Algebra Homework Help


# Description Question

Math 090 Wk 8 TU Individual Worksheet


1.  Are the following factored correctly or incorrectly? If they are correct, mark "correct", and if they are incorrect, factor it correctly.


a. x2   5x   6

b. 4m2 + 20m + 25

c.  x2 + 16x   60

= (x  2)(x  3)

= (2m + 5)2

= (  x  10)(x + 6)














2.  Factor the following fully. Remember, it is possible that they may not be able to be factored, in which case they are called prime.


z2 + 2z   24                                                                            a2    9ab + 18b2













12p3    12p2 + 3p                                                                     6a3    12a2 + 90a













x2    25                                                                                     2x3    x2    8x + 4

50x2y3    18y

9w2    42w + 49
















x4    64                                                                                     x4yz   x2yz

















x2 + 16                                                                                     x3 + 27

















64m3    125n3                                                                          x2 + x + 5

Math 090 Wk 8 TU Individual Worksheet



1.       Consider the two points:

a.       Plot the two points on the x-y coordinate system





b.      Find the distance between A and B



c.       Find the midpoint between A and B



2.       Graph the relation:








3.       a. Is the point (-1, 1) on the graph of  ?

Show work.





b. Find the x and y intercepts for the graph of









4.       Justify each answer you give:

a.      Is the graph of a line a function?



b.      Is the graph of a circle a function?



5.       Given the following functions




a.       (f+g)(1) and (f-g)(1)



b.      Domain of f(x) and g(x)



c.       (f+g(1))(x)


Tasha just started a job as a nurse.She is told that her starting salary will be $41,500 per year.She is also told that her salary will increase to $49,000 in 6 years.Assume that = the years worked and = Tasha’s Salary in dollars. Using this information, find the following answers:

MAT1222 - Algebra

Module 02 Creating Linear Equations


Instructions: Using the knowledge from the Module 02 live lectures, answer the following questions and show ALL work for full credit.  It’s a good idea to also explain your steps! Make sure you are using the equation editor!

Description: Image result for nurse

Tasha just started a job as a nurse.  She is told that her starting salary will be $41,500 per year.  She is also told that her salary will increase to $49,000 in 6 years.  Assume that  = the years worked and  = Tasha’s Salary in dollars. Using this information, find the following answers:

1)      What is the rate of change of Tasha’s salary?
Hint: Find the slope by first creating two points in the form (years, salary).

Text Box: Show all work, explanations, and answer here.

2)      Create the slope-intercept form of the line that represents Tasha’s salary.
Hint: Start by using your answer from (1) and find the y-intercept (AKA starting value).
Text Box: Show all work, explanations, and answer here.

3)      Using your equation in (2), find the value of Tasha’s salary in 13 years.

Text Box: Show all work, explanations, and answer here.

Module 02 Creating Linear Equations

SOLVE them with a separate PDF & WORD documents with their codes written in the document

For every problem, provide

 The MATLAB script files/Command window screenshots that solve the problems.

 Final answers. Run the prepared script file in the MATLAB command window in order to obtain the answers.

for this time>>Please note that all problems in this HW must be solve by hand, without MATLAB!, so attached ur answer via a picture into the PDF & WORD documents

plz finish it ASAP


For every problem, perform all calculations by hand. Provide all details of calculations in the report.

Problem 1: Find matrix product AB for


1    —4   2                 2      0

a)  A = [                ] ,    B = [—1    —2] .

2    —1    7

4     —2

2     —1    —3

b)  A = [—2   —3   1/2],    B = [ 2      0      4 ].

—2   —5     3



2     —1    —3              —2

c)   A = [

2      0      4

—2   —5     3

1    0   0

] , B = [—3]



2     —24   —3

d)  A = [0    1    0] , B = [ 0       0       1

7        0       8 ].

—2   —15     3


Problem 2: Find the transpose of the following matrices


2     —1    —3

a)  A = [ 2      0      4 ]

—2   —5     3

2      0

b)  B = [—1    —2]

4     —2


Problem 3: Consider a system of linear equations


x3 + 2x2 =  5 2x2 + 2x3x1 = 0

2x2 + 5x1 = 2

1.      Find the matrix of coefficients A of this system and vector of right hand sides B and write this system in the matrix form.

2.      Find solution of this system using the Gauss elimination.


Problem 4: Find the solution of the system of linear equations AX = B by the Gauss elimination:

1.      Find the matrix of coefficients and vector of left hand sides after the forward sweep.

2.      Find the solution of the system.


1    —1     2     4                     —2

A = [ 1     3      0   —1],         B = [ 1 ].

—2     0     —1    5                     1

0     —4     0     2                     0



Problem 5: Consider the matrices


1     1       1

A = [1    —3     0

1     3

],        B = [0     2


],        C = [2].

