Linear Algebra Questions and Answers

9 Let v and v be nonzero vectors in 3 space having direction angles a B1 71 and a2 82 72 respectively Moreover suppose the vectors are orthogonal Show their direction cosines satisfy cos a cos a cos 3 cos cos cos 2 0

A shirt was originally priced at 65 The store is having a 5 off sale How much will you pay for the shirt after the discount not including tax

State the amplitude period phase shift and vertical shift of the function f x 4 sin Amplitude Period Phase shift Vertical shift 1 3 X 3 37 2 1

7 An engineer makes different size samples of a new material The table shows volumes and their related masses a What would be the mass of 100 cubic centimeters of the material 1 000 megap b What would be the mass of 500 cubic centimeters of the material 5 000 8 Higher Order Thinking The number of pizzas y and the weight of the shredded cheese topping x on the pizzas have a proportional relationship When shredded a 50 lb block of cheese is enough to make 150 large pizzas a Find the constant of proportionality 3x y Assessment Practice b How can you use the constant of proportionality to find how much cheese is on one slice of pizza if there are 8 slices per pizza Explain 34 3 h mundan solen ser murine ne sme 9 For every 3 lemons Chrissy buys at a farm stand the total cost increases by 1 80 The constant of proportionality is Volume in Cubic Centimeters x 8 3 An equation that relates the total cost y and the number of lemons x is y invi Use the equation you wrote to complete the table X olguer TPU 10 For every dozen bagels you buy the cost increases 15 Which equation represents the cost y and the number of bagels x Ay 1 25 x y 15x x 15y 14 25 96 9 X JO 140 144 CXL PY 150 150 16 8 det st Inokady 150 3 Alleno 40adre Mass in Grams y 90 10 tushoitoong to thetines Number of Lemons x 4 250 50 110 1 3 jeher 18 fis 21 Cost of Lemons ew to of 10 sathw Total Cost y 4 20 9 00

3 Jacob North wants to buy a four year old Palomino sedan His friend has a V8 four door that he will sell Jacob at wholesale The car has a manual transmission a DVD player leather seats a power sunroof and 53 480 miles Premier Certified Pre Owned Autos has a V6 four door that is being sold at retail That car has power mirrors front bucket seats aluminum wheels and 73 840 miles It does not have air conditioning Which car will cost Jacob less and how much less

The Venn diagram shows sets A B C and the universal set U Shade B n C UA on the Venn diagram U B

A 657 000 property is depreciated for tax purposes by its owner with the straight line depreciation method The value of the building y after x months of use is given by y 657 000 1800x dollars After how many months will the value of the building be 396 000 months Read It Need Help Watch It MY NOTES

Problem 2 1 points Is the set W of all polynomials of the form W p t 2 t at a R a vector space over R with respect to the standard addition and scalar multiplication

3 5 140 Height Above the Ground f 1 2 3 4 5 6 7 Time minutes is the difference in feet between the minimum and maximum heights of a car on the Ferris wheel 0 150 554 120 110 100 90 80 70 60 50 40 30 20 10 0

Solve the inequality for x OA OB OC OD 5 3232 x X 289 01 0 WIF

Music Mania Number of Total Downloads Cost 4 50 7 50 10 50 3 5 7 Total Cost dollars Least expensive 765 M N L 0 Song Central 1 2 3 4 Number of Downloads Che websites from least expensive price per song to most expensive price per song the websites you want to select and drag them into the boxes Most expensive Song Factory 14 for 8 downloads

A mountaineer climbed 1 000 feet at a rate of x feet per hour He climbed an additional 5 000 feet at a different rate This rate was 10 feet per hour less than twice the first rate Which expression represents the number of hours the mountaineer climbed OA 6 000 3x 10 OB 6 000 3x 10 OC 1 000 OD 1 000 5 000 2x 10 5 000 2x 10

What does the remainder theorem conclude given that f x x 3 has a remainder of 11

4 c y x 4 d y 4x 2 What is the equation for the parabola a y x 4 b y x 4

A cone has a diameter of 3 inches The cone holds 12 cubic inches of water To the nearest inch what is the height of the cone OA 1 OB 4 OC 5 OD 8

Solve the equation for x 5x 4x 6 2 26 5 OA OB OC OD X X 2 34 2 5 x 2 2 26 5 X 2 34 5

