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### Library Home CBSE - IX (Change Class)
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Basic Constructions
In earlier classes you might have learnt to construct perpendicular bisector of a line segment, angles of 300,450 600, 900, 1200 and also to draw bisector of the given angle. An angle bisector is a ray, which divides an angle in to two equal... |
# L.C.M concepts and formula
## L.C.M concepts and formula
One of the most prevalent quantitative aptitude topics asked in government tests is L.C.M. This is one of the most fundamental topics that students are already aware of before they begin studying for competitive exams.
Although the concepts of LCM remain the... |
# Lesson Explainer: Möbius Transformations Mathematics
In this explainer, we will learn how to interpret Möbius transformation in the complex plane.
Möbius transformations form an interesting class of the transformations of the complex plane. They have a number of deep properties and connections to other areas of mat... |
# Class 8 RD Sharma Solutions – Chapter 15 Understanding Shapes Polygons – Exercise 15.1
Last Updated : 18 May, 2021
### Question 1. Draw a Rough diagram to illustrate the Following.
(i) Open curve
(ii) Closed curve
Solution:
i) Open curve: A curve in which the beginning point and the ending point do not meet eac... |
?> Identity Property Worksheet | Problems & Solutions
# Identity Property Worksheet
Identity Property Worksheet
• Page 1
1.
Which symbol would you use to balance the number sentence?
a. I don′t know. b. × c. - d. +
#### Solution:
The product of any number and 1 is the number itself.
So, 8 × 1 = 8.
2.
Multiply:... |
# RS Aggarwal Class 8 Math Ninth Chapter Percentage Exercise 9A Solution
## EXERCISE 9A
(1) Express each of the following as a fraction:
(2) Express each of the following as a decimal:
(3) Express each of the following s a percentage:
(4) Convert the ratio 4 : 5 to percentage.
(5) Express 125% as a ratio.
(7)(i)... |
# Computing the area under a curve
Page 1 / 2
Basic Numerical Integration with MATLAB
This chapter essentially deals with the problem of computing the area under a curve. First, we will employ a basic approach and form trapezoids under a curve. From these trapezoids, we can calculate the total area under a given cur... |
A set of equations for which we get a common solution is known as system of equations. System of equations can be either linear or non-linear.
Two set of equations will have two variables, three set of equations will have three variables and so on. System of equations can have any number of variables which can be line... |
# How do you factor m^2-10my+25y^2?
##### 1 Answer
May 11, 2016
$\left(m - 5 y\right) \left(m - 5 y\right) = {m}^{2} - 10 m y + 25 {y}^{2}$
#### Explanation:
One of our first clues in factoring this expression is that the first and last terms are perfect squares:
$\sqrt{{m}^{2}} = m$
and
$\sqrt{25 {y}^{2}} = 5 y... |
Section 14.4 Trees
1 / 22
# Section 14.4 Trees - PowerPoint PPT Presentation
## Section 14.4 Trees
- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
##### Presentation Transcript
1. Section 14.4Trees
2. What You Will Learn • Trees • Spanning Trees • ... |
English
# Solving Cubic Equations With Worked Examples
Cubic equation is a third degree polynomial equation. To solve this equation, write down the formula for its roots, the formula should be an expression built with the coefficients a, b, c and fixed real numbers using only addition, subtraction, multiplication, di... |
# Question 4 & 5, Review Exercise 1
Solutions of Question 4 & 5 of Review Exercise 1 of Unit 01: Complex Numbers. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.
If ${{z}_{1}}=2-i$,${{z}_{2}}=1+i,$ find $|\dfrac{{{z}_{1}}+{{z... |
Exploring Box Plots - PowerPoint PPT Presentation
1 / 22
Exploring Box Plots. Using the Key components of the Box plot to compare variability . Bell Ringer (review - calculate median). Ashley’s Dress shop posted sales for one week of \$874, \$1471, \$1275, \$1078, \$993, \$471, and \$1125. Find the median sales for t... |
# 2003 AMC 12B Problems/Problem 21
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
## Problem
An object moves $8$ cm in a straight line from $A$ to $B$, turns at an angle $\alpha$, measured in radians and chosen at random from the interval $(0,\pi)$, and moves $5$ cm in a straight line to ... |
