This document provides instructions for an assignment on parallel and perpendicular lines. Students are asked to find the equations of lines parallel and perpendicular to given lines and passing through given points. They are also asked to define what makes lines parallel and perpendicular and to incorporate math vocabulary words into their responses. The vocabulary words are origin, ordered pair, x-intercept, slope, and reciprocal.
This powerpoint presentation discusses about the first lesson in Grade 10 Math. It is all about Number Pattern. It also shows the definition, examples and how to find the nth term and general formula.
This slide focuses on finding the values of the specific term and the common difference of an arithmetic sequence described by a given succession of numbers and patterns.
iServe is a community ministry of The Lutheran Church of Webster Gardens, Missouri. Our members have committed to spend 10 percent or more of member contributions within our neighborhood. This presentation describes how we do that.
This powerpoint presentation discusses about the first lesson in Grade 10 Math. It is all about Number Pattern. It also shows the definition, examples and how to find the nth term and general formula.
This slide focuses on finding the values of the specific term and the common difference of an arithmetic sequence described by a given succession of numbers and patterns.
iServe is a community ministry of The Lutheran Church of Webster Gardens, Missouri. Our members have committed to spend 10 percent or more of member contributions within our neighborhood. This presentation describes how we do that.
A digital portfolio of work including Multi-Media Marketing Campaigns, Company/Service Marketing, Individual Business Marketing, Marketing for Sales, Charity and Non-Profit Marketing, Content/SEO Strategy, Technology Training, Corporate Events, Billboard Design, Postcard Design, Ad Design, Brochure Design, Digital Imaging, Promo Item Design, Photography
At AnswerModules we think your corporate investments in technology are important. That's the reason why we are not willing to sell you yet another Enterprise Content Management solution. What we really want to do is help you leverage your investment by enhancing your existing platform with new, cutting edge functionalities. We decided to stand on the shoulders of the giants, and created our Module Suite for OpenText Content Suite, the world-leading EIM solution.
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� EMBED Equation.3 ���-5
� EMBED Equation.3 ���5
Sum=b
0
Product=a x c
1x (-25)
x2+0x-25=0 substitute the value of bx to facilitate factorization
The denominator is a constant term
(x2+5x)(-5x-25)=0
x (x+5)-5(x+5)=0
(x+5)(x-5) are the factors for the domain
All values of x in the expression are included as dividing by the domain will yield a solution
Thus D=� EMBED Equation.3 ���
� EMBED Equation.3 ���The Domain is Integer 2 which divides any factor in the numerator. We factorize the Numerator to obtain the factors.
� EMBED Equation.3 ���-6
� EMBED Equation.3 ���5
Sum=b
-1
Product=a x c
1x (-30)
k2+5k-6k-30=0 substitute the value of bx to facilitate factorization
(k2+5k)(-6k-30)=0
k (k+5)-6(k+5)=0
(k+5)(k-6) are the factors for the domain
k=-5 and k=6 are the excluded values in the expression since they will equal 0 in any range of values.
Thus D={K:K� EMBED Equation.3 ���� EMBED Equation.3 ���,K� EMBED Equation.3 ���(-5) ,k� EMBED Equation.3 ���6}
L
� EMBED Equation.3 ���Factorizing the domain in the form we find factors:
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INSTRUCTOR GUIDANCE EXAMPLE: Week One Discussion
Domains of Rational Expressions
Students, you are perfectly welcome to format your math work just as I have done in
these examples. However, the written parts of the assignment MUST be done about
your own thoughts and in your own words. You are NOT to simply copy this wording
into your posts!
Here are my given rational expressions oh which to base my work.
25x2 – 4
67
5 – 9w
9w2 – 4
The domain of a rational expression is the set of all numbers which are allowed to
substitute for the variable in the expression. It is possible that some numbers will not be
allowed depending on what the denominator has in it.
In our Real Number System division by zero cannot be done. There is no number (or
any other object) which can be the answer to division by zero so we must simply call the
attempt “undefined.” A denominator cannot be zero because in a rational number or
expression the denominator divides the numerator.
In my first expression, the denominator is a constant term, meaning there is no variable
present. Since it is impossible for 67 to equal zero, there are no excluded values for the
domain. We can say the domain (D) is the set of all Real Numbers, written in set
notation that would look like this:
D = {x| x ∈ ℜ} or even more simply as D = ℜ.
For my second expression, I need to set the denominator equal to zero to find my
excluded values for w.
9w2 – 4 = 0 I notice this is a difference of squares which I can factor.
(3w – 2)(3w + 2) = 0 Set each factor equal to zero.
3w – 2 = 0 or 3w + 2 = 0 Add or subtract 2 from both sides.
