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How do you simplify 2 ^ 2 + (13 - 8/4) * 2- (6b - 4) ^ 2?
Jun 6, 2017
$- {\left(6 b - 4\right)}^{2} + 26$ or
$2 \left(- 18 {b}^{2} + 24 b + 5\right)$
Explanation:
Whether you use BODMAS, BIDMAS OR PEDMAS, brackets and parentheses always come first in an expression, followed by exponents and roots, after which comes... |
# What are the critical points of f(x) = sqrt(e^(sqrtx)-sqrtx)?
Feb 25, 2017
$x = 0$
#### Explanation:
$f \left(x\right) = {\left({e}^{{x}^{\frac{1}{2}}} - {x}^{\frac{1}{2}}\right)}^{\frac{1}{2}}$
Through the chain rule:
$f ' \left(x\right) = \frac{1}{2} {\left({e}^{{x}^{\frac{1}{2}}} - {x}^{\frac{1}{2}}\right)}^... |
Home / The science / Mathematics / How fast to count in the mind
# How fast to count in the mind
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Many schoolchildren are appalled at the mere mention of the solution of mathematical examples.
Sometimes the calculations seem so complicated that you can not do without a calculator.
But mathematics ... |
Home | | Maths 8th Std | Rational numbers in Standard form
# Rational numbers in Standard form
Observe the following rational numbers: 4/5, -3/7, 1/6, -4/13, -50/51.
Rational numbers in Standard form
Observe the following rational numbers: . Here, we see that
i) the denominators of these rational numbers are all p... |
# The supergiant star Betelgeuse has a measured angular diameter of 0.044 arcsecond. Its distance has been measured to be 427 light-years. What is the actual diameter of Betelgeuse?
Dec 13, 2015
$861 , 000 , 000 \text{ km}$
#### Explanation:
This is a pretty straight forward trigonometry problem. We can set up a di... |
# How do you solve 3x - 2/7 = (3x)/4 + 4?
Dec 20, 2015
$x = \frac{40}{21}$
#### Explanation:
$3 x - \frac{2}{7} = \frac{3 x}{4} + 4$
Make each term have a denominator of $7$ on the left side and $4$ on the right side.
$\frac{7 \left(3 x\right)}{7} - \frac{2}{7} = \frac{3 x}{4} + \frac{4 \left(4\right)}{4}$
$\fra... |
# 9.2 Mole-Mass and Mass-Mass Calculations
## Learning Objectives
By the end of this section, you will be able to:
• From a given number of moles of a substance, calculate the mass of another substance involved using the balanced chemical equation
• From a given mass of a substance, calculate the moles of another su... |
# Operations with Rational Exponents
## Simplify expressions with negative and fractional exponents.
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The period (in seconds) of a pendulum with a length of L (in meters) i... |
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# 11.16: Coordinate Locations on a Map
Difficulty Level: At Grade Created by: CK-12
Estima... |
# Storybook Guide Based on Robie H. Harris’s “Crash! Boom! A Math Tale”
Topic:
## Activity Summary
Use this storybook guide with the book “Crash! Boom! A Math Tale.”
Many public libraries have this book.
Elephant is playing with blocks and decides to build a tower as tall as itself. Elephant makes a stack of one, t... |
# The maxima for the function is
## Introduction
In mathematics, maxima and minima (the plural of maximum and minimum) are points of a function at which the function takes its largest value (maximum) or smallest value (minimum), respectively. In the case of a local maximum or minimum, this value is also the largest v... |
# Decoding Mathematical Symbols: Understanding the Meaning Behind the Signs
**Short answer in math what does this symbol mean:**
In mathematics, symbols are used to represent numerical quantities, mathematical operations or relations. The meaning of a specific symbol depends on the context it is used. Common mathemat... |
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# Probability Problems
Probability is an important branch of mathematics which basically deals with the phenomena of chances or randomness of events. Probability of an event measures how likely it is expected to happen. An event is said to be "most likely" if it has higher probability and "least likely" if it has... |
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1 DERIVATIVES: RULES Part 1: Derivatives of Polynomial Functions We can use the definition of the derivative in order to generalize solutions and develop ... Read More
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# Conditional Probability
## P(B|A) = P(A and B)/ P(A)
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# RS Aggarwal Solutions Class 10 Chapter 18 Areas of Circle, Sector and Segment
In this chapter, we provide RS Aggarwal Solutions for Class 10 Chapter 18 Areas of Circle, Sector and Segment Maths for English medium students, Which will very helpful for every student in their exams. Students can download the latest RS ... |
How Do You Reduce Fractions?