# How do you find the sides of a triangle given the angle and hypotenuse?
## How do you find the sides of a triangle given the angle and hypotenuse?
If you have the hypotenuse, multiply it by sin(θ) to get the length of the side opposite to the angle. Alternatively, multiply the hypotenuse by cos(θ) to get the side a... |
# Evaluate
Question:
Evaluate
$\lim _{h \rightarrow 0}\left(\frac{\sqrt{x+h}-\sqrt{x}}{h}\right)$
Solution:
To evaluate:
$\lim _{h \rightarrow 0} \frac{\sqrt{x+h}-\sqrt{x}}{h}$
Formula used:
L'Hospital's rule
Let $f(x)$ and $g(x)$ be two functions which are differentiable on an open interval $I$ except at a po... |
Arithmetic
Additive Identity
Associative Property
Averages
Brackets
Closure Property
Commutative Property
Conversion of Measurement Units
Cube Root
Decimal
Distributivity of Multiplication over Addition
Divisibility Principles
Equality
Exponents
Factors
Fractions
Fundamental Operations
H.C.F / G.C.D
Integers
L.C.M
Mult... |
# Net force word problems
Find here in this lesson some easy and challenging net force word problems.
Problem #1:
What is the net force on the airplane in the figure below?
The airplane is moving with a force of 800 N. However, there are two forces moving in the opposite direction on the airplane.
Just add these ... |
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### Chapter1.7
1. 1. Commutative andComm... |
Let's continue exploring integer addition, but this time we will progress from using colour alone to represent the opposite signs of positive and negative values and explicitly write out these expressions and equations mathematically!
In the previous posts, we have primarily used colour to differentiate between positi... |
# Video: Differentiating a Combination of Rational Functions Using the Quotient Rule
If π¦ = ((π₯ + 5)/(π₯ β 5)) β ((π₯ β 5)/(π₯ + 5)), find dπ¦/dπ₯.
01:48
### Video Transcript
If π¦ is equal to π₯ plus five over π₯ minus five minus π₯ minus five over π₯ plus five, find dπ¦ by dπ₯.... |
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# Greatest Common Factor Using Factor Trees
## Multiplying only the same prime factors on each tree
Estimated4 minsto complete
%
Progress
Practice Greatest Common Factor Using Factor Tr... |
## Perimeter
It is the outside boundary of any closed shape. To find the perimeter we need to add all the sides of the given shape.
The perimeter of a rectangle is the sum of its all sides. Its unit is same as of its length.
Perimeter = 3 + 7 + 3 + 7 cm
Perimeter of rectangle = 20 cm
## Area
Area of any closed fi... |
## Algebraic Equations
### Introduction
The fundamental idea on which algebraic equation are based is that an equation is exactly like a set of balance scales. If you do exactly the same thing to both sides of the equation then the equation will always balance. If you add the same amount to both sides or subtract the... |
# How do you integrate int dx/(x^2+25) using trig substitutions?
Dec 8, 2016
Let $x = 5 \tan \left(\theta\right)$, then dx = sec^2(theta)d"theta. To reverse the substitution, use $\theta = {\tan}^{-} 1 \left(\frac{x}{5}\right)$
#### Explanation:
$\int \frac{\mathrm{dx}}{{x}^{2} + 25}$
Let $x = 5 \tan \left(\theta\... |
# Lesson 13
Exponential Functions with Base $e$
## 13.1: $e$ on a Calculator (5 minutes)
### Warm-up
In this lesson, students are expected to use calculators with an $$e$$ button. This warm-up is meant to smooth out any technical difficulties with using their calculator to perform desired calculations.
Students ma... |
# Ordinal Numbers From Left T
It is possible to enumerate infinite sets using ordinal numbers. They also aid in generalize ordinal numbers.
## 1st
Ordinal numbers are among the most fundamental ideas in mathematics. It is a number that indicates the place of an object within an array of objects. Ordinal numbers are ... |
# Find the sum of the series:
Question:
Find the sum of the series:
$(3 \times 8)+(6 \times 11)+(9 \times 14)+\ldots$ to $n$ terms
Solution:
In the given question we need to find the sum of the series.
