Although not obvious, learning equations is important in our daily life. Without them we wouldn't have the computers, GPS, satellite television and other inventions that make modern society what it is.
SomeEquations that changed the way we liveThey are the Pythagorean Theorem, the Fundamental Theorem of Analysis, and Newton's Universal Law of Gravitation, to name a few.
The equation is important for medicine, business, computer science, engineering and more. Read on for more information on this dynamic concept.
Types of Equations - Algebraic
cubic equation
A cubic equation is a polynomial equation in which the largest sum of the exponents of the variables in each term is three. In other words, it's an equation.with a cubic polynomial; that is, one of the forms. It has the following form:
Machado3+ bx2+ cx + d = 0 for a ≠ 0
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exponential equation
Exponential equations have variables instead of exponents and can be solved using this property: axax = ayay => x = y. Examples for this are:
- 4X= 0
- 8X= 32
- andb= 0 (where "a" is the base and "b" is the exponent)
Irrational polynomial equation
Irrational polynomial equations are those equations with at least one polynomial under the root sign.
linear equation
Linear equations are those in which each term is a constant or the product of a single variable and a constant. When there are two variables, the graph of the linear equation is always a straight line. A linear equation typically looks like this:
y = mx + c, Metro ≠≠ 0
In this example, m is known as the slope and c represents the point where it intersects the y-axis.
In linear equations with different variables:
Single Variable Equation: An equation that has only one variable. Examples for this are:
- 8a – 8 = 0
- 9a = 72
The equation has two variables: An equation that has only two types of variables. Examples for this are:
- 9a + 6b – 82 = 0
- 7x + 7a = 12
- 8a - 8d = 74
The three variable equation: This is an equation with only three types of variables in the equation. Examples for this are:
- 13a - 8b + 31c = 74
- 5x + 7a - 6z = 12
- 6p + 14q – 74 + 82 = 0
logarithmic equation
These are equations where the unknown is always affected by a logarithm.
polynomial equation
Contain polynomial equationsVariables or indeterminate and coefficients. They are involved in operations such as addition, subtraction, multiplication, and non-negative integer exponents. Examples for this are:
- ax + by + c = 0 ax + by + c = 0 with degree = 1 and two variables
- Machado2+ bx + c = 0ax2+ bx = c = 0 with degree = 2 and one variable
- ax + b = 0 with degree = 1 and one variable
- axy + c = 0axy + c = 0 with degree = 2 and two variables
quadratic equation
A quadratic equation is aA second class equationwhere a variable contains the variable that has an exponent of two. Below is an example and the general form.
Machado2+ bx + c = 0, a ≠≠ 0
Other examples are:
- 5a2- 5a = 35
- 8x2+ 7x – 75 = 0
- 4 years2+ 14 years – 8 = 0
quadratic equation
Quadratic equations are quadratic equations and an equation that equates to zero a quadratic polynomial in this form:
f(x) = ax4+ bx3+ CX2+ dx + e = 0 und a ≠ 0
The derivative of a quadratic function is a cubic function.
quintic equation
A quintic equation is a polynomial equation where five is the highest power of the variable. The formula used is:
ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0
Examples for this are:
- x^5 + x^3 + x
- y^5 + y^4 + y^3 + y^2 + y + 1
radical equation
Radical equations are those that have a maximum exponent in the variable that is 12 and that have more than one term. A radical equation can also be said to be one in which the variable is enclosed in a radical symbol, usually in the form of a square root. Examples for this are:
- + 10 = 26
- +x – 1
rational equation
A rational equation implies rational expressions.
transcendent equations
Transcendent equations are equations thatcontain transcendent functions. Exponential equations are examples of transcendental equations.
trigonometric equation
Simply put, trigonometric equations are the equations that involvetrigonometric functions, usually from unknown angles, such as B. cos B = ½.
An example of a trigonometric equation can be found here:
x=
More examples of trigonometric equations can be found hereon here.
Other examples of algebraic equations can be foundon here.