# How Do You Reduce Fractions?
To reduce or simplify fractions, look for common factors in the numerator (the term on top) and the denominator (the term on the bottom). Divide both terms by the greatest common factor to reduce the fraction to its lowest terms.
1. Identify the prime facto... |
# Logarithm Formula
Logarithm are the inverse phenomena of exponential. Log function “undo” the exponential function. Consider a number x in the exponent equals to a fixed number b, the logarithmic value of b will be equal to the number x. Such as:
$\large e^{x} = b$
Taking log on both the sides, we have
$\large lo... |
# How many 13 card hands having exactly 11 diamonds can be dealt?
Here’s information about what you’re looking for in How many 13 card hands having exactly 11 diamonds can be dealt?. While every brand has a “Help Center” (or “Support Center”), when we look for relevant information or links, there are often the answers... |
# Learn how to subtract ordinary fractions: theory, steps and a practical example. Fractions with different (like) or unlike denominators
## How to: Subtracting ordinary (simple, common) math fractions. Steps.
There are two cases regarding the denominators when we subtract ordinary fractions:
• A. the fractions have... |
# Ex.4.3 Q1 Quadratic Equations Solutions - NCERT Maths Class 10
Go back to 'Ex.4.3'
## Question
Find the roots of the following quadratic equations, if they exist, by the method of completing the square.
(i) $$2x^2-7x+3=0$$
(ii) $$2x^2+x-4=0$$
(iii) $$4x^2+ 4\sqrt {\left( 3 \right)} x +3=0$$
(iv) $$2x^{2}+x+4=... |
# Maharashtra Board 10th Class Maths Part 1 Practice Set 1.4 Solutions Chapter 1 Linear Equations in Two Variables
## Maharashtra Board 10th Class Maths Part 1 Practice Set 1.4 Solutions
Question 1.
Solve the following simultaneous equations.
Solution:
i. The given simultaneous equations are
∴ Equations (i) and (ii... |
# Free math homework help
Here, we will be discussing about Free math homework help. We will also look at some example problems and how to approach them.
## The Best Free math homework help
There are a lot of Free math homework help that are available online. this analysis method is called time domain analysis metho... |
Learn the basics of exactly how to calculate percentages of quantities in this easy lesson! To find a percentage of any type of number, usage this generic reminder of TRANSLATION: readjust the percentage into a decimal, and also the word "of" into multiplication. See countless examples below.
You are watching: 80 of w... |
# 1950 AHSME Problems/Problem 24
## Problem
The equation $x + \sqrt{x-2} = 4$ has:
$\textbf{(A)}\ 2\text{ real roots }\qquad\textbf{(B)}\ 1\text{ real and}\ 1\text{ imaginary root}\qquad\textbf{(C)}\ 2\text{ imaginary roots}\qquad\textbf{(D)}\ \text{ no roots}\qquad\textbf{(E)}\ 1\text{ real root}$
## Solutions
##... |
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# Euler-Lagrange Equation and How to Use it in 5 Easy Steps
Level 3 (with higher mathematics)
Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.
Updated by Alexander Fufaev on
## Video - Euler-Lagrange Equation
Let us consider a p... |
# Party Preparations: How Many Ways Can Susan Assign Tasks to Her Helpful Friends?
When it comes to party preparations, assigning tasks to friends can be a tricky business. It’s not just about who can do what, but also about how many different ways tasks can be assigned. This is a question that Susan, who is planning ... |
# GRE Subject Test: Math : Factorials
## Example Questions
← Previous 1
### Example Question #1 : Factorials
Simplify the following expression:
Explanation:
Recall that ! means facotrial in math. This means we multiply the number by all positive integers less than itself. In other words, this...
Becomes
This is... |
# Eureka Math Geometry Module 1 Lesson 2 Answer Key
## Engage NY Eureka Math Geometry Module 1 Lesson 2 Answer Key
### Eureka Math Geometry Module 1 Lesson 2 Exercise Answer Key
Opening Exercise
You need a compass, a straightedge, and another student’s Problem Set.
