text stringlengths 22 1.01M |
|---|
# Mock AIME 5 2005-2006 Problems/Problem 12
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
## Problem
Let $ABC$ be a triangle with $AB = 13$, $BC = 14$, and $AC = 15$. Let $D$ be the foot of the altitude from $A$ to $BC$ and $E$ be the point on $BC$ between $D$ and $C$ such that $BD = CE$... |
# AS sequence
In an arithmetic sequence is given the difference d = -3 and a71 = 455.
a) Determine the value of a62
b) Determine the sum of 71 members.
Correct result:
a62 = 482
s71 = 39760
#### Solution:
$a_{ 71} = 455; d=-3 \ \\ a_{ 71} = a_1 + (71-1)d \ \\ 455 = a_1 + (71-1)\cdot (-3) \ \\ a_1 = 455 - (-210)... |
Courses βeta
Job Preparation
## Time Speed Distance
#### Description:
Another important topic for clearing the written round of the placements is here. Time, Speed and Distance problems are the ones which you can crack easily with little attention to them
Time, Speed and Distance (popularly known as TSD) is an impo... |
80
Q:
# A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?
A) 1/4 B) 1/2 C) 3/4 D) 7/12
Explanation:
Let A, B, C be the respective events of solving the problem and be the respective events of not solving the... |
## Archive for March 16th, 2018
Someone I know IRL recently wrote, “I didn’t use algebra at all today.” That was probably not true, but no matter.
The Daughter is studying algebra right now in 8th grade and it’s a real PITA. Because she was so good in 7th grade math, she skipped over 8th grade math, what that was, an... |
# How Do You Find A Slope And Y-intercept?
How do you find a slope and y-intercept? The slope-intercept form of a line is: y=mx+b where m is the slope and b is the y-intercept. The y-intercept is always where the line intersects the y-axis, and will always appear as (0,b) in coordinate form.
## How do you find the sl... |
# If 3x2 - 3y2 - 18x + 12y + 2 = 0 represents a hyperbola, find the equation of the directrix.
This question was previously asked in
DSSSB Patwari Question Paper 16th June 2019 Shift 1
View all DSSSB Patwari Papers >
1. $$x=3\pm\sqrt{\dfrac{6}{13}}$$
2. $$x=2\pm\sqrt{\dfrac{13}{6}}$$
3. $$x=2\pm\sqrt{\dfrac{6}{13}}$$
... |
# 2009 AMC 10A Problems/Problem 10
## Problem
Triangle $ABC$ has a right angle at $B$. Point $D$ is the foot of the altitude from $B$, $AD=3$, and $DC=4$. What is the area of $\triangle ABC$?
$[asy] unitsize(5mm); defaultpen(linewidth(.8pt)+fontsize(8pt)); dotfactor=4; pair B=(0,0), C=(sqrt(28),0), A=(0,sqrt(21)); p... |
<meta http-equiv="refresh" content="1; url=/nojavascript/"> Inequalities with Multiplication ( Read ) | Algebra | CK-12 Foundation
You are viewing an older version of this Concept. Go to the latest version.
Inequalities with Multiplication
%
Best Score
Practice Inequalities with Multiplication
Best Score
%
Solve Ineq... |
#### Multiplication - Multiples and Powers of Ten
Quick! Count by tens in your head. Each number that you recited is referred to as a multiple of ten. By the way, regardless of how far you count, each number has a zero at the end. It may be obvious, but I needed to point this out to make a point later.
10, 20, 30, 40 ... |
What is the pattern when dividing by 10 and 100?
What is the pattern when dividing by 10 and 100?
When dividing by ten, move the decimal point one place to the left. When dividing by 100, move the decimal place two places to the left. And, remember, if there’s no decimal point, assume that the decimal falls at the en... |
# 1661 A Little About Palindromes
### Today’s Puzzle:
A number is a palindrome if it reads the same backward as it does forward. For example, 1661 is a 4-digit palindrome. Today’s puzzle asks you to explore number palindromes and their factors.
Half of the time when a 4-digit palindrome is divided by 11, we get a 3-... |
Question
What fraction of an hour is 40 minutes?
Hint: Convert hour into minutes and find the value of fraction by taking 40 minutes in the numerator and one hour in the denominator (converted into minutes). Reduce the fraction into lowest terms by taking out common terms from numerator and denominator.
