The solution to fill the blank in the statement so that the resulting statement is true. The statement in which we have to fill the blank is "The degree of the monomial $-18{x}^{4}{y}^{2}$ is ___________________"

sjeikdom0
2021-08-21
Answered

The solution to fill the blank in the statement so that the resulting statement is true. The statement in which we have to fill the blank is "The degree of the monomial $-18{x}^{4}{y}^{2}$ is ___________________"

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SabadisO

Answered 2021-08-22
Author has **108** answers

Given:

Fill in the blank of the statement "The degree of the monomial$-18{x}^{4}{y}^{2}$ is ____" so that the resulting statement is true.

Algebraic expressions are created by combining numbers and variables using arithmetic operations such as addition, subtraction, multiplication, division, and exponentiation. Using these mathematical operations, we can create an expression called a polynomial.

A polynomial is a sum of or difference of terms, each consisting of a variable rose to a nonnegative integer power. A polynomial which contains only one term is called Monomial, polynomial which contains two terms is called Binomial, and a polynomial which contains three terms is called Trinomial.

A polynomial is a sum of monomials where each monomial is called a term. It is usually written with the term with the highest exponent of the variable first and then decreasing from left to right. The first term of a polynomial is called the leading coefficient. The number term of a polynomial which is not multiplied by a variable is called a constant.

The basic building block of a polynomial is a monomial. A monomial is one term which can be a number, a variable, or the product of a number and variables with an exponent. The number part of the term is called the coefficient. The coefficient can be any real number, including 0. Exponent of the variable must be a whole number. We should keep in mind that a monomial cannot have a variable in the denominator or a negative exponent. The value of the exponent is the degree of a monomial. We should also consider that a variable that appears to have no exponent really has an exponent of 1 and a monomial with no variable has a degree of 0.

In a monomial of the form$a{x}^{m}{y}^{n}$ , a is the coefficient of the monomial and $m+n$ be the degree of the monomial.

There by the given momonial$-18{x}^{4}{y}^{2}$ , the degree of monomial is $6(4+2)$

Conclusion:

The degree of the monomial$-18{x}^{4}{y}^{2}$ is 6.

Fill in the blank of the statement "The degree of the monomial

Algebraic expressions are created by combining numbers and variables using arithmetic operations such as addition, subtraction, multiplication, division, and exponentiation. Using these mathematical operations, we can create an expression called a polynomial.

A polynomial is a sum of or difference of terms, each consisting of a variable rose to a nonnegative integer power. A polynomial which contains only one term is called Monomial, polynomial which contains two terms is called Binomial, and a polynomial which contains three terms is called Trinomial.

A polynomial is a sum of monomials where each monomial is called a term. It is usually written with the term with the highest exponent of the variable first and then decreasing from left to right. The first term of a polynomial is called the leading coefficient. The number term of a polynomial which is not multiplied by a variable is called a constant.

The basic building block of a polynomial is a monomial. A monomial is one term which can be a number, a variable, or the product of a number and variables with an exponent. The number part of the term is called the coefficient. The coefficient can be any real number, including 0. Exponent of the variable must be a whole number. We should keep in mind that a monomial cannot have a variable in the denominator or a negative exponent. The value of the exponent is the degree of a monomial. We should also consider that a variable that appears to have no exponent really has an exponent of 1 and a monomial with no variable has a degree of 0.

In a monomial of the form

There by the given momonial

Conclusion:

The degree of the monomial

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Why do logarithms produce such difficult problems

This was inspired by Fun logarithm question, because it made me remember a question I accidentally asked on a quiz some time ago. It was suppose to have both log bases the same, 3 or 5.

${\mathrm{log}}_{5}(x+3)=1-{\mathrm{log}}_{3}(x-1)$

After apologizing to my students, I talked to some people about it and we could not find an analytical solution... other than to realize that $x=2$ is a solution by just trying it. So, my questions are: Is there an analytical solution to this specific problem? And, more importantly, why do variables in exponents/logarithms that are seemingly easy to state produce such difficult problems? I would like some insight into the second question more than the first, as answering the second will also answer the first, I think.

This was inspired by Fun logarithm question, because it made me remember a question I accidentally asked on a quiz some time ago. It was suppose to have both log bases the same, 3 or 5.

${\mathrm{log}}_{5}(x+3)=1-{\mathrm{log}}_{3}(x-1)$

After apologizing to my students, I talked to some people about it and we could not find an analytical solution... other than to realize that $x=2$ is a solution by just trying it. So, my questions are: Is there an analytical solution to this specific problem? And, more importantly, why do variables in exponents/logarithms that are seemingly easy to state produce such difficult problems? I would like some insight into the second question more than the first, as answering the second will also answer the first, I think.