Answer:

Step-by-step explanation:
We need to first simplify the expression using rationalization(i.e. if a square root term exists in the denominator, then multiply and divide the whole expression by the denominator(but the change the sign of its middle term))
here, we need to find:

first we'll rationalize our expression:





this is our simplified expression, now we can apply our limits:




the limit does exists and it is 2.
Answer:

Step-by-step explanation:
Hello!
Use the distributive property and multiply like terms.
<h3>Simplify</h3>
The simplified form is
.
Answer:
Option c, A square matrix
Step-by-step explanation:
Given system of linear equations are



Now to find the type of matrix can be formed by using this system
of equations
From the given system of linear equations we can form a matrix
Let A be a matrix
A matrix can be written by
A=co-efficient of x of 1st linear equation co-efficient of y of 1st linear equation constant of 1st terms linear equation
co-efficient of x of 2st linear equation co-efficient of y of 2st linear equation constant of 2st terms linear equation
co-efficient of x of 3st linear equation co-efficient of y of 3st linear equation constant of 3st terms linear equation 
which is a
matrix.
Therefore A can be written as
A= ![\left[\begin{array}{lll}3&-2&-2\\7&3&26\\-1&-11&46\end{array}\right] 3\times 3](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Blll%7D3%26-2%26-2%5C%5C7%263%2626%5C%5C-1%26-11%2646%5Cend%7Barray%7D%5Cright%5D%203%5Ctimes%203)
Matrix "A" is a
matrix so that it has 3 rows and 3 columns
A square matrix has equal rows and equal columns
Since matrix "A" has equal rows and columns Therefore it must be a square matrix
Therefore the given system of linear equation forms a square matrix
Answer:
41 years old.
Step-by-step explanation:
Let x represent age of younger child.
We have been given that a mother has two children whose ages differ by 5 years. So the age of older child would be
.
The sum of the squares of their ages is 97. We can represent this information in an equation as:

Let us solve for x.



Divide both sides by 2:






Since age cannot be negative, therefore, age of younger child is 4 years.
Age of older child would be 
Therefore, the age of older child would be 9 years.
We have been given that the square of the mother's age can be found by writing the squares of the children's ages one after the other as a four-digit number.
Square of 4: 
Square of 9:
.
Square of mother's age: 
To find mother's age, we need to take positive square root of 1681 as:

Therefore, the mother is 41 years old.
F(2)= 4(16) - 6(4) + 8(2) - 15
F(2)= 64 -24 + 16 - 15
F(2)= 41