Directions:
Follow the directions from another st... |
Home » Math Theory » Operations of Numbers » Addition Of Numbers Within 100
# Addition Of Numbers Within 100
## Introduction
Addition is one of the most important arithmetic operations used in mathematics. It is the method of calculating the total of two or more numbers to know the sum of the numbers. We use additio... |
# 9.3 Double-angle, half-angle, and reduction formulas (Page 4/8)
Page 4 / 8
Given that $\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\alpha =-\frac{4}{5}\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\alpha \text{\hspace{0.17em}}$ lies in quadrant IV, find the exact value of $\text{\hspace{0.17em}}\... |
# RD Sharma Chapter 1 Class 10 Maths Exercise 1.4 Solutions
RD Sharma Chapter 1 Class 10 Maths Exercise 1.1 Solutions -Real Number is written by expert mathematics teachers. The solutions in the chapter are written according to RD Sharma’s latest Class 10 Mathematics Solutions course. This chapter will introduce you t... |
# Random variables: How would you explain it to a beginner?
Different types of random variables: (discrete) Binomial, hypergeometric, geometric, Poisson (continuous) Uniform, normal, exponential
Random variables are very useful tools when solving simple and complex problems related to probability. They're used in div... |
## What is the formula to solve for circumference?
C = 2πr
The circumference is the distance around a circle. In other words, it’s the perimeter of the circle. And we find the circumference by using the formula C = 2πr.
## How do you find the radius with the circumference?
To calculate the circumference, you need th... |
# 5.4: The Exponential Distribution
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$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$
( \newcommand{\kernel}{\mathrm{null}\,}\)... |
How to Find the Mode of Grouped Data (With Examples)
Often we may want to calculate the mode of data that is grouped in some way.
Recall that the mode represents the value that occurs most frequently.
For example, suppose we have the following grouped data:
While it’s not possible to calculate the exact mode since ... |
# Vectors
## Describing translations using vectors
Vectors are used to describe movement. We often use them to describe the movement of shapes on or off of graphs.
We also write vectors like this
which refers to vector AB, this can be a line or two points, point A and point B,. It can also be referred to as a or as... |
# Question 88ca9
Oct 20, 2017
$c = 3$
#### Explanation:
$0.2 \left(10 - 5 c\right) = 5 c - 16$
In order to solve this, we need to isolate $c$, which means get it by itself. So, let's start by getting rid of those parentheses and distributing that $0.2$.
$0.2 \left(10 - 5 c\right) = 5 c - 16$
$2 - 1 \cdot c = 5 c... |
# Cpm mathematics homework help
In addition, Cpm mathematics homework help can also help you to check your homework. Our website can help me with math work.
## The Best Cpm mathematics homework help
Best of all, Cpm mathematics homework help is free to use, so there's no sense not to give it a try! Solving a Rubik's... |
# Amarge the following in descending order.(i) $\frac{2}{9}, \frac{2}{3} \cdot \frac{8}{21}$(ii) $\frac{1}{5}, \frac{3}{7}+\frac{7}{10}$In a magic square"
Given:
$(i)\ \frac{2}{9}, \frac{2}{3} \times \frac{8}{21}$
$(ii)\ \frac{1}{5}, \frac{3}{7},\ \frac{7}{10}$
Solution::
$(i)\ \frac{2}{9}, \frac{2}{3} \times \fra... |
# Factors of 25
The number 25 is a composite number, meaning it has factors other than 1 and itself. The factors of 25 are the numbers that divide 25 evenly, leaving no remainder.
The factors of 25 are: 1, 5, 25.
Here’s a breakdown of the factors:
1: 1 is a factor of every number.
5: 5 divides 25 evenly, as 25 ÷ 5 ... |
# Applications of Systems of Linear Equations Example 1: Steve invested \$12,000 for one year in two different accounts, one at 3.5% and the other at 4%.
