You will learn how to factor the difference of two squares.
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This powerpoint presentation discusses or talks about the topic or lesson Functions. It also discusses and explains the rules, steps and examples of Quadratic Functions.
Mathematics 9 Lesson 1-D: System of Equations Involving Quadratic EquationsJuan Miguel Palero
This powerpoint presentation discusses or talks about the topic or lesson System of Equations involving Quadratic Equations. It also discusses and explains the rules, steps and examples of System of Equations involving Quadratic Equations
You will learn how to factor the difference of two squares.
For more instructional resources, CLICK me here! 👇👇👇
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here! 👍👍👍
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
This powerpoint presentation discusses or talks about the topic or lesson Functions. It also discusses and explains the rules, steps and examples of Quadratic Functions.
Mathematics 9 Lesson 1-D: System of Equations Involving Quadratic EquationsJuan Miguel Palero
This powerpoint presentation discusses or talks about the topic or lesson System of Equations involving Quadratic Equations. It also discusses and explains the rules, steps and examples of System of Equations involving Quadratic Equations
Final Exam Name___________________________________Si.docxcharlottej5
Final Exam Name___________________________________
Silva Math 96 Spring 2020
YOU MUST SHOW ALL WORK AND BOX YOUR ANSWERS FOR CREDIT. WORK ALONE.
Solve the absolute value inequality. Write your answer
in interval notation.
1) |2x - 12 |> 2
Solve the compound inequality. Graph the solution set.
Write your answer in interval notation.
2) -4x > -8 and x + 4 > 3
Solve the three-part inequality. Write your answer in
interval notation.
3) -1 < 3x + 2 < 14
Solve the absolute value equation.
4) 4x + 9 = 2x + 7
Solve the compound inequality.
5) 3( x + 4 ) ≥ 0 or 4 ( x + 4 ) ≤ 4
Solve the inequality. Graph the solution set and write
your answer in interval notation.
6) |5k + 8| > -6
Solve the inequality graphically. Write your answer in
interval notation .
7) x + 3 ≥ 1
x-8 -6 -4 -2 2
y
8
6
4
2
x-8 -6 -4 -2 2
y
8
6
4
2
1
Graph the system of inequalities.
8) 2x + 8y ≥ -4
y < - 3
2
x + 6
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Find the determinant of the given matrix.
9) 10 5
0 -4
Use Cramer's rule to solve the system of linear
equations.
10) 6x + 5y = -12
2x - 2y = -4
Write a system that models the situation. Then solve the
system using any method. Must show work for credit.
11)A vendor sells hot dogs, bags of potato chips,
and soft drinks. A customer buys 3 hot dogs,
4 bags of potato chips, and 5 soft drinks for
$14.00. The price of a hot dog is $0.25 more
than the price of a bag of potato chips. The
cost of a soft drink is $1.25 less than the price
of two hot dogs. Find the cost of each item.
Use row reduced echelon form to solve the system.
12) x + y + z = 3
x - y + 4z = 11
5x + y + z = -9
2
Find the domain of f. Write your answer in interval
notation.
13) f(x) = 13 - 9x
If possible, simplify the expression. If any variables
exist, assume that they are positive.
14) 2x + 6 32x + 6 8x
Match to the equivalent expression.
15) 100-1/2
A) 1
1000
B) 1
10
C) 1
100
D) 1
10
Write the expression in standard form.
16) (5 + 8i) - (-3 + i)
Simplify the expression. Assume that all variables are
positive.
17) 5 t
5
z10
Solve the equation.
18) 3x + 1 = 3 + x - 4
Write the expression in standard form.
19) 3 + 3i
5 + 3i
3
Write the equation in vertex form.
20) y = x2 + 5x + 2
The graph of ax2 + bx + c is given. Use this graph to solve
ax2 + bx + c = 0, if possible.
21)
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
Solve the equation. Write complex solutions in standard
form.
22) 4x2 + 5x + 5 = 0
Graph the quadratic function by its properties.
23) f(x) = 1
3
x2 - 2x + 3
x
y
x
y
Solve the equation. Find all real solutions.
24) 2(x - 1)2 + 11(x - 1) + 12 = 0
Solve the problem.
25) The length of a table is 12 inches more than its
width. If the area of the table is 2668 square
inches, what is its length?
4
Solve the equation..
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
In today's fast-changing business world, Companies that adapt and embrace new ideas often need help to keep up with the competition. However, fostering a culture of innovation takes much work. It takes vision, leadership and willingness to take risks in the right proportion. Sachin Dev Duggal, co-founder of Builder.ai, has perfected the art of this balance, creating a company culture where creativity and growth are nurtured at each stage.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
Smart TV Buyer Insights Survey 2024 by 91mobiles.pdf91mobiles
91mobiles recently conducted a Smart TV Buyer Insights Survey in which we asked over 3,000 respondents about the TV they own, aspects they look at on a new TV, and their TV buying preferences.
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
5. You can see in the graph of f(x) = x2 + 1 below
that f has no real zeros. If you solve the
corresponding equation 0 = x2 + 1, you find
that x = ,which has no real solutions.
However, you can find solutions if you
define the square root of negative
numbers, which is why imaginary
numbers were invented. The
imaginary unit i is defined
as . You can use the imaginary
unit to write the square root of
any negative number.
6. Example 1A: Simplifying Square Example 1B: Simplifying Square Roots of
Roots of Negative Numbers Negative Numbers
Express the number in terms of i. Express the number in terms of i.
4 6i 4i 6
7. Check It Out! Example 1a Check It Out! Example 1c
Express the number in terms of i. Express the number in terms of i.
