Maths-
General
Easy

Question

# Write recursive formula. -5,-8.5,-12,-15.5,-19,....

Hint:

## The correct answer is: a_n=a_(n-1)-3.5.

General
Maths-

### Write an equation of a line that passes through the given line and is perpendicular to the given line.

• We have to write an equation of a line that passes through the given line and is perpendicular to the given line.
Step 1 of 1:
We have to find a line passes through a point (-2, 5) and perpendicular to a line x = 3
Since product of two perpendicular lines is equal to -1.
So,

m × ∞ = -1
m = 0
Therefore the equation of the line will be

y - 5 = 0 (x + 2)
y = 5.

### Write an equation of a line that passes through the given line and is perpendicular to the given line.

Maths-General
• We have to write an equation of a line that passes through the given line and is perpendicular to the given line.
Step 1 of 1:
We have to find a line passes through a point (-2, 5) and perpendicular to a line x = 3
Since product of two perpendicular lines is equal to -1.
So,

m × ∞ = -1
m = 0
Therefore the equation of the line will be

y - 5 = 0 (x + 2)
y = 5.

General
Maths-

### Find the vertical and horizontal asymptotes of rational function, then graph the function.

1.Find the asymptotes of the rational function, if any.
2.Draw the asymptotes as dotted lines.
3.Find the
x -intercept (s) and y -intercept of the rational function, if any.
4.Find the values of y for several different values of x .
5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
2x + 1 = 0
x =
The vertical asymptote of the rational function is x =
We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is  x= and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = =0.5

### Find the vertical and horizontal asymptotes of rational function, then graph the function.

Maths-General
1.Find the asymptotes of the rational function, if any.
2.Draw the asymptotes as dotted lines.
3.Find the x -intercept (s) and y -intercept of the rational function, if any.
4.Find the values of y for several different values of x .
5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
2x + 1 = 0
x =
The vertical asymptote of the rational function is x =
We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is  x= and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = =0.5
General
Maths-

### Write recursive formula. 2,6,10,14,18,....

• We have given a sequence 2,6,10,14,18,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given a sequence 2,6,10,14,18,...
The given sequence is an AP
And we know the recursive formula of any AP is .
Where d is common difference.
Here the common difference is 4.
So, The recursive formula is

### Write recursive formula. 2,6,10,14,18,....

Maths-General
• We have given a sequence 2,6,10,14,18,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given a sequence 2,6,10,14,18,...
The given sequence is an AP
And we know the recursive formula of any AP is .
Where d is common difference.
Here the common difference is 4.
So, The recursive formula is

General
Maths-

### Write an equation of a line that passes through the given line and is perpendicular to the given line.

• We have to write an equation of a line that passes through the given line and is perpendicular to the given line.
Step 1 of 1:
We have to find a line passes through a point (0, 3) and perpendicular to a line 3x - 4y = -8
Since product of two perpendicular lines is equal to -1.
So,

Therefore the equation of the line will be

### Write an equation of a line that passes through the given line and is perpendicular to the given line.

Maths-General
• We have to write an equation of a line that passes through the given line and is perpendicular to the given line.
Step 1 of 1:
We have to find a line passes through a point (0, 3) and perpendicular to a line 3x - 4y = -8
Since product of two perpendicular lines is equal to -1.
So,

Therefore the equation of the line will be

General
Maths-

### Tell whether the given sequence is an arithmetic sequence. -6,5,16,27,38,....

• We have given a sequence -6,5,16,27,38,....
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence -6,5,16,27,38,....
The difference in first two terms is

Now the difference in next two terms is

Then, The difference between next two terms will be

Since the difference is constant
The given sequence is an arithmetic sequence.

### Tell whether the given sequence is an arithmetic sequence. -6,5,16,27,38,....

Maths-General
• We have given a sequence -6,5,16,27,38,....
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence -6,5,16,27,38,....
The difference in first two terms is

Now the difference in next two terms is

Then, The difference between next two terms will be

Since the difference is constant
The given sequence is an arithmetic sequence.

General
Maths-

### Tell whether the given sequence is an arithmetic sequence. 48,45,42,39,....

• We have given a sequence 48,45,42,39,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 48,45,42,39,...
The difference in first two terms is

Now the difference in next two terms is

Then, The difference between next two terms will be

Since the difference is constant
The given sequence is an arithmetic sequence.