UGC NET Paper 1 Mathematical Reasoning & Aptitude.pdfNirmal Dwivedi
This Presentation is about the Unit 5 Mathematical Reasoning of UGC NET Paper 1 General Studies where we have included Types of Reasoning, Mathematical reasoning like number series, letter series etc. and mathematical aptitude like Fraction, Time and Distance, Average etc. with their solved questions and answers.
This provides support material for PSA (Problem Solving Assessment) conducted by CBSE. It has tutorials as well as guidelines along with sample papers
These guidelines are extremely genuine as they are issued by Directorate of Education, Delhi.
Math 235 - Summer 2015Homework 2Due Monday June 8 in cla.docxandreecapon
Math 235 - Summer 2015
Homework 2
Due Monday June 8 in class
Remember: In this course, you must always show reasoning for your answers. You can use any result we have
proved in class, in textbook reading, or in a previous homework.
Problem 1 For each of the following problems, you must justify your answer by finding the general solution
to the corresponding system of linear equations, or by showing that no solution exists.
(a) In the vector space P3(R), can −2x3 − 11x2 + 3x+ 2 be written as a linear combination of vectors in
{x3 − 2x2 + 3x− 1, 2x3 + x2 + 3x− 2}?
(b) In the vector space M2×2(R), can
(
1 0
0 1
)
be written as a linear combination of vectors
in
{(
1 0
−1 0
)
,
(
0 1
0 1
)
,
(
1 1
0 0
)}
?
Problem 2 Show that a subset W of a vector space V (over a field F ) is a subspace of V if and only if
span(W ) = W .
Problem 3 You are given a subset S of a vector space V . Determine whether S is linearly dependent or
linearly independent using exclusively methods developed in this course, and justify your answers.
(a) V = R3 and S = {(1, 2,−1), (2,−3, 1), (2, 3,−5)}.
(b) V = P3(R) and S = {1, 1 + 2t+ t2, 1− 2t+ t3, t2 + t3}.
(c) V = F(R,R) and S = {t, et, sin(t)}.
Problem 4 Prove that a subset S of a vector space V is linearly dependent if and only if there exists a
proper subset S′ ( S with the same span as S.
Problem 5 Exercise 1.6.13 from the textbook.
Problem 6 You are given a subspace S of M2×2(F ), the vector space of 2 × 2 matrices with entries in a
field F . You are required to find a basis for this subspace, and to find the dimension of this subspace.
For each problem, you DO NOT need to prove that S is a subspace, but you DO need to prove that your
conjectured basis is, in fact, a basis (that is, you need to show it is a linearly independent generating set for
S).
(a) S is the subspace of all diagonal 2× 2 matrices with entries in F .
(b) S is the subspace of all symmetric 2× 2 matrices with entries in F .
(c) S is the subspace of all skew-symmetric 2× 2 matrices with entries in F .
Problem 7 Let W1 and W2 be subspaces of a finite-dimensional vector space V . Prove that dim(W1∩W2) ≤
min{dim(W1),dim(W2)} and dim(W1 +W2) ≥ max{dim(W1),dim(W2)}.
Problem 8 Each of the maps below goes from one vector space to another (where both vectors spaces are
over the same field). For each map: prove that it is linear, determine whether it is one-to-one or not (prove
your answer), and determine whether it is onto or not (prove your answer).
(a) T : P3(R)→M2×2(R) defined by T (p) =
(
p(0) p′(0)
p′′(0) p′′′(0)
)
.
(b) T : M2×2(F ) → F defined by T (A) = tr(A), where F is a field. (Recall that for an n × n matrix,
tr(A) =
∑n
i=1Aii.)
1
(c) T : R2 → R3 defined by T ((a, b)) = (a, b, a+ b).
(Hint: You may find an analysis of rank and nullity useful here.)
Problem 9 Suppose that T : R2 → R2 is linear and that T ((1, 2)) = (3, 4) and T ((1, 3)) = (0, 1). Find
T ((1, 0)). Is T one-to-one? Justify your answer.
Problem 10 Let ...
Wk 5 Individual Preparing for Working in Teams [due Day#]Top of.docxhelzerpatrina
Wk 5 Individual: Preparing for Working in Teams [due Day#]
Top of Form
Bottom of Form
Assignment Content
1.
Top of Form
Collaboration is everywhere, especially in the health care industry. It is important to learn how to work and communicate in a collaborative environment. As you progress through your program, you will experience learning teams in your courses. Learning teams provide you with valuable experiences that will prepare you for working collaboratively in the health care industry.
Navigate to the University Library homepage.
Locate the Learning Team Toolkit on the upper right side of the homepage.
Create a 7- to 10-slide Microsoft® PowerPoint® presentation that identifies the Learning Team resources provided by the University and the importance of working effectively in a team. A presentation format has been provided for this assignment; however, you may choose to format your presentation in another professional manner.