## Presentation on theme: "Applications of Systems of Linear Equations Example 1: Steve invested \$12,000 for one year in two different accounts, one at 3.5% and the... |
Ashley Jones
Assignment 4: Activity- Exploration of Medians
Many of us know that the medians of a given triangle can be found by connecting opposite vertices to the midpoint of each side of the triangle. This process can be achieved by using a compass, ruler, and pencil, but can also be achieved by using the mathemat... |
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#### Online Quiz (WorksheetABCD)
Questions Per Quiz = 2 4 6 8 10
### High School Mathematics - 210.2 Heights and Distances
Introduction One of the most important applications of trigonometry is the application of meas... |
# Disjoint sets Information
(Redirected from Disjoint set)
https://en.wikipedia.org/wiki/Disjoint_set
Two disjoint sets
In mathematics, two sets are said to be disjoint sets if they have no element in common. Equivalently, two disjoint sets are sets whose intersection is the empty set. [1] For example, {1, 2, 3} and ... |
Question Video: Finding the Range of a Given Sine Function | Nagwa Question Video: Finding the Range of a Given Sine Function | Nagwa
# Question Video: Finding the Range of a Given Sine Function Mathematics • First Year of Secondary School
## Join Nagwa Classes
Find the range of the function π(π) = 3 sin (π... |
# 1989 AIME Problems/Problem 4
## Problem
If $a are consecutive positive integers such that $b+c+d$ is a perfect square and $a+b+c+d+e$ is a perfect cube, what is the smallest possible value of $c$?
## Solution
Since the middle term of an arithmetic progression with an odd number of terms is the average of the seri... |
# Algebra II : Solving Equations
## Example Questions
### Example Question #1 : Linear Systems With Three Variables
Solve this system of equations.
, ,
, ,
, ,
, ,
, ,
, ,
Explanation:
Equation 1:
Equation 2:
Equation 3:
Adding the terms of the first and second equations together will yield .
Then, add t... |
Review question
# Can we calculate the total time taken for this car journey? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource
Ref: R7250
## Solution
The diagram shows a speed-time graph of a car.
1. Calculate the acceleration of the ... |
# 10.3: Surface Area of Prisms
Difficulty Level: At Grade Created by: CK-12
## Introduction
The Doll House
On her first day wrapping boxes, Candice had a customer come up to the counter with a huge box in her arms.
“This is a doll house for my niece,” the woman said. “Can you please wrap it?”
“Certainly,” Candice... |
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# Parallelograms
## Quadrilateral with two pairs of parallel sides.
Estimated7 minsto complete
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# Lesson 11
Introducing the Number $i$
• Let’s meet $$i$$.
### 11.1: Math Talk: Squared
Find the value of each expression mentally.
$$\left(2\sqrt{3}\right)^2$$
$$\left(\frac12 \sqrt{3}\right)^2$$
$$\left(2\sqrt{\text- 1}\right)^2$$
$$\left(\frac12 \sqrt{\text- 1}\right)^2$$
### 11.2: It is $i$
Find the solut... |
A linear pair is a pair of angles that lie next to each other on a line and whose measures add to equal 180 degrees. Linear pair: Two adjacent angles are said to be linear pair if their sum is equal to 180°. S(1) is an exception, but S(2) is clearly true because 2 is a prime number. If we apply a function to every elem... |
Factors that 40 are numbers that, when multiplied in pairs give the product together 40. There room 8 factors of 40, which room 1, 2, 4, 5, 8, 10, 20 and also 40. Here, 40 is the biggest factor. The element Factors and also Pair factors of 40 room 1, 2, 4, 5, 8, 10, 20, 40 and also (1, 40), (2, 20), (4, 10) and (5, 8) ... |
# How do you graph y=sqrt(x-0.5), compare it to the parent graph and what is the domain and range?
May 3, 2017
See explanation
$x \in \mathbb{R} \mathmr{and} y \in \mathbb{R} \leftarrow \text{ what is called Real Numbers}$
Domain $\to \text{ input } \to x \ge 0.5 \to \left[0.5 , + \infty\right)$
Range $\to \text{ o... |
## Time and Work Questions - 1
A can do a piece of work in 12 days; B can do it in 18 days. Then how many days both working together can complete the work ?