### Tell whether the given sequence is an arithmetic sequence. 48,45,42,39,....

Maths-General
• We have given a sequence 48,45,42,39,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 48,45,42,39,...
The difference in first two terms is

Now the difference in next two terms is

Then, The difference between next two terms will be

Since the difference is constant
The given sequence is an arithmetic sequence.

General
Maths-

### Find the vertical and horizontal asymptotes of rational function, then graph the function.

1.Find the asymptotes of the rational function, if any.
2.Draw the asymptotes as dotted lines.
3.Find the
x -intercept (s) and y -intercept of the rational function, if any.
4.Find the values of y for several different values of x .
5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
x - 3 = 0
x = 3
The vertical asymptote of the rational function is x = 3
We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is  x = 3 and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = =1

### Find the vertical and horizontal asymptotes of rational function, then graph the function.

Maths-General
1.Find the asymptotes of the rational function, if any.
2.Draw the asymptotes as dotted lines.
3.Find the x -intercept (s) and y -intercept of the rational function, if any.
4.Find the values of y for several different values of x .
5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
x - 3 = 0
x = 3
The vertical asymptote of the rational function is x = 3
We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is  x = 3 and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = =1
General
Maths-

### Which sequence is an arithmetic sequence?

• We have given a sequence 1,3,5,7,11,....
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
Option(A):
We have given a sequence 1,3,5,7,11,....
The common difference here is not constant, as 3 - 1 ≠ 11 - 7
So, This is not an AP.
Option(B):
We have given a sequence 4,6,9,13,18,....
The common difference here is not constant, as 6 - 4 ≠ 9 - 6
So, This is not an AP.
Step 2 of 2:
Option(c):
We have given a sequence 8,15,22,29,36,....
The common difference here is constant.
So, This is an AP.
Option(D):
We have given a sequence 3,6,12,24,48,....
The common difference here is not constant, as 6 - 3 ≠ 12 - 6
So, This is not an AP.

### Which sequence is an arithmetic sequence?

Maths-General
• We have given a sequence 1,3,5,7,11,....
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
Option(A):
We have given a sequence 1,3,5,7,11,....
The common difference here is not constant, as 3 - 1 ≠ 11 - 7
So, This is not an AP.
Option(B):
We have given a sequence 4,6,9,13,18,....
The common difference here is not constant, as 6 - 4 ≠ 9 - 6
So, This is not an AP.
Step 2 of 2:
Option(c):
We have given a sequence 8,15,22,29,36,....
The common difference here is constant.
So, This is an AP.
Option(D):
We have given a sequence 3,6,12,24,48,....
The common difference here is not constant, as 6 - 3 ≠ 12 - 6
So, This is not an AP.
General
Maths-

### Write an equation of a line that passes through the given line and is perpendicular to the given line.

• We have to write an equation of a line that passes through the given line and is perpendicular to the given line.
Step 1 of 1:
We have to find a line passes through a point (-6, -3) and perpendicular to a line
Since product of two perpendicular lines is equal to -1.
So,

Therefore the equation of the line will be

.

### Write an equation of a line that passes through the given line and is perpendicular to the given line.

Maths-General
• We have to write an equation of a line that passes through the given line and is perpendicular to the given line.
Step 1 of 1:
We have to find a line passes through a point (-6, -3) and perpendicular to a line
Since product of two perpendicular lines is equal to -1.
So,

Therefore the equation of the line will be

.

General
Maths-

### When will the graph of a rational function have no vertical asymptotes ? Give an example of such a function.

For example, function f ( x ) = ​ has no vertical asymptote.

### When will the graph of a rational function have no vertical asymptotes ? Give an example of such a function.

Maths-General
• If both the polynomials have the same degree, divide the coefficients of the leading terms. This is your asymptote.
• If the degree of the numerator is less than the denominator, then the asymptote is located at y = 0 (which is the x-axis).
• If the degree of the numerator is greater than the denominator, then there is no vertical asymptote.