We have to f... |
#### Explanation:
She spended 10% of her savings, that can also be said as per every $100 she had, she spended$10 of them.
This can be written as
$73 \cancel{0} \times \frac{1 \cancel{0}}{1 \cancel{0} \cancel{0}} = x$
Where $x$ is the money spended in phone
$73 = x$
She spended $73 on her phone Nov 13, 2017 See a solu... |
# What does the intermediate value theorem mean?
Jan 5, 2016
It means that a if a continuous function (on an interval $A$) takes 2 distincts values $f \left(a\right)$ and $f \left(b\right)$ ($a , b \in A$ of course), then it will take all the values between $f \left(a\right)$ and $f \left(b\right)$.
#### Explanation... |
# Lesson 18
Modeling Price Information
These materials, when encountered before Algebra 1, Unit 4, Lesson 18 support success in that lesson.
## 18.1: What’ll It Be? (10 minutes)
### Warm-up
This warm-up helps students get oriented to the situation they will be working with throughout this lesson. Students also mak... |
$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$... |
Let's Discover Great Ideas
# How to Write a Rule to Define a Transformation
Let’s look at some examples of the transformation of a function. First, we’ll describe how we can mirror a graph. This means flipping the x-values around the x-axis. Next, we’ll look at how we can mirror the graph in the y-axis. In both cases... |
# Question Video: Differentiating Root and Exponential Functions Mathematics
Differentiate the function π¦ = 3π^(π₯) β 5/βπ₯.
02:42
### Video Transcript
Differentiate the function π¦ equals three π to the power of π₯ minus five over the cube root of π₯.
The first thing weβre gonna do is act... |
<meta http-equiv="refresh" content="1; url=/nojavascript/">
You are reading an older version of this FlexBook® textbook: CK-12 Algebra - Basic Go to the latest version.
# 12.6: Addition and Subtraction of Rational Expressions
Difficulty Level: At Grade Created by: CK-12
Like numerical fractions, rational expressions... |
# The Three Musketeers: Simplifying the Quadratic Formula
10 teachers like this lesson
Print Lesson
## Objective
SWBAT use the completing the square method to transform a quadratic equation. SWBAT solve quadratic equations using completing the square and the quadratic formula. SWBAT recognize and write complex solut... |
# Case Study Questions for Class 12 Maths Chapter 1 Relations and Functions
Home » CBSE Class 12 Maths » Case Study Questions for Class 12 Maths » Case Study Questions for Class 12 Maths Chapter 1 Relations and Functions
## Case Study Questions for Class 12 Maths Chapter 1 Relations and Functions
Question 1:
Sherli... |
6.5 Concurrent lines of triangles:
Definition:
The perpendicular drawn from the vertex of a triangle to its opposite side is called ‘altitude’. In the adjoining figure C is the vertex. CM is perpendicular to the opposite side AB (extended). CM is called Altitude. Similarly we can draw 2 altitudes from other vertic... |
## Sunday, November 1, 2015
### Arctan and Euler
Communicating Math
Leonard Euler has made many contributions to math, and one of them is a formula for arctan. To see and investigate Euler's formula, I used GeoGebra's An Equation of Euler by timteachesmath (Link). There are 5 sets of examples of the formula in each ... |
# Names of the Numbers
Names of the numbers are discussed here in this topic. Students can learn from here how to name a number. The number is named on the basis of the place values of the concerned digits. The name is taken according to place values of the digits, starting from highest place value to lowest place val... |
# What are the asymptote(s) and hole(s), if any, of f(x) =x^2/(2x^2-x+1)?
Apr 1, 2017
$\text{horizontal asymptote at } y = \frac{1}{2}$
#### Explanation:
The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be and if t... |
Mathematics » Introducing Integers » Multiply and Divide Integers
# Simplifying Expressions with Integers
## Simplifying Expressions with Integers
Now we’ll simplify expressions that use all four operations–addition, subtraction, multiplication, and division–with integers. Remember to follow the order of operations.... |
Author:
Material Type:
Lesson Plan
Level:
Middle School
6
Provider:
Pearson
Tags:
Language:
English
Media Formats:
Text/HTML
# Inequalities
## Overview
Students identify whether an inequality statement is true or false using a number line to support their reasoning.