The data represents the number of cars that the sales staff at Templeton Motors sold this week 4 7 6 8 3 5 4 3 4 5 2 3 Which line plot correctly displays the data OA B Number of Cars Sold X X X X X X X X X X X X 0 1 2 3 4 5 6 7 8 9 10 Number of Cars Sold X X X X X X X 0 1 2 3 4 5 6 7 8 9 10 D Number of Cars Sold X X X X X X X X X X X X X X X 0 1 2 3 4 5 6 7 8 9 10 Number of Cars Sold XX XXX 0 1 2 3 4 5 6 7 8 9 10

Let f x Vz Use the local linear approximation to f at x 8 to approximate V7 94

In this stage of the Computational Thinking process you try to reca a problem that you have solved in the past that is similar to the problem you need to solve now

Which equation would be best to use to convince someone that 36 is a perfect square 36 A 361 B 6 6 36 C 3 12 36 D 2 18 36

Find the directional derivative of f x y z z3 x y at the point 5 5 5 in the direction of the vector v 1 1 3

13 A place near 181st and Stark St will rent a roto tiller at a price of 35 for the first 3 hours then 9 for each additional hour a Let h represent the total number of hours you rent the roto tiller and let c represent the cost for renting it Complete the table of values h 3 4 5 6 h C b Write an equation that shows the relationship between h and c c Suppose you budgeted 120 for renting the roto tiller How long could you rent it for Show how you arrived at your answer with algebra d Graph the equation on the grid below Label and scale your axes appropriately Finally show the solution to problem c on your graph

1 4 7 10 13 Add 3 4 6 9 13 18 DRAG AND 3 6 10 15 21 Multiply by 3 6 9 12 15 18 CLEAR 3 9 27 81 243 Neither

the sum of the first n terms is 3n 2n oldu u metik Dizi Bir aritmetik dizide ilk n terimin top na g re bu dizinin genel terimi a a dakilerden hangisi dir A 7n 1 D 5n 2 B 6n 1 E 5n 2 C 6n 1 what is the general term

1 point Find the scalar and vector projections of b onto a where a 1 1 2 and b 2 6 9 1 comp b 2 proj b

What is the probability that if you guessed randomly from the four answers to this question you would choose an incorrect answer O 25 75 30 50

graphical methods to solve the linear programming problem mimize z 2x 4y subject to x 2y210 3x y210 x20 and y20 OA Minimum of 0 when x 0 and y 0 OB Minimum of 20 when x 2 and y 4 as well as when x 10 ar and all points in between OC Minimum of 20 when x 10 and y 0 OD Minimum of 20 when x 2 and y 4

The reduced row echelon form of the augmented matrix of a system of equations is given Find the solutions of the system 1000 2 0 1 0 0 18 0010 6 0001 2 0000 0 H OA 2 18 6 2 w for any real number w OB 2 18 6 2 2196701

Graph the function Give the equations of the vertical and horizontal asymptotes 2 5x 1 f x Give the equations of any vertical asymptotes for the graph of the rational function Select the correct choice below and fill in any answer boxes within you OA x Simplify your answer Use a comma to separate answers as needed OB There is no vertical asymptote Give the equations of any horizontal asymptotes for the graph of the rational function Select the correct choice below and fill in any answer boxes within yo OA OA y Simplify your answer Use a comma to separate answers as needed OB There is no horizontal asymptote Choose the correct graph below C OB C OC C OD

e the solution set in both interval and graph form 6 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is OB The solution set is Choose the correct graph of the solution set below OA Type your answer in interval notation Simplify your answer Use integers or fractions for any numbers in the expression 20 OB 20 O D OC 20 20 15 15 15 15 10 10 10 10 5 5 5 5 0 5 5 10 10 Submit test 10 10 15 15 15 15 20 20 20 20

The Acme Class Ring Company designs and sells two types of rings the VIP and the SST They can produce up to 24 rings each day using up to 60 total man hours of labor It takes 3 man hours to make one VIP ring versus 2 man hours to make one SST ting How many of each type of ring should be made daily to maximize the company s profit if the profit on a VIP ring is 30 and on an SST ring is 40 OA 0 VIP and 24 SST OB 8 VIP and 16 SST OC 16 VIP and 8 SST OD 12 VIP and 12 SST

Find the order of the matrix product AB and the product BA whenever the products exist A is 2x2 B is 2x2 OA AB is 2x2 BA is 2x2 OB AB is 2x4 BA is 2x4 OC AB is 1x1 BA is 1x1 OD AB is 4x2 BA is 4x2

Solve the system by back substitution 1 2x 4y z 3w y 6z 2w 8 5z 5w 10 5w 15 The solution set is 0 Type an integer or a simplified fraction