Include the following in your presentation:
Slide One: Title Slide
· Title of presentation
· Your name
· Course abbreviation and course number
· Due date
· Your facilitator’s name
Slide Two: Introduction
· Describe what the Learning Team Toolkit is.
· Provide screenshots of the Learning TeamToolkit.
Slides Three and Four: Review the Learning Team Charter
· Explain the importance of the Learning Team Charter.
· Why is it created?
· Why is it important in collaborative environments?
· How can it be used during team conflicts?
· Why is it important to communicate with your faculty?
Slides Five and Six: Review the Learning Team Evaluation
· Explain the importance of the Learning Team Evaluation form.
· Why is it important to rate the members of your team?
· Why is it important that your faculty know how you would rate your team members?
Slide Seven: Learning Team Toolkit Resources
· Explain the resources available in the LearningTeam Toolkit.
Slide Eight: Importance of Team Work
· Explain the importance of team work in education and the workplace.
· Identify some strategies you would use when working in a team.
· Identify effective communication you would use when working in a team.
Slide Nine: References
· Cite 3 peer-reviewed, scholarly, or similar references.
· Format your references according to APA guidelines.
Note: Speaker notes are to be provided for each slide. Refer to the “Tutorial: Adding Speaker Notes to Microsoft® PowerPoint® Presentations” document for more information on how to add speaker notes to your presentation.
Note: The University’s Center for Writing Excellence provides samples of different deliverables. Under Samples, you will find a sample Microsoft® PowerPoint® presentation to use as a reference while creating your presentation.
Cite 3 peer-reviewed, scholarly, or similar references to support your presentation.
Format your assignment according to APA guidelines. Include a title slide, detailed speaker notes, and a reference slide.
Submit your assignment.
Bottom of Form
PLEAS ...
Wk 5 Individual Preparing for Working in Teams [due Day#]Top of.docx
It 221 week 3 dq1
1. To get more course tutorials visit
https://bitly.com/1xpymvf
This file of IT 221 Week 3 Discussion Question 1 comprises:
How does the design phase of the project management life
cycle differ in content and importance from the other
phases?
Mathematics - Discrete Mathematics
Parallel and Perpendicular.
Read the following instructions in order to complete this
discussion, and review the example of how to complete the
math required for this assignment:
a. Given an equation of a line, find equations for lines parallel
or perpendicular to it going through specified points. Find the
appropriate equations and points from the table below.
Simplify your equations into slope-intercept form.
If your first name starts with
Write the equation of a line parallel to the given line but
passing through the given point.
Write the equation of a line perpendicular to the given line
but passing through the given point.
A or N
y = ½ x + 3; (-2, 1)
y = ¾ x – 1; (4, 0)
B or O
– 4; (1, 3)
+ 3; (1, 1)
C or P
y = ¼ x – 2; (8, -1)
– 5; (0, -1)
2. D or Q
+ 3; (-2, -2)
⅔ x + 2; (9, -3)
E or R
⅓ x – 4; (-6, -3)
– 1; (2, -2)
F or S
½ x + 1; (4, 2)
– 6; (-1, 5)
G or T
y = ¾ x – 1; (4, 0)
+ 4; (-7, 1)
H or U
+ 3; (1, 1)
y = ½ x + 3; (-2, 1)
I or V
– 5; (0, -1)
– 4; (1, 3)
J or W
⅔ x + 2; (9, -3)
y = ¼ x – 2; (8, -1)
K or X
– 1; (2, -2)
+ 3; (-2, -2)
L or Y
– 6; (-1, 5)
⅓ x – 4; (-6, -3)
M or Z
+ 4; (-7, 1)
½ x + 1; (4, 2)
b. Discuss the steps necessary to carry out each activity.
3. Describe briefly what each line looks like in relation to the
original given line.
c. Answer these two questions briefly in your own words:
What does it mean for one line to be parallel to another?
What does it mean for one line to be perpendicular to
another?
d. Incorporate the following five math vocabulary words into
your discussion. Use bold font to emphasize the words in
your writing (Do not write definitions for the words; use
them appropriately in sentences describing your math
work.):
Origin
Ordered pair
X- or y-intercept
Slope
Reciprocal
Your initial post should be 150-250 words in length. Respond
to at least two of your classmates’ posts by Day 7 in at least a
paragraph. Make sure you choose people who don’t have the
same equations as you worked. Do you agree with how they
used the vocabulary? Do their equations seem reasonable
given what they started with?
Although college can be very frightening, it can also be an
incredible experience. The following guide has tricks and tips
that you could use in order to graduate from college.
Consider this advice, along with that of friends and family,
very carefully. The decisions you make today will impact the
rest of your life....
https://bitly.com/1xpymvf