# Algebra

### Featured Answers

### Expressions, Equations, and Functions

- Variable Expressions
- Expressions with One or More Variables
- PEMDAS
- Algebra Expressions with Fraction Bars
- Patterns and Expressions
- Words that Describe Patterns
- Equations that Describe Patterns
- Inequalities that Describe Patterns
- Function Notation
- Domain and Range of a Function
- Functions that Describe Situations
- Functions on a Cartesian Plane
- Vertical Line Test
- Problem-Solving Models
- Trends in Data
- Properties of Rational Numbers
- Additive Inverses and Absolute Values
- Addition of Integers
- Addition of Rational Numbers
- Subtraction of Rational Numbers
- Multiplication of Rational Numbers
- Mixed Numbers in Applications
- Expressions and the Distributive Property
- When to Use the Distributive Property
- Division of Rational Numbers
- Applications of Reciprocals
- Square Roots and Irrational Numbers
- Order of Real Numbers
- Guess and Check, Work Backward
- One-Step Equations and Inverse Operations
- Applications of One-Step Equations
- Two-Step Equations and Properties of Equality
- Multi-Step Equations with Like Terms
- Distributive Property for Multi-Step Equations
- Equations with Variables on Both Sides
- Equations with Ratios and Proportions
- Scale and Indirect Measurement Applications
- Conversion of Decimals, Fractions, and Percent
- Percent Equations
- Percent of Change
- Formulas for Problem Solving
- Graphs in the Coordinate Plane
- Graphs of Linear Equations
- Horizontal and Vertical Line Graphs
- Applications of Linear Graphs
- Intercepts by Substitution
- Intercepts and the Cover-Up Method
- Slope
- Rates of Change
- Slope-Intercept Form
- Graphs Using Slope-Intercept Form
- Direct Variation
- Applications Using Direct Variation
- Function Notation and Linear Functions
- Graphs of Linear Functions
- Problem Solving with Linear Graphs
- Write an Equation Given the Slope and a Point
- Write an Equation Given Two Points
- Write a Function in Slope-Intercept Form
- Linear Equations in Point-Slope Form
- Forms of Linear Equations
- Applications Using Linear Models
- Equations of Parallel Lines
- Equations of Perpendicular Lines
- Families of Lines
- Fitting Lines to Data
- Linear Interpolation and Extrapolation
- Problem Solving with Linear Models
- Dimensional Analysis
- Inequality Expressions
- Inequalities with Addition and Subtraction
- Inequalities with Multiplication and Division
- Multi-Step Inequalities
- Compound Inequalities
- Applications with Inequalities
- Absolute Value
- Absolute Value Equations
- Graphs of Absolute Value Equations
- Absolute Value Inequalities
- Linear Inequalities in Two Variables
- Theoretical and Experimental Probability
- Graphs of Linear Systems
- Systems Using Substitution
- Mixture Problems
- Linear Systems with Addition or Subtraction
- Linear Systems with Multiplication
- Consistent and Inconsistent Linear Systems
- Linear Programming
- Probability and Permutations
- Probability and Combinations
- Exponential Properties Involving Products
- Exponential Properties Involving Quotients
- Negative Exponents
- Fractional Exponents
- Scientific Notation
- Scientific Notation with a Calculator
- Exponential Growth
- Exponential Decay
- Geometric Sequences and Exponential Functions
- Applications of Exponential Functions
- Polynomials in Standard Form
- Addition and Subtraction of Polynomials
- Multiplication of Monomials by Polynomials
- Multiplication of Polynomials by Binomials
- Special Products of Polynomials
- Monomial Factors of Polynomials
- Zero Product Principle
- Factorization of Quadratic Expressions
- Factor Polynomials Using Special Products
- Factoring by Grouping
- Factoring Completely
- Probability of Compound Events
- Quadratic Functions and Their Graphs
- Vertical Shifts of Quadratic Functions
- Use Graphs to Solve Quadratic Equations
- Use Square Roots to Solve Quadratic Equations
- Completing the Square
- Vertex Form of a Quadratic Equation
- Quadratic Formula
- Comparing Methods for Solving Quadratics
- Solutions Using the Discriminant
- Linear, Exponential, and Quadratic Models
- Applications of Function Models
- Graphs of Square Root Functions
- Simplification of Radical Expressions
- Addition and Subtraction of Radicals
- Multiplication and Division of Radicals
- Radical Equations
- Pythagorean Theorem and its Converse
- Distance Formula
- Midpoint Formula
- Measures of Central Tendency and Dispersion
- Stem-and-Leaf Plots
- Box-and-Whisker Plots
- Inverse Variation Models
- Graphs of Rational Functions
- Division of Polynomials
- Excluded Values for Rational Expressions
- Multiplication of Rational Expressions
- Division of Rational Expressions
- Addition and Subtraction of Rational Expressions
- Rational Equations Using Proportions
- Clearing Denominators in Rational Equations
- Surveys and Samples
- Question #06856
- Question #20f62
- Question #5a793
- How do you divide #(x^3-2x+5)/(x^2+4x+3)# ?
- Question #f472a
- #x^4-10x^2+1=0# has one root #x=sqrt(2)+sqrt(3)#. What are the other three roots and why?
