Quadratic equations Questions and Answers

The demand D for a new rollerball pen is given by D 0 007p 0 4p 120p where p is the price in dollars a Find the rate of change of quantity with respect to price dD dp b How many units will consumers want to buy when the price is 25 per unit c Find the rate of change at p 25 and interpret this result d Would you expect dD dp to be positive or negative

18 4x 2y 7z 26 5x 3y 5z 50 7x 8y 3z 49

11 15 23 P5 Answer the following constructed response question Follow all directions to receive full points A Write two expressions that can be used to find the area of the figure below Expression 1 4x 4x 8x 1 Expression 2 B If x 3 find the area of the rectangle using one of your expressions from Part A All measurements are in feet Show all of your work

Factor the expression Use the fundamental identities to simplify if necessary There is more than one correct form of each answe sin x 6 cos x 15

d x 2i x 2 x 1 x 1 x 2 x 2 e 9 Use the definition of the logarithmic function to find x log4x 3 a x 12 b x 4 c x 81 d x 64 e none of these

iven the functions f x and g x below find all solutions to the equation f x g x to the earest hundredth f x 0 2x x x 4 8 g x 0 3x 3 9

Challenge x 1 10 12 S 15 2

8 x 8 7

6 3 x 2

1 x 90

5 Jada measures the growth of 10 tomato plants and lists the data in a table Use the data in the table to create a line plot a Plant Growth inches A 2 8 0 B 7100 8 C 318 J D 218 1 8 E 5100 8 13234 F 13 G 00011 8 H 48 7 8 618 1 778 b What is the difference in inches between the growth of the plant with the greatest amoun of growth and the plant with the least amount of

2 2x 5 41

Given sin 0 5 and cos 0 find the exact values of the following 7 sin 20 cos 20 tan 20

x 1 Ella and Alicia are comparing scores on their college entrance exams Ella s SAT score is 1380 Alicia s CT score is 32 The mean SAT score is 1000 with a standard deviation of 200 The mean ACT score is 21 with standard deviation of 5 Who has the better score

Use the given function f to answer parts a through f below X 4 f x 4 5 B There is no horizontal asymptote d Find f the inverse of f f x 4 log 4 x 5 Simplify your answer e Find the domain and range of f The domain of f is 1 Type your answer in interval notation

Use the given function f to answer parts a through f below f x log x 4 3 d Find f the inverse of f f x 10x 3 4 Simplify your answer e Find the domain and range of f1 The domain of f is

Add 4i 2 8i

5 2i

2 2i 9 5i

Use the given function f to answer parts a through f below X 4 f x 4 5 via w grupis v MVIVIR O A 10 Q 10 Q X

in 15 0

6 5i 3 10i

17 61 9 10i

3x2 8 19

7 9 7 41n 2214n 71 n 54 76 A 41m n 1 n 54 70 n 54 B 41n n 2 71 n 54 C 41m D 41m 1 71 n 54 8 8 66x 2912x x 3036 96 x 41 A x 30x 29 96 x 39 B x 30x 35 96 x 37 C x 30x 33 96 x 36 D x 30x 32 96 x State if the given binomial is a factor of the given polynomial 9 x 3x 8 x 3 B No 10 A Yes 10 2m 5m 30m 12 6 m A No B Yes

2 13

8 Software LLC REVIEW REVIEW Divide 8 11x 57x 21x 27 11x 9 A x 6x 3 B x 6x 5 1 11x 9 C x 6x 4 D x 6x 6 5 11x 9 Find each product 10 3p p 8 4p 7p 5 A 12p 17p 54p 51p 40 B 12p 25p 40p 2 61p 40 C 12p 17p 54p 51p 40 D 12p 7p 40 All rights reserved 9 9 8x 57x 33x 5 8x 1 A x 7x 5 B x 5x 3 C x 7x 8 D x 5x 2 1 8x 1 4 8x1 ZOC

