Algebra Questions

The total revenue for Jane s Vacation Rentals is given as the function R x 100x 0 5x2 where x is the number of apartments booked What number of apartments booked produces the maximum revenue Answer How to enter your answer opens in new window Keypad Keyboard Shortcuts

Please help with this Q before 18 9 thanks Consider the mapping function w 3z determine and sketch the images of the followings a a unit square with one vertex at the origin b a square grid formed by repeating the above unit square along x and y A 5 x 5 or 6 x 6 grid is fine viole

Determine the domain and range of each relation Sketch a graph if it will help De Rangemel 1 y 3x 5 2 y x 3 3 y 2x 4 y 3x 2 7 5 y 2 x 3 2 6 y x 2 7 7 14 x 6 3 Domain

1 the 3 y 3x 5 1 2 y x 3 y 2x 4 y 3x 7 5 y 2 x 3 6 y x 2 7 7 y 4 x 6 3 1 8 y 3 9 y 10 y 1 x 4 3 x 5 11 y x 12 y x 3 x 4 13 y 5 14 y 2x 4 Domain Range of

13x 12 5x 15x 3 6x 3x 7 8x 5x 70 2x 100 17x 45 7x 48 9 x 16 x 7 9 x 1 11 5x 8 11 8x 44 8x 59 7x

Determine the real root of f x 5x 5x 6x 2 A Graphically B Using the bisection to locate the root 1 Discuss the descriptive algorithm with your team II Draw a schematic algorithm flow diagram III Select initial guesses of x and x and iterate until the estimated error falls below a level of E 10 C Prepare a findings report

e Fiesch Reading Fase Test is a test that ranks the reading level of passagest Let W be the total number of words in the passage S the number of sentences and the number of syllables Then he Fiesch test calculates the score of the passage using the formula F 206 835 1015 846 a Calculate for the paragraph above the one that describes the Fleich Reading Ease Test Omit the formula itself Round your answer to the nearest whole number We count 3 sentences 51 words and 71 sylables b for the rest of this exerse we consider passages that have 10 sentences and 400 sylaties Find a formula expressing as a function of w for such passages 846 400 206 835 1015 10 Assage thought to be easily understandable by 13 to 15 year old students of the resch score rounded to one decimar place is 60 or higher For the passages considered in part b how many words should be in the passage to make it easily understood bv 13 to 15 year old students Suppestion First use a table increment of 20 to get an estimate of the answer Then change to lable increment of L 1 What is the maximum number of words in the passages considered in part b Can there be more words than syllables 400 wants 4 Bear in mind your answer from part 0 and ortering

Use the piecewise defined function to find the following values for f x f x f 0 4 3x 3x 5x 2 if x 2 if 2 x 7 if x 7

A Describe how the process of solving a linear inequality with 1 variable is different from solving a linear equation also with 1 variable B Consider the difference in meaning between inclusive and exclusive inequality symbols Describe or demostrate how they relate to the following words open closed solid dashed brackets and parentheses Suggested Vocabulary negative inequality symbol number line graph interval notation open closed Solid dashed Include exclude Brackets parentheses

2 0 2 Points DETAILS PREVIOUS ANSWERS SCOLALG7 2 FOM 022 10 30 Submissions Used A graphing calculator is recommended In this problem you are asked to find a function that models a real life situation and then use the model to answer questions about the situation Use the guidelines on page 273 to help you A rancher with 850 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle see the figure a Find a function A that models the total area of the four pens Use w to represent the width of the field A w 1700 8w b Find the largest possible total area of the four pens

Can a 2x2 system of linear equations have exactly two solutions Explain why or why not by describing the 3 types of linear systems and their solutions Suggested vocabulary Point of intersection Slope Lines Equation

Convert the following angle to decimal degrees x 326 16 31 0 Round to three decim

Convert the angle measure 34 33 18 to decimal degrees O 34 33 18 Type an integ r or decimal rounded to the nearest thousandth as needed

Consider the equation P 2Q 3 This equation represents a supply Instructions Enter your answer as a whole number Use a negative sign if necessary This curve has a slope of Instructions Use the Line tool to draw the line by plotting the y intercept and the price when the quantity is 5 2 points total Price 15 14 13 12 11 10 9 43210 8 76543 curve 2 Tools Line

Domain Range

Theorem 1 If lim f x L and lim f x M then L M x p x p IL MI Proof Suppose L M then IL MI 0 Since lim f x L if we take 2 then 38 0 such that x p Ix pl 8 f x LI E Similarly since lim f x M 38 0 such that x p Ix pl 8 If x MI e If we choose 8 min 8 8 then Ix pl 8 will mean that ix pl 8 and lx pl 8 In this case we will have both I f x LI e as well as I f x MI e So that IL MI L f x f x MISI f x LI f x MI E 2 IL MI That is we get L MI IL MI which is a contradiction Therefore our supposition is wrong Hence L M We now state and prove a theorem whose usefulness will be clear to you in Unit 4 Theorem 2 Let f g and h be functions defined on an interval I containing a except possibly at a Suppose i f x g x h x x I a ii lim f x L lim h x X 48 Then lim g x exists and is equal to L 243 Proof By the definition of limit given e 0 38 0 and 8 0 such that If x LI e for 0 ix al 8 and Ih x LI e for 0 lx al 8 Let 8 min 8 8 Then 0 lx al 8 lf x LI e and I h x LI E L ESf x SL E and L esh x SL E We also have f x g x Sh x xE I a Thus we get 0 1x al 8 L ES f x g x h x L In other words 0 lx al 8 Ig x Li e Therefore lim g x L 113 Theorem 2 is also called the sandwich theorem or the squeeze theorem because g is