• 7 $\displaystyle\frac{1}{5}$ days
• 8 $\displaystyle\frac{1}{2}$ days
• 8 days
• 7 $\displaystyle\frac{1}{2}$ days
• 7 days
Explanation
One day work of A = $\d... |
# Difference between revisions of "The Fourth Dimension"
## Explorations
Begin learning about flatland and the fourth dimesion with:
## Introduction to Dimensions
Webster’s Dictionary gives a description of dimensions 1, 2 , 3, and 4. We will also give a description of the 0th dimension.
• Space of zero dimensions... |
## MATHEMATICS FORM TWO TOPIC 2:ALGEBRA
### MATHEMATICS FORM TWO TOPIC 2:ALGEBRA
Monday, January 16, 2023
When we play games with computers we play by running, jumping and or finding secret things. Well, with Algebra we play with letters, numbers and symbols. And we also get to find secret things. Once we learn some... |
# Indefinite Integrals
Dear all, you might all be afraid of integration though it is quite fascinating topic… Well, here we bring up few important concepts in integration, by which you can make your preparation interesting…!!
Indefinite Integrals:
A function ∅ (x) is called a primitive (or) an anti-derivative of a f... |
# Calculating rate of change for simple models is commonsense
Calculating rate of change of a car [1]
Calculating rate of change is the first of calculus’s two principal operations
…the two principal symbols that are used in calculating… are:
1. d which merely means “a little bit of.”
Thus dx means a little bit of ... |
# Solution For Split Array Largest Sum
The Split Array Largest Sum problem on LeetCode asks you to divide an array of integers into m subarrays such that the maximum sum of any subarray is minimized.
For example, given the array [7,2,5,10,8] and m = 2, the optimal solution would be to split the array into [7,2,5] and... |
# Does solving a recurrence relation by iteration have two different meanings?
I've seen iteration used by plugging numbers in and not simplifying and guessing the explicit formula, e.g., $t_n$ plug $n=1,2,3,4$ in and guess the explicit formula. The other way I've seen is plugging the variables in e.g. plug $t_{n+1}$ ... |
# What The Numbers Say About Teresa Giudice (11/16/2019)
How will Teresa Giudice do on 11/16/2019 and the days ahead? Let’s use astrology to perform a simple analysis. Note this is not scientifically verified – don’t get too worked up about the result. I will first calculate the destiny number for Teresa Giudice, and ... |
Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 2 Complex Numbers Ex 2.8 Textbook Questions and Answers, Notes.
## Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 2 Complex Numbers Ex 2.8
Question 1.
If to ω ≠ 1 is a cube root of unity, then show that
Solution:
L.H.S
Question ... |
Question
# The values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Give the exponential models for those that are
Exponential models
The values of two functions, f and g, are given in a table. One, both, or neither of them may be exponential. Give the exponential... |
Thomas' Calculus 13th Edition
$f^{-1}(x)=2x+7$ Domain of $f^{-1}$ is $(-\infty,\infty)$ Range of $f^{-1}$ is $(-\infty,\infty)$
Given $$f(x) = \frac{1}{2}x-\frac{7}{2}$$ Find the inverse: \begin{aligned} y &= \frac{1}{2}x-\frac{7}{2} \\2y &=x-7 \\ x&=2y+7 \\ \text {Switch }& x \ and\ y:\\ y=&2x+7 =f^{-1}(x) \end{align... |
Kids Math
Glossary and Terms: Angles
Acute angle - Any angle smaller than 90°. Adjacent angles - Adjacent angles are two angles that share a common vertex and one common side. They do not overlap. In the picture to the right, angles ∠cad and ∠cab are adjacent angles.
Adjoining - When two objects share a common bound... |
# Rectangular Coordinate System
## Presentation on theme: "Rectangular Coordinate System"— Presentation transcript:
Rectangular Coordinate System
Definitions X-axis – the horizontal axis Y –axis – the vertical axis
Rectangular coordinate system: where the x-axis and the y-axis intersect Ordered pair: identifies the ... |
# 9.3 Geometric sequences (Page 4/6)
Page 4 / 6
## Verbal
What is a geometric sequence?
A sequence in which the ratio between any two consecutive terms is constant.
How is the common ratio of a geometric sequence found?
What is the procedure for determining whether a sequence is geometric?
Divide each term in ... |
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# Find the square root of 7+4sqrt(3). <br> (b) Find the square root of 10+sqrt(24)+sqrt(60)+sqrt(40)
Khareedo DN Pro and dekho sari videos bina kisi ad ki rukaavat ke!
