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# Geometric series/Ratio test/R/Section
The series ${\displaystyle {}\sum _{k=0}^{\infty }x^{k}}$ is called geometric series for ${\displaystyle {}x\in \mathbb {R} }$, so this is the sum
${\displaystyle 1+x+x^{2}+x^{3}+\ldots .}$
The convergence depends heavily on the modulus of ${\displaystyle {}x}$.
## Theorem
F... |
Home > Technology > Computer Science > Computer Architecture > Binary-Decimal conversion with floating point
# Binary-Decimal conversion with floating point
Chapter I – Numeral systems
Binary-Decimal conversion with floating point
We have learned in the previous post how to convert a number between numeral systems ... |
of 18 /18
Warm-Up - Artists Vito Acconci is a popular American sculptor and artist. One of his furniture creations called the Name Calling Chair uses a variety of geometric shapes, such as squares and triangles. The back of the chair is shown in the diagram. • What do you know about angles FCB and CFE? Are triangles AB... |
# Relations and Functions – Class XI – Exercise 2.2
1. Let A = {1, 2, 3… 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, co-domain and range.
Solution:
The relation R from A to A is given as R = {(x, y): 3x – y = 0, where x, y ∈ A}
i.e., R = {(x, y): 3x = y, ... |
# Find the intervals in which the following functions are increasing or decreasing.
Question:
Find the intervals in which the following functions are increasing or decreasing.
$f(x)=\log (2+x)-\frac{2 x}{2+x}$
Solution:
Given:- Function $f(x)=\log (2+x)-\frac{2 x}{2+x}$
Theorem:- Let $f$ be a differentiable real ... |
# NCERT Notes for Class 10 Maths Chapter 15 Probability
#### Class 10 Maths Chapter 15 Probability Notes
Chapter Name Probability Notes Class CBSE Class 10 Textbook Name Mathematics Class 10 Related Readings Notes for Class 10Notes for Class 10 MathsRevision Notes for Probability
### Probability
Probability is the... |
INSTRUCTORS Carleen Eaton Grant Fraser
Start learning today, and be successful in your academic & professional career. Start Today!
• ## Related Books
### Properties of Logarithms
• Use the properties either to convert the log of a complex expression into a combination of logs of simple expressions, or vice versa.
... |
# Equations Reducible to Quadratic by Substitution
Equations Reducible to Quadratic by Substitution to Learn Math are made easy to solve by substitution to simplify the equations.
## Question 1
Solve $(x+2)^2-3(x+2)-4 = 0$.
\begin{aligned} \displaystyle \require{AMSsymbols} \require{color} \text{Let } A &= x+2 \\ A... |
## Thinking Mathematically (6th Edition)
In order to arrive at the answer of 2 cups of water, we first need to find the amount of water needed for one serving of instant potatoes. To do this, we use the information given in the problem: 2$\frac{2}{3}$ cups of water is needed to make 8 servings of instant potatoes. We ... |
2001 USAMO Problems/Problem 3
Problem
Let $a, b, c \geq 0$ and satisfy
$a^2 + b^2 + c^2 + abc = 4.$
Show that
$0 \le ab + bc + ca - abc \leq 2.$
Solution
Solution 1
First we prove the lower bound.
Note that we cannot have $a, b, c$ all greater than 1. Therefore, suppose $a \le 1$. Then $$ab + bc + ca - abc = a... |
Question 1
Present age of Vinod and Ashok are in ratio of 3:4 respectively. After 5 years, the ratio of their ages becomes 7:9 respectively. What is Ashok’s present age is ?
A 40 years B 28 years C 32 years D 36 years
Arithmetic Aptitude 3 Ratio and Proportion Age
Discuss it
Question 1 Explanation:
Let the pres... |
## Engage NY Eureka Math Grade 6 Module 5 Lesson 2 Answer Key
### Eureka Math Grade 6 Module 5 Lesson 2 Exploratory Challenge Answer Key
Exploratory Challenge:
Question a.
