Quadratic equations Questions and Answers

5 Use the Heron s formula to find the area of the triangle Round your answer upto two decimal pla a 12 42 b 8 56 c 15 15 29 44 12 51

5 Select a value for b such that a triangle with A 33 and a 4 has no soluti A A 3 67 14 68 1 84 O 1 47 7 24

6 Use the figure below to determine the exact value of the given function csc 20 2 8

6 5 4 3 2 1 7 6 5 4 3 2 41 1 2 3 Slope m 7 6 7 1 Find the slope of the line 2 3 4 5 6

Which of the following points are on the graph of f x 11 Mark all the correct ones 0 1 1 0 O 1 11 1 11 1 0 1 11 1 1 11

Write an expression for the general or nth term an for the arithmetic sequence 3 8 13 18 The general term of the arithmetic sequence is an Do not factor Use integers or fractions for any numbers in the expression

Use long division or synthetic division to divide the following polynomials 3x x 3x 1 x 3

Which point is not on the Unit Circle O 5 3 2 3 3 5 4 5 O 3 4 7 4 O 2 7 3 7

Find the degree measure of the given angle with the given radian measure TU 10 70 degrees 98 degrees 10 degrees 18 degrees

What are the vertical asymptotes of the following rational function y x 5 x 2 x 5 x 7x 10 x 2 and 5 x 2 and 5

Find the zeros of the following function f x x 17x 60x

Select the line that is perpendicular to the following line 4x 2y 2 This is supposed to say parallel not perpendicular y 2x 5 Oy 4x 3 Oy 2x 3 y 4x 2

8 If 5x 6 10 what is the value of 10x 3

Which transformation changed f x to g x f x 2x 2 g x 2x 7 Vertical translation of 5 units Reflection across the x axis Reflection across the y axis Horizontal translation of 5 units

Completely simplify the following expression x y z x y

Solve the following quadratic equation x 2x 3 0

Name the property of real numbers illustrated by the equation 3 7 12 3 7 12 Distributive Property Commutative Property Multiplicative Inverse Associative Property

21 FOTO 437 HAN CO wil sin int zoom in 7 What does this puzzle represent Type a response

4 Her izginin e imini belirlemek i in grafi i kullan n 1 1 3 2 4 4 3 2 01 4 3 2 1 5 6 E im 20 3 4 5 3 O 9 6 49 y 2 9 1 2 3 x 1 2 3 4 5 x 2 5 3 2 1 2 1 5 1 6 4 2 E im F im 2 1 2 3 4 6 4 2 4 6 y 1 2 3 x 3 1 y 5 3 2 4 6 x 3 6 1 3 3 2 1 3 3 2 IN E im 1 2 1 y 2 3 1 3 Ay 3 2 1 1 2 3 x 1 2 E im I 2 3 x

2a A certain video streaming service allows users to rent movies for a flat monthly fee but re quires them to pay a charge per movie that they d like to purchase The equation for the cost c of purchasing m movies through the service is c 10 5m How many movies could be pur chased for 45 2b How much would it cost to buy 10 movies

3 The normal systolic blood pressure P in millimeters of mercury for an adult male x years old can be modeled by the equation below 220 2 If a male has a systolic blood pressure of 120 millimeters of mercury how old is he

Practice 1a The ounces of cereal in a box can be represented by the equation y 120 8x where y is the ounces of cereal in the box and x is the number of days since purchase After 8 days how many ounces of cereal are left in the box 1b How many days will it be until the box is empty 1c After 5 days how many ounces of cereal have been eaten

Try It 1 A taxi costs 2 25 plus an additional 75 per mile This cost y can be expressed by the ex pression y 2 25 75x where x is the number of miles One day Carl has to travel to the air port How much will it cost him to travel 35 miles 2 The cost c of renting a boat for h hours is c 15 12h If Emily receives a bill for 111 how many hours did she spend the boat

Partner Example 4 The speed of a sound wave in the air depends on the air temperature The formula a 1 052 1 08t shows the relationship between a the speed of a sound wave in feet per second and t the air temperature in degrees Fahrenheit Q1 If the air temperature is 50 what is the speed of the sound wave Q2 If the speed of the sound wave is 1 089 8 feet per second what is the air temperature Q3 Write an equation for t in terms of a