Write the domain and range of each function 2 a y x 5 Domain Range

he linear function with the following properties r Correct f 4 11 f 9 9

ver linear function with the following properties 2 15 Correct f 0 1 Slope off 6

K Money is borrowed at 7 simple interest After one year 771 47 pays off the originally borrowed The amount of the original loan was an How II

Part 1 of 2 Use the given graph to find each of the following a the zero of the function b the x intercept What is the zero of the function O Points 0 of 1

The perimeter of a college athletic field is 92 meters and the length is 18 m more than the width Find the length and width What is the width m o D

Use the given graph to find each of the following a the zero of the function b the x intercept What is the zero of the function D

An airplane that travels 400 mph in still air encounters a 50 mph headwind How long will it take the plane to travel 1050 mi into the wind hours to travel 1050 mi into the wind The airplane takes Type an integer or decimal

he perimeter of a rectangular held is 380 ya he smaller of the two sides is yd length is ya longer than the width Find the dime

5 Extra Credit What is your favorite movie and why is it all three Lord of the Rings movies with the extended edition and cut content

c Now that we have two equations that are about the same at what point do these two lines intersect one another Give the answer as an ordered pair x y

a Silva looks down at her computer on the floor with an angle of depression being 30 degrees Since she knows she is 5 feet tall how far away is the computer

5 2 20 pts Using the rule of similar triangles solve for the missing sides and angles of each 16 18 21 y N 8 18 21

a Use the product rule to find the derivative of the given function b Find the derivative by expanding the product first h z 3 2 3z 4 a Use the product rule to find the derivative of the given function Select the correct answer below and fill in the answer box es to complete your choice OA The derivative is 3 z O B The derivative is 3 z z 3z 4 OC The derivative is 3 z z 3z 4 OD The derivative is 2 3z 4 The derivative is 3 z z 3z 4 b Expand the product 3 2 z 3z 4 Using either approach dz TILB Simplify your answer 3 z z 3z 4

a Use the Product Rule to b Find the derivative by expanding the product first f x x 6 x 3 a Use the product rule to find the derivative of the function Select the correct answer below and fill in the answer box es to complete your choice O A The derivative is x 6 x 3 OB The derivative is x 6 x 3 O c The derivative is x 6 1x 3 OD The derivative is x 6 O E The derivative is x 1x 3 b Expand the product x 6 x 3 Simplify your answer Using either approach x 6 x 3 d dx

4 20 pts We learned before that we can find the equation of a line if we are given a point and a degree of elevation or depression a Find the equation of a line that passes through the point 3 7 at an angle of elevation of 35 Degrees

b Steven looks at the top of the lat pulldown machine with an angle of elevation being 50 degrees He is 2 feet away from the machine what is the height from his sight line to the handles

1 Calculate the length of the unknown side for the following right triangle if a 7 and b 63 27 O 4 7 O 7 7 14 b 63

A vector with a magnitude of 12 0 m is directed at an angle of 25 0 above the x axis What is the component of this vector Provide your answer below

Use a graphing calculator to find all solutions in 0 2x x 2 sinx x 3 cos x 0 The solution set is Round to four decimal places as needed Use a comma to separate answers as nee

13 Sketch on separate graph of the derivative of the function whose graph is shown Note the vertical lines are the asymptotes 15 10 20 10 15

b sin 2 cos 1

3 Let u and 7 be two unit vectors that are orthogonal Show that ar 7 7 are orthogonal too

1 Exercise 7 2 A plane P in R is defined by x 2y 3y 0 It has v 2 and w b For u 1 3 T vectors a Find 3 vectors v and w so that v v and w w are orthogonal bases for P there are many possible answers as basis 1 B 1 compute Projp u in terms of the bases v v and w w that you found in part a i e find scalars a b and c d for which Projp u av bv and Projp u cw dw c Consider the two forms for Projp u that you derived in part b Show that they describe the same vector

1 3 S I sina I 2x 1 x x 1 dr da 5 cos a sina da 2 1 2x 100 4 sin r cosa 6 3x e dz da

The graph of the quadratic function y ax 2x chas x intercepts 2 and 3 and y intercept 12 Find a and c a

The length of a rectangular garden is 7 meters longer than its width If the garden s perimeter is 190 meters what is the area of the garden in square meters m

hich of the following is equal to ultiple choice 6 2 A B C D 1 3 1 1 3 1 6 2 4 6 2 4 E 1 F G H 1 6 2 2 6 2 2 1 3 1 J 3 1

For what value s of a do the curve y 4x2 6x 4 and the line y 2x 1 intersect f your answer contains more than one value please use a comma to separate the values of the two curves do not intersect enter DNI

et f x 3x 1 be a composite function Which is the correct decomposition of f x Multiple choice A a x 3x 1 b x 3x 1 f x b a x B a x 3x 1 b x x7 f x a b x c a x 3x 1 b x 3x 1 f x a b x D a x 3x7 b x x 1 f x b a x E a x 3x 1 b x x f x a b x F None of these G a x 3x 1 b x x f x b a x H a x 3x7 b x x 1 f x a b x

onsider the graph of the function y f t as drawn below If f x 3 find x lick the image for a larger version H 88 f t H

The perimeter of a square must be greater than 70 inches but less than 106 inches Find the range of possible side lengths that these conditions Hint The perimeter of a square is given by P 4s where s represents the length of a side Express your answer in interval notation Use decimal form for numerical values Answer

w w43 3w 4 W 2 For what values of wis A W B w 2 C w 2 D EV 2 E 2 w 2 and w 2 0

Let f x x 4x and g x x 8 Evaluate the following 1 fog x 2 gof x 3 fof x 4 gog x