Use the shapes labeled with an X to predict the formula needed to calculate the area of a right triangle. Explain your prediction.
Formula for th... |
# 7.1 Kinetic energy
Page 1 / 7
• Explain work as a transfer of energy and net work as the work done by the net force.
• Explain and apply the work-energy theorem.
## Work transfers energy
What happens to the work done on a system? Energy is transferred into the system, but in what form? Does it remain in the syste... |
Home » Blog » Find the extreme values for the perimeter of an isosceles triangle inscribed in a circle
# Find the extreme values for the perimeter of an isosceles triangle inscribed in a circle
1. Consider a circle of radius with an inscribed isosceles triangle. If the angle at the apex of the isosceles triangle is ,... |
Polynomial and Rational Functions
# Power Functions and Polynomial Functions
### Learning Objectives
In this section, you will:
• Identify power functions.
• Identify end behavior of power functions.
• Identify polynomial functions.
• Identify the degree and leading coefficient of polynomial functions.
Suppose a c... |
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You are viewing an older version of this Concept. Go to the latest version.
Applications Using Rational Equations
Word problems including fractions with variables in the denominator
Est... |
## What are the 9 types of factoring?
Types of Factoring polynomials
• Greatest Common Factor (GCF)
• Grouping Method.
• Sum or difference in two cubes.
• Difference in two squares method.
• General trinomials.
• Trinomial method.
## How do you factor polynomials step by step?
1. Step 1: Identify the GCF of the pol... |
# How do you solve x+3y=6, 4x-5y=7 by graphing?
##### 1 Answer
Jun 14, 2018
$x = 3 , y = 1$
#### Explanation:
We seek a graphical solution of:
$\setminus \setminus x + 3 y = 6 \implies y = \frac{6 - x}{3}$
$4 x - 5 y = 7 \implies y = \frac{4 x - 7}{5}$
Thus we graph each of the functions on the same axis:
graph{... |
# Search by Topic
#### Resources tagged with Limits similar to Fractional Calculus III:
Filter by: Content type:
Stage:
Challenge level:
### There are 19 results
Broad Topics > Pre-Calculus and Calculus > Limits
### Fractional Calculus III
##### Stage: 5
Fractional calculus is a generalisation of ordinary calcul... |
Tag: Fractions
# Get On My Fraction Level!
Many students have trouble with fractions. When I taught at a high school, my 10th and 11th grade students regularly had difficulty performing operations with fractions. As an 8th grade teacher, I’ve tried to help my students develop, refine, and maintain strong fraction ski... |
# What is the dot product of 5i and 8j?
Dec 13, 2016
$0$
#### Explanation:
A property of the scaler (or dot) product is that it is zero if the vectors are perpendicular which $5 \underline{\hat{i}}$ and $8 \underline{\hat{j}}$ clearly are, so without any calculation we know the answer is zero.
We can show this if ... |
# Rounding the Mean – Definition, Applications, and Examples
In this article, we will delve into the reasons for rounding the mean, the different rounding methods available, and the potential implications of rounding on data analysis and decision-making processes
## Definition
Rounding the mean refers to the process... |
# Lines in Geometry(Definition, Types & Examples)
This post is also available in: हिन्दी (Hindi)
In geometry, points and lines are the two fundamental concepts that you need to learn before learning about different shapes and sizes. A line is a one-dimensional figure, which has length but no width. It is made of a se... |
chain rule with square root December 24, 2020 – Posted in: Uncategorized
The Chain Rule. Watch the video for a couple of chain rule examples, or read on below: The formal definition of the chain rule: = 2(3x + 1) (3). Let's introduce a new derivative if f(x) = sin (x) then f '(x) = cos(x) It’s more traditional to rewr... |