For that, first, we need to find the nth term of the series so that we can use summation of the series with stan... |
# A weight of 500 N is supported by two metallic ropes as shown in the figure. The values of tensions T1 and T2 are respectively:
1. 433 N and 250 N
2. 250 N and 433 N
3. 353.5 N and 250 N
4. 250 N and 353.5 N
## Answer (Detailed Solution Below)
Option 1 : 433 N and 250 N
## Detailed Solution
Concept:
Lami's Theo... |
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### PRODUCT DESCRIPTION
4th Grade MAFS Study Guide is a tool to review the Mathematics Florida Standards as a Test Prep. The study guide uses examples from the FSA Test Item Spec... |
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Finding the Area of Irregular Figures
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# HCF AND LCM WORKSHEET
HCF and LCM Worksheet :
Worksheet given in this section will be much useful to the students who would like to practice solving problems on HCF and LCM.
Before look at the worksheet, if you would like to learn the stuff HCF and LCM,
## HCF and LCM Worksheet - Problems
Problem 1 :
Find the H... |
# Helping solve mod problems
I am having trouble solving the below problems. My teacher taught us to write out the solutions by hand.. but I really think there is an easier way to do the higher numbers. Thanks!
• The last one you can do it using Chinese Remainder Theorem. – Alexei0709 Jun 3 '14 at 20:46
Hints: $$\te... |
# An Inequality with Two Sets of Cevians
### Solution 1
Let be $x,y,z\in [0,1];$ $BA'=xa;$ $CA'=(1-x)a;$ $CB'=yb;$ $AB'=(1-y)b;$ $AC'=zc$; $BC'=(1-z)c.$
\displaystyle\begin{align} \frac{[A'B'C']}{[ABC]}&=\frac{[ABC]-[AB'C']-[BA'C']-[CA'B']}{[ABC]}\\ &=1-\frac{\frac{1}{2}z(1-y)bc\sin A }{\frac{1}{2}bc \sin A}-\frac{\... |
toseeifitworksforream
2022-04-04
Let a and b be coprime integers, and let m be an integer such that a | m and b | m. Prove that ab | m
alenahelenash
To prove that $ab\mid m$, we need to show that $m$ is a multiple of $ab$, which means that $m=abn$ for some integer $n$.
Since $a\mid m$, we can write $m=ak$ for some ... |
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# SAT Math: Problem Solving and Data Analysis ๐
kritika gautam
kritika gautam
## SAT Math Overview
Welcome to another SAT Math guide! The Problem Solving & Data Analysis portion of the SAT Math exam makes up 17/58 questions, or about 30% of the math section. You should be ... |
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# Graphs of Functions based on Rules
## Graph functions using value tables
Estimated6 minsto complete
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Progr... |
# How do you solve 3x - 3= 8- 2( x + 3)?
May 29, 2018
Work backwards PESADM to find the lost unknown.
#### Explanation:
To find something that is lost it usually best to work backwards.
The order of operation is PEMDAS backwards PESADM.
Think about it this way if you lose something in PE you are a SAD M(an, am)
F... |
# What is the Greatest Common Factor (GCF) of 2 and 399?
Are you on the hunt for the GCF of 2 and 399? Since you're on this page I'd guess so! In this quick guide, we'll walk you through how to calculate the greatest common factor for any numbers you need to check. Let's jump in!
Want to quickly learn or show student... |
# If two chords of a circle are equally inclined to the diameter through their point of intersection, prove the chords are equal.
Given:
Two chords of a circle are equally inclined to the diameter through their point of intersection.
To do:
We have to prove that the chords are equal.
Solution:
$AB$ and $AC$ are tw... |
## 2 + 3
means;
If we bring together 2 apples and 3 apples, we have 5 apples.
If we put them all in a bag, we have 5 apples.
## Before starting:
You should know the place values of the numbers.
In modeling, shapes and their meanings.
In modeling, shapes and their meanings can be used to represent mathematical co... |
# How do find the vertex and axis of symmetry, and intercepts for a quadratic equation y=x^2 +2x -5?
Jul 11, 2015
The vertex is at ($- 1 , - 2$).
The axis of symmetry is $x = 1$.
The $y$-intercept is at ($0 , 5$).
The $x$-intercepts are at $x = - 1 - \sqrt{6}$ and $x = - 1 + \sqrt{6}$.
