Maths-
General
Easy

Question

# Write recursive formula and find the first term.

Hint:

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

General
Maths-

### Are graphs of the equations parallel, perpendicular or neither?

• We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.
Step 1 of 1:
We have given two equations

y = 4x + 1
y = -4x - 2
Slope of both lines are 4, -4 respectively
Since slope are not equal then both are not parallel.
Product of both slope is 4 × -4 = -16
So, both are not perpendicular also.
So,
Both are nor parallel neither perpendicular.

### Are graphs of the equations parallel, perpendicular or neither?

Maths-General
• We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.
Step 1 of 1:
We have given two equations

y = 4x + 1
y = -4x - 2
Slope of both lines are 4, -4 respectively
Since slope are not equal then both are not parallel.
Product of both slope is 4 × -4 = -16
So, both are not perpendicular also.
So,
Both are nor parallel neither perpendicular.

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-

### Are graphs of the equations parallel, perpendicular or neither?

• We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.
Step 1 of 1:
We have given two equations

x - 3y = 6
x - 3y = 9
Slope of both lines are  respectively
Since slope are  equal then both are parallel.

### Are graphs of the equations parallel, perpendicular or neither?

Maths-General
• We have been given two equations in the question for which we have to tell are graphs of the equations parallel, perpendicular or neither.
Step 1 of 1:
We have given two equations

x - 3y = 6
x - 3y = 9
Slope of both lines are  respectively
Since slope are  equal then both are parallel.

General
Maths-

### What is the graph of

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 .
x2 + 2x - 15= 0
x2 + 5x -3x - 15= 0
x(x + 5) - 3 (x + 5) = 0
(x – 3) (x + 5) = 0
x – 3 = 0   or    x + 5 = 0
x = 3   or   x = -5
The vertical asymptote of the rational function is x = 3 and x = -5  .
This function has the x - intercept at (1.667,0) and y -intercept at (0,1) . We will find more points on the function and graph the function.

### What is the graph of

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 .
x2 + 2x - 15= 0
x2 + 5x -3x - 15= 0
x(x + 5) - 3 (x + 5) = 0
(x – 3) (x + 5) = 0
x – 3 = 0   or    x + 5 = 0
x = 3   or   x = -5
The vertical asymptote of the rational function is x = 3 and x = -5  .
This function has the x - intercept at (1.667,0) and y -intercept at (0,1) . We will find more points on the function and graph the function.

General
Maths-

### Find the equation for a path that passes through the point (-4, 9) and is parallel to .

• We have been given an equation that represents y-axis.
• We have to find an equation for a path that passes through the point (-4,9) and is perpendicular to
Step 1 of 1:
We have given a line passes through a point (-4, 9) and parallel to a line
Since two parallel lines have same slope.
So, Slope of the line will be
Therefore the equation of the line will be

### Find the equation for a path that passes through the point (-4, 9) and is parallel to .

Maths-General
• We have been given an equation that represents y-axis.
• We have to find an equation for a path that passes through the point (-4,9) and is perpendicular to
Step 1 of 1:
We have given a line passes through a point (-4, 9) and parallel to a line
Since two parallel lines have same slope.
So, Slope of the line will be
Therefore the equation of the line will be

General
Maths-

### Write explicit formula.

• We have given
• We have to find the explicit formula of the given sequence.
Step 1 of 1:
We know that the recursive formula of an AP is , where d is common difference.
Here we have
So, d = -7
Also, We have a1 = -3
So, The explicit formula will be

.

### Write explicit formula.

Maths-General
• We have given
• We have to find the explicit formula of the given sequence.
Step 1 of 1:
We know that the recursive formula of an AP is , where d is common difference.
Here we have
So, d = -7
Also, We have a1 = -3
So, The explicit formula will be

.

General
Maths-

### Write explicit formula.

• We have given
• We have to find the explicit formula of the given sequence.
Step 1 of 1:
We know that the recursive formula of an AP is , where d is common difference.
Here we have
So, d = 1
Also, We have a1 = 12
So, The explicit formula will be

### Write explicit formula.

Maths-General
• We have given
• We have to find the explicit formula of the given sequence.
Step 1 of 1:
We know that the recursive formula of an AP is , where d is common difference.
Here we have
So, d = 1
Also, We have a1 = 12
So, The explicit formula will be

General
Maths-

### Write explicit formula.

• We have given
• We have to find the explicit formula of the given sequence.
Step 1 of 1:
We know that the recursive formula of an AP is , where d is common difference.
Here we have
So, d = -21
Also, We have a1 = 56
So, The explicit formula will be

### Write explicit formula.

Maths-General
• We have given
• We have to find the explicit formula of the given sequence.
Step 1 of 1:
We know that the recursive formula of an AP is , where d is common difference.
Here we have
So, d = -21
Also, We have a1 = 56
So, The explicit formula will be

General
Maths-

### Graph each function

Hint :-
Solution:-
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 - 1= 0
x = 1
The vertical asymptote of the rational function is x= 1
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 = 1 and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = =3

### Graph each function

Maths-General
Hint :-
Solution:-
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 - 1= 0
x = 1
The vertical asymptote of the rational function is x= 1
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 = 1 and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = =3
General
Maths-

### Find the equation for a path that passes through the point (6, 6) and is perpendicular to .

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

Therefore the equation of the line will be

### Find the equation for a path that passes through the point (6, 6) and is perpendicular to .

Maths-General
• We have been given an equation that represents y-axis.
• We have to find an equation for a path that passes through the point (6, 6) and is perpendicular to
Step 1 of 1:
We have given a line passes through a point (6, 6) 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-

### Write explicit formula.

• We have given
• We have to find the explicit formula of the given sequence.
Step 1 of 1:
We know that the recursive formula of an AP is , where d is common difference.
Here we have
So, d = -2
Also, We have
So, The explicit formula will be

### Write explicit formula.

Maths-General
• We have given
• We have to find the explicit formula of the given sequence.
Step 1 of 1:
We know that the recursive formula of an AP is , where d is common difference.
Here we have
So, d = -2
Also, We have
So, The explicit formula will be

General
Maths-

### Write explicit formula.

• We have given
• We have to find the explicit formula of the given sequence.
Step 1 of 1:
We know that the recursive formula of an AP is , where d is common difference.
Here we have
So, d = 6
Also, We have a1 = 9
So, The explicit formula will be

### Write explicit formula.

Maths-General
• We have given
• We have to find the explicit formula of the given sequence.
Step 1 of 1:
We know that the recursive formula of an AP is , where d is common difference.
Here we have
So, d = 6
Also, We have a1 = 9
So, The explicit formula will be

General
Maths-

### Write explicit formula.

• We have given
• We have to find the explicit formula of the given sequence.
Step 1 of 1:
We know that the recursive formula of an AP is , where d is common difference.
Here we have
So, d = 15
Also, We have a1 = 8
So, The explicit formula will be

### Write explicit formula.

Maths-General
• We have given
• We have to find the explicit formula of the given sequence.
Step 1 of 1:
We know that the recursive formula of an AP is , where d is common difference.
Here we have
So, d = 15
Also, We have a1 = 8
So, The explicit formula will be

General
Maths-

### Graph each 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 + 8= 0
x = -8
The vertical asymptote of the rational function is x=-8
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= -8 and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = = 4

### Graph each 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 + 8= 0
x = -8
The vertical asymptote of the rational function is x=-8
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= -8 and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = = 4
General
Maths-

### What is the graph of 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 .
3x - 4= 0
3x = 4
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) =

### What is the graph of 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 .
3x - 4= 0
3x = 4
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) =