# Key Concepts
• The meaning of m
• The meaning ... |
# Section 6 5 The Central Limit Theorem Distribution
• Slides: 15
Section 6. 5 The Central Limit Theorem
Distribution of Sample Means Population (with mean µ and standard deviation σ) Distribution of Sample Means Normal (for any sample size n) Not normal with n > 30 Normal (approximately) Not normal with n ≤ 30 Not ... |
Mathematics » Introducing Graphs » Use the Rectangular Coordinate System
# Finding Solutions to Linear Equations in Two Variables
## Finding Solutions to Linear Equations in Two Variables
To find a solution to a linear equation, we can choose any number we want to substitute into the equation for either $$x$$ or $$y... |
## Tod und Leben (Life and Death)
In this lesson, children will play a card game and try to accumulate as many cards as possible by identifying the higher-ranking cards.
### Lesson for:
Toddlers/Preschoolers
(See Step 5: Adapt lesson for toddlers or preschoolers.)
### Content Area:
Algebra
Numbers and Operations
... |
# Problem Statement
Problem 53 asks about values of the binomial coefficient, a.k.a. n-choose-k. For some values of n and k, the resulting n-choose-k value can exceed 1 million. This question asks how many binomial coefficients n-choose-k exceed 1 million, for n = 1 to 100.
# Solution Explanation
The solution here c... |
Rating
Ø 5.0 / 2 ratings
The authors
Team Digital
CCSS.MATH.CONTENT.1.OA.A.2
## Adding Using a Chart – Introduction
Mr. Squeaks and Imani have found themselves captured as pets! To escape, they need to solve equations using a hundreds chart. This method is a fantastic tool to help solve addition problems, see patter... |
# FIND THE INDICATED ANGLE IN THE PARALLELOGRAM WITH DIAGONALS
Find the measure of the indicated angle in each parallelogram.
Example 1 :
Solution :
In the given figure, ∠JKM = 30° and ∠MOL = 115°
By alternate angles,
∠JKM = ∠KML
30° = ∠KML
In ΔLOM,
We know that,
The sum of the interior angles of a triangle i... |
# 1st Grade Comparison of Numbers
We will learn how to compare two numbers. Compare a one-digit number and a two-digit number and Compare 2 two-digit numbers.
I. A two-digit number is always greater than a one-digit number.
(i) Compare 26 and 8.
26 8 26 has two digits. 8 has one one-digit. 26 is greater than 8.
(... |
# 009C Sample Midterm 3, Problem 3 Detailed Solution
Test if each the following series converges or diverges.
Give reasons and clearly state if you are using any standard test.
(a) ${\displaystyle {\displaystyle \sum _{n=1}^{\infty }}\,{\frac {n!}{(3n+1)!}}}$
(b) ${\displaystyle {\displaystyle \sum _{n=2}^{\infty... |
# The inverse of 3 x 3 matrix with determinants and adjugate
### The inverse of 3 x 3 matrix with determinants and adjugate
In this lesson, you will learn the long way of computing the inverse of a 3 x 3 matrix. This method requires 4 steps. The first step is the matrix of minor. Each entry in the matrix is a 2 x 2 m... |
# How do you solve 1/a=2/14?
Jan 29, 2017
$a = 7$
#### Explanation:
The right side of the equation can be simplified.
$\Rightarrow \frac{2}{14} = {\cancel{2}}^{1} / {\cancel{14}}^{7} = \frac{1}{7}$
Since the fractions are equal.
$\frac{1}{a} = \frac{1}{7} \Rightarrow a = 7$
Jan 29, 2017
See the entire solution... |
# College Algebra (MATH-1150)
The main idea that separates College Algebra from previous algebra courses is an emphasis on functions. While you should have seen that concept before, you may not have concentrated on it very much. Now you will.
An expression like 3x + 2 literally stands for a real number; you simply do... |
# Algebra of Quadratic Functions – Factoring
Document Sample
``` Lesson 5 – Algebra of Quadratic
Functions - Factoring
IB Math SL1 - Santowski
(1) Review of Factoring trinomials
(2) Develop the graphic significance of
factors/roots
(3) Solving Eqn (algebra/graphic connection)
11/13/2011 2
BIG PI... |
# How do you use the remainder theorem and synthetic division to find the remainder when 2x^3-7x^2 div x-5?
Feb 20, 2017
The remainder is $= 75$
#### Explanation:
The remainder theorem states that when a polynomial $f \left(x\right)$ is divided by $x - c$
$f \left(x\right) = \left(x - c\right) q \left(x\right) + r... |
Get A+ with YaClass!