# How do you solve the following linear system 3x-2y=8, 2x-3y=-6 ?
Jun 9, 2016
(x,y)=color(green)(""(7.2,6.8))
#### Explanation:
Given
[1]$\textcolor{w h i t e}{\text{XXX}} 3 x - 2 y = 8$
[2]$\textcolor{w h i t e}{\text{XXX}} 2 x - 3 y = - 6$
Multiplying [1] by $3$ and [2] by $2$
[3]$=$[1]$\times 3 \textcolor{w h ... |
Rules of inequalities I
Solving Inequalities Rules
A mathematical expression which involves symbols >, <, ≥ and ≤ is an inequality. To solve such we need go find a range of values that an unknown variable can take and then satisfy the in-equality. The rules for solving such are that, if the same number is added to bo... |
Question
# A closed iron tank 12 m long, 9 m wide and 4 m deep is to be made. Determine the cost of iron sheet used at the rate Rs. 5 per meter sheet, sheet being 2 m wide.
Hint – In this question first find out, total surface area of the closed iron tank which is given as $S.A = 2\left( {lb + bh + hl} \right)$ whe... |
# Barbara Palazzo 9/24/09 ED 637 Title: Multiplication Commutative operations in math Two well-known examples of commutative The addition
of real numbers, is commutative; For example 3 + 2 = 2+ 3, since both expressions equal 6. y+z = z+y The multiplication of real numbers, is commutative For example, 3 × 5 = 5 × 3, s... |
# Precalculus : Products and Quotients of Complex Numbers in Polar Form
## Example Questions
### Example Question #1 : Find The Product Of Complex Numbers
Find the value of ,where the complex number is given by .
Explanation:
We note that by FOILing.
We also know that:
We have by using the above rule: n=2 , m=... |
1. ## inequality confucion
Solve this inequality .
$\displaystyle \frac{6}{|x|+1}<|x|$
squarring both sides , i got
$\displaystyle \frac{36}{x^2+2|x|+1}<x^2$ , rearranging them
$\displaystyle \frac{36}{x^2+2|x|+1}-\frac{x^2(x^2+2|x|+1)}{x^2+2|x|+1}<0$
$\displaystyle \frac{36-x^4-2x^2|x|-x^2}{x^2+2|x|+1}<0$ , till... |
×
# CHEFST - Editorial
Author: Tapas Jain
Tester: Sergey Kulik
Editorialist: Kevin Atienza
# PROBLEM:
Consider a single-player game on two piles of stones. One has $n_1$ stones and the other has $n_2$ stones. Before the start of the game, we choose an integer $m$.
In a move, we choose a number between $1$ and $m$,... |
As I said in the previous post, there is a duality:
Points on a Curve (Geometry) $\Leftrightarrow$ Solutions of an Equation (Algebra)
This means we can answer geometric questions using algebra and answer algebraic questions using geometry.
### Problem
Consider the following two questions:
1. Find the tangents to a... |
## SOLVING QUADRATIC EQUATIONS
Note:
• A quadratic equation is a polynomial equation of degree 2.
• The ''U'' shaped graph of a quadratic is called a parabola.
• A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions.
• There are several meth... |
# Exponents and Fractions Online Quiz
Following quiz provides Multiple Choice Questions (MCQs) related to Exponents and Fractions. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next... |
# Conic Sections/Circle
The circle is the simplest and best known conic section. As a conic section, the circle is the intersection of a plane perpendicular to the cone's axis.
The geometric definition of a circle is the locus of all points a constant distance ${\displaystyle r}$ from a point ${\displaystyle (h,k)}$ ... |
P. 1
003 - Fractions and Their Forms (Smt I)
# 003 - Fractions and Their Forms (Smt I)
|Views: 406|Likes:
To write a fraction in a percent form
To write a fraction in a decimal form
To compare fractions
and its inverse
number into fractions
To change a mixed
To simplify fractions
To write a fraction in a percent form... |
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# The Peculiar Puzzle of Geometrical Transformation-Insights into Transformation Geometry
Updated: Apr 11, 2021
Aloha! Excited about Geometric Math? Transformation? Dilation? Well, I am! Transformation is used everywhere! From operating a Mars rover to running a mile, transforma... |
# What is the distance between (-4,-11) and (13,-41)?
Mar 26, 2018
Distance$= 34.482 \ldots$
#### Explanation:
Apply Pythagorean theorem, where $d$ is the distance between the two points.