Types of Equations - Geometric
Numbers - Volume (V) and Surface Area (SA) Formulas
prism in general
- V = Bh = base x height
- SA = sum of the areas of the faces
Prism rectangular
- V = lbh = length x width x height
- SA = 2lw + 2hw + 2lh
- = 2 (length x width) + 2 (height x width) + 2 (length x height)
right circular cone
- V = Bh = x base x height
- SA = B + C
- = area of base + (x perimeter of base x slope height)
right circular cylinder
- V = Bh = base x height
- SA = 2B + Ch = (2 x base area) + (circumference x height)
she was
- V =3= x x Kubikradius
- SA = 42= 4 x x Square of Radius
square pyramid
- V = Bh = x base x height
- SA = B + P
- = area of base + (x perimeter of base x slope height)
Shapes: Area (A) and Perimeter (C) Formulas
Kreis
and =2= x to the square of the radius
C = 2r = 2xx ratio
C = = x diameter
Parallelogramm
A = bra = base x height
rectangle
A = LW = length x width
trapeze
and =(b1+b2)h = x sum of bases x height
triangle
A = bra = x base x height
equations of a line
Standard form
Ax + By = 0, where A and B are non-zero
Point Gradient Shape
and and1= m(x – x1) where m = slope, (x1, She1) = point on the line
Intercept form for gradients
y = mx + b or y = b + mx where m = slope b = y - intercept
geometric formulas
circle area:2(= 3.14 approximately)
Area of a rectangle: length x height
Area of the square: length2(Length x Length)
area of a triangle: ½ x wide x high
Circumference of a circle: 2 (x diameter)
Cone volume: 1/3 x base x height; 1/3x (d/2)2xh
Cylinder volume: base x height; (d/2)2xh
Rectangular prism volume: length x height x depth
Check out our article"7 Different Types of Triangles". (Or you like"7 Different Types of Fractions")
types of chemical reactions
chemical combination reactions
In this reaction, two or more reactants form a product.
Also, more than one product can be formed in a combined chemical reaction, depending on the conditions or the relative amounts of the reactants.
combustion chemical reactions
Chemical combustion reactions take place when a compound, usually containing carbon, combines with gaseous oxygen from the air. This process is called combustion because heat is the most important product in most chemical combustion reactions.
Propane is part of the compounds called hydrocarbons, which are compounds made up of only carbon and hydrogen. Heat is the result of this reaction. In addition, combustion chemical reactions are also a type of chemical redox reaction.
chemical decomposition reactions
In reality, chemical decomposition reactions are the exact opposite of combination reactions. In decomposition reactions, a single compound breaks down into two or more substances of a simpler nature, mostly compounds and/or elements.
Double displacement chemical reactions
Single displacement reactions involve the displacement of a single chemical species; However, in double displacement reactions, also called metathesis reactions, two species are displaced, usually ions.
Very often such chemical reactions take place in a solution, forming water (neutralization reactions) or an insoluble solid (precipitation reactions).
Chemical neutralization reactions
This is another type of chemical double displacement reaction that occurs between a base and an acid. This type of chemical double displacement reaction is called a neutralization reaction and it forms water. Examples for this are:
The mixture of sodium hydroxide (lye) and sulfuric acid (car battery acid) is a reaction that shows up as follows:
Chemical polymerization reactions
Polymerization is a process in which monomer molecules react with each other in a chemical reaction, resulting in the formation of polymer chains, also known as three-dimensional networks. There are numerous forms of polymerization, as well as different systems that categorize each of them. Examples for this are:
N.H.2C=CH2→ [-CH2CH2-]Norte
This equation represents the union of thousands of ethylene molecules resulting in polyethylene.
In both cellulose and starch, glucose molecules are joined with the simultaneous removal of one water molecule for each bond formed. An example of this is demonstrated as follows:
North Carolina6H12Ö6→ -[-C6H10Ö5-]-n + n2Ö
Precipitation chemical reactions
Mixing a silver nitrate solution with a potassium chloride solution gives an insoluble white. When an insoluble solid forms in solution, it is called a precipitate, and the insoluble white solid that forms is called silver chloride.
Redox chemical reactions
These reactions are also known as chemical oxidation-reduction reactions and involve the exchange of electrons.
These are also examples of other types of reactions, including combined, individual exchange, and combustion reactions, but they are all redox reactions. All involve the transfer of electrons from one chemical species to another.
Redox chemical reactions are also involved in oxidation, photosynthesis, combustion, batteries, respiration, and more.
chemical reactions with one turn
Simple displacement reactions occur when a more active element displaces or displaces a less active element from a compound. An example would be if you put some metallic zinc in a copper sulfate solution, the zinc will actually displace the copper.
In this equation, the notation (aq) means that the compound dissolves in water, which is an aqueous solution. Since zinc replaces copper in this case, it is considered more active. If you put a piece of copper in a zinc sulfate solution, nothing happens.
You can view more information about chemical reactions.on here.
Glossary of Algebraic Terms
Absolute value:It tells how far away a number is from 0.
Algebra:A type of mathematics that uses mathematical symbols and the rules for manipulating those symbols.
Associated law of addition:This states that for any three numbers a, b and c, the following always applies: (a+b)+c=a+(b+c)
Base:Raised number.
roof function:Ceiling(x) is the nearest integer greater than or equal to x.
Coefficient:This is a constant that is multiplied by an expression or variable.
Composition:The composition of two functions, f and g, is the function f∘g, which transforms x into f(g(x)).
Coordinates:A point on a two-dimensional plane is always described by a pair: (x, y). In this example, the x-coordinate is given by the labels below the grid and the y-coordinate is given by the labels to the left of the grid.
