Match the reasons with the statements in the proof.
2 answers:
Answer:
Given: and
To prove that:
1. [Given]
Substitution property of equality says that:
If x = y, then x can be substituted in y, or y can be substituted in x.
2 [ By Substitution Property]
Alternate interior angles states that when two lines are crossed by transversal , a pair of angles on the inner sides of each of these two lines on the opposite sides of the transversal line.
3. and
are alternate interior angles [By definition Alternate interior angle].
Alternating interior angles theorem states that if two parallel lines are intersected by third lines, then the angles in the inner sides of the parallel lines on the opposite sides of the transversal are equal.
4. ; then the lines are parallel [By Alternate interior angles theorem]
Correct match is as follows:
1. [Given]
2. [Substitution]
3. and
are alternate interior angle [By definition of alternate interior angles ]
4. the lines are parallel [If alternate interior angles are equal]
You might be interested in
Option A) Is the answer. 
For this question; You are needed to expose yourselves to popular usages of radical rules. In this we distribute the squares as one-and-a-half fractions as the squares eliminate the square roots. So, as per the use of fraction conversion from roots. It becomes relatively easy to solve and finish the whole process more quicker than everyone else. More easier to remember.
Starting this with the equation editor interpreter for mathematical expressions, LaTeX. Use of different radical rules will be mentioned in between the steps.
Radical equation provided in this query.
Divide the numbered values of 900 and 100 by cancelling the zeroes to get "9" as the final product in the next step.
Imply and demonstrate the rule of radicals. In this context we will use the radical rule for fractions in which a fraction with a denominator of variable "a" representing a number or a variable, and the denominator of variable "b" representing a number or a variable are square rooted by a value of "n" where it can be a number, variable, etc. Here, the radical of "n" is distributed into the denominator as well as the numerator. Presuming the value of variable "a" and "b" to be greater than or equal to the value of zero. So, by mathematical expression it becomes:
![\boxed{\mathbf{Radical \: \: Rule: \sqrt[n]{\dfrac{a}{b}} = \dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}, \: \: a \geq 0 \: \: \: b \geq 0}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cmathbf%7BRadical%20%5C%3A%20%5C%3A%20Rule%3A%20%5Csqrt%5Bn%5D%7B%5Cdfrac%7Ba%7D%7Bb%7D%7D%20%3D%20%5Cdfrac%7B%5Csqrt%5Bn%5D%7Ba%7D%7D%7B%5Csqrt%5Bn%5D%7Bb%7D%7D%2C%20%5C%3A%20%5C%3A%20a%20%5Cgeq%200%20%5C%3A%20%5C%3A%20%5C%3A%20b%20%5Cgeq%200%7D%7D)
Apply the radical exponential rule. Here, the squar rooted value of radical "n" is enclosing another variable of "a" which is raised to a power of another variable of "m", all of them can represent numbers, variables, etc. They are then converted to a fractional power, that is, they are raised to an exponent as a fractional value with variables constituting "m" and "n", for numerator and denominator places, respectively. So:
![\boxed{\mathbf{Radical \: \: Rule: \sqrt[n]{a^m} = a^{\frac{m}{n}}, \: \: a \geq 0}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cmathbf%7BRadical%20%5C%3A%20%5C%3A%20Rule%3A%20%5Csqrt%5Bn%5D%7Ba%5Em%7D%20%3D%20a%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%7D%2C%20%5C%3A%20%5C%3A%20a%20%5Cgeq%200%7D%7D)
Exhibit the radical rule for two given variables in this current step to separate the variable values into two new squares of variables "a" and "b" with a radical value of "n". Variables "a" and "b" being greater than or equal to zero.
![\boxed{\mathbf{Radical \: \: Rule: \sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}, \: \: a \geq 0 \: \: \: b \geq 0}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cmathbf%7BRadical%20%5C%3A%20%5C%3A%20Rule%3A%20%5Csqrt%5Bn%5D%7Bab%7D%20%3D%20%5Csqrt%5Bn%5D%7Ba%7D%20%5Csqrt%5Bn%5D%7Bb%7D%2C%20%5C%3A%20%5C%3A%20a%20%5Cgeq%200%20%5C%3A%20%5C%3A%20%5C%3A%20b%20%5Cgeq%200%7D%7D)
So, the square roots are separated into root of 9 and a root of variable of "f" raised to the value of "6".