#### Explanation:
The standar... |
# An Introduction to Mathematical Induction: The Sum of the First n Natural Numbers, Squares and Cubes.
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
## Sigma Notation
In math, we frequently deal with large sums. For example, we can write
${\displaystyle 1+2+3+4+5+6+7+8+9+10+11+12+13,}$... |
$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$... |
Geometric Progression, GP
Geometric progression (also known as geometric sequence) is a sequence of numbers where the ratio of any two adjacent terms is constant. The constant ratio is called the common ratio, r of geometric progression. Each term therefore in geometric progression is found by multiplying the previous ... |
# Indefinite integral
Let $f$ be any function and $F$ its antiderivative. The set of all antiderivatives of $f$ is called indefinite integral of the function $f$ denoted by
$$\int f(x) dx = F(x) + C.$$
Every two primitive functions differ by a constant $C$. This means, if we know the one antiderivative $F$ of the fu... |
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# 5.10: Proportions Using Cross Products
Difficulty Level: At Grade Created by: CK-12
Estimated6 minsto complete
%
Progress
Practice Proportions Using Cross Products
MEMORY METER
This i... |
Instructor: Maria Blojay
Maria has taught College Algebra and has a master's degree in Education Administration.
This lesson will show how to solve radical inequalities using radical definitions and properties. Key terms and radical notes are included to share step by step the method to solve these special types of i... |
1) Arrange both the polynomial is same order of exponent . It would be good to have terms arrange from highest exponent to lowest exponent i.e
For example
S(x) = x2 + 5x3 + 1 +10x
P(x) = x3 + x2 + 5 +10x
Arranging them as per suggestion above
S(x) = 5x3 +x2+ 10x +1
P(x) = x3 + x2 + 10x +5
2) Add the like term . By l... |
In this post we are going to learn to analyze, think about, and solve addition problems. Usually, failure in mathematics comes from not understanding well the problems that we are given. This is why we are going to analyze 5 problems which require addition to solve.
There were 8 cars in the parking lot of a hotel. 5 m... |
# Dao's Six Point Circle
### What Might This Be About?
6 June 2014, Created with GeoGebra
### Problem
The centers of the six circles tangent to the medians of $\Delta ABC$ at the centroid and through the vertices of the triangle are concyclic:
### Solution
Let $A', B', C'$ be the midpoints of the sides of $\Delta... |
# Algebra: Solving Rational Inequalities
## Solving Rational Inequalities
At the end of Quadratic Equations and Inequalities, I showed you how to solve and graph one-variable quadratic inequalities. Do you remember the process? Basically, you factored the quadratic, found critical numbers, split the number line into ... |
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Solutions
Abstract Algebra
# Abstract Algebra (3rd Edition)Solutions for Chapter 1.3
• 1574 step-by-step solutions
• Solved by publishers, professors & experts
• iOS, Android, & web
Looking for the textbook?
Over 90% of students who use Chegg Study report better grades.
May 2015 Survey of Chegg Stu... |
# Thread: Optimization Problem
1. ## Optimization Problem
Find the maximum horizontal overhang for a 15 foot ladder over an 8 foot fence
The ladder base is always on the ground, the fence is vertical and ground it horizontal
2. Originally Posted by Exiab
Find the maximum horizontal overhang for a 15 foot ladder ove... |
# How do you factor 12x^2+7x-5?
Sep 20, 2015
color(blue)((12x-5)(x+1) is the factorised form.
#### Explanation:
$12 {x}^{2} + 7 x - 5$
We can Split the Middle Term of this expression to factorise it.
In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers... |
### 26-SNC2D-MirrorAndMagnification
```(10.3/10.4) Mirror and
Magnification Equations
(12.2) Thin Lens and
Magnification Equations
Mirror and Magnification Equations
The characteristics of an image can be
predicted by using two equations:
◦ Mirror Equation:
Allows us to determine the focal point, distance of
the i... |
# Search by Topic
#### Resources tagged with Generalising similar to Flip Flop - Matching Cards:
Filter by: Content type:
Stage:
Challenge level:
### There are 81 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Generalising
### Nim-7
##### Stage: 1, 2 and 3 Challenge Level:
Can you work ... |
How do you draw a 200 degree angle with a protractor?
1. Given : angle 200 degree.
2. To Find : draw angle 200 degree with protractor
3. Solution: Step 1 : Draw a line segment AB. Step 2 : Draw an angle of 160° at B on AB and mark C. ∠ABC = 160° Step 3 : Mark angle out side of angle that will be ∠ABC = 360° – 160° = ... |
# Algorithm and Flowchart to check whether a number is twisted prime or not
[166 views]
### Prime Numbers:
A number is said to be a prime number when it has only two factors, that is, when the factors of the number are 1 and the number itself. Example: 2, 3, 11, 17, etc.