$d = \sqrt{{\left(13 - - 4\right)}^{2} + {\left(- 41 - - 11\right)}^{2}}$
$\textcolor{w h i t e}{d} = \sqrt{{\left(17\right)}^{... |
# How do you solve and check your solutions to 3/2k=18?
Mar 11, 2018
$k = 12$
#### Explanation:
$\text{multiply both sides by 2 to eliminate the fraction}$
$\cancel{2} \times \frac{3}{\cancel{2}} k = 2 \times 18$
$\Rightarrow 3 k = 36$
$\text{divide both sides by 3}$
$\frac{\cancel{3} k}{\cancel{3}} = \frac{36}... |
How do you graph y=-2x+7?
Jun 2, 2018
See a solution process below:
Explanation:
First, solve for two points which solve the equation and plot these points:
First Point: For $x = 2$
$y = \left(- 2 \cdot 2\right) + 7$
$y = - 4 + 7$
$y = 3$ or $\left(2 , 3\right)$
Second Point: For $x = 4$
$y = \left(- 2 \cdot ... |
### Mean, Median and Mode
#### Mean
##### Definition
The mean of a set of numbers in a data set is obtained by adding up all the numbers then dividing by the size of the data set. When people use the word 'average' in everyday conversation, they are usually referring to the mean.
#### Worked Example 1
###### Worke... |
# What is the distance between (3, –1, 1) and (2, –3, 1) ?
Apr 3, 2018
Distance b/w the pts.=$\sqrt{5}$ units.
#### Explanation:
let the pts. be A(3,-1,1) & B(2,-3,1)
so, By distance formula
$A B = \sqrt{\left({\left({x}_{2} - {x}_{1}\right)}^{2}\right) + {\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({z}_{2} - {z}... |
# How to get percentage of 2 numbers: Real-Life Applications
0
903
We use percentages daily, often without even realizing it. Whether calculating tips at a restaurant or working out a sale price at the store, percentages are a part of our lives. So how to get a percentage of 2 numbers? This blog post will look at som... |
Q&A
# what does inverse operation mean
Inverse operationsare pairs of mathematical manipulations in which one operation undoes the action of the other—for example, addition and subtraction, multiplication and division.
## What is an inverse operation example?
The set of two opposite operations is called inverse ope... |
# Teaching for mastery in primary maths
Year 1
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Autumn
Autumn
Spring
Summer
All Topics
## Numbers up to 20
• Year group: Year 1
• Term: Autumn
• Topic: Number and place value
• Duration: 2 weeks
• Keystage: KS1
• Age Range: 5 to 6 yrs
• Unit can be taught out of sequence: N
•... |
# What is the probability of getting at least 35 cents?
$$3$$ nickels, $$1$$ dime and $$2$$ quarters are in a purse. In picking three coins at one time (without replacement), what is the probability of getting a total of at least $$35$$ cents?
I know that the total ways of selecting 3 coins out of 6 is $${6\choose 3}... |
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# 4.6: Triangle Congruence using AAS
Difficulty Level: At Grade Created by: CK-12
## Learning Objectives
• Understand and apply the AAS Congruence Theorem.
## AAS Congruence
Another ... |
Concept: Factorial
CONTENTS
INTRODUCTION
Factorial, in mathematics, is the product of all positive integers less than or equal to a given positive integer and is denoted by that integer and an exclamation point.
