Receiving a heart transplant is Select Primary prevention Secondary prevention Tertiary prevention Physical therapy for those who have suffered a stroke is Select A condom distribution program at the UNCG Rec Center is Select

12 What is the factored form of the expression 25x 16y over the complex numbers

365 days 1 year Units of weight volume Weight 16 ounces 1 pound 2000 pounds 1 ton 1 gram 1000 milligrams 1000 grams 1 kilogram Must be memorized Volume 1000 milliliters 1 liter 1 cup 8 fluid ounces 1 pint 2 cups 1 quart 4 cups 1 gallon 4 quarts

If the incidence rate of pancreatic cancer is 33 new cancers per 100 000 P Y and the prevalence is 18 per 100 000 population what is the average duration time from diagnosis to death

A person is a member of this type of population only as long as he or she has the defining state or condition When the person stops having the defining condition they stop being counted as part of the population O Fixed population O Dynamic population O Candidate population O Catchment population

Macmillan Learning Solve the following equation for x log 3x log 4 x 1 Give an exact answer Use symbolic notation and fractions where needed Enter NO SOLUTION a solution

20 Solve the following equation for x 25 ln x 4ln x Express numbers in exact form Use symbolic notation and fractions where need

Apply It Group Problem Solving Tasks G In a class there is a 2 3 ratio of boys to girls If there are 30 students in the class how many boys are there

60 The terminal velocity for an object dropped near the surface of Earth is the maximum downward velocit by the falling object For a man of average size the terminal velocity is about 176 feet per second It is f velocity v in feet per second t seconds into his fall before he opens his parachute is given by v 176 1 0 75 How long does it take the skydiver to achieve 99 of terminal velocity Give your answer to the nearest second Macmillan Learnir

Write the expression below as a trigonometric function of a single angle Then evaluate cos 10 cos 18 sin 10 sin 18

Solve for a d r Type a response

Evaluate 4x 3xy for x 3 and y 4

Find the measure in radians of a central angle of a sector of area 12 square inches in a circle of radius 3 2 inches The central angle measures approximately radians Round to the nearest tenth

Find the area of the sector of a circle having radius r and central angle 8 T r 10 6 cm 0 4 Points 0 OT 1 The area is approximately cm Round to the nearest tenth

Use the figure to determine the radian measure of angle 8 0 radians C CLB

2 Factor 81x8 36y 2 3 Factor 5x 23x 12 4 Factor 125x6 27y15