Quadratic equations Questions and Answers

Let f z 3 Evaluate the following expressions Solutions should be exact Do not round f 1 f 5 f 4 f 0

Which expression is equal to O 8 m 3 m 2 2m m 2 4m m 6 m 8 2m 2 m 2 m 2 m m 3 m 4m

Enter the simplified form of the complex fraction in the box Assume no denominator equals zero 2 x 3 3 x 3 3 X

Which expression is equal to 3x x 3 3x 2x 6 x x 3 4x x 6 x x 3 x 42 6 x x 3 4x x 6 T x 3 x 2 I

Which expression is equal to O r 3x 10 x 2 x 5 x 9x 6 x 2 x 5 3x 11x 6 x 2 x 5 2 11x 6 x 2 x 5 2x x 2 x 3 x 5

Marcus states that the polynomial expression 3x 4x y 2 is in standard form Ariel states that it should be y 4x y 3x 2 Explain which student is correct and why 1

Identify the expression which is not equivalent to the others A 1 B x6 x C 2 2 3 D E x15 x3 6 x 4

17 26 19 2x y 21 23 25 27 29 2r 3n 3n 3m m 3 2 4x y z 4x 4 3 3 4m n p 224 3m n P 18 x y 20 3m 2 22 24 4 m 2m 26 4 3 2x y z 3x y z 28 2h j k 3 jk 30 1 1 3x y z 4 00 x y z

ASUW is equilateral and ZTSU ZUWV Complete the proof that AUVW T S 1 2 U 3 Statement V ZVUW ZSUT UW SU SAUVW AUTS W ASUW is equilateral ZTSU ZUWV Reason AAS Additive Property of Angle Measure Additive Property of Length All right angles are congruent

Which of the integers below is the least integer value that will make the following inequality 2x 6 18 true 8 O 20 6 6

If 13 144 O 24 54 5 4 zd then what is the value of 6d 3

Solve for y 6 y 5 O y O y O Y 9 19 6 y 1 24 19 6

24 x 30 100 9

Find the domain of the given function Enter the solution using interval notation 5 25 x n x Domain Find the domain of the given function Enter the solution using interval notation 8 49 T s x

p x x 8x 19x 19x 13x 24

Find fog x and gof x and the domain of each 2 f x x 1 g x 6x 5x 1 fog x Simplify your answer The domain of fog x is Type your answer in interval notation gof x Simplify your answer The domain of gof x is Type your answer in interval notation

22 How many solutions does the following system have 1x 2y 11 3x 6y 33 O two O one O infinite

pq Express log b 5 9 m b OA log b 46 OB log b 46 pq 5 9 mb 46 pq mb 4 log p 6log bq 5logm 9 log 4 6 logpq log 5 logbm log9 5 9 46 pq OC log 5 9 m b in terms of sums and differences of logarithms 46 p q OD log 5 9 mb log 4p log6q log 5m 9 4 logpq 6 5 logbm 9 logb

Simplify the expression by using an appropriate identity Do not use a calculator cos21 cos69 sin21 sin69 cos21 cos69 sin21 sin69 1

Completely factor and find all roots of the following polynomial Use the given partial graph of f identify a root of f f x 15x 73x 37x 129x 36

26 Determine whether the inequality shown below matches the graph y 2 11 no yes 11 x

For the given functions find fog x and gof x and the domain of each 3 1 7x f x g x 1 X fog x 0 5 Simplify your answer

14 Choose the correct graph for the inequality y24 c

The demand for lumber is increasing exponentially The amount of timber N in billion cubic feet consumed t years after 1997 can be approximated by N t 65 1 018 where t corresponds to 1997 How much lumber was consumed in 1998 billion cubic feet Round to the nearest hundredth

ST H E A J 17 23 88 9 F 11 13 33 325 F 90 W 19 7 25 97 75 W 16 7 v 15 2 15 3 8 x 50 18 3 16 9 k 21 d 15 crico B 24 x 30 100 9 19 8 12 t 5 22 3 n 25 2m 7 m 40 27 The sum of the angle measures of any triangle is 180 If one angle of a triangle measures 35 and another angle measures 72 what is the measure of the third angle 7 28 63 17 10 q 3 6 5 20 43 7 x 16 0 23 3 b 1 12 26 0 3y 10 4y 28 The perimeter of this quadrilateral is 100 in What is the length of the side not given 27 in 23 in 32 in

1 n 3 10 4 d 16 5 7 18 k 1 10 11 x 44 2 y 8 15 5 6 u 22 8 7 p 12 11 5 m 92 13 In 3 way light bulbs the highest wattage is the sum of the two lower ones If the lowest is 60 watts and the highest is 150 watts what is the middle wattage 3 9 x 2 6 a 11 14 9 3 b 60 12 y 27 4 14 It was an extremely cold day on the mountain The temperature dropped 22 to 13 F What was the temperature before the drop

EG bisects ZFEH and ZFGH Complete the proof that AEGH AEGF F 1 2 E Statement G EG bisects ZFEH EG bisects ZFGH ZFEGZGEH 3 4 ZEGF ZEGH EG EG AEGHAEGE H Reason Given Given Definition of angle bisector Reflexive Property of Congruence