### What are Twisted Prime Numbers?:
A prim... |
# Puzzle – The Hands of a Clock First Overlap
• Difficulty Level : Basic
• Last Updated : 18 Jan, 2023
Question:
An hour hand and a minute hand are standard on a clock. At 12 midnight the hands are exactly aligned. When will they next precisely align or overlap? How frequently will they cross paths each day?
Soluti... |
# 750 in words
750 in words is written as Seven hundred and Fifty. 750 represents the count or value. The article on Counting Numbers can give you an idea about count or counting. The number 750 is used in expressions that relate to money, days, distance, length, weight and so on. Let us consider a few examples for 75... |
# Divisibility
Many people know about testing numbers for divisibility by 3 or 9: you add the digits and if (and only if) the sum is divisible by 3, so is the original number; if (and only if) the sum is divisible by 9, so is the original number. Not as many people know how to prove that, though. There are a number of... |
# How do you find the sum of the first 25 terms of the sequence: 7,19,31,43...?
$3775$
#### Explanation:
The given series:
$7 , 19 , 31 , 43 , \setminus \ldots$
Above series is an arithmetic progression with a common difference
$d = 19 - 7 = 31 - 19 = 43 - 31 = \setminus \ldots = 12$
First term: $a = 7$
The sum... |
# How do you find all relative extrema and points of inflection for the equation: y=x^2 log_3x?
Jul 5, 2015
Find extrema using the derivative and points of inflection using the second derivative.
#### Explanation:
We will make use of: ${\log}_{3} x = \ln \frac{x}{\ln} 3$ and
$\frac{d}{\mathrm{dx}} {\log}_{3} x = \... |
## Wednesday, May 20, 2015
### Another method to prove $7 ≥ \sqrt 2+\sqrt 5 + \sqrt {11}$
Show with proof which of these two values is smaller:
$7$, or $\sqrt 2+\sqrt 5 + \sqrt {11}$
In my (few) previous blog post (Which is greater), I mentioned of how I proved for $\sqrt 2+\sqrt 5 + \sqrt {11}$ is smaller than $7$... |
# Ch 1: Real Numbers: Types and Properties
Watch video lessons and learn about the different types of numbers and their properties. Complete the quizzes that follow each lesson to measure your learning.
## Real Numbers: Types and Properties - Chapter Summary and Learning Objectives
The lessons in this chapter explor... |
# Section 1.1: Integer Operations and the Division Algorithm - PowerPoint PPT Presentation
1 / 17
Section 1.1: Integer Operations and the Division Algorithm. MAT 320 Spring 2008 Dr. Hamblin. Addition. “You have 4 marbles and then you get 7 more. How many marbles do you have now?”. 4. 11. 7. Subtraction. “If you have ... |
# Diagonal Count
The purpose of this page is to help you count a number of non-intersecting diagonals in a convex polygon. I won't give you the formula right away. You are to come up with the right one by experimenting with the applet below. Once you surmise the right result, try to prove it before looking into the ex... |
# Geometric Series Formula
## Geometric Series Formula
Number sequences follow certain patterns and laws. Any routine pattern that is transferable from one term to the next may be this pattern. The Geometric Series Formula is one in which more multiplication is required to obtain the following term. The sum of the se... |
# Understanding Ordering of Numbers and Applying the Rules of Ascending & Descending Order Value
One of the most important topics for early Math learners is to identify the order of numbers and correctly arrange them from small to big and big to small. Ordering is basically arranging numbers in a sequence where the su... |
# Linear Thinking Solving First Degree Equations - Ship
Linear Thinking Solving First Degree Equations - Ship
0011 0010 1010 1101 0001 0100 1011
Linear Thinking
Solving First Degree Equations
9/21/09
MAT 400
Chessa Horomanski
Jessica DiPaul
4 2 1
0011 0010 1010 1101 0001 0100 1011
The Rhind Papyrus
• Named ... |
# Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8, how do you simplify R - S + T?