Thus, factorial four is written 4!, which means 1 × 2 × 3 × 4
Hence, n! = 1 × 2 × 3 × ... × (n-1) × n
... |
# KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.1
KSEEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.1 are part of KSEEB Solutions for Class 9 Maths. Here we have given Karnataka Board Class 9 Maths Chapter 1 Number Systems Exercise 1.1.
## Karnataka Board Class 9 Maths Chapter 1 Number... |
# What is the equation of the line passing through (9,2) and (9,14)?
May 8, 2016
$x = 9$
#### Explanation:
As it is a line that passes through $\left(9 , 2\right)$ and $\left(9.14\right)$, when either abscissa or ordinate is common, we can easily find the equation of the line - as it will of the form $x = a$, if ab... |
1. ## HELPfocus of parabola!!
could someone please walk through the steps of solving this problem....?
find the focus of the conic section y=-3x^2-12x-5
2. Hello, emetty90!
Find the focus of the parabola: .$\displaystyle y\:=\:-3x^2-12x-5$
We must get the equation into the form: .$\displaystyle (x-h)^2 \:=\:4p(y-k... |
<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.
Theoretical and Experimental Spinners
Using APPS on the TI 84 calculator for spinner simulations
0%
Progress
... |
Advice 1: How to learn to divide a two-digit number
One of the most important topics in math elementary school division of two-digit numbers. Usually this action is done by selection or in a column, if the job is written. In any case a good tool is the multiplication table.
Instruction
1
Are two-digit numbers from 10 ... |
# How do you find the median of a data set?
## How do you find the median of a data set?
Finding the median
1. Arrange the data points from smallest to largest.
2. If the number of data points is odd, the median is the middle data point in the list.
3. If the number of data points is even, the median is the average ... |
# Log Formulas
Logarithm is a convenient way to express large numbers. The logarithm of a product is the sum of the logarithms of the numbers being multiplied. Log Formulas are available below for the convenience of the students. Here you can find Logarithms Formulas including Basic & Special Case Log with Examples Eq... |
## Engage NY Eureka Math 6th Grade Module 1 Lesson 9 Answer Key
### Eureka Math Grade 6 Module 1 Lesson 9 Example Answer Key
Example 1.
To make paper mache, the art teacher mixes water and flour. For every two cups of water, she needs to mix in three cups of flour to make the paste.
Find equivalent ratios for the rat... |
There are some special situations that have special methods of factoring. Once such situation is the factoring the difference of two perfect squares. You need to know this formula!
Factoring the Difference of Two Squares
We already know that by multiplying: (a + b)(a - b) = a2 - b2.
If we use the commutative pro... |
# MSBSHSE Solutions For Class 8 Maths Part 1 Chapter 3- Indices and Cube Root
MSBSHSE Solutions For Class 8 Maths Part 1 Chapter 3 Indices and Cube Root is one of the best reference material students can rely on. The MSBSHSE Solution for Class 8 module contains all the important topics that can help students score wel... |
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If you want to set points via some algebraic equation, then you are probably doing the equation of line. So, the equation of a line is setting the points with an algebraic equation, which forms a line in a coordinate system. There are numerous points that are placed together known as the variables which ar... |
# November 1998 Winner
Question:
1. Find the sum of the angles formed at the tips of both stars
2. Find a formula for the sum of the sum of the angle measurements at the tips of an n-pointed star.
1. The sum of the angles formed at the tips of the five pointed star is 180; the sum of the angles formed at the tips of ... |
# Math Snap
## A group of 41 people are going to a concert together in 7 vehicles. Some of the vehicles can hold 7 people each, the rest can hold 5 people each. Assuming all the vehicles are filled to capacity, exactly how many of these vehicles can hold 7 people?
#### STEP 1
Assumptions1. The total number of people... |
# Math Tutorial 1.5 - Multiples, Factors, Prime Numbers and Prime Factorization including LCM and GCF
There are 7 lessons in this math tutorial covering Multiples, Factors, Prime Numbers and Prime Factorization including LCM and GCF. The tutorial starts with an introduction to Multiples, Factors, Prime Numbers and Pri... |
#### You may also like
What is the relationship between the arithmetic, geometric and harmonic means of two numbers, the sides of a right angled triangle and the Golden Ratio?
