Algebra Questions

What is the horizontal asymptote of the following rational function x 1 x3 6x 2 y There is no horizontal asymptote y 2 3 y 0 y 3 2 A

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

Which transformation changed f x to g x f x 3x 1 g x 3x 1 Vertical translation of 6 units Horizontal translation of 6 units Reflection across the x axis Reflection across the y axis

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

Name the property of real numbers illustrated by the equation 2 x 5 2x 10 Distributive Property Associative Property Commutative Property Multiplicative Inverse 1

D If six less than three times x is equal to 8 more than 4 what is the value of x squared

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

9 The cost c of renting a lane at a bowling alley can be modeled by the equation c 8 5h where h is the number of hours that the alley is rented for If Janet wants to rent 4 lanes for 3 hours each for her birthday party how much will it cost

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

Solve the triangle a 4 32 m c 5 73 m B 29 6 What is the length of side b m Simplify your answer Type an integer or a decimal Round to four decimal places if needed What is the measure of angle A Simplify your answer Type an integer or a decimal Round to the nearest tenth if needed What is the measure of angle C 0 Simplify your answer Type an integer or a decimal Round to the nearest tenth if needed

K Determine the remaining sides and angles of the triangle ABC What is the measure of angle B 0 Simplify your answer Type an integer or a decimal What is the length of side a ft Simplify your answer Type an integer or a decimal Round to the nearest tenth as needed What is the length of side b ft Simplify your answer Type an integer or a decimal Round to the nearest tenth as needed B B 50 4 ft 35 69 114 4

5 5 13 k 5 10 4k 56

Her nokta ifti aras ndaki e imi hesaplay n 7 1 2 and 4 4 8 4 2 and 2 5 9 2 4 and 0 2

3 5m 1 6 a 1 8 8a a 5 4 4 3r 3r 12 4x 9 3x 8 7x 2x 10

5 5 135 10 4k 56 E 6 6 2 k 1 4k 2k 1

Graph the function y 3 sin 2x Give the period and the amplitude Choose the correct graph of the function OA Ay 3 8T OB Ay 4 0 The amplitude is Simplify your answer Type an exact answer using as needed The period is Simplify your answer Type an exact answer using as needed X 81 C Ay 4 b THU X 8x o O D 3 0 3 8

20 22 Kuta Software LLC All rights reserved Subtracting Rational Expressions 2 Simplify each expression 2 1 10m 1 10 5m 1 8 2 7 3r 9r 3r

sec sec T R 6 Simplify your answer including any radicals Use integers or fractions for any numbers in the expressi

Find the exact function value tan tan 3T 4 3T 4 Simplify your answer including any radicals Use integers or fractions for any numbers in the ex

Select the correct choice below and if necessary fill in the answer box to complete your choice O A csc 8 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OB The function is undefined

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

Rewrite the system as an augmented matrix then use your calculator to write the matrix 10 in row echelon form REF Use back substitution to solve the system Give exact answers in fraction form If the system has no solution state this If the system has an infinite number of solutions give one solution x 5y z 1 3x 11y4z 1 3x 10y 7z 5

7 The measure A in degrees of an exterior angle of a regular polygon is related to the number of sides n of the polygon by the formula nA 360 If the measure of an exterior angle of a regu lar polygon is greater than 50 what is the greatest number of sides it can have

Example 1 Kathy is a repair technician for a phone company Each week she receives a batch of phones that need to be repaired The number of phones that she has left to fix at the end of each day can be estimated with the equation P 108 23d where P is the number of phones left and d is the number of days she has worked this week Q1 Define your variables below in your own words if possible P d Q2 Complete a table for this equation P 0 2 63 0 Q3 What patterns do you see in the table above Q4 How many cell phones will Kathy have left to repair after 3 days 05 How many days will it take Kathy to repair all of the cell phones

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

4 Use the formula asin Bo bcos B0 expression in the following form y a b cos Be C a b cos Be C where C arctan a b a 3 b 7 B 2 to rewrite the trigonometri

O sin u v O O 8 Find the exact value of sin u v given that sin u 25 O sin u v sin u v sin u v sin u v 204 325 204 325 253 325 36 325 36 and cos v 13 Both u and v are in Quadrant II

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

O 2 Simplify the expression algebraically 3 3 sin COS X 2 1 O o cosx COS X 3 O 3 cos x O 3 sin x O cosx 3

6 Write the given expression as the tangent of an angle tan 7x tan4x 1 tan 7x tan 4x tan 3x tan 5x Otan 17x Otan 11x tan 7x

1 Find the expression as the tangent of an angle O tan 60 tan 20 1 tan 60 tan 20 O O tan 40 1 O tan 80 tan 60 tan 40 tan 20

Let a h 20 10 and a2 H For what value s of h will the set a a span R X

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

10 A student works the following problem and then stops Explain what is wrong with the problem 6 cos x 2 1 cos x cos x 3 1 V 3 1 ANSWER 1

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

4 2cosx 1 0 O x 5T 3 0 x 1 O x X 6 7 O x 15 6 7 O x 1 4 of te 0 x 31 O 4 Is a to the equation