$14 - 3 m - 4 n$
#### Explanation:
Given that
$R = 11 - 2 m , \setminus S = n + 5$ & $T = - m - 3 n + 8$
$\setminus \therefore R - S + T$
$= 11 - 2 m - \left(n + 5\right) + \left(- m - 3 n + 8\right)$
$= 11 - 2 m - ... |
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# Vở bài tập Toán lớp 3 Tập 2 trang 32, 33 Bài 53 Tiết 1 | Kết nối tri thức
Have you been looking for effective and detailed solutions for your 3rd grade math homework from Exercise Book 2, specifically on Pages 32-33, Lesson 1? Look no further! At Kienthucykhoa.com, we provide top-notch assistance to help stude... |
Find a Nonsingular Matrix Satisfying Some Relation
Problem 280
Determine whether there exists a nonsingular matrix $A$ if
$A^2=AB+2A,$ where $B$ is the following matrix.
If such a nonsingular matrix $A$ exists, find the inverse matrix $A^{-1}$.
(a) $B=\begin{bmatrix} -1 & 1 & -1 \\ 0 &-1 &0 \\ 1 & 2 & -2 \end{bmatri... |
# Math Clip Art--Base Ten Blocks--50
Number Models
## Description
This image is a crucial component of the base ten blocks series, demonstrating the modeling of the number 100. It employs a template in the form of a placemat where base ten blocks representing thousands, hundreds, tens, and ones are strategically pla... |
# The Second Derivative
The second derivative of a quadratic function is constant.
In calculus, the second derivative, or the second order derivative, of a function f is the derivative of the derivative of f. Roughly speaking, the second derivative measures how the rate of change of a quantity is itself changing; for... |
## How do you find the roots of an equation?
The roots of any quadratic equation is given by: x = [-b +/- sqrt(-b^2 – 4ac)]/2a. Write down the quadratic in the form of ax^2 + bx + c = 0. If the equation is in the form y = ax^2 + bx +c, simply replace the y with 0. This is done because the roots of the equation are the... |
# How do you write a rule for the nth term of the geometric sequence given the two terms a_2=-153, a_4=-17?
Jan 19, 2018
${u}_{n} = \pm 459 \cdot {\left(\pm \frac{1}{3}\right)}^{n - 1}$
#### Explanation:
geometric sequence: ${u}_{n} = a {r}^{-} 1$
where $a$ is the starting term
and $r$ is the number by which one ... |
# Multiplication Facts 0-10 Memory Tips
## MULTIPLICATION FACTS 0-12
When students learn multiplication, it starts out easy.
Too easy, as 0 times anything equals 0 (e.g. 0 x 8 = 0, while anything times 1 equals itself (e.g. 4 x 1 = 4).
But it doesn’t stay easy. Most students struggle to remember multiplication fact... |
Prove that, for any polygon, taking all pair of adjacent angles, subtracting 180 from their sum, and adding all the results together equals $180(n-4)$
Take any simple polygon. Extend all sides in both directions. Note the angles where these sides meet, if at all. What is the sum of these angles?
For example, consider... |
# Unlocking the Magic of 5.25 as a Fraction: Exploring Its Meaning, Uses, and Applications
## Understanding 5.25 as a Fraction: A Comprehensive Guide
### What is a Fraction?
A fraction is a way of representing a part of a whole. It consists of two numbers separated by a line, with the top number called the numerator... |
# Show the identity can be derived from a sum or a difference identity and the pythagorean identity?
## $\cos \left(2 a\right) = 1 - 2 {\sin}^{2} a$
Jun 3, 2018
See explanation
#### Explanation:
Remember the angle sum identity
color(blue)(cos(x+y)=cos(x)cos(y)-sin(x)sin(y)
Now let color(red)(x=y=a
$\cos \left(a... |
# Search by Topic
#### Resources tagged with Addition & subtraction similar to Primary Advent Calendar 2010:
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##### Other tags that relate to Primary Advent Calendar 2010
Interactivities. Games. Generalising. Mental addition & subtraction. Working systematically. Addit... |
# Factorising
[mathjax]
Expanding Brackets
Removing the brackets is known as distributive law. To remove the brackets, multiply each term outside the bracket.