Register now to understand any school subject with ease and get great results on your exams!
### Theory:
Steps to find the irrational numbers between two numbers:
Step 1: Express the provided number in decimal form.
Step 2: Keep in mind that we need to construct irrational numbers between the pr... |
Name: ___________________Date:___________________
Email us to get an instant 20% discount on highly effective K-12 Math & English kwizNET Programs!
### MEAP Preparation - Grade 4 Mathematics1.36 More Fraction Problems
The fractional part of a collection is determined by dividing the collection into subgroups equal... |
# To graph : The circle x 2 + y 2 = 9 by solve for y .
### Precalculus: Mathematics for Calcu...
6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
### Precalculus: Mathematics for Calcu...
6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
#### Solutions
Ch... |
# Equivalent Fraction and their Identification
Contributed by:
Equivalent fractions and how to identify them. Equivalent fractions are two or more fractions that are all equal. A fraction is a part of a whole: the denominator (bottom number) represents how many equal parts the whole is split into; the numerator (top n... |
Q.1. Find the remainder when x3 + 3x2 + 3x + 1 is divided by
(i) x + 1 (ii) x - $\frac{1}{2}$ (iii) x (iv) x + π (v) 5 + 2x
Solution:
The remainder can be obtained by either long division method or by remainder theorem.
(i) Dividing x3 + 3x2 + 3x + 1 by x + 1
p(x) = x3 + 3x2 + 3x + 1
g(x) = x + 1
Put g(x) = 0,
... |
# Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.15
## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.15
10th Maths Exercise 3.15 Solutions Question 1.
Graph the following quadratic equations and state their nature of solutions,
(i) x2 – 9x + 20 = 0
Solution:
Step 1:
Points to be ... |
# Today’s Lesson: What: transformations (rotations)... Why: To perform rotations of figures on the coordinate plane.. What: transformations (rotations)...
## Presentation on theme: "Today’s Lesson: What: transformations (rotations)... Why: To perform rotations of figures on the coordinate plane.. What: transformations... |
I love using roll and cover games with my students because they make it so fun to practice different math skills: addition, subtraction and even number recognition.
Scroll below to grab your free flower-themed game boards! Then, for more math fun, grab our Number Formation Pack in our shop!
## Math Game Differentiati... |
# How do you find the axis of symmetry, and the maximum or minimum value of the function y=x^2+3x-5?
Apr 23, 2018
The axis of symmetry is $x = - \frac{3}{2}$ or $- 1.5$.
The vertex is $\left(- \frac{3}{2} , - \frac{29}{4}\right)$ or $\left(- 1.5 , - 7.25\right)$.
#### Explanation:
Given:
$y = {x}^{2} + 3 x - 5$ i... |
# How Do You Calculate the Median of a Set of Numbers?
Credit: Khoa Vu/Moment/Getty Images
Calculate the median of a set by putting the numbers in order from least to greatest and finding the middle number, when there is an odd number of values in the set. When there is an even number of values, find the median by av... |
# 13.3: Units of Concentration
The Learning Objective of this module is to describe the concentration of a solution in the way that is most appropriate for a particular problem or application.
There are several different ways to quantitatively describe the concentration of a solution. For example, molarity was introd... |
# Prim’s Algorithm for Minimum Spanning Tree (MST)
## Introduction to Prim’s algorithm:
We have discussed Kruskal’s algorithm for Minimum Spanning Tree. Like Kruskal’s algorithm, Prim’s algorithm is also a Greedy algorithm. This algorithm always starts with a single node and moves through several adjacent nodes, in o... |
# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01R) | Year 2014 | June | Q#11
Question
A sketch of part of the curve C with equation
, x>0
is shown in Figure.
Point A lies on C and has an x coordinate equal to 2
a. Show that the equation of the normal to C at A is ... |
It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results.
# Calculus
## The Definite Integral
As discussed in the previous section, the pro... |
# How do you evaluate the integral int 1/(x^2-4)?
Mar 26, 2017
$\frac{1}{4} \ln \left\mid \frac{x - 2}{x + 2} \right\mid + C$
#### Explanation:
This can be done with partial fractions, but this will be done with a trigonometric substitution.