2     2     —2                  2    —1                   1


1.      Calculate AB.

2.      Calculate BT.

3.      Calculate AC.

4.      Calculate BTA.

5.      Solve the SLE AX = C by hand using Gauss elimination technique.

MATLAB easy 5 questions

All Triangles are Isosceles!


1. Start with a random triangle 4ABC.









2. Locate it's mid-point D. (Prop 10)










3. Create a perpendicular line through AB, going through D. (Prop 11)











4.  Construct a line bisecting \ACB and locate the intersection between this line and the previously drawn perpendicular to AB going through D. Call this point E. (Prop 9)










5.  Construct perpendicular line segments to the two sides AC and BC through E. That is, construct line segments EF and EG that are perpendicular to the corresponding sides of 4ABC. (Prop 12)











6. Connect EA and EB (i.e. draw those line segments).











Now something whacky is about to happen!


Let's start by looking at 4CFE and 4CGE.










They share a side, and have two angles equal. So by AAS (Prop 26), they are congruent. And so









Now consider 4EAD and 4EBD.










These two have ED in common, and by construction, AD = BD. So by SAS (Prop 4), they are congruent. And so


AE = BE                                                                    (3)


Finally, look at 4AFE and 4BGE.













These are both right angled triangles with two sides equal (equation 2 and equation 3). So by RASS (proved today in class!) they are congruent. And so





So now we have:





(Equation 1)


(Equation 4)

CF + FA = CG + GB

(Adding equations 1 and 4)





Thus the \random triangle" we started with, is actually isosceles! So all triangles are isosceles. And actually by the same argument on di erent sides, equilateral! YIKES!!!













































1) Work through propositions 27 through 34 (this is the second part of Book of Euclid the elements I which introduces results involving the parallel postulate) . This time create a dependency map This will help you get a sense of how the propositions build on one another. Don't worry about being completely accurate (but do your best!) - the point is to see how the propositions support each new result, and to see why Euclid chose to introduce the results in the order he selected.


2)      Here are a few more "rusty compass" constructions to take care of. These can be useful to give to students who are already used to "regular constructions" and as a way of changing perspectives a bit. Suppose you've got a straightedge and a compass, but your compass has rusted in position and now has a permanent one inch radius (i.e. you can only draw circles with a radius equal to one inch). The straightedge is "normal" in that you can draw line segments of any length. First, given a line L, and a point A on the line, you're asked to construct a line perpendicular to L that goes through A. As part of your answer please be sure to describe your construction so someone else could do the same thing (i.e. provide the steps taken instead of just turning in a finished diagram on its own - writing things such as "draw circle at B with radius BC" ... "label new intersection as point D" etc.)


3)  And one last rusty compass construction - this one's a bit more involved than the previous ones, and a reasonable answer can take upwards of 12 construction steps (if you can get it down to under 12 steps, great, if not try to get to as close to it as you can - and there are some solutions that are even lower!). So... again, suppose you've got a straightedge

and a compass and that your compass has rusted in position with a one inch radius. Now given a line L and a point A that is around 3 inches away from the line construct a line through A and perpendicular to L. Note that the line might be a bit more or less than 3 inches - you can't just assume that it's exactly 3 inches in your work. When writing up your solution, again be sure to write down the steps you took (and number them) - so that anyone else could recreate your work precisely.


4) with an erroneous theorem that all triangles are isosceles (and so in fact must be equilateral). This is obviously complete baloney! To figure out what's going wrong with this construction "proof" (which is attributable to W.W. Rouse Ball in 1940), please take time to draw a carefully executed diagram of the construction steps to find out where the error occurred (as a hint - it has to do with where the lines that are supposed to be perpendicular to the sides of the triangle should actually end up going - if you have to extend one of the sides of the triangle to create the perpendicular, then go ahead and do that to see how the problem in the final conclusion shows up). As a bit of a hint - this construction problem involves the issue of "betweenness" - where things actually intersect, and how depending on diagrams can end up leading to problems - we saw that show up in the diagram for Proposition 7 as well. Here's a description of the steps: All Triangles Are Isosceles. As part of your answer, you should try to figure out what's up with the (misleading!) equation CF + FA = CG + GB. Note that it is in fact true that CF = CG and that FA = GB, so there's something else wrong with the equation as it’s written here...(?) Make sure that you explain what's going on with the erroneous "proof" in enough detail so that it's clear what this "proof" has actually

shown. Big hint - point E won't show up where you drew it in the triangle - but just saying that point E must end up somewhere else isn't the end of the story - create the diagrams, find out where E must be located and then, still, figure out what's wrong with the argument I showed you - if necessary (and it will be!) extend the sides (CA and CB) of the triangle so that you can do the construction out completely, finding points F and G (one of which will be forced to lie on one of the extended triangle sides).