Suppose P C 048 P Mn C 044 and P MUC 524 Find the indicated probability P M OA 528 OB 480 OC 472 520

For the given pair of equations give the slopes of the lines and then determine whether the two lines are parallel perpendicular or neithe 6x 16y 9 6x 8y 4 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The slope of 6x 16y 9 is B ype an integer or a simplified fraction The slope of fx 16v 9 is undefined

Under her cell phone plan Vani pays a flat cost of 69 per month and 4 per gigabyte She wants to keep her bill at 76 60 per month Which tape diagram could be used to represent the context if a represents the number of gigabytes of data Vani can use while staying within her budget A B C D 4 4 69 4 4 4x 4 4x 69x 69 72 6 69 76 6 4 72 6 4 69 76 6 69 69x 69 69 69 4

Under his cell phone plan Logan pays a flat cost of 38 per month and 5 per gigabyte He wants to keep his bill at 56 per month Which equation or tape diagram could be used to represent the context if g represents the number of gigabytes of data Logan can use while staying within his budget A B C D 38 5 38g 38 38 51 5g 56 38 38 56 38 38g 56 5 38g 38 5

0 There is a one to one correspondence between S and St conclude that any two right cosets of S have the same number of elements

Find a state space equivalent for the following linear system G s 10s5 48 68 882 12s 20 85 2s 7s 6s2 10s 11

ch one doesn the value o What is the value of 50 2019 Illustrative Mathematics All Rights Reserved Type your answer below as a number example 5 3 1 4 1 2 or 3 2 Submit Answer

Problem ID PRABMQ2U Which expression is equal to 38 Select one OA 1 6 OB 3 6 Oc 3 4 OD 3 6 32 2019 Illustrative Mathematics All Rights Reserved

Problem ID PRABMRYU Are You Ready For More Han notices 11 121 and x 1 x 2x 1 11 1331 while x 1 x 3x 3x 1 The digits in the powers of 11 correspond to the coefficients of the polynomials Is this still true for 114 and x 1 4 2019 Illustrative Mathematics All Rights Reserved Select one Otrua

Correct Submit Answer Problem ID PRABM6BU 3 37 311 b Next Problem Type your answer below as a number example 5 3 1 41 2 or 3 2 4 Correct Submit Answer Next Problem Problem ID PRABM6BU

The volume of a sphere is increasing at a constant rate of 3177 cubic feet per minute At the instant when the volume of the sphere is 911 cubic feet what is the rate of change of the radius The volume of a sphere can be found with the equation V Round your answer to three decimal places

When playing American roulette the croupier attendant spins a marble that lands in one of the 38 slots in a revolving turntable The slots are numbered 1 to 36 with two additional slots labeled nd 00 that are painted green Assume a single spin of the roulette wheel is made Find the probability of winning with the given bet in example of a line bet is betting that the marble will land in a slot numbered 27 28 29 30 31 or 32 the probability of winning with the given line bet is Cam

6 Complete the following statements to summarize the relationship between the a and k values in the quadratic function rule y ax k and the parabola that is the function s graph the parabola stretches vertically k 0 the parabola compresses vertically the vertex shifts up the y axis a When the a value is positive b When the a value is negative c When the a value increases d When the a value decreases 0 k the parabola opens upward e When the k value increases f When the k value decreases g The vertex of the parabola has coordinates the vertex shifts down the y axis the parabola opens downward

Table for 1 by 1 sandstone tile Area covered Edge length of laid tile in feet x 1 2 3 4 5 10 x sq ft 1 4 9 16 25 100 x Number of sandstone tiles y 1 4 9 16 25 100 y x 4 Compare the data in both tables a What patterns do you see Table for 2 by 2 granite tile Area covered sq ft Edge length of laid tile in feet x 2 4 6 80 4 16 36 64 64 Number of granite tiles y 1 4 9 16 b According to this pattern how many granite tiles will Carly need for a 10 foot by 10 foot floor c Write a function rule that represents the relationship between the edge length in feet and the number of granite tiles

rules 7 What happens to the parabola when the a value is increased a 1 function 8 For values of a between 1 and 0 0 a 1 what happens to the parabola as the a value decreases 9 What happens to the parabola when the a value becomes negative a 0

6 How will the 13 extra tiles affect Carly s rule y x 6 for the total number of tiles they need to buy Build a new function rule that considers the 13 extra tiles 7 Graph all three rules on your graphing calculator How do the 13 extra 1 by 1 tiles transform or change the graph of the function rules the parabolas y x and y x 6 8 What is the meaning for the problem situation of points that lie in quadrants III and IV

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