Quadratic equations Questions and Answers

Express in terms of sums and differences of logarithms 2 In In 3 3x y 2 3 3x y

Determine the number of cycles the sine function shown to the right has in the interval from 0 to 2x Find the amplitude and the period of the function The given sine function has 4 cycle s Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression For the given sine function the amplitude is 1 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression For the given sine function the period is Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression 4

1 Find the domain of the given logarithmic function f x log 3 X 2 x 2 Solve the following exponential equations algebraically Do not approximate your solutions e 4x 2e 2x 16 0

The graph of a function is shown below Find 4

The measure of the angle in standard position is ty X 3 3v3

Find the measure of the angle in standard position The measure of the angle is

the sun is 58 above the horizon find the length of the shadow cast by a building 91 ft tall Round your answer to the nearest tent 000 070 58 a

e measure of the angle in standard position is 5 5 Ay X degrees

Find the lateral surface area and volume of the solid object shown below 17 7 s 18 1 The base is a square The lateral surface area is Round to the nearest whole number as nem

34 5 Log ny k 11 2 is given below D Below is a graph of g x a linear transformation of f What is the expression for g x

Which of the following are exponential functions Select all correct answers Select all that apply Of x 8 9 g x 15 3 Oh x 9 j x 7 11 Ok x 5 11

Solve the following system by graphing x y 1 x 2y 4 Use the graphing tool to graph the system Click to enlarge graph www Click the graph choose a tool in the palette an 10 B 6 4 2 10 8 to Ay 6 4 2 2

The revenue equation for a certain brand of toothpaste is y 2 3x where x is the number of tubes of toothpaste sold and y is the total income for selling x tubes The cost equation is y 0 7x 2000 where x is the number of tubes of toothpaste manufactured and y is the cost of producing x tubes The following set of axes shows the graph of the cost and revenue equations Find the coordinates of the point of intersection or break even point by solving the system shown below y 2 3x y 0 7x 2000 Dollars y 4000 3000 2000 1000 Cost Revenue 500 1000 1500 Tubes of toothpaste The break even point is Type an ordered pair 20

Use the given graph to solve the following inequality f x g x The solution set for f x g x is Type your answer in interval notation 10 10 200 22

1 Graph by hand in the interval 0 to 2n Upload a photo Identify the amplitude and period a y 2 sin x 2 b y cos x 1

Score 18 27 10 13 answered Question 7 The function f x x bx cis graphed below 29 H 20 18 16 Y 12 10 8 6 19 2 24 4 6 8 10 12 14 16 18 20 q What are the solutions to the equation z bx c 0 f x can be factored into the form zm x n where m and n are integers Fill in the values below to write the factored form of f x f x x

Find the logarithm using the change of base formula log 720 log 720 Round to four decimal places as needed

N 1 z f t z 2 6 5 0 5z 1 0 5 0 5z 1 z 0 5 0 5z 1 2 0z 5 I 2 0 5x 1 z 2 2 0 5 0 5z 1 z 2 AV 2 z 6z 5 0 5z 1 z 2 IN 2 7 6 5 z 2 0 5z 1 HM 2 2 62 5 0 5z 1 I 2 AV 2 z 2 I 2 I 2 IM 2 IN 2 F 2

Find the graph of the given function over a one period interval y 2 tanx Which of the following is the graph of y 2 tanx7 OA iz A od 14 A Cair OG Apt al

The midline is y Ay umum 4 2 0 2 2 Check X A person s pulse rate is the number of time his or her heart

Write an equation of a cosine function for the gra 4 8

Probability Trent has 12 marbles as shown in the diagram below Each marble is either blue labeled with a B red labeled with an R or yellow labeled with a Y R B Trent chooses one of the marbles at random Determine the following probabilities Enter your probabilites as fractions and simplify any fractions as needed What is the probability that Trent will choose a yellow marble 4 What is the probability that Trent will choose a blue marble 6 What is the probability that Trent will choose a red marble What is the probability that Trent will choose a red or blue marble What is the probability that Trent will choose a marble that is not blue D

s s x s 3 1 x 0 5 x5 2 0 Br 1 2 2 r 5 0 5 1 M z 5 z 2 0tr 1 ZM 2 z 5 z 2 0tr 1 z 2 z 6 5 x 2 05r 1 FM 2 7 6 5 I 2 0 5 1 I 2 z 6z 5 I 2 05r 1 r z z 5 I 2 05 1 I 2 123

Identify the equation of the graph y X

For the following function briefly describe how the graph can be obtained from the graph of a basic logarithmic function Then graph the function and state the domain and the vertical asymptote f x log x 1 Describe how the graph of f x can be obtained from the graph of a basic logarithmic function The graph of f x log x 1 could be obtained by translating the graph of y log 2x unit s to the right

Find the following for the graph below 61Y A 0 20 4 maximum minimum period midline 00 8 X

Fill in the missing numbers X 1 0 273 60 95 30 27 O 3 4 45 1 3 9 K 27 1 1 9 1 27 m 27 27 7 4 34 4 5 7 0 6 0 3 0 a 143 in 1 1 9 5 C 13 51 13 In 3476 4 34 13 7 0 3 0 3486 45 4 3 4 3 0 750 100 3 6 2 750 100 9 0 4 C

Find the value of k such that A is singular 105 2 1 0 36 k

Use the given values of k and n to complete the table for the inverse variation model y k k 7 n 1 x 4722 2 Plot the points in a rectangular coordinate system 3 SIN 4 10 10 X 10 2 3 1 10