First, we need to add $\mathrm{dx}$ to the integral:
$I = \int \frac{1}{{... |
Saturday, September 23, 2023
# What Is Cpctc In Math
## Corresponding Parts Of Congruent Triangles Are Congruent
CPCTC
In this video, you will learn how to use Corresponding Parts of Congruent Triangles are Congruent to prove line segments or angles are congruent to each other.
When writing proofs, we are not alwa... |
# Operations with integers
## The sum of integers
As the integers have $$+$$ or $$-$$ before, when we operate with them we will write these numbers in brackets in order to not confuse them with $$+$$ and $$-$$ while adding up and subtracting.
For example, if we want to add $$+5$$ and $$-6$$ we will write: $$(+5)+(-6... |
# ACT Math : How to find the equation of a parallel line
## Example Questions
← Previous 1
### Example Question #1 : Coordinate Geometry
There is a line defined by the equation below:
There is a second line that passes through the point and is parallel to the line given above. What is the equation of this second ... |
# 17.1 Second-Order Differential Equations
## 17.1.1 Introduction
The easiest second-order differential equations to solve are those which we can integrate directly, for example
$\frac{d^{2}y}{dx^{2}}=\cos(x)$ (17.1)
When we integrate this once, we get that
$\displaystyle\int\frac{d^{2}y}{dx^{2}}dx=\int\cos(x)dx$... |
Practice With Points
# Practice With Points
Want more basic practice with the coordinate plane and points first? Locating Points in Quadrants and on Axes
As discussed in Locating Points in Quadrants and on Axes, an ordered pair $\,(x,y)\,$ is a pair of numbers, separated by a comma, and enclosed in parentheses. Th... |
$$\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 \|}$$ $$... |
## How do you convert to standard form?
To convert small normal numbers into standard form, you have to find the first non 0 digit after the decimal point. After this digit, you place your new decimal point ignoring everything that is in front of this digit. In the example on the right, the digit would be 5 and the de... |
# [Maths Class Notes] on Sequences and Series Pdf for Exam
Focused on dealing with a list of objects and events (in a certain fashion), sequences and series teach students all about different functions that dominate a sequence chain. Further, sequences and sets also provide a description of different operations that a... |
### Straight-line Graphs
We all know how straight line graphs span across graph papers - or grids. These graphs have two things in common. They are Gradient and Intercept.
The slope or steepness of a graph is called the gradient. It is calculated by dividing a change in 'y' by change in 'x' between two points.
The g... |
# Find Trigonometric Functions Given Their Graphs With Phase Shift (2)
Find the amplitude, period and phase shift of a trigonometric functions given by their graphs. Then find its equation. Questions are presented along with detailed solutions and explanations. Interactive tutorials on Phase Shift and Periodof trigono... |
# How do you find the center of the radius of (x-4)^2 +y^2 =16?
Jun 2, 2016
Center: (4,0)
#### Explanation:
The circle formula is
${\left(x - {x}_{1}\right)}^{2} + {\left(y - {y}_{1}\right)}^{2} = {r}^{2}$
The center of all circles is $\left({x}_{1} , {y}_{1}\right)$, without the negative. The radius is the r. So... |
# Question #5f8be
Sep 15, 2017
$\left(5 x - 4\right) \left(3 x + 1\right)$
#### Explanation:
I remember receiving this problem before . . . Here's how my math teacher explained it:
You can't factor this the way you normally would with quadratic equations, becuase there are no two numbers whose sum is 7 and whose p... |
ORDERING FRACTIONS WITH DIFFERENT DENOMINATORS
Ordering Fractions with Different Denominators :
In this section, you will learn, how to order fractions with different denominators.
Ordering Fractions with Different Denominators - Steps
To order fractions in the order from least to greatest or greatest to least, the... |
Let's Connect
>
# Comparing Fractions Calculator
Comparing fractions can get difficult if done manually, especially with complex pair of fractions. This calculator can help you with the comparison easily. It can tell you which is the bigger and which is the smaller fraction among with given set of fractions.
## How... |
# Converting Complex Numbers To Polar Co-ordinates
A vast array of sets can be listed by using ordinal numbers as a tool. They can also be used to generalize ordinal numbers.
## 1st
The ordinal number is among the most fundamental ideas in mathematics. It is a numerical number that defines the location of an object ... |
Chapters
In algebra, algebraic fractions are the fractions that have algebraic expressions (the expressions which have one or more variables and arithmetic operations) both in the numerator and the denominator.