Factor out –1.
Product Property. Factor out –1.
Product Property. Product Property.
Simplify.
Simplify.
Express in terms of i.
Multiply.
Example 2A: Solving a Quadratic
Equation with Imaginary Solutions Express in terms of i.
Solve the equation.
Take square roots.
Express in terms of i.
Check
x2 = –144 x2 = –144
(12i)2 –144 (–12i)2 –144
144i 2 –144 144i 2 –144
144(–1) –144 144(–1) –144
8. Example 2B: Solving a Quadratic Equation with
Imaginary Solutions
Solve the equation.
5x2 + 90 = 0
Add –90 to both sides.
Divide both sides by 5.
Take square roots.
Express in terms of i.
Check 5x2 + 90 = 0
0
5(18)i 2 +90 0
90(–1) +90 0
9. Check It Out! Example 2a
Solve the equation.
x2 = –36
Take square roots.
Express in terms of i.
Check
x2 = –36 x2 = –36
(6i)2 –36 (–6i)2 –36
36i 2 –36 36i 2 –36
36(–1) –36 36(–1) –36
10. Check It Out! Example 2b
Solve the equation.
x2 + 48 = 0
x2 = –48 Add –48 to both sides.
Take square roots.
Express in terms of i.
Check x2 + 48 = 0
+ 48 0
(48)i 2 + 48 0
48(–1) + 48 0
11. Check It Out! Example 2c
Solve the equation.
9x2 + 25 = 0
9x2 = –25 Add –25 to both sides.
Divide both sides by 9.
Take square roots.
Express in terms of i.
12. A complex number is a number that can be written in the form a + bi, where a and b are
real numbers and i = . The set of real numbers is a subset of the set of complex numbers
C.
Every complex number has a real part a and an imaginary
part b.
Real numbers are complex numbers where b = 0. Imaginary numbers are complex
numbers where a = 0 and b ≠ 0. These are sometimes called pure imaginary numbers.
Two complex numbers are equal if and only if their real parts are equal and their
imaginary parts are equal.
Example 3: Equating Two Complex Numbers
Find the values of x and y that make the equation 4x + 10i = 2 – (4y)i true .
Real parts
4x = 2 Equate the real parts. 10 = –4y Equate the imaginary parts.
4x + 10i = 2 – (4y)i Solve for x. Solve for y.
Imaginary parts
13. Check It Out! Example 3a
Find the values of x and y that make each
equation true.
2x – 6i = –8 + (20y)i
Real parts
2x – 6i = –8 + (20y)i
Imaginary parts
Equate the Equate the
2x = –8 –6 = 20y
real parts. imaginary parts.
x = –4 Solve for x. Solve for y.
14. Check It Out! Example 3b
Find the values of x and y that make each
equation true.
–8 + (6y)i = 5x – i 6
Real parts
–8 + (6y)i = 5x – i 6
Imaginary parts
Equate the
–8 = 5x Equate the real
imaginary parts.
parts.
Solve for y.
Solve for x.
15. Example 4A: Finding Complex Zeros of Quadratic
Functions
Find the zeros of the function.
f(x) = x2 + 10x + 26
x2 + 10x + 26 = 0 Set equal to 0.
x2 + 10x + = –26 + Rewrite.
x2 + 10x + 25 = –26 + 25 Add to both sides.
(x + 5)2 = –1 Factor.
Take square roots.
Simplify.
16. Example 4B: Finding Complex Zeros of Quadratic
Functions
Find the zeros of the function.
g(x) = x2 + 4x + 12
x2 + 4x + 12 = 0 Set equal to 0.
x2 + 4x + = –12 + Rewrite.
x2 + 4x + 4 = –12 + 4 Add to both sides.
(x + 2)2 = –8 Factor.
Take square roots.
Simplify.
17. Check It Out! Example 4a
Find the zeros of the function.
f(x) = x2 + 4x + 13
x2 + 4x + 13 = 0 Set equal to 0.
x2 + 4x + = –13 + Rewrite.
x2 + 4x + 4 = –13 + 4 Add to both sides.
(x + 2)2 = –9 Factor.
Take square roots.
x = –2 ± 3i Simplify.
18. Check It Out! Example 4b
Find the zeros of the function.
g(x) = x2 – 8x + 18
x2 – 8x + 18 = 0 Set equal to 0.
x2 – 8x + = –18 + Rewrite.
x2 – 8x + 16 = –18 + 16 Add to both sides.
Factor.
Take square roots.
Simplify.
19. The solutions and are related. These solutions are a complex conjugate
pair. Their real parts are equal and their imaginary parts are opposites. The complex
conjugate of any complex number a + bi is the complex number a – bi.
If a quadratic equation with real coefficients has nonreal roots, those roots are complex
conjugates.
Helpful Hint
When given one complex root, you can always find the other by finding its conjugate.
Example 5: Finding Complex
Zeros of Quadratic Functions
Find each complex conjugate.
A. 8 + 5i C. 9 - i
8 + 5i Write as a + bi. 9 + (-i) Write as a + bi.
8 – 5i Find a – bi. 9 – (-i) Find a – bi.
9+i Simplify.
B. 6i D. -8i
0 + 6i Write as a + bi. 0 + (-8)i Write as a + bi.
0 – 6i Find a – bi. 0 – (-8)i Find a – bi.
–6i Simplify. 8i Simplify.
20. Lesson Quiz
1. Express in terms of i.
Solve each equation.
2. 3x2 + 96 = 0 3. x2 + 8x +20 = 0
4. Find the values of x and y that make the
equation 3x +8i = 12 – (12y)i true.
5. Find the complex conjugate of