Algebra Questions

of Rudy Meangrurow Find the difference quotient Assume h 0 f x h f x h 2 for the following function below 700

ind the domain of each of the following functio 3 x x 6 4 x 9 1 f x 2 h x 3 g x 4 p x 3x x x 4 5x x 2 x 4 x 3 r 2

Bonus Give an example of a function with domain 0 1 and range consists of 1 1 and 2 3

Solve 4x 21 Graph the solutions on the number line 26 14 45 H 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10

Matt is five years older than twice his cousin Andy s age The sum of their ages is less than 35 Let x represent Andy s age Which inequality represents Andy s possible age 00 z 25 00 z 10 0 0 x 10 25

What is the solution to the compound inequality in interval notation 4 x 1 4 or 2x 4 10 O 3 or 2 0 O 3 or 2 O 3 2 O 2 or 3

Which graph represents the solution set of the compound inequality 5 a 15 2 10 8 6 4 2 0 2 4 6 8 10 19 10 8 6 4 2 0 2 4 6 8 10 0 2 4 6 8 10 12 14 16 18 20

Solve for n 3 n 6 3n 8 O no solution all real numbers

Solve for x 410 7x 0x2 Ox 2 x 2 0x 2

Use your calculator to evaluate cos 0 56 to at least 3 decimal places Give the answer in radians

Verify the identity algebraically Use a graphing utility to check your result graphically 7 csc x csc x sin x 7 sin x 7 cos x 7 cot x 7 csc x sin x Expand the expression and then use the Reciprocal Identities to simplify Simplify your answers completely 7 csc x sin x sin x 7 csc x 7 7 7 csc x csc x sin x 7 sin x 7 cos x sin x 7 cot x 7 cot x 7 7 7 cot x

Graph Mean Of Leaves 20 15 10 5 0 9 8 10 12

The Mars company says that before the introduction of purple yellow candies made up 20 of their plain M M s red another 20 and orange blue and green each made up 10 The rest were brown Complete parts a and b b Assume you have an infinite supply of M M s from which to draw Suppose you pick three M M s in a row 1 What is the probability that they are all brown 2 What is the probability that the third one is the first one that is blue 3 What is the probability that none are orange 4 What is the probability that at least one is red 1 The probability of picking three brown M M s is Type an integer or a decimal Do not round 2 The probability of the third one being the first blue one is Type an integer or a decimal Do not round 3 The probability that none are orange is Type an integer or a decimal Do not round 4 The probability of at least one red M M is Type an integer or a decimal Do not round Submit test

A line has a slope of 7 and a y intercept of 15 What is the equation of the line in slope intercept form A y 7x 15 B y 7x 15 C y 7x 15 D y 15x 7

Solve the equation for x 125 3 5 8 The solution set is Simplify your answer Type an integer or a fraction

The solution set is MEIER Use a comma to separate answers as needed

Find each quotient 1 1 2 3 4 15 7 5 25 10 13 0 25 4 00 w 3 14 1 12 2 6 5 24 3 2 8 3 3 Fill in the blank with a number to make a true statement 1 0 25 14 2 4 2 11 2 4 3 4 7 3 5 3 6 10 10 6 0 125 0 5 6 9 Write a division problem for each situation Then solve it 16 How many quarter pound 4 packets of plant food can a garden shop make out of 8 pounds of the plant food 12 34 5100 8 1 15 7 3 17 The assembly of a machine takes 4 hour There are twelve steps in the assembly process What is the average time for each step 3 18 A 35 meter length of cable is cut into pieces that measure 1 25 meters each Into how many pieces is the cable cut 4 2 19 8 tons of gravel is spread evenly across 6 acres How many tons of gravel are on each acre 5 16

The light vehicle market share in percent in a particular country for pickup trucks is shown in the graph Let x 0 represent 1995 x 4 represent 1999 and so on a Use the points on the graph to write equations for the line segments in the intervals 0 4 and 4 8 b Define this graph as a piecewise defined function f x Percent Ay Pickup Truck Market Share 45 43 0 42 4 41 39 37 35 33 31 1995 1997 4 39 7 8 32 1 1999 2001 2003 Year a The equation for the line segment in the interval 0 4 is y Simplify your answer Use integers or decimals for any numbers in the expres