Updated On: 27-06-2022
Text Solution
So... |
Level-3 Mixed Graph Practice Test -1 Hard
Directions : Study the following pie chart and line chart carefully and answer the questions given beside.
The pie chart shows the number of students study in five different schools as a percentage of the total number of students studies in all five schools A, B, C, D, and E.... |
# Constructions Class 10 Maths Formulas
For those looking for help on Constructions Class 10 Math Concepts can find all of them here provided in a comprehensive manner. To make it easy for you we have jotted the Class 10 Constructions Maths Formulae List all at one place. You can find Formulas for all the topics lying... |
# 5.2 Unit circle: sine and cosine functions
Page 1 / 12
In this section, you will:
• Find function values for the sine and cosine of and $\text{\hspace{0.17em}}{60°}^{}\text{or}\left(\frac{\pi }{3}\right).$
• Identify the domain and range of sine and cosine functions.
• Use reference angles to evaluate trigonometric... |
# Lehmer's GCD algorithm
Lehmer's GCD algorithm, named after Derrick Henry Lehmer, is a fast GCD algorithm, an improvement on the simpler but slower Euclidean algorithm. It is mainly used for big integers that have a representation as a string of digits relative to some chosen numeral system base, say β = 1000 or β = ... |
29
Q:
# Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 km/h
A) 90 km/h B) 160 km/h C) 67.5 km/h D) Non... |
# CLASS-8SIMULTANEOUS LINEAR EQUATION - ELIMINATION METHOD
SIMULTANEOUS LINEAR EQUATION -
Elimination Method –
This method is also called the addition subtraction method
Step.1) Decide which variable will be easier to eliminate, try to avoid fractions
Step.2) Multiply one or both the equations by suitable numbers ... |
Exponential Functions
You can move the red dots to see the graph of different exponential functions.
Exponential functions are related to geometric progressions:
Geometric sequences graphic representations. Sum of terms of a geometric sequence and geometric series.
Exponential functions can be seen as extensions of... |
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# Pick-a-Bar: Finding Values in the Tenths Place
This little decimal activity has you looking for values in specific places. Start by remembering that whole numbers are found on the left side of the decimal point and... |
Polar Coordinates
# Polar Coordinates - Polar Coordinates Up to this point weve...
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Polar Coordinates Up to this point we’ve dealt exclusively with the Cartesian (or Rectangular, or x-y ) coordinate system. However, as we will see, this is not always the... |
# If A= <8 ,-5 ,6 > and B= <7 ,1 ,0 >, what is A*B -||A|| ||B||?
Mar 14, 2018
$\boldsymbol{\underline{A}} \cdot \boldsymbol{\underline{B}} - | | \boldsymbol{\underline{A}} | | \setminus | | \boldsymbol{\underline{B}} | | = 51 - 25 \sqrt{2}$
#### Explanation:
We start with the vectors $A$ and $B$
$\boldsymbol{\unde... |
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# Division and Multiplication Relationship
Do you need extra help for EL students? Try the Multiplication and Division: What's the Connection?Pre-lesson.
EL Adjustments
GradeSubjectView aligned standards
No standards associated with this content.
No standards associated with this content.
Which set of stan... |
Applying Reasoning and Proof
Reasoning About Fractions | Reasoning About Fractions in Action | Classroom Practice | Reasoning and Proof in Action | Classroom Checklist | Your Journal
Think about the Fraction Tracks game and consider the following questions. Select "Show Answer" to reveal our commentary.
Question: H... |
# NCERT Class 8 Maths Chapter 7 – Cubes and Cube roots solutions
### Access Answers of Maths NCERT Class 8 Chapter 7 – Cubes and Cube roots
Exercise 7.1 Page: 114
1. Which of the following numbers are not perfect cubes?
(i) 216
Solution:
By resolving 216 into prime factor,
216 = 2×2×2×3×3×3
By grouping the fact... |
# Brief Introduction to Vectors and Matrices
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## Transcription
1 CHAPTER 1 Brief Introduction to Vectors and Matrices In this chapter, we will discuss some needed concepts found in introductory course in linear algebra. We will introduce matrix, vector, vector-valued... |
# How do you prove sec(x) + 1 + ((1-tan^2(x)) / (sec(x)-1)) = cos(x)/(1-cos(x))?
Jul 10, 2016
Do some conjugate multiplication, make use of trig identities, and simplify. See below.
