Quadratic equations Questions and Answers

Joey works at a coffee shop on weekends Every now and then a customer will order a hot tea and ask Joey to surprise them with the flavor The teas are categorized by flavor and caffeine level Mint Fruity Chai Caffeine free Caffeinated 7 2 8 7 8 5 What is the probability that a randomly selected tea is fruity given that the tea is caffeinated Simplify any fractions

Consider the function f x x 4 x 1 x 5 x 36 Find the nonreal complex roots of f x

Suive each inequality 7 9x 7 38 10 50 8 6x 13 15 5k 0 16 11w 62 182 11 6 3 14 3 4 17 X 5 112 14 9 12 8x 18 22 18 30 30 6x 15 2x 14 86 7 4q 9

Determine the discharge through the following sections for a normal depth of 4 6 ft n 0 012 and blttom slope S 0 20 Solution a A rectangular section 18 4 ft wide 1 Section area A 2 Wetted perimeter Pw 3 Hydraulic radius Rh 4 Discharge flow rate Q b A circular section 18 4 ft in diameter 1 Inner angle 2 Section area A 3 Hydraulic radius Rh 4 Discharge flow rate Q c A right angled triangular section 1 Side slope m 2 Section area A 3 Hydraulic radius Rh 2 Wetted perimeter Pw rad 3 Hydraulic radius Rh 4 Discharge flow rate Q ft ft ft ft ft ft 4 Discharge flow rate Q d A trapezoidal section with a bottom width of 18 4 ft and side slope of V H 1 2 1 Section area A 2 ft cfs cfs ft cfs cfs

Determine which equation corresponds to the graph shown below

ertical asymptotes if any on the graph ymptotes is selected that number of lines are available to plot Select a location on the grid to plot a line Lines can be m Number of Vertical Asymptotes A O None One OTwo V 10 5 Enable Zoom Pan 10 x

Synthetic division to determine whether 4 is an upper or lower bound of the real zeros of the following polynom f x x4 x 16x 4x 48 ver O upper bound O lower bound O no determination can be made

Vrite the word name for the value of the underlined digit in each whole number For example the value of 2 in 524 is twenty a 3451 four hundred b 11 534 thirty c 45 259 forty thousand d 5 755 965 e 49 432 000 thirty thousand f 268 665 408 Found Work Revert to Last Response

onstruct a polynomial function with the stated properties Reduce all fractions to lowest terms Answer Second degree with zeros of 7 and 5 and goes to as x 0 p x

DETAILS The mass of a hydrogen atom is approximately 0 00000000000000000000000167 gram Write the mass in scientific notation

omplete the table to show the approximate area of the region using n number of rectangles of equal width Round your answers to three decimal places 1 n f x 9 1 y 8 6 2 4 1 2 8 3 4 20 X 50

Use synthetic division to determine if the given value for k is a zero of this polynomial If not determine p k p x 4x 3 7i x 15 9i k 3i Answer Selecting an option will display any text boxes needed to complete your answer Isk a zero of this polynomial Yes No

Let n be a positive real number Use the fact that 2 n n to find each value of n a n 64 b c d n 25 n 36 n

Write each expression as a product of two powers a 23a 2 26a2 46a2 2 a 25a 45a2 b 5c3 4 204c81 54c12 20 7 20 c12 54c7 ww

Consider the following Write the volume of the cube in exponential form OV 67 V 37 OV 6 V 76 V 73 Find the volume units 3

ASK YOUR TEACHER percent of change is the percent that a quantity changes from the original amount When the original amount increases the percent of change is called a percent of increase and can be alculated using the formula new amount original amount original amount a What is the percent of increase from 60 to 84 Percent of increase b A class size increases from 23 students to 28 students Calculate the percent of increase Round your answer to the nearest tenth of a percent

Fill in the blanks to demonstrate the Multiplicative Inverse Property a b 3 c 3 1 1

Which of the following rational numbers are equal to 1 1 2 Select all that apply 199 0 3 TO THO 031

Set models can be created using tiles like the ones shown below Determine which set models could be used to represent each of the following fractions Select all that apply a 0 0 0 0 0 b AA

Step 2 of 2 Test each interval to find the solution of the polynomial inequality Express your answer in interval notation Answer ON W 3 E R 56 5 T MacBook Pro 6 Y 7 C 8 O

Decide whether the two fractions are equivalent by writing them in simplest form 48 59 a and 80 81 Yes these are equivalent fractions No these are not equivalent fractions b c d 38 14 76 and 28 Yes these are equivalent fractions No these are not equivalent fractions 452 63 and 668 100 Yes these are equivalent fractions No these are not equivalent fractions 87 and 45 261 135 Yes these are equivalent fractions No these are not equivalent fractions

Tell whether each statement is true or false xk 1 X True False a b xk ank akn True False H

d 13 Click and drag each point to its appropriate position Some points might be unused 13 4 49 MO 2 1 0 2 N NO SOL Help

S T 10 An initial investment of 2000 doubles in value in 8 1 years Assuming continuous compounding what was the interest rate Round to the nearest tenth of a percent

a Consider the following Describe how the model is used to add two integers positive counters and Combine Select Write the addition problem represented by the model 5 2 O 5 2 3 5 5 2 2 5 in problem negative counters and remove them Because there are Select counters left the sum is

