Maths-
General
Easy

Question

Write explicit formula.

Hint:

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) =

General
Maths-

Write recursive formula and explicit formula. -15,-6,-3,12,21,...

• We have given a sequence -15,-6,-3,12,21,.....
• We have to find the recursive and explicit formula of the given sequence.
Step 1 of 2:
We have given a sequence -15,-6,-3,12,21,.....
The given sequence is an AP.
We know that the recursive formula for any AP is  , where d is common difference.
Here the common difference is 9
So, The recursive formula is

Step 2 of 2:
The given sequence is an AP.
So, The explicit formula will be

Write recursive formula and explicit formula. -15,-6,-3,12,21,...

Maths-General
• We have given a sequence -15,-6,-3,12,21,.....
• We have to find the recursive and explicit formula of the given sequence.
Step 1 of 2:
We have given a sequence -15,-6,-3,12,21,.....
The given sequence is an AP.
We know that the recursive formula for any AP is  , where d is common difference.
Here the common difference is 9
So, The recursive formula is

Step 2 of 2:
The given sequence is an AP.
So, The explicit formula will be

General
Maths-

The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is perpendicular to the north path.

• We have been given an equation that represents the north path on a map.
• We have to find an equation for a path that passes through the point (6, 3) and is perpendicular to the north path.
Step 1 of 1:
We have given 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

The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is perpendicular to the north path.

Maths-General
• We have been given an equation that represents the north path on a map.
• We have to find an equation for a path that passes through the point (6, 3) and is perpendicular to the north path.
Step 1 of 1:
We have given 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-

Write recursive formula and explicit formula. 62,57,52,47,42,...

• We have given a sequence 62,57,52,47,42,....
• We have to find the recursive and explicit formula of the given sequence.
Step 1 of 2:
We have given a sequence 62,57,52,47,42,....
The given sequence is an AP.
We know that the recursive formula for any AP is  , where d is common difference.
Here the common difference is -15
So, The recursive formula is

Step 2 of 2:
The given sequence is an AP.
So, The explicit formula will be

Write recursive formula and explicit formula. 62,57,52,47,42,...

Maths-General
• We have given a sequence 62,57,52,47,42,....
• We have to find the recursive and explicit formula of the given sequence.
Step 1 of 2:
We have given a sequence 62,57,52,47,42,....
The given sequence is an AP.
We know that the recursive formula for any AP is  , where d is common difference.
Here the common difference is -15
So, The recursive formula is

Step 2 of 2:
The given sequence is an AP.
So, The explicit formula will be

General
Maths-

Write recursive formula and explicit formula. -4, 5,14,23,32,...

Step 1 of 2:
We have given a sequence -4,5,14,23,32,...
The given sequence is an AP.
We know that the recursive formula for any AP is  , where d is common difference.
Here the common difference is 9
So, The recursive formula is

Step 2 of 2:
The given sequence is an AP.
So, The explicit formula will be

.

Write recursive formula and explicit formula. -4, 5,14,23,32,...

Maths-General
Step 1 of 2:
We have given a sequence -4,5,14,23,32,...
The given sequence is an AP.
We know that the recursive formula for any AP is  , where d is common difference.
Here the common difference is 9
So, The recursive formula is

Step 2 of 2:
The given sequence is an AP.
So, The explicit formula will be

.

General
Maths-

What are the vertical and horizontal asymptotes of the graph of 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 .
3x2 -12= 0
3x2 = 12
x2 = 4
x = -2  or  x = 2
The vertical asymptote of the rational function is x = −2 and x = 2
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= -2 and x = 2. and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) =

What are the vertical and horizontal asymptotes of the graph of 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 .
3x2 -12= 0
3x2 = 12
x2 = 4
x = -2  or  x = 2
The vertical asymptote of the rational function is x = −2 and x = 2
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= -2 and x = 2. and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) =
General
Maths-

The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is parallel to the north path.

• We have been given an equation that represents the north path on a map.
• We have to find an equation for a path that passes through the point (6, 3) and is perpendicular to the north path.
Step 1 of 1:
We have given a line passes through a point (6, 3) and parallel to a line y = 2x + 7
Since two parallel lines have same slope.
So, Slope of the line will be 2
Therefore the equation of the line will be

y - 3 = 2(x - 6)
y = 2x - 9

The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is parallel to the north path.

Maths-General
• We have been given an equation that represents the north path on a map.
• We have to find an equation for a path that passes through the point (6, 3) and is perpendicular to the north path.
Step 1 of 1:
We have given a line passes through a point (6, 3) and parallel to a line y = 2x + 7
Since two parallel lines have same slope.
So, Slope of the line will be 2
Therefore the equation of the line will be

y - 3 = 2(x - 6)
y = 2x - 9

General
Maths-

Write recursive formula and explicit formula. 12,19,26,33,40,...

• We have given a sequence 12,19,26,33,40,....
• We have to find the recursive and explicit formula of the given sequence.
Step 1 of 2:
We have given a sequence 12,19,26,33,40,....
The given sequence is an AP.
We know that the recursive formula for any AP is  , where d is common difference.
Here the common difference is 7
So, The recursive formula is

Step 2 of 2:
The given sequence is an AP.
So, The explicit formula will be

.

Write recursive formula and explicit formula. 12,19,26,33,40,...

Maths-General
• We have given a sequence 12,19,26,33,40,....
• We have to find the recursive and explicit formula of the given sequence.
Step 1 of 2:
We have given a sequence 12,19,26,33,40,....
The given sequence is an AP.
We know that the recursive formula for any AP is  , where d is common difference.
Here the common difference is 7
So, The recursive formula is

Step 2 of 2:
The given sequence is an AP.
So, The explicit formula will be

.