C F 32 The equation above represents the relationship between a measurement of temperature in de grees Fahrenheit F and the measurement of a temperature in degrees Celsius C If a room is 20 Celcius what is the temperature in degrees Fahrenheit

7 Write the given expression as an algebraic expression cos arccos x arcsin x I O 0 O O 2x 1 x x 1 x x x 1 x 1 O x 1 x x 1

5 Write the given expression as the cosine of an angle cos 45 cos 40 sin 45 sin 40 cos 45 cos 40 cos 85 cos 80 cos 5

3 Simplify the expression algebraically 6 sin 26 co COS X 6 cos x 1 x 6 sin x 6 cos x 1

1 Find all solutions of the following equation in the interval 0 27

Factoring Trinomials a 1 Factor each completely 1 b 8b 7 3 m m 90 5 n 10n 9 7 m 2m 24 9 k 13k 40 11 n n 56 Name 2 n 11n 10 4 n 4n 12 Date 6 b 16b 64 8 x 4x 24 10 a 11a 18 12 n 5n 6

9 There are at least two different trigonometric ways to solve this equation Choose the method you understand best and explain step by step how y would solve this equation 2 sin x 6 cos x

0 6 Solve the following equation

3 Determine whether the statement is true or false Justify your answer The equation 2 sin 4t 1 0 has four times the number of solutions in the interval 0 27 as the equation 2 sin t 1 0 False True

5 Solve the following equation

An element decays at the rate of S t se 0 062t where s is the initial amount in grams and t is the time in years since this initial amount was present If you have a 45 gram piece of this element how many grams will you have 4 years from now Round your answer to the nearest tenth of a gram

10 Verify that each equation is an identity algebraically Remember your answer is not a yes or no answer Verify means Prove and this whole proof needs to be part of your answer sec tan cos B 1 sin

8 Perform the indicated operations and simplify the result sin e cos e 1 cot 0 cos e sin e sin 0 tan 0 O 2 tan e sec 8 csc 0

7 Use the fundamental identities to simplify the expression tan 0 csc 0 cos 0 tan e Osec 0

1 Evaluate the following expression x 8 n where n is a whole number 3 tan 4x 3 cot 4x O 3 tan 4x cot 4x O4 tan 4x cot 4x O 3 tan 4x cot 4x O tan 4x cot 4x tan 4x cot 4x

4 Decide whether the expression is or is not an identity sec x tan x O Identity Not an identity 0

10 Use fundamental identities to write a simpler version of the expression sin a csc a sin a and explain your process Be sure to tell which fundamental identity you used

6 Which of the following is equivalent to the given expression cos x 1 sinx

An arctic village maintains a circular cross country ski trail that has a radius of 2 2 kilometers A skier started skiing from the position 1 989 0 94 measured in kilometers and skied counter clockwise for 3 3 kilometers where he paused for a brief rest Consider the circle to be centered at the origin Determine the ordered pair in both kilometers and radii on the coordinate axes that identifies the location where the skier rested Hint Start by drawing a diagram to represent this situation x y 2 199246115 0 05758928628 radii kilometers

Find Gl H 5 69 Write your answer as an integer or as a decimal rounded to the nearest tenth GI Submit

Simplify the following rational expression x 6x 8 x 1 X 4 x 1 State the restrictions on the variable Express your answers as integers or fractions in lowest terms Seperate multiple answers with a comma x

The population of a town is increasing by 601 people per year State whether this growth is linear or exponential If the population is 1800 today what will the population be in five years Is the population growth linear or exponential O linear O exponential What will the population be in five years

Write a short statement that expresses a possible relationship between the variables travel time from Denver to Chicago average speed of a car Choose the correct answer below OA As the time to drive from Denver to Chicago increases the average speed of a car decreases OB As the average speed of a car increases the time to drive from Denver to Chicago decreases OC As the time to drive from Denver to Chicago increases the average speed of a car increases O D As the average speed of a car increases the time to drive from Denver to Chicago increases

What are the three basic ways to represent a function Choose the correct answer below OD OA The three basic ways to represent a function are a table a graph and an expression OB The three basic ways to represent a function are an ordered pair a graph and an expression OC The three basic ways to represent a function are a table an ordered pair and an equation OD The three basic ways to represent a function are a table a graph and an equation

32 f x 18 fit x 3 Ay 8 2 6 4 2 2 8 6 8

36 f x 8 2 6 x 3x 4 2x 6 4 2 8 6 4 2 4 6 8 X