For example, function f ( x ) = ​ has no vertical asymptote.
General
Maths-

### Write an equation of a line that passes through the given line and is parallel to the given line.

• We have to write an equation of a line that passes through the given line and is parallel to the given line.
Step 1 of 1:
We have to find a line passes through a point (6, 4) and parallel to a line 2x + 3y = 18
Since two parallel lines have same slope.
So, Slope of the line will be
Therefore the equation of the line will be

### Write an equation of a line that passes through the given line and is parallel to the given line.

Maths-General
• We have to write an equation of a line that passes through the given line and is parallel to the given line.
Step 1 of 1:
We have to find a line passes through a point (6, 4) and parallel to a line 2x + 3y = 18
Since two parallel lines have same slope.
So, Slope of the line will be
Therefore the equation of the line will be

General
Maths-

### Asthon said the graph of  has a horizontal asymptote at  . Describe and correct Asthon's error.

1. Find the asymptotes of the rational function, if any.
2. Draw the asymptotes as dotted lines.
3. Find the x -intercept (s) and y -intercept of the rational function, if any.
4. Find the values of y for several different values of x .
5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
2x2 + 4x - 6= 0
x2 + 2x - 3= 0
x2 + 3x – x – 3 = 0
x(x + 3) – (x - 3) = 0
(x - 1) (x + 3) = 0
x = -3  or  x = = 1
The vertical asymptote of the rational function is x= 2.24 and x= -2.24  .
We will find more points on the function and graph the function.

the degree of the numerator is less than the denominator, then the horizontal asymptote is located at y = 0 (which is the x-axis).

### Asthon said the graph of  has a horizontal asymptote at  . Describe and correct Asthon's error.

Maths-General
1. Find the asymptotes of the rational function, if any.
2. Draw the asymptotes as dotted lines.
3. Find the x -intercept (s) and y -intercept of the rational function, if any.
4. Find the values of y for several different values of x .
5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.
The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .
2x2 + 4x - 6= 0
x2 + 2x - 3= 0
x2 + 3x – x – 3 = 0
x(x + 3) – (x - 3) = 0
(x - 1) (x + 3) = 0
x = -3  or  x = = 1
The vertical asymptote of the rational function is x= 2.24 and x= -2.24  .
We will find more points on the function and graph the function.

the degree of the numerator is less than the denominator, then the horizontal asymptote is located at y = 0 (which is the x-axis).
General
Maths-

### Write an equation of a line that passes through the given line and is parallel to the given line.

• We have to write an equation of a line that passes through the given line and is parallel to the given line.
Step 1 of 1:
We have to find a line passes through a point (-3, 2) and parallel to a line y = -4
Since two parallel lines have same slope.
So, Slope of the line will be 0
Therefore the equation of the line will be

y - 2 = 0 (x + 3)
y = 2

### Write an equation of a line that passes through the given line and is parallel to the given line.

Maths-General
• We have to write an equation of a line that passes through the given line and is parallel to the given line.
Step 1 of 1:
We have to find a line passes through a point (-3, 2) and parallel to a line y = -4
Since two parallel lines have same slope.
So, Slope of the line will be 0
Therefore the equation of the line will be

y - 2 = 0 (x + 3)
y = 2

General
Maths-

### Write recursive formula and find the first term.

• We have given a explicit function .
• We have to find the recursive formula and first term.
Step 1 of 2:
We have given explicit formula .
First term will be

Step 2 of 2:
Now for recursive formula we will calculate .
So,

### Write recursive formula and find the first term.

Maths-General
• We have given a explicit function .
• We have to find the recursive formula and first term.
Step 1 of 2:
We have given explicit formula .
First term will be

Step 2 of 2:
Now for recursive formula we will calculate .
So,

General
Maths-

### How can you graph a rational function ?

A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) =, where p(x) and q(x) are polynomials such that q(x) ≠ 0.
Rational functions are of the form y=f(x)y=fx , where f(x)fx is a
rational expression .
1. Find the asymptotes of the rational function, if any.
2. Draw the asymptotes as dotted lines.
3. Find the x -intercept (s) and y -intercept of the rational function, if any.
4. Find the values of y for several different values of x .
5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.

### How can you graph a rational function ?

Maths-General
A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) =, where p(x) and q(x) are polynomials such that q(x) ≠ 0.
Rational functions are of the form y=f(x)y=fx , where f(x)fx is a rational expression .
1. Find the asymptotes of the rational function, if any.
2. Draw the asymptotes as dotted lines.
3. Find the x -intercept (s) and y -intercept of the rational function, if any.
4. Find the values of y for several different values of x .
5. Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.