Place the correct symbol or between the two rational numbers a b c d 15 40 C 30 8 11 32 11 14

Which subtraction expression is represented by the integer counters model below 3 6 O 6 3 3 6 6 3

A solution of a polynomial equation is given Use synthetic division to find any remaining solutions x 13x 16x 192 0 3 The remaining solution s of the equation is are Simplify your answer Use a comma to separate answers as needed Type each solution only once

11 Aubrey is painting a mural of an ocean scene The triangular sail on a sailboat has a base of 6 feet and a height of 4 feet Aubrey will paint the sail using a special white paint A container of this paint covers 10 square feet and costs 6 79 per container How much will Aubrey spend on the white paint 12 Silas is a making a wildflower meadow with the dimensions shown He plans to cover the entire meadow with a wildflower seed mix One bag of wildflower seed mix covers 22 square yards and costs 12 79 How much will Silas spend on the wildflower seed mix 4 ft 15 yd 6 ft 10 ye

Apply 7 Kamesh is planting grass in the backyard of his new house A roll of 4 5ft sod costs 0 36 per square foot If his backyard has the dimensions sh shown how much will he pay for the grass 8 FIND THE ERROR Tia determined that the area of the parallelogram shown is 90 square meters Find her error and correct it 10 m 15 m 9 ml 9 Describe a parallelogram that has the same area but a different perimeter than the parallelogram shown Then find the perimeter and area of the new parallelogram 14 in 10 in 10 ft 12 in 1 4 5 ft allang an E colored

1 3 5 6 yd 9 in 5 yd 8 in 9 cm 1 14 cm ples 1 and 2 Asgave liw URA TOURTEMOS AT 2 4 6 8 ft 13m w 2 ft 7 ft 8 m 8 ft ofbuw

Rewrite the system of inequalities adding slack variables or subtracting surplus variables as needed X X 15 2x 4x 227 OA x x 5 15 2x 4x 5 27 OB x x 5 15 2x 4x 27 OC x x 5 27 2x 4x 5 15 OD x x S 15 2x 4x 27 GALLER 12

aking into account both 1 second reaction time braking distance Once you decide to stop when riving at 52 MPH what will the overall stopping distance be

answers Work must be shown for full credit 15 A music concert is organized at a memorial auditorium The first row of the auditorium has 16 seats the second row has 24 seats the third row has 32 seats and so on increasing by 8 seats each row for a total of 50 rows Find the number of people that can be accommodated in the sixteenth row

continuously since the investment was made 10 years ago How much was invested originally Page 1

Desenberg 8 5 Date Period 1 Let Q represent a mass of radioactive radium 226Ra in grams whose half life is 1599 years The quantity of radium present after 1 years is Q 2 1 1599 Determine the quantity present after 100 years Round to the nearest hundredth of a gram

2 How long will it take an investment that pays 6 compounded annually to double in value Round to the nearest tenth of a year

Look at the grap 10 50 10 5 0 5 10 5 What is the excluded value for this function X 10

A theater group made appearances in two cities The hotel charge before tax in the second city was 500 higher than in the first The tax in the first city was 10 and the tax in the second city was 7 The total hotel tax paid for the two cities was 1012 50 How much was the hotel charge in each city before tax First city Second city 3750 2250 X

Look at the graph 10 5 Submit Bos 5 0 10 5 X 10 What is the equation of the horizontal asymptote

Look at the graph 10 5 2014 5 0 5 10 5 XA 10 What is the equation of the vertical asymptote

Look at the graph 10 5 Bofy 5 0 5 X 10 What is the equation of the horizontal asymptote

4 Which graph has a domain of x 5 and a range of y 2 A B C I D 3

14 The graph below shows the function f x Sketch the graph of 2f x 3 1 on the grid provided 491 X 4 2 2 10 T 6 W Y 6 5 5 4 6 0 9 12 100 8 T 20 70 to X 4 2 44 J 2 10 2 10 Y 4 10

5 You have a lemonade stand on the side of the road A car drives at a constant speed down the road toward your stand and then away from your stand as it passes A Linear B Quadratic C Square Root D Absolute Value

An unknown radioactive element decays into non radioactive substances In 580 days the radioactivity of a sample decreases by 45 percent a What is the half life of the element half life days b How long will it take for a sample of 100 mg to decay to 87 mg time needed days

8 A school is building a rectangular soccer field that has an area of 6000 square yards The soccer 4 points field must be 40 yards longer than its width Write an equation for the area of the soccer field and determine algebraically the dimensions of the soccer field in yards

5 There is a nerf gun that shoots a dart into the air from the roof of a house in such a way that the height can be modeled by the equation h t 16t2 122t 25 h t is the height of the dart in feet after t seconds a When will the height be 45 feet in the air b When will the dart hit the ground X b b 4ac 2a

4 Sketch a graph that would only have one solution There is more than one answer for this 10 5 5

Short Answer Clearly indicate the necessary steps including appropriate formulas and substitutions A correct numerical answer with no work shown will receive only 1 point 6 A golf ball is hit from the ground and its flight can be modeled by h t 16t 48t where his height in feet and is time in seconds Find the time it takes for the golf ball to return to the ground 2 points