We can apply the operations of addition, subtraction, multiplication, and division on these algebraic fract... |
# Solve expression
In addition, there are also many books that can help you how to Solve expression. Our website will give you answers to homework.
## Solving expression
In this blog post, we will show you how to Solve expression. Solving for a side of a triangle is actually quite simple. We can take the given side ... |
# Section 2.4 Question 1
## What is a matrix?
A matrix is simply a table of numbers enclosed by a set of square brackets. These numbers may correspond to inventory levels, production quotas, or almost anything. We specify the size of a matrix by giving the number of rows and columns in the matrix.
An m x n matrix (r... |
# Calculate: (6x-2)/((x+3) * (x-2))
## Expression: $\frac{ 6x-2 }{ \left( x+3 \right) \times \left( x-2 \right) }$
For each factor in the denominator, write a new fraction using the factors as new denominators. The numerators are unknown values
$\frac{ ? }{ x+3 }+\frac{ ? }{ x-2 }$
Since the factor in the denominat... |
Smartick is an online platform for children to master math in only 15 minutes a day
Sep29
# Follow 8 Easy Steps to Factor a Number
In this entry, we’re going to explain how to break down or factor a number to its prime numbers step by step.
Before we start anything, feel free to look at these entries where we expla... |
# Trigonometric Functions
Trigonometric functions are functions which represent the relationship between sides and angles in right triangles. There are three main “trig” functions: sine, cosine, and tangent, and a mnemonic often used to remember what they represent is SohCahToa:
• • The SINE of an angle is the ratio ... |
# Quadratic Functions and Their Graphs
## Key Questions
• There are two forms a quadratic function could be written in: standard or vertex form. Here are the following ways you can determine the vertex and direction dependent on the form:
Standard Form ($f \left(x\right) = a {x}^{2} + b x + c$)
1. Direction of the p... |
Ex 9.1
Chapter 9 Class 11 Straight Lines
Serial order wise
### Transcript
Ex10.1, 6 Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle. Let the 3 points of triangle be A (4, 4) , B (3, 5) , C (–1, –1) Lets calculate slope of AB, BC and A... |
P l a n e G e o m e t r y
An Adventure in Language and Logic
based on
# First Principles
Definitions
IT IS NOT POSSIBLE to prove every statement; we saw that in the Introduction. Nevertheless, we should prove as many statements as possible. Which is to say, the statements we do not prove should be as few as possi... |
# Areas of Regular Polygons
Author:
hertelm
Topic:
Area, Polygons
Recall the definition of a regular polygon. Welearned earlier in the semester that regular polygons are both _________________________ and _________________________.
## Construction
Step 1: Construct a Circle (circle with Center through Point) Step 2... |
# How do you graph y> -2 |x-1| + 3?
Aug 3, 2018
$\text{ }$
#### Explanation:
$\text{ }$
We are given an absolute value function:
color(red)(y=f(x)=-2|x-1|+3
The standard form of an absolute value function:
color(blue)(y=a|x-h|+k, where
If color(blue)(a>0, then the graph Opens Up
If color(blue)(a<0, then the gr... |
# Algebraic Identities
The algebraic equations which are true for all values of variables in them are called algebraic identities. They are also used for the factorization of polynomials. This is how they find utility in the computation of algebraic expressions.
## Standard Algebraic Identities List
All the standard... |
# What is the equation of the line that is perpendicular to 2x + 4y = 1 and that passes through the point (6, 8)?
Dec 12, 2016
$y = 2 x - 4$
#### Explanation:
Step 1) Solve for $y$ in order to find the slope of the line in the equation given:
$2 x + 4 y = 1$
$2 x - 2 x + 4 y = 1 - 2 x$
$0 + 4 y = - 2 x + 1$
$4 ... |
# How many three-digit numbers with distinct digits can be formed using the digits 1, 2, 3, 5, 8, and 9? What is the probability that both the first digit and the last digit of the three digit number are even numbers?
Jun 27, 2017
We can make $120$ three digit distinct numbers. The probability, that both the first di... |
Update all PDFs
Extending the Definitions of Exponents, Variation 2
Alignments to Content Standards: F-LE.A N-RN.A.1
A biology student is studying bacterial growth. She was surprised to find that the population of the bacteria doubled every hour.