### Classical Means
Use the diagram to investigate the classical Pythagorean means.
# Pythagorean Golden Means
##### Stage: 5 Challenge Lev... |
# Normal Form Games¶
## Motivating example: Coordination Game¶
Game theory is the study of interactive decision making. One example of this is the following situation:
Two friends must decide what movie to watch at the cinema. Alice would like to watch a sport movie and Bob would like to watch a comedy. Importantly,... |
# Circumcentre, Incentre, Orthocentre and Centroids
Contributed by:
This ppt includes the following topics:-
Medians
Centroid
Angle Bisector
Incentre
Altitude
Orthocentre
Perpendicular Bisector and many more.
1. Centers of Triangles or
Points of Concurrency
Prepared for Ms. Pullo’s
Geometry Classes
2.
3. Example 1
In ... |
Draw ∆ABC, right-angled at B, such that AB = 3 cm and BC = 4 cm.
Question:
Draw $\triangle A B C$, right-angled at $B$, such that $A B=3 \mathrm{~cm}$ and $B C=4 \mathrm{~cm}$. Now, construct a triangle similar to $\triangle A B C$, each of whose sides is $\frac{7}{5}$ times the corresponding sides of
ABC.
Solution... |
How To Factor Trinomials How To Factor Trinomials Today in this session we are going to discuss about Factoring Trinomials. Trinomials are the very interesting and important part of the elementary algebra. Trinomial is a polynomial which has three terms. The three terms can be any variable. For instance 2x + 4y +9z and... |
# What Is 33/60 as a Decimal + Solution With Free Steps
The fraction 33/60 as a decimal is equal to 0.55.
Proper fractions, improper fractions, and mixed fractions are the three types of Fractions. Proper fractions are those in which the numerator is less than the denominator, whereas Improper fractions are those in ... |
# Projectile word problems
A few carefully chosen projectile word problems to help you see how to solve these problems.
Problem #1:
A ball is dropped from a helicopter traveling with a speed of 75 m/s. After 2 seconds, the ball lands in the pool. Assuming no air resistance, what was the horizontal distance between t... |
### Home > CCAA > Chapter 1 CC2: Unit 1 > Lesson CC2: 1.1.2 > Problem1-15
1-15.
Maria was playing a game with her brother. She said, “I’m thinking of a number. When you multiply my number by six and add seven, you get twenty-five. What is my number?”
1. Find Maria’s number.
How big do you expect her number to be? C... |
# NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.5
These NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.5 Questions and Answers are prepared by our highly skilled subject experts.
## NCERT Solutions for Class 10 Maths Chapter 6 Triangles Exercise 6.5
Question 1.
Sides of triangles are given... |
Thinking Mathematically (6th Edition)
Published by Pearson
Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2 - Page 362: 17
{-17}
Work Step by Step
4x -14 = -82 Step 1: Add 14 on both the sides 4x -14 +14 = -82 +14 Step 2: Simplify 4x = -68 St... |
Home MATHEMATICS TOPIC 1: EXPONENTS AND RADICALS ~ MATHEMATICS FORM TWO
2388
0
# TOPIC 1: EXPONENTS AND RADICALS ~ MATHEMATICS FORM TWO
Exponents
Exponents tell how many times to use a number itself in multiplication. There are different laws that guides in calculations involving exponents. In this chapter we are g... |
### Free Educational Resources
+
2 Tutorials that teach Basic Quadratic Factoring
##### Rating:
(0)
Author: Sophia Tutorial
##### Description:
In this lesson, students will learn how to factor quadratic expressions.