14 refer to the following information In 2006 180 million pounds of crab were sold In 2011 80 million pounds were sold In 2006 the price of king crab was 8 per pound at the beginning of the year and dropped to 7 per pound toward the end of the year If 60 of the king crab supply was sold at the higher price per pound and the rest was sold at the lower price per pound what was the total revenue generated in millions of dollars from the sales of king crab in 2006 gridded response Your answer In 2011 the price of king crab was 17 per pound In 2012 x million pounds of king crab were sold at 16 per pound If the total money generated from sales each year was the same what is the value of x

The amount of protein supplied by five different food products A B C D and E costs are 2 00 2 20 2 50 4 00 5 00 respectively for 10 grams of product Which of the five food products supplies the most protein per dollar O A OB

Boyd grows only tomatoes and raspberries in his garden Last year he grew 140 pounds of tomatoes and 60 pounds of raspberries This year the production by weight of tomatoes decline by 20 percent and the production by weight of raspberries declined by 50 By what percentage did the total yield by weight of Boyd s garden decline O29 percent 30 percent O 35 percent 70 percent

A high school basketball team won exactly 65 percent of the games it played during last season Which of the following could be the total number of games the team played last season no calculator O 22 O 20 18 14

Which of the following numbers are equivalent 1 05 II 15 TA 0000

k Marty owns an electronics store One week he decides to have a sale in which he decreases the price of a TV from 500 to 425 What was the percent decrease in the price rounded to the nearest whole percentage point if needed O 7 O 15 18 75

You can retry this question below 5 4 3 5 3 2 29 S 6 1 2 3 The function graphed above is Increasing on the interval s 1 1 5 13 Decreasing on the interval s 0 1 U 15 80

8 What are the factors of the polynomial function Use the rational root theorem to determine the factors f x x x2 10x 8 The possible rational roots are 2 11 12 14 18 o x 1 o x 1 0 x 2 o x 2 0 x 4 o x 4 o x 5

3 Which graph represents f x 2x8 Explain how you know based on the sign of the leading coefficient and degree of function

Following surgery a patient has been receiving a pain relief medication intravenously The concentration C in milligrams per liter of the medication in the patient s bloodstream t hours after this process started is given by C t 50t 10 5 a The patient will not receive pain relief unless the concentration of the medication is 15 or more milligrams per liter Use this function to determine the time interval for which the concentration of the medication C will be greater than or equal to 15 milligrams per liter The time interval for which the patient will receive pain relief is Express your answer in interval notation and round any decimals to the nearest tenth of an hour hours b If the intravenous medication continues to be given to the patient that is as time goes on and t approaches oo the concentration will approach milligrams per liter Question Help

500t The population of Sasquatch in Salt Lake County was modeled by the function P t t 50 t 0 represents the year 1803 When were there fewer than 75 Sasquatch in Salt Lake County 4 Present your answer to the nearest whole year in interval notation There were fewer than 75 Sasquatch in Salt Lake City between the years Quortion Helps where

3 Which graph represents f x 2x Explain coefficient and degree of function

1 arch Algebra Prep 222 Ke Seftware LLC Graph linear Inequalities Sketch the solution to each system of inequalities 1 y2 x 3 y23x 1 A 2 D 21 B

9 1 5x 2y 10y Xx 46 A 3 7 C 1 7 B 3 7 D 3 7 10 10 24 9x 2y 0 5y 29 7x A 2 3 G 2 9 B 9 2 D 2 9

For the function f x x 1 construct and simplify the difference quotient 5 Simplify your answer Use integers or fractions for any numbers in the expression f x h f x h Answer

For the given functions find fog x and gof x and the domain of each f x x 5x 3x 10 g x x 1 a Find fog x b What is the domain of fog x Use interval notation c Find gof x d What is the domain of gof x Use interval notation

The point 16 3 is on the graph of y f x Find the corresponding point on the graph of y g x where g x f x Simplify your answer Type an ordered pair x y

Directions Fill in the table The first one is done for you as an example 1 Example y 10 10 201 30 40 W M y 84 67 ut al 6 8 Value of the zero s 3 0 2 Value of the y intercept s 0 Identify the interval s where the function is negative 3 x 0 2 x Identify the interval s where the function is positive x 3 0 x 2

7 2r 1 11 9 2n 6 6

1 2m 2m 3 4 2 2 m 2m 4 4n 2n 2x v3 2x7 6 2x

The amount of a sample remaining after t days is given by the equation P t A 3 where A is the initial amount of the sample and h is the half life in days of the substance A scientist has a 10 mg sample of a radioactive isotope The isotope has a half life of 8 days After 16 days how much of the radioactive isotope remains 2 0 mg 7 1 mg 5 7 mg 2 5 mg

Solve the inequality 2r 9 7 or 7z 5 30 In the blanks below fill in the inequality symbol and number to your solution

Given the absolute value inequality which of the following are part of the solution Select all that apply 10p 4 34 A B D 1 C 7 1 3 LL 10 1 E 3 5 1 2