Graph the following function f x 3 x 5 2 Select all that apply A Vertical stretch or shrink B Horizontal stretch or shrink C Reflect across y axis D Reflect across x axis E Vertical translation up F Horizontal translation to the right G Horizontal translation to the left H Vertical translation down Use the graphing tool to graph the function Click to enlarge graph

Use the piecewise defined function to find the following values for f x f x 5 4x 3x 5x 3 f 2 13 f 1 if x 1 if 1 x 9 if x 9

h x x 3 Which transformations are needed to graph the function h x x 3 Choose the correct answer below A The graph of y x should be shifted to the left by 3 units and reflected across the y axis B The graph of y x should be shifted to the right by 3 units and reflected across the x axis OC The graph of y x should be shifted to the left by 3 units and reflected across the x axis OD The graph of y x should be shifted to the right by 3 units and reflected across the y axis

6x 3x 35 x 4 Select the correct choice below and fill in the answer box to complete your choice OA No because the polynomial 6x 3x 35 evaluated at 4 is equal to OB Yes because the polynomial 6x 3x 35 evaluated at 4 is equal to OC No because the polynomial 6x 3x 35 evaluated at 4 is equal to OD Yes because the polynomial 6x 3x 35 evaluated at 4 is equal to

Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first 4x4 12x 11x 25x 20 x 4 Is x 4 a factor of 4x4 12x 11x 25x 20 O No OYes

Use the remainder theorem and synthetic division to find f k for the given value of k f x x 9x 21x 13 k 5 f 5

Express f x in the form f x x k q x r for the given value of k f x 2x4 3x 11x 16 k 1 2x4 3x 11x 16

For the given equation and graph of the quadratic function do the following Complete parts a through e f x x 4 4 The domain is Type your answer in interval notation The range is Type your answer in interval notation b Give coordinates of the vertex The vertex is Type an ordered pair c Give the equation of the axis of symmetry The axis of symmetry is x d Find the y intercept s The y intercept s is are Type an ordered pair Use comma to separate answers as needed e Find the x intercept s The x intercept s is are Type an ordered pair Use a comma to separate answers as needed b 10 b

4 32 2 4 32 2 Type your answer in the form a bi Type an exact answe

Use any method to determine if the series converges or diverges Give reasons for your answer 2 0 1 21 Select the correct choice below and fill in the answer box to complete your choice OA The series converges because the limit used in the nth Term Test is OB The series diverges because the limit used in the nth Term Test is OC The series converges because the limit found using the Ratio Test is OD The series diverges because the limit found using the Rafin TI 1

M8 n 1 n4 Verges or diverges Give a reason for your answer Does the series converge or diverge 1 OA The Direct Comparison Test with shows that the series converges n OB The Direct Comparison Test with Oc The Direct Comparison Test with n 1 80 1 n 1 n 1 40 n 1 shows that the series converges shows that the series diverges 1 OD The Direct Comparison Test with E shows that the series diverges n

Find the series interval of convergence and within this interval the sum of the series as a function of x n 0 8 The interval of convergence is Type an exact answer using radicals as needed Type your answer in interval notation Within the interval 8 8 4 S

Determine whether the alternating series 00 1 1 n 1 5 n 3 INC converges or diverges Choose the correct answer below and if necessary fill in the answer box to complete your choice OA The series does not satisfy the conditions of the Alternating Series Test but converges because it is a geometric series with r B The series does not satisfy the conditions of the Alternating Series Test but diverges by the Root Test because the limit used does not ex OC The series does not satisfy the conditions of the Alternating Series Test but diverges because it is a p series with p OD The series converges by the Alternating Series Test OE The series does not satisfy the conditions of the Alternating Series Test but converges because it is a p series This question 8 p with