Kubikwurzel: The cube root of a, which is written as3a, is the number whose cube is a; in other words, (3a)3= a.
Data: A collection of related measures.
Domain:The set of inputs (x-coordinates) of a function or relation.
Equation:A mathematical theorem with an equals sign; for example 3x+5=11.
Exponent:In powers, it represents the number of times the base is multiplied by itself.
Expression:A combination of numbers and variables using arithmetic; for example 6x.
Factor:An expression that is, or can be, multiplied by another expression to produce a specific result.
Profession:A relation in which no x-coordinates occur in more than one ordered pair (x,y). In other words, think of a function as a transformation that takes each x-coordinate to its unique corresponding y-coordinate.
Inequality:This is a mathematical sequence using one of the following symbols: <, >, ≤, or ≥.
all:An integer or the negative of an integer; For example, 37 and 0 and -5 are integers, but 2.7 is not.
Isolate:That a variable appears alone on one side of the inequality or equation and does not appear on the other side of the inequality or equation.
Common frequency:This refers to the number of events that meet both parts of two specific criteria.
Board Relative Frequency:This is a joint frequency divided by the total number of events.
Monika:A polynomial whose first or leading coefficient is 1.
Monom:A product of numbers and variables; for example 3x or 5x2. It is also sometimes referred to as a term.
n-te Wurzel:An nth root of a is a number b raised to an nth power of a. In other words, b.Norte= a.
Origin:This is the point on a coordinate plane where the x-axis and y-axis intersect. It is always represented by coordinates (0,0).
Function defined by parts:This is a function defined by different formulas for different inputs.
Point:A point is a location on the coordinate plane. It has coordinates (x,y), where x is given by the labels below the coordinate grid and y by the labels to the left of a coordinate grid.
To get:A set of outputs, i. H. y-coordinates, a function or relationship.
Relationship:This term refers to a set of ordered pairs, ie (x,y).
Relative Frequency:A frequency divided by the total number of events. It is usually given as a percentage.
Sequence:A list of numbers that can be generated by a rule.
Define:An unordered collection of numbers or other objects of a mathematical nature with no repetitions.
Similar:Two geometric figures are considered similar if they have the same shape but possibly different sizes and corresponding lengths that differ by a single common scale factor.
Simplify:This refers to rewriting an expression so that it means the same thing but is shorter or simpler. For example, you can simply convert 3x-x+6 to 2x+6.
Tilt:This is a number that measures the slope of a line. Displays the change in height of a line as it moves one unit to the right. For example, the slope of the line y=mx+b is the letter m.
Incline cut shape:For a linear equation, the form y=mx+b, where b and m are constants. The numbers b and m indicate the slope and y-intercept of the line being graphed at that particular section.
Solution:For both inequalities and equations, the variable can be replaced with numbers to make that equation or inequality true. When the inequality equation contains more than one variable, a solution refers to a list of numbers that, when substituted for the list of variables, make the inequality or equation true. For systems with more than one inequality or equation, the solution must make all of the inequalities or equations true. A solution also refers to a liquid mixture in chemistry.
solution set:This refers to all solutions of the inequality, equation or system.
Resolution:Solving means finding solutions to an inequality, equation, or system.
Quadratwurzel:The square root of a is a number b whose square is a. In other words, b2=a. If b is a square root of a, then so is -b.
standard deviation:This term refers to the square root of the variance.
Standard form:In a linear equation, the form Ax+By=C, where A, B, and C are constants. For quadratic equations, the form ax2+bx+c=0 or the form y=ax2+bx+c, where a, b, and c are constants.
The statistics:A statistic is a number that describes or summarizes data.
The statistics:Statistics is the study of data; it also refers to the methods used to summarize or describe data.
step function:This refers to a function defined by parts, where the formula of each part is constant; that is, it does not change with x. In fact, the graph of a function looks like the rungs of a ladder.
Ersatz:This is the elimination of a variable in an equation or expression; This is done by replacing it with another expression that is the same.
System:For inequalities or equations, two or more are enough to be true.
low hill:A mathematical term that implies a rectangular arrangement of columns and rows.
Deadline:A term is an element in a difference, sum, or sequence.
Translation:Translation is a rigid motion over a constant distance that goes in only one direction; that is, without reflection or rotation.
Unit:This refers to a standard measurement; for example an hour or a meter.
Bravery:This refers to a number that can be matched by an expression or variable.
Variable:A letter (e.g. x) used to refer to different numbers at different times.
Variation:The mean square distance of the data values from their mean m. can be calculated by adding x(x-m)2 to each data value and then dividing by the number of data values n. When you measure samples from a population (e.g., people's height), the sample variance is often different from the variance of the entire population.
vertex:This is the point where a parabola crosses its axis of symmetry, or an endpoint on the side of a polygon, or even the vertex of an angle.