(more)
Sophia’s self-paced online courses are a great way to save time and money as you earn credit... |
Guided Lessons
# Parts of a Set: Fractions
Get your students excited to learn about fractions with this hands on lesson. Working in groups will help students learn from each other and share ideas.
No standards associated with this content.
Which set of standards are you looking for?
Students will be able to divide... |
Solve Quadratic equations: 4x ^ 2 – 5x – 12 = 0
4x ^ 2 – 5x – 12 = 0 is an example of a quadratic equation. This equation is a mathematical equation and it requires a formula to solve it. This is one of the mathematical equation-based questions where variables and numbers are given. In this equation, we have to simply... |
Contents of this Precalculus episode:
Absolute value of complex numbers, Sets on the complex plane, Equation of line, Equation of circle.
Text of slideshow
The absolute value of a complex number is its distance from zero.
We can compute this distance using the Pythagorean Theorem.
Let's see one more.
Instead of t... |
# Learn How to Find Prime Factors and Factor Pairs of 36 in Detail
Factors are whole numbers that are multiplied together to generate another number. If a × b = c, then a and b are c’s factors.
• A factor is an integer that divides a given whole number exactly with no remainder.
• Every whole number greater than one ... |
@professionalbronco Ohh, I see! Very clever to think about units digits, since with bigger numbers, it can save you a lot of time. Still, I think that the best way to do the problem is to notice that all of $$\frac{18}{396},\frac{15}{396},\frac{9}{396}$$ aren't simplified.
BUT, let's talk about the units digit method ... |
2006 AMC 12A Problems/Problem 24
Problem
The expression
$$(x+y+z)^{2006}+(x-y-z)^{2006}$$
is simplified by expanding it and combining like terms. How many terms are in the simplified expression?
$\mathrm{(A) \ } 6018\qquad \mathrm{(B) \ } 671,676\qquad \mathrm{(C) \ } 1,007,514\qquad \mathrm{(D) \ } 1,008,016\qqua... |
# Fractions: Computing the Total Purchase Cost
(*)(*)(*)(*)(*) ( 4.3, 379 students)
• Price per ClassroomFREE
• Grade Levels 4, 5, 6, 7
• Topics Numbers & Operations, Fractions
• Duration 15 Minutes
• Auto Scored? Yes
• Teacher Evaluation Needed? No
### Activity Description
In this activity, students will use their ... |
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LINEAR EQUATIONS IN ONE VARIABLE
21
Linear Equations in
One Variable
2.1
Introduction
CHAPTER
2
In the earlier classes, you have come across several algebraic expressions and equations.
Some examples of expressions we have so far worked with are:
5x, 2x – 3, 3x + y, 2xy + 5, xyz + x... |
# How to Find the Perimeter of a Shape
Perimeter is a measure of the area or distance around a two-dimensional shape. On a rectangle, for instance, the perimeter is the total length of the rectangle's outline, including the two widthwise borders and the two lengthwise borders. To determine the perimeter of a shape, th... |
# Understanding Variables. Algebra/Standard GLE 0506.3.2 Develop and apply the concept of variable. √ 0506.3.1 Evaluate an expression by substituting non-negative.
## Presentation on theme: "Understanding Variables. Algebra/Standard GLE 0506.3.2 Develop and apply the concept of variable. √ 0506.3.1 Evaluate an express... |
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# Circumcenter of a Triangle
• Last Updated : 26 May, 2022
The point of intersection, or the meeting point of the perpendicular bisectors of a triangle, is the circumcenter of a triangle and is usually represented by the letter “O”. In simple words, the circumcenter of a triangle is the point of ... |
# NCERT Solutions class 12 Maths Exercise 7.9 (Ex 7.9) Chapter 7 Integrals
## NCERT Solutions for Class 12 Maths Exercise 7.9 hapter 7 Integrals – FREE PDF Download
NCERT Solutions for integrals Class 12 exercises 7.9 are accessible in PDF format which is available at CoolGyan’s online learning portal. The solutions ... |
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Logarithmic Functions
# Logarithmic Functions
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## Logarithmic Functions
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##### Presentation Transcript
1. Logarithmic Functions
2. The logarith... |
# Understanding Show Me Cash Chances
You may already know that the chances of winning the Show Me Cash jackpot are 1 in 575,757. But many people wonder how those chances of winning are determined.