For the series below a find the series radius and interval of convergence For what values of x does the series converge b absolutely c conditionally 49x D 1 Type a company my you awe Use eyes analyse expression OB The series converges only at x Type an integer or a simplified fraction C The series converges for all values of x b For what values of x does the series converge absolutely Select the correct choice below and if necessary fill in the answer box to complete your choice OA The series converges absolutely for Type a compound inequality Simplify your answer Use integers or fractions for any numbers in the expression OB The series converges absolutely at x Type an integer or a simplified fraction OC The series converges absolutely for all values of x c For what values of x does the series converge conditionally Select the correct choice below and if necessary fill in the answer box to complete your choice OA The series converges conditionally for Type a compound inequality Simplify your answer Use integers or fractions for any numbers in the expression OB The series converges conditionally at x Type an integer or a simplified fraction Use a comma to separate answers as needed OC There is no value of x for which the series converges condi

enes 2 n 1 converge or diverge Choose the correct answer below OA The series diverges because it is a p series with p 1 OB The series converges because it is a geometric series with r 1 OC The series diverges because it is a geometric series with r 21 OD The series converges her

Consider the solid obtained by rotating the region bounded by the given curves about the specified line y x 1 y 0 x 6 about the x axis Set up an integral that can be used to determine the volume V of the solid v f 1 2x10 20 20 Jav dx X Find the volume of the solid 92 7 x 4

Solve the inequality Write the solution set in interval notation t2 8t 16 20 Select one a 00 00 b 4 U 4 c 0 4 U 4 d 4 U 4 s

e graph of a polynomial function is given What is the smallest degree that the polynomial could have

The graph of a polynomial function is given What is the smallest degree that the polynomial could have

Use the simplex method to find the optimal solution Assume all variables are nonnegati Minimize f 3x 2y subject to the following constraints x y 15 x y 2 25 x y 35 f

Fill in the blank to correctly complete the following sentence The graph of f x x is a reflection of the graph of y x across the x axis

Simplify function cotx CSC x 1 cot x csc x 1 to a single trig 2cot x csc x 1 csc x Preview

Use the graph below of a function to find all integer values of x for which f x 4 Separate multiple answers with a comma 6 MN 2 1 2 4 6 46 Enable Zoom Pan 8 6

The plot below represents the function f z 10 9 8 7 6 34 Find the indicated values a f 1 b if f 2 4 then z A Ra 10 9 for the tavs6 S 2 7593992 6 7 NE 9 10 to 5 6 7 8 9 10

Find which the first tem of of the exceeds 1400 d 7 sequence 6 6 2 12 12 2

Find the standard equation y a x h k of the parabola shown in the figure Be sure to answer in the specified format V 1 2 2 3 H

Find a polynomial of the specified degree that satisfies the given conditions Degree 4 zeros 1 1 6 integer coefficients and constant term 18 30x319x 30x 18 f x 4 X

actor the polynomial and use the factored form to find the zeros Enter your answers as a comma separated list Enter all answers including repeti P x x5 9x3 X ketch the graph 3 2 y 3 2 1 40 20 20 40 y 40 20 20 1 2 40 X O 2 1 y 20 10 20 10 NAV X 2 3 2 1 10 10 20 y 1 2 20 1 2 3 X X

Identify and estimate the x and y values of the extrema Round to the nearest tenth if necessary y O X

Terry is skiing down a steep hill Terry s elevation E t in feet after t seconds is given by the equation E t 2200 40t Complete the following sentence describing Terry s starting elevation and how it is changing over time He is starting from a height of feet and is skiing downhill at a speed of numbers Note to get the problem correct you must provide the correct answer to every part per E

Graph the line that passes through the point 4 5 with a slope of Give an equation for this line What is the y intercept for this line Y use exact numbers no decimals give your answer as a point use exact numbers no decimal

Fernando is walking home from a friend s house at a constant speed After 4 minutes he is 2 miles from home 14 minutes after leaving he is 1 2 miles from home What is his rate in miles per hour mph mph help numbers