For bonus credit - dive in and check out this construction using GeoGebra


(Links to an external site.) Links to an external site.


(it's free and you can download a copy). Print out your construction to show that you were successful at using GeoGebra! We'll continue to see GeoGebra at various times in class, so it's nice to get comfortable with the software.


5)   Now it's time to use the power of triangles(!) to prove that the two diagonals of a rectangle are congruent and that they bisect each other. Here use a definition of a rectangle as just being a quadrilateral with four right angles. In your answer you should work solely with the results we've seen so far in Euclid - i.e. you can use results from any of the propositions up through Prop 34 at this point in your proof.


6)     Finally, given a line segment, then (using a straightedge and compass as usual) construct a square based on that given line segment (i.e. with the line segment as one of its sides). Note that you have to assume that your straightedge is just a straightedge, not a ruler so it can't be used to measure distances, but you can assume that given the

existence of Proposition 2 (Euclid book 1 the elements), that your compass can in fact transfer distances now (as most modern compasses do anyway) . The important part of this question is that you need to do your construction in such a way so that you can prove that your square construction does in fact yield a square (i.e. a quadrilateral with four equal sides and four equal angles). In doing this, please just use the results from any of the first 34 propositions (including, for example, the result from proposition 32 that the sum of the angles in a triangle is 180 degrees - or as Euclid would put it "equal to two right angles"!). This type of construction/proof mirrors many of Euclid's Propositions. It's one thing to construct a particular type of figure, quite another, sometimes, to then prove that the figure actually has the desired properties(!)


7) Back to multidimensional fence building! Suppose you've fallen into a hole in the space time continuum and you've ended up in some weird universe with five dimensions(!) You run across a fence builder who's putting up four dimensional fences splitting up this bizarre five dimensional space. Using what you've learned from the fence problem solutions we looked at in class, write down the maximum number of regions that can be produced by 1, 2, 3, 4, 5, 6, 7 and 8 fences respectively in this five dimensional world. Don't even bother trying to "picture" five dimensional space - you can do all the work just by using the patterns that we've worked out so far (you'll need to extend some of the sequences a bit to nail this down).


8) Now you're really in trouble - you've fallen into another hole in the spacetime continuum and you've ended up in a universe with 2018 dimensions(!) You run across a fence

builder who's putting up fences (each one is 2017 dimensional!) splitting up this bizarre 2018 dimensional space. Using all that you know of these weird situations, write down the maximum number of regions that can be produced if the fence builder builds (a) 2018 of these fences, and then (b) the maximum number produced by 2019 of these fences (hint, your answers will be absolutely huge - you won't be able to write down the actual digits for them). Note, there are no real calculations required to answer this - as we did in class, just take a look at what's happening with all of the earlier fence building information and figure out how the pattern must continue.


All Triangles are Isosceles!

The table lists the average annual cost of tuition and fees at private 4-year colleges for selected years.

Year Tuition and Fees (in dollars)

1994 11,719

 1996 13,994

 1998 17,709

2000 16,233

 2002 21,116

2004 24,101

2006 32,218 

1.  Given any two data points with each consisting of the year and its corresponding tuition and fees, describe in detail how you would find a linear function that models the data shown in the table. Be sure to clearly define and interpret all components involved in your model.

2.  Determine a linear function that models the data, where 0 x= represents 1994, and 1 x= represents 1995, and so on. Use the points ( ) 0,11719 and( ) 12,32218 . Choose two more combinations of points and use them to create two additional linear functions that model the data. Record the three linear functions below. 

  Function 1: 

 Function 2: 

 Function 3:

 3.  How would you go about using these functions to predict the average annual cost of tuition and fees for a future year? Suppose you are in the marketing department for a college and you are trying to determine which function to use to encourage future students attend your college. Explore and state the messages that can be sent to prospective students by each function.

 4.  Use all three functions to approximate tuition and fees in 2035. State your results below. Next, choose the function you would use to encourage prospective students and explain the reasoning behind your choice. 

  Function 1: 

 Function 2: 

  Function 3: 

 Function of choice: 


The table lists the average annual cost of tuition and fees

Tom has just received a new job offer. He is told that his starting salary will be $75,000 per year. He is also told that his salary will probably be $83,000 in four years. We will use this data to try and anticipate his future earnings in any given year. Assume that y = Tom’s salary amount in dollars and x = the number of years worked. 1. Use the data given to find the rate of change, or the salary increase per year. (Hint: compute the slope.) We are now going to use a line to model Tom’s salary growth. 2. Use the data given and the slope value from Step 1 to write the slope-intercept form of the line. Based on your equation from Step 2 what will Tom’s salary be in ten years?

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