Show Me Cash is played by selecting five numbers out of 39 possible choices (the numbers from 1 to 39). During each drawi... |
Solution of Digit Problem2
In this page solution of digit problem2 we are going to see solution for question 3 and question 4 with detailed steps.
Question 3:
The unit's digit of a two digit number is twice its ten's digit. If 18 is added to the number, the digits interchange their places. Find the number.
Solution... |
# How to Simplify Fractions With Decimals
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Fractions and decimals are parts of whole numbers written in two different forms. A fraction has a numerator over a denominator, which represents the number of parts you have of a whole number over the number of parts by whic... |
How do you solve lnx + ln(x+1) = ln12?
Oct 23, 2015
$x = 3$
Explanation:
In general
$\textcolor{w h i t e}{\text{XXX}} \log \left(A\right) + \log \left(B\right) = \log \left(A B\right)$
(this is one of the basic logarithmic rules)
Specifically
$\textcolor{w h i t e}{\text{XXX}} \ln \left(x\right) + \ln \left(x + ... |
# Dividing Rational Expressions – Techniques & Examples
Rational expressions in mathematics can be defined as fractions in which either or both the numerator and the denominator are polynomials. Just like dividing fractions, rational expressions are divided by applying the same rules and procedures.
To divide two fr... |
# Question Video: Finding the Algebraic Form of a Vector That Makes Equal Angles with the Axes Given Its Norm Mathematics • 12th Grade
Find the algebraic form of a vector π if its norm is 31, given that it makes equal angles with the positive directions of the Cartesian axes.
02:52
### Video Transcript
Find the ... |
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# 3 Forms Of A Quadratic Function
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### 3 Forms Of A Quadratic Function
1. 1. 3 Forms of a Quadratic Function!<br />
2. 2. Key Ideas<br /><u... |
# Left hand limit
The value of a function as its input approaches some value from left hand side is called the left-hand limit, and also called as the left sided limit.
## Introduction
Assume, $x$ is a variable, a function is defined in terms of $x$ and the function is expressed as $f(x)$ simply. Let $a$ represents ... |
# How do you find the derivative of (x^4 - 1)^10 (2x^4 + 3)^7?
Dec 30, 2015
$56 {x}^{3} {\left({x}^{4} - 1\right)}^{10} {\left(2 {x}^{4} + 3\right)}^{6} + 40 {x}^{3} {\left(2 {x}^{4} + 3\right)}^{7} {\left({x}^{4} - 1\right)}^{9}$
#### Explanation:
Use the product rule :
$\frac{d}{\mathrm{dx}} \left(f \left(x\right... |
# High School Math : Quadratic Functions
## Example Questions
### Example Question #23 : Quadratic Functions
Based on the figure below, which line depicts a quadratic function?
None of them
Blue line
Red line
Purple line
Green line
Red line
Explanation:
A parabola is one example of a quadratic function, rega... |
# Finding Distances on Maps
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## Objective
SWBAT solve map scale problems using a double number line
#### Big Idea
Remember planning trips before Mapquest or Google Maps? Students find distances using rulers and map scales.
## Introduction
10 minutes
I will start by askin... |
Binomials Cubed – Examples and Practice Problems
Binomials cubed exercises can be solved using two methods. The first method consists in multiplying the binomial three times and fully expanding the expression. The second method is to use a standard formula that can simplify the resolution process.
Here, we will look ... |
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# GMAT Tip: Let It Cancel Out
When faced with Geometry problems with variables, many test takers will approach the question with fear, believing they are forgetting some obscure geomet... |
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