Just factor out the value of "3" as 3 × 3 and join them to a raised exponent as they are having are similar Base of "3", hence, powered to a value of "2".
The radical value of square root is similar to that of the exponent variable term inside the rooted enclosement. That is, similar exponential values. We apply the following radical rule for these cases for a radical value of variable "n" and an exponential value of "n" with a variable that is powered to it.
![\boxed{\mathbf{Radical \: \: Rule: \sqrt[n]{a^n} = a^{\frac{n}{n}} = a}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cmathbf%7BRadical%20%5C%3A%20%5C%3A%20Rule%3A%20%5Csqrt%5Bn%5D%7Ba%5En%7D%20%3D%20a%5E%7B%5Cfrac%7Bn%7D%7Bn%7D%7D%20%3D%20a%7D%7D)
Again, Apply the radical exponential rule. Here, the squar rooted value of radical "n" is enclosing another variable of "a" which is raised to a power of another variable of "m", all of them can represent numbers, variables, etc. They are then converted to a fractional power, that is, they are raised to an exponent as a fractional value with variables constituting "m" and "n", for numerator and denominator places, respectively. So:
Hope it helps.
For this question; You are needed to expose yourselves to popular usages of radical rules. In this we distribute the squares as one-and-a-half fractions as the squares eliminate the square roots. So, as per the use of fraction conversion from roots. It becomes relatively easy to solve and finish the whole process more quicker than everyone else. More easier to remember.
Starting this with the equation editor interpreter for mathematical expressions, LaTeX. Use of different radical rules will be mentioned in between the steps.
Radical equation provided in this query.
Divide the numbered values of 900 and 100 by cancelling the zeroes to get "9" as the final product in the next step.
Imply and demonstrate the rule of radicals. In this context we will use the radical rule for fractions in which a fraction with a denominator of variable "a" representing a number or a variable, and the denominator of variable "b" representing a number or a variable are square rooted by a value of "n" where it can be a number, variable, etc. Here, the radical of "n" is distributed into the denominator as well as the numerator. Presuming the value of variable "a" and "b" to be greater than or equal to the value of zero. So, by mathematical expression it becomes:
Apply the radical exponential rule. Here, the squar rooted value of radical "n" is enclosing another variable of "a" which is raised to a power of another variable of "m", all of them can represent numbers, variables, etc. They are then converted to a fractional power, that is, they are raised to an exponent as a fractional value with variables constituting "m" and "n", for numerator and denominator places, respectively. So:
Exhibit the radical rule for two given variables in this current step to separate the variable values into two new squares of variables "a" and "b" with a radical value of "n". Variables "a" and "b" being greater than or equal to zero.
So, the square roots are separated into root of 9 and a root of variable of "f" raised to the value of "6".
Just factor out the value of "3" as 3 × 3 and join them to a raised exponent as they are having are similar Base of "3", hence, powered to a value of "2".
The radical value of square root is similar to that of the exponent variable term inside the rooted enclosement. That is, similar exponential values. We apply the following radical rule for these cases for a radical value of variable "n" and an exponential value of "n" with a variable that is powered to it.
Again, Apply the radical exponential rule. Here, the squar rooted value of radical "n" is enclosing another variable of "a" which is raised to a power of another variable of "m", all of them can represent numbers, variables, etc. They are then converted to a fractional power, that is, they are raised to an exponent as a fractional value with variables constituting "m" and "n", for numerator and denominator places, respectively. So:
Hope it helps.
We have that the total length of paper needed to cover all the tables is
From the question we are told that:
Number of tables
Length of table
Extension
Generally, the equation for the Total length tables is mathematically given by
Therefore with an extension of 0.25ft at both end we have the Total length of tablecloths to be
In conclusion
The total length of paper needed to cover all the tables is
For more information on this visit
Answer:
Step-by-step explanation:
We have
this equals to
now we try to agrupate to have exponent of 2 that we can cancel
we can take out the ones with exponent from the root