1. Complete the following table and plot the data.
Hours into study ... |
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
You are viewing an older version of this Concept. Go to the latest version.
Single Variable Division Equations
Solve one - step equations using division.
Estimated4 minsto complete
%
Pr... |
16
Q:
The concentration of petrol in three different mixtures (petrol and kerosene) is 1/2 , 3/5 and 4/5 respectively. If 2 litres, 3 litres and 1 litre are taken from these three different vessels and mixed. what is the ratio of petrol and kerosene in the new mixture?
A) 4:5 B) 3:2 C) 3:5 D) 2:3
Explanation:
Conc... |
# ADDITION AND SUBTRACTION OF DECIMALS
LESSON PLANNING OF ADDITION AND SUBTRACTION OF DECIMALS
Subject Mathematics
Students` Learning Outcomes
Information for Teachers
• If you know how to add and subtract whole numbers, then you can add and subtract decimals. Just be sure to line up the terms so that all the deci... |
# Math 108 Exam 3 Solutions Spring 00
Save this PDF as:
Size: px
Start display at page:
## Transcription
1 Math 108 Exam 3 Solutions Spring An ecologist studying acid rain takes measurements of the ph in 12 randomly selected Adirondack lakes. The results are as follows: Give 90% confidence intervals for a) the aver... |
# What is an example of a proportional relationship on a graph?
## What is an example of a proportional relationship on a graph?
The graph of the proportional relationship equation is a straight line through the origin. Example 1: Given that y varies proportionally with x , with a constant of proportionality k=13 , f... |
A subspace is a vector space that is contained within another vector space. So every subspace is a vector space in its own right, but it is also defined relative to some other (larger) vector space. We will discover shortly that we are already familiar with a wide variety of subspaces from previous sections. Here's the... |
## Calculus with Applications (10th Edition)
$$y = {e^{\frac{{1 - x}}{x}}}$$
\eqalign{ & {x^2}\frac{{dy}}{{dx}} = y;\,\,\,\,\,\,\,\,\,\,\,y\left( 1 \right) = - 1 \cr & {\text{Separating variables leads to}} \cr & \frac{{dy}}{y} = \frac{{dx}}{{{x^2}}} \cr & \frac{{dy}}{y} = {x^{ - 2}}dx \cr & {\text{To solve this equat... |
# RD Sharma Class 9 Solutions Chapter 20 Surface Areas and Volume of A Right Circular Cone MCQs
In this chapter, we provide RD Sharma Solutions for Chapter 20 Surface Areas and Volume of A Right Circular Cone MCQS for English medium students, Which will very helpful for every student in their exams. Students can downl... |
# Math Insight
### The determinant of a matrix
A matrix is an array of many numbers. For a square matrix, i.e., a matrix with the same number of rows and columns, one can capture important information about the matrix in a just single number, called the determinant. The determinant is useful for solving linear equati... |
# Find the area bounded by the curve
Question:
Find the area bounded by the curve $x^{2}=4 y$ and the line $x=4 y-2$
Solution:
The area bounded by the curve, $x^{2}=4 y$, and line, $x=4 y-2$, is represented by the shaded area $\mathrm{OBAO}$.
Let A and B be the points of intersection of the line and parabola.
Coo... |
# 3.4 Composition of functions (Page 6/9)
Page 6 / 9
## Finding the domain of a composite function involving radicals
Find the domain of
Because we cannot take the square root of a negative number, the domain of $\text{\hspace{0.17em}}g\text{\hspace{0.17em}}$ is $\text{\hspace{0.17em}}\left(-\infty ,3\right].\tex... |
# Confused about $(-1) \times (-1) = (+1)$ [duplicate]
Why the product of two negative numbers is a positive number? We all learn about it, and I'm not sure why it is like that. Is it a convention or what?
• So: you can define "Bre multiplication" in another way if you like. No one is stopping you. But then (see the ... |
###### Brian McCall
Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
##### Thank you for watching the video.
To unlock all 5,300 videos, start your free trial.
# Two Column Proofs - Problem 4
Bri... |
In mathematics outside of school we use radians instead of degrees for convenience. I have found that many undergraduate students don’t understand what a radian is.
An angle of 1 radian is created when the length of the arc created by the angle is equal to the length of the radius. Thus, a radian is the angle that occ... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.