Example:
$$3(x + 2)$$ Multiply each term inside the bracket by 3.
$$3 (x) + 3 (2) = 3x + 6$$
Example 2: $$2x(x + 2)$$
$$2x (x) ... |
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A B C
Solutions for Session 10, Part B
See solutions for Problems: B1 | B2 | B3 | B4 | B5
Problem B1 The largest possible perimeter is 22 units; the smallest is 14 units. This is because all but one pentomino have a perimeter of 12 units. One pentomino has a perimeter of 10 units. A method for determining perimeter... |
# 13.7 Quadratic Equations and Problem Solving
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## Transcription
1 13.7 Quadratic Equations and Problem Solving Learning Objectives: A. Solve problems that can be modeled by quadratic equations. Key Vocabulary: Pythagorean Theorem, right triangle, hypotenuse, leg, su... |
# Working With Money Yorubah Banks. Content Area: Mathematics Grade Level: Grade 2 Summary: The purpose of this power point is to give the students.
## Presentation on theme: "Working With Money Yorubah Banks. Content Area: Mathematics Grade Level: Grade 2 Summary: The purpose of this power point is to giv... |
# Lesson 7
Graphs of Proportional Relationships
## 7.1: Notice These Points (5 minutes)
### Warm-up
This warm-up prepares students for graphing proportional relationships in the coordinate plane. They practice graphing coordinate points and notice that all points lie on a straight line.
### Launch
Give students 3... |
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# In a college, 70 % students pass in physics, 75 % pass in mathematics and 10 % students fail in both. One student is chosen at random. What is the probability that the student passes in mathematics given that he passes in physics?
Last updated ... |
# 6.1 Point Estimation and Sampling Distributions
Learning Objectives
By the end of this chapter, the student should be able to:
• Understand point estimation
• Apply and interpret the Central Limit Theorem
• Construct and interpret confidence intervals for means when the population standard deviation is known
• Und... |
# Understanding the Ohm’s Law Wheel
If you’re looking for a comprehensive guide to the Ohm’s Law Wheel, look no further! In this blog post, we will discuss everything you need to know about electricity. We’ll start by talking about the different parts of Ohm’s Law Wheel and what they mean. Then, we’ll go over some com... |
### One-to-One
##### 1. One-to-one and uniqueness
After the discussion about the relation between onto and existence, we turn to uniqueness from the transformation viewpoint. Again the relation can be seen through everyday life questions.
Example For the transformation
Capital City: country → city
we already know ... |
BY DR. JULIA ARNOLD The Algebra of Functions What does it mean to add two functions? If f(x) = 2x + 3 and g(x) = -4x - 2 What would (f+g)(x) be? (f+g)(x)
Presentation on theme: "BY DR. JULIA ARNOLD The Algebra of Functions What does it mean to add two functions? If f(x) = 2x + 3 and g(x) = -4x - 2 What would (f+g)(x) ... |
# Perimeter of Rectangle
A rectangle can be explained as a 4-sided quadrilateral which contains equal opposite sides. In a rectangle, the opposite sides are always parallel to each other and commonly classified as equiangular quadrilateral. As the rectangle has no equal adjacent sides, we always get 2 different measur... |
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# Anshul moves towards East a distance of 5 meters, then he turns to his left and walks 20 meters, then again he turns left and walks 15 meters. Now, he turns ${45^0}$ towards his right and goes straight to cover $20\sqrt 2$ meters. How far is he ... |
# Chapter 4 First and second order ODEs
Not all ODEs are analytically solvable. In this section we discuss some types of first and second order ODEs that are analytically solvable and see some examples.
## 4.1 First order ODEs
A first order ODE has only the first derivative represented. The general implicit form for... |
# If y varies inversely with x and y = 8 when x = 5, then what is y when x = 2?
Apr 29, 2017
$y = 20$
#### Explanation:
"varies inversely means " 1/("variable")
$\text{the initial statement is } y \propto \frac{1}{x}$
To convert to an equation, multiply by k, the constant of variation.
$\Rightarrow y = k \times ... |
# Class 7: Systems of linear equations and SAGEmath
Overview: This part introduces you to an essential skill in any mathematician's or cryptographer's tool chest. Using linear algebra (matrices) to find answers to linear systems. This talent will unlock the ability to break the LCGs and LFSRs from the last lesson.
##... |
# Difference between revisions of "2011 AMC 10B Problems/Problem 23"
## Problem
What is the hundreds digit of $2011^{2011}?$
$\textbf{(A) } 1 \qquad \textbf{(B) } 4 \qquad \textbf{(C) }5 \qquad \textbf{(D) } 6 \qquad \textbf{(E) } 9$
## Solution 1
Since $2011 \equiv 11 \pmod{1000},$ we know that $2011^{2011} \equi... |
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