Determine whether each function is or is not periodic A Graph A Graph B Graph C 4 Choose Choose Choose B y 02 4 8 X C r 21Y 2 2 IX

cos a 5 12 3 a 2 and tan 8 2 3 NE B 7 find sin a B

Consider the graph of the function of the form f x ax a Solve f x 0 b Solve f x 0 a Solve f x 0 Choose the correct answer below O A x 1 or x 2 B 1 x 2 OC x 1 or x 2 OP x 1 orx 2 bx c on the right 3 4 8

4 Let I be the interval of numbers x s where x is more than 3 but less 5 J 1 6 and K 4 8 find and draw JNK UI Write the answer in inequalities

of triangles The pair of trian 14 K T 78 x 13 130 AJKL ATUV 78 91 X 13 130 are J 14 14 3 1 2 4 13 X 13 200 13 X 1 w 13 13 X 7 R 72 45 14 70 n L 50 Q

Q1 Austenitized 40 mm diameter 5140 alloy steel bar is quenched in agitated oil Predict what is the Rockwell hardness of this bar will be at a its surface and b its center c What do you think about the difference in hardness number between the center and surface d Differentiate between hardness and hardenability e Rank the steels in the figure below from lowest to highest hardenability and explain why 600 Bar diameter mm 100 80 60 40 20 0 300 0 0 Cooling rate at 700 C C sec 150 5 25 125 8 S 34 R 10 M R Agitated oil 15 20 LL 5 5 2 3 4 Distance from quenched end De Jominy distance 4 3 19 Bar diameter in LLO 25 mm 1 in Where C center S surface M R mid radius Hardness Rockwell C 288928 65 60 55 50 45 40 30 25 20 JI 15 10 0 1 2 10 5140 20 30 Distance from quenched end mm 4340 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Distance from quenched end sixteenths of an inch 40 9840 4140 8640 50

Sketch the graph of each function and identify the vertex 8 y x 2x 5 4 3 2 1 y 1 2 3 4 x 9 y x 2x 3 14 q F 4 5 3 5 3 2 5 y

Simplify the expression Write your answer with positive exponents only 20 2312 10x y Select one 5y 219 O a O b 227 22 C 2y 2 219 Od

Solve for x 17 a 15 140 122 22 152 X x 20 x 35 8 10 1X Q X 3x 4 25 Tx 3 2x 97 x 6 x 5

The Friendly Driver Taxi Company estimated on the basis of collected data that the number of taxi miles driven each day can be modeled by the function Q 294L day a Graph this function for 0 L 15 b How many taxi miles are driven each day if there are 10 drivers employed c Does this model indicate that the number of taxi miles increases or decreases as the number of drivers increases a Choose the correct graph below A AQ 700 0 15 Q B AQ 700 13 0 0 b If 10 drivers are employed miles are driven per day Round to the nearest integer as needed 15 GLEER AQ 700 21 04 15 U 0 0 3 OD AQ 700 Tim 0 when they employ L drivers per 15 2

Let T R R2 be the linear operator defined by X1 T 2 X2 and let B u u be the basis for which u Find TB T B 5x1 x2 5x1 x2 B 3 U2

In a class of 149 students 95 are taking math M 75 are taking science S and 51 are taking both math and science One student is picked at random Find the probability P taking math or science or both P taking math or science or both Round to three decimal places as needed

Let p be a prime number The polynomial p x x x 1 is irreducible over Zp if and and only if either p 5 mod 12 or p 11 mod 12

Knowing the basic function shapes for power functions and the absolute value function will be very helpful when you work on graphing piece wise defined functions in college algebra Use your college algebra notes or do a web search to find the graphs of each function below and copy down the shapes Power functions y xn Root functions y x x Reciprocal functions y x x n Absolute value function y x y x y x x a 11 AIX y x y x y x x y 2 y x y x 3 y x3 2

hoose the function below that best represents this following graph 10 10 5 Select one O a f x O b f x O C f x O d f x 3 2 1 x 2 2 1 I I 2 5 0 5 10 5 10

Click on the graph of the function f x 2 if 3 x 1 if 1 x 1 1 3 if 1 x 3 B O J O

1 6 0 0 4 1 2 3 Drag and drop options on the right hand side and submit For kayboard navigation SHOW MORE Y 4 for the given function The graph of the function extends infinitely to the left and right 4 3 1 m 444 2 0 4 1 61 T E III E E III 23 4 III TI Relative maxime Not a relative extremum Relative minime Relative maxime Relative minime Not a relative extremum Note relative extremum

First give the exact answer expressed as a simplified radical expression Then give an approximation rounded to the nearest tenth The surface area of a cone is given by the formula Sary where r is the radius of the base and is its height Use this formula to find the number of square feet of waterproof cloth used to make the umbrelia Assume hand exact answer S n Approximation 5 All 1

Consider the following 6 5 Identify the parent function y 4 3 2 1 3 2 1 1 X Identify the transformation represented by the graph Select all that apply vertical stretch vertical shift of 4 units upward horizontal shift of 4 units to the right vertical shift of 4 units downward reflection in the x axis horizontal shift of 4 units to the left Write an equation for the function represented by the graph

The diameter of a circle is given by the function d A 2 where A is the area of the circle Cooking area 243 in right grill a Use the function to find the diameter of each grill left grill right grill Need Help a Use the function to find the diameter of each grill left grill in approximation in Wish b Find the difference between the diameters of the barbecue grills Give an exact answer and an approximation to the nearest tenth exact answer in in Cooking area 75 in in in

Find the value of b if any that would cause the graph of f x b to look like the graph indicated If an answer does not wrist witer DN KDY 0 1