- How do you simplify surds in brackets?
- The price of two bags of popcorn and three drinks is #$18.25#. The price of four bags of popcorn and two drinks is #$27.50#. What is the price of one bag of popcorn and one drink?
- Can someone explain Remainder Theorem to me?
- Question #48167
- Question #aabf4
- Question #3fd94
- In #2006# the deficit was #$248bn#. By #2013# the deficit was #$680bn#. What is the average annual rate of change?
- The product of the first ten prime numbers must be divisible by? a. 16 b. 18 c. 20 d. 22 e. 24
- How do you solve #log_5(2x-1) < 1# ?
- Question #cfb72
- What is the best way of finding #sqrt(13)# without using a calculator?
- How do you solve #abs(5x + 13) = –7#?
- How to solve #4^(x^2)=(1/32)^((x+6)/5)# ?
- The quadratic equation in x is x2 + 2x.cos(A) + K=0. &also given summation and difference of solutions of above equation are -1 & -3 respectively. Hence find K & A?
- What are relatively prime multinomials and how do they relate to factorability?
- How do you define two divergent sequences whose termwise product is a convergent sequence?
- What is the wavelength of violet light?
- How do you define a function?
- What is the difference between an othonormal frame and an orthoganol frame of reference?
- How many different anagrams can you form with the word POLYTECHNIQUE?
- Question #452f5
- Question #8a4ec
- What is the new Transforming Method to solve quadratic equations?
- How do you find the slope of #f(x) = 0.5x^2+6x+7.5# at #x=-6# by first principles?
- Solve (3x+y)/8 = (x-y)/5 = (x²-y²)/5. What is the values for x and y?
- What is an example of an infinite group in which every element is of finite order?
- Question #addf9
- Question #e7833
- Question #289b5
- Solve (z+3)(2-z)(1-2z)>0?
- How to solve (x^2 - 4x +3)(x^2 -3)<0?
- Question #1fec9
- The function #f(x) = 1/(1-x)# on #RR# \ #{0, 1}# has the (rather nice) property that #f(f(f(x))) = x#. Is there a simple example of a function #g(x)# such that #g(g(g(g(x)))) = x# but #g(g(x)) != x#?
- Does #z(x) = sqrt(x^2-5x-6)# have an inverse function?
- Question #ee1fb
- Question #b0e8c
- Question #517e5
- Question #3d967
- Wheat runs out of a silo at a constant rate, forming a conical heap. After #1# minute the height of the heap is #20"cm"#. At what rate is its height increasing at that time?
- Question #f7d59
- Question #44424
- How many planes pass through #3# distinct points in #3# dimensional space?
- Question #9ba75
- How can you evaluate #(y+3)/(4y^2)+y-3#?
- How do you find the square root of #100# ?
- Solve |x²-3|<3 . This looks simple but i could not get the right answer. The answer is (-√5,-1)U(1,√5). How to solve this inequality?
- Question #87f67
- Question #05984
- Question #b85b6
- Question #8cff4
- Question #e72dc
- Question #68395
- How do you prove that zero exists?
- Question #d632b
- How to factor cubic trinomials? x^3-7x-6
- How do I factor #i^2-4t-21# completely?
- How do I factor #6x^2-7x-3# completely?
- How do I simplify #(5x^2)(2x^5)#?
- How do I simplify #(-2c^3)^2#?
- How do I simplify #(t^3)(t^(n-3))#?
- How do I simplify #(10*2^6)/(8*2^(-2))#?
- Question #bafcb
- What is the largest prime factor of #(25!)^3 - (24!)^3 #?
- How do you simplify #3a-14a#?
- Question #2ab73
- How do you factor #4y^2-11y-3#?
- Question #5b380
- Question #8a625
- What is #(sqrt(2x+4))^2#?
- What is the domain of #f(g(x))# if #f(x)=x^2-4# and #g(x)=sqrt(2x+4)# ?
- How do I simplify #(x^2-25)/(x^2+7x+10)#?
- How do I simplify #(x^2-5x+6)/(x^2-4)*(x^2+3x+2)/(x^2-2x-3)#?
- How do I simplify #(2x)/(x+5)÷(6x^2)/(2x+10)#?
- How do I simplify #(2x)/(x-3)-(x)/(x+3)#?
- Question #60254
- Question #df084
- Cot theta+tan theta=k, where theta is an acute angle and k is a constant, has real value of tan theta, show that k«2 or k»2?
- Question #fedfc
- What is the union symbol (#uu#) used for?
- If #100# cats kill #100# mice in #100# days, then how long does it take #4# cats to kill #4# mice ?
- Question #e5f13
- Question #e8fc7
- How do you simplify #(-27/8)^(-4/3)#?
- Question #92987
- What is the new Transforming Method to solve quadratic equations?
- Question #2d2b0
- Question #301cc
- Alan had thrice as many stickers as Janani. After Alan and Janani had given 40% and 20% of their stickers to Wendy respectively, the number of stickers that Wendy had increasedby1/4.Wendyhad1680stickersintheend.HowmanystickerdidJanani have in the end?
- Suppose #x# varies directly as both #y# and #z# (and #y# and #z# vary inversely with each other. If #x=6# when #y=6# and #z=123#, what is the value of #z# when #x=7# and #y-8#?
- How do you solve #3/4x^2-2x+1/2=0# using the quadratic formula?
- How do you solve #-42 < -7x < -35# ?
- How do you factor #x^2-17x+72# ?
- For maximum safety, the distance between the base of a ladder and a building should be 25% of the length of the ladder. Find the safest angle between the ladder and the ground?
- Find all exact angles x in the interval [0,360°] that satisfy the following equations without the use of calculator a)sin x +cos 2x=0 b)cos 2x= sin52 ?