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 Real Numbers

• 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

Linear Equations

• 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 of Linear Equations and Functions

• 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

Forms of Linear Equations

• 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

Linear Inequalities and Absolute Value

• 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

Systems of Equations and Inequalities

• 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

Exponents and Exponential Functions

• 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 and Factoring

• 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 Equations and Functions

• 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

Radicals and Geometry Connections

• 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

Rational Equations and Functions

• 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

Uncategorized Questions

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• Question #0b637
• Sam receives a paycheck every other Friday. His yearly salary is #$84500.00#. How much is his gross paycheck each payday?
• How do you factor quadratic equations box method?
• Question #13354
• Question #05482
• Question #24247
• How do you simplify #(-7x^4y^2)(-2x^2y^2)#?
• What is the last digit in the number #7^(7^(7^(7^(7^(7^7)))))# ?
• How do u know if an equation is combined transformation is it when you have all the variables a, k, d and c?
• Can you please explain the rational root theorem and the factor theorem?
• Question #d1034
• Question #c7129
• How do you know if a triangle is ambiguous?
• Given that #z # is a complex number and that#|z|> 0# Show that #|z + 1|>=1#?
• Question #fcc28
• Question #ef706
• Question #357ad
• Question #d90f9
• Question #b1688
• What is #2^(3^2)#?
• Question #9b0dd
• What is the new AC Method to factor trinomials?
• If #x = 5 - 5 ^ ( 2/3) - 5 ^ (1/3)# Prove that# x ^3 - 15x^2 + 60 x - 20 = 0# ?
• What is algebra useful for in real life?
• Question #081ca
• Question #3863c
• Question #38732
• What is the new Transforming Method to solve quadratic equations?
• What is the new Transposing Method to solve linear equations?
• Question #3e37f
• Question #43427
• Question #79a9f
• Question #15fa0
• If# x = (a/b)^((2ab)/(a^2-b^2))# Prove that #( (ab)/(a^2+b^2) )(x^(a/b) + x ^ (b/a))=(a/b)^((a^2+b^2)/(a^2 - b^2))#?
• Question #f12fd
• If # p ^ (a^3 - b^3 ) = q^ (a^3 + b^3 ) = r ^ ( a^2- b^2)# Then prove that# (p/q)^(a^2 + b^2) = (r^ (2b ))/((pq)^(ab))# ?
• What is #x^(2/3)# divided by #x^(1/2)#?
• If# (y/z)^a * (z/x)^b*(x/y)^c = 1# Then prove #(y/z)^(1/(b-c))=(z/x)^(1/(c-a)) = (x/y)^(1/(a-b))#?
• Prove that #(x+y)(x^2 +y^2)(x^4 +y^4).......(x^{2^(n-1 )} + y^{2^(n-1 )}) = {x^(2^(n)) -y^(2^(n))}/(x-y)#?
• Question #9e5f7
• Question #9ea92
• How do you write #y= x^2-18x+52 into vertex form?
• Question #9fc71
• Question #2aff7
• What is the value of #x# if #sqrt(5x+1) = x+1#?
• Question #4c87b
• Question #2555b
• If #(5-sqrt(x))^2 = y-20sqrt(2)# where #x, y# are integers, then what are #x# and #y# ?
• Question #43eb0
• Question #1ab06
• Question #99e41
• Question #56298
• Question #fdc59
• Find the roots of #e^(xcoshx)=3#?
• Question #c2e26
• Question #c5c0c
• Question #7eb8c
• Question #15e3f
• If #4/10=10/m# what is the value of #m#?
• What is the average rate of change of the function #y = x^2+1# over the interval #[5, 5+a]# ?
• Question #72fd4
• How do you solve #a^2-sqrt(3)a+1 = 0# ?
• How do you solve #(x+1)^2+2 = 7# ?
• Question #c78ad
• Question #0e123
• If you were to produce a 3 digit multiple of 7 that has a final digital sum of 7 using the formula; 7(1+9k). How do you calculate what k is?
• How do you write #Y=-7(x-3)^2+12# in standard form?
• How do you combine # [(3x - 5)/(3 - x)] + [(1)/(1 - x)] - [(x^2 - 1)/(x^2 - 4x + 3)]#?
• Why does the equation #4x^2-25y^2-24x-50y+11=0# not take the form of a hyperbola, despite the fact that the squared terms of the equation have different signs? Also, why can this equation be put in the form of hyperbola#(2(x-3)^2)/13 - (2(y+1)^2)/26=1#
• Question #46f24
• Question #e4ce0
• Why are so many people under the impression that we need to find the domain of a rational function in order to find its zeros? Zeros of #f(x) = (x^2-x)/(3x^4+4x^3-7x+9)# are #0,1#.
• Question #4e512
• Given a circle with equation #x^2+(y-1)^2 = 10#, what are the equations of the two tangents to the circle that run through the point #(4, -1)# ?
• What is the least common multiple of #p# and #q# if #p, q# are prime numbers ?
• Question #c9e1c
• How do you FOIL #(3x - 2)(2x + 5)#?
• Question #6bd54
• Question #6c523
• How do you find the percentage of stock X originally invested?
• How do you write an equation in standard form given a line that passes through (2,9) and (1,3)?
• Question #5ff03
• An arched window formed from the union of a semicircle and a rectangle has total perimeter #540"cm"#. What is the maximum possible area of the window?
• Question #3b1bd
• How do you show that #kx^2+2x-(k-2) = 0# has at least one real root for any value of #k# ?
• Question #0e900
• Question #3b27d
• Squares are cut from each corner of a #0.5m xx 0.5m# square of cardboard and the sides folded up to make an open box. What is the maximum possible volume of the box?
• Is #5 * 7 * 11 + 13 * 17# odd or even, prime or composite?
• If #x^2+bx+40# has a turning point at #x=-7# then what is #b# ?
• What is the history of FOIL? and why does it seem to be emphasized over more general methods of multiplication (like use of the distributive property or tabular multiplication)?
• How do I factor a polynomial (e.g. cubic)?
• How can you find the GCF of two polynomials?
• Question #1ca2d
• How to simplify algebraic fractions?
• What is the equation of a circle of radius 1, which is also tangent to the line 3x-4y+1=0 at the y-axis value = 1 ?
• How do you solve the system #y=2x-3# and #x+y=15#?
• Question #fc123
• How do you factor #64-y^2#?
• How do you factor #9t^2-1# ?
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