4 6 Simplify each sum 4 2x 5 6 2x A 1 C 1 5x 6 A Simplify Your answer should contain only positive exponents a b 2a b 2a 7 2a b C 266 1 16a 10 B B 1 x D 3 5x D b 16a lo 64a12 b 1971 00 LLC K 5 AIL 5 2x 6x 3x x A 7x x C 8x x 7 2a bab ab C 64a 4 14 B D B 15x x D 14x 8b 16b 20 Maki 3

10 Find each product 10 3p p 8 4p 7p 5 A 12p 17p 54p 51p 40 B 12p 25p 40p 61p 40 C 12p 17p 54p 51p 40 D 12p 7p 40 State if the given binomial is a factor of the given polynomial 11 11 4x5 24x 5x 27 x 6 12 A No B Yes 12 x 8 7x 7 x A Yes B No

REVIEW REVIEW Simplify each difference 2 3n 6 3n 4n 7 7n A n 4n 12 6n B n 4n 14 6n C n 4n 12 13 D n All rights reserved 3 3 6n 5 2n 4n 5 8n A 10n 7n 5 B 10n 8n 5 C 10n 2n 5 D 10n 2n 2

x 1 x 15 2x zoom in 3x 2 1 What is the expression that represen the area of the shaded part of the figure Type a response

Synthetic Division Divide 11 3 2v 2 v A v 3 B 2 v 3 C v v 3 3 D 2 1 6 2 v 4 2 v 2 2 2n 3n 2 n 1 A 2n n 1 B 2n n 2 C 2n n 3 D 2n n 3 n 1 3 n 1 3 n 1 3 n 1

The formula S SA 6 gives the length of the side s of a cube with a surface area SA How much longer is the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters 30 2 5 meters 30 2 5 meters 8 5 meters 5 6 2 5 meters

5 3 3 5 3 A 12 2 15 B 12 C 8 2 15

Multiply 5 4 3 10 A 2 3 2 B C D 4 5 15 2 30 2 3 3 2 2

The population of Fort Pierce can be modeled by the function P 45481e0 008266t where t is the number of years since 2020 Use the above function to answer the following questions What was the population of Fort Pierce in 2020 In what year is the population of Fort Pierce projected to reach 74 589 Round the solution to the ne whole number

State if the given binomial is a factor of the given polynomial 9 x 3x 8 x 3 A Yes B No 10 10 2m 5m 30m 12 6 m A No B Yes

Synthetic Division Divide 1 3 2 1 v 2 v 6 2 v A v v 3 4 2 v B v v C v v 3 3 D 2 v 3 3n n n 5 2 n A n n 3 B n 2 C n 2 D n 1 1 2 n 2 2 n 3 2 n 5 2 n 2 4 2 2n 3n 2 n 1 A 2n n 1 B 2n 2n 2 n 1 3 n 3 n 1 3 C 2n n 3 D 2n n n 1 3 n 1 4 8v5 2v 11v4 10v 2 v 7 A 8v4 5v 2v 1 2 v B 8v4 5v 2 C 8v4 5v 2v 5 D 8v4 5v 4 2 2 v 4 2 v 1 2 v

i 7

0 16

CAJ N

On the moon the distance d in feet that an object falls in time t in seconds is modeled by the function d t t Suppose an astronaut on the moon drops a tool How long does it take the tool to fall 4 feet 000

x 7x 6 0

x 7x 6 0

y 10 3x 5x y 6

x 16 0

x 16 0 AIRIE

As age increases so does the likelihood of a particular disease The fraction of people x years old with the disease is modeled by f x 0 8 1 271e 0 122x a Evaluate f 25 and f 65 Interpret the results b At what age does this likelihood equal 60 a Select the correct choice below and fill in the answer boxes within your choice OA 25 and f 65 COLLE This means that among Round to three decimal places as needed people age 25 have the disease while among people age 65 have the disease OB 1 25 and f 65 Round to three decimal places as needed This means that among people age 25 have the disease while among people age 65 have the diconco

Find the value log 355 log 31 log 355 log 31 Round to four decimal places as needed

Write the given statement in an equivalent exponential form log 6216 6 The equivalent exponential form of the given statement is Type your answer using exponential notation Do not simplify