#### Explanation:
Recall the Pythagorean Identity ${\sin}^{2} x + {\cos}^{2} x = 1$. Divide both sides by ${\cos}^{2} x$:
$\frac{{\sin... |
### 2: Quadratic Relations of the Form y = ax² + bx + c
#### 2.1: Overall Expectations
2.1.1: determine the basic properties of quadratic relations;
2.1.2: relate transformations of the graph of y = x² to the algebraic representation y = a(x - h)² + k;
2.1.4: solve problems involving quadratic relations.
#### 2.2:... |
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## Staging content lifeboat
### Course: Staging content lifeboat>Unit 14
Lesson 4: Fractions and ... |
Lesson 3
# Lesson 3 - by an even number from this maximum So f x = 3 x...
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Finding Roots of Polynomials Let’s start with a quadratic: p q x 2 + r s x + t u = 0 with p,q,r,s,t,u all integers Then find a common denominator and a common factor and divide them o... |
# What is the power of a quotient property?
Dec 25, 2014
The Power of a Quotient Rule states that the power of a quotient is equal to the quotient obtained when the numerator and denominator are each raised to the indicated power separately, before the division is performed.
i.e.: ${\left(\frac{a}{b}\right)}^{n} = {a... |
# 20 Is What Percent of 52? Round Your Answer to the Nearest Tenth.
20 Is What Percent of 52? Round Your Answer to the Nearest Tenth.
When faced with the question “20 is what percent of 52?” it might seem daunting at first, especially if you haven’t dealt with percentages in a while. However, with a little bit of kno... |
# Topic 1.1: Modulus Functions
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Category: Education
## Presentation Description
Absolute value, Solving modulus equations, modulus inequalities, quadratic modulus inequalities.
## Presentation Transcript
### Modulus functions :
Modulus functions |4| = |-4| = |a| = b => |x - a| = b => |a| = |b| => |x - a| =... |
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Study these two triangles. How are they alike? If we rotated the pink triangle and slid it on top of the green one, the two would fit on top of each other exactly. All the sides and all the angles are equal, so these two triangles are congruent.
I... |
Lost Car Key Puzzle
# Lost Car Key Puzzle
I drive to work, and put my car keys in my pocket. Whenever I sit down in a meeting there is a 20% chance that my car keys might fall out of my pocket (unnoticed). At lunchtime, I reach for my keys and find out they are missing. If I’ve had three sit-down meetings that mor... |
# The Holistic Approach to Absolute Values – Part V
We will continue our holistic approach to absolute values and add more complications to these types of questions. This article should set you up for any question of this kind. Note that this is a 750+ level concept, so if you are targeting a lower score, it may not b... |
# Math help from the Learning Centre
This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.
## Introduction to Annuities
What is an annuity? It is a series of equal payments w... |
## Lesson: Ordering Greater Numbers Introducing the Concept
Before students order greater numbers, use this lesson to reinforce their understanding of place value of greater numbers.
Materials: transparency made from Learning Tool 4 in the Learning Tools Folder
Preparation: Write the value of each place on Learning ... |
1975 AHSME Problems/Problem 28
Problem 28
In $\triangle ABC$ shown in the adjoining figure, $M$ is the midpoint of side $BC, AB=12$ and $AC=16$. Points $E$ and $F$ are taken on $AC$ and $AB$, respectively, and lines $EF$ and $AM$ intersect at $G$. If $AE=2AF$ then $\frac{EG}{GF}$ equals
$[asy] draw((0,0)--(12,0)--(1... |
# Lesson Video: Arc Length by Integration Mathematics • Higher Education
In this video, we will learn how to use integration to find the length of a curve.
14:26
### Video Transcript
In this video, weβll learn how to use integration to find the length of a curve. By this stage, you might be aware of some of the k... |
Gauthmath
# How to Rationalize the Denominator
## How to Rationalize the Denominator
#### Context of this video
Gauthmath helps with your math. Welcome to Gauthmath.
In this video, we're going to introduce a key skill called the rationalization of denominator.
What does rationalization mean?
We know that the cor... |
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