Maths-
General
Easy

Question

Write a recursive formula for the given sequence. 47, 39, 31, 23, 15, ....

Hint:

The correct answer is: a_n=a_(n-1)-8.

General
Maths-

Write a recursive formula for the given sequence. 81,85,89,93,97,....

Explanation:
• We have given a sequence 81,85,89,93,97,...
• We have to find the recursive formula.
Step 1 of 1:
We have given a sequence 81,85,89,93,97,...
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 4
So, The recursive formula is

Write a recursive formula for the given sequence. 81,85,89,93,97,....

Maths-General
Explanation:
• We have given a sequence 81,85,89,93,97,...
• We have to find the recursive formula.
Step 1 of 1:
We have given a sequence 81,85,89,93,97,...
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 4
So, The recursive formula is

General
Maths-

Write a recursive formula for the given sequence. 81,85,89,93,97,....

Explanation:
• We have given a sequence 4,7,10,14,..
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 4,7,10,14,...
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 not constant
The given sequence is not an arithmetic sequence.

Write a recursive formula for the given sequence. 81,85,89,93,97,....

Maths-General
Explanation:
• We have given a sequence 4,7,10,14,..
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 4,7,10,14,...
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 not constant
The given sequence is not an arithmetic sequence.
General
Maths-

How do you find vertical and horizontal asymptotes of a rational function? What are the vertical asymptotes for 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 +7x + 12 = 0
x2 + 3x + 4x + 12 = 0
x(x + 3) + 4 (x + 3) = 0
(x + 3)(x + 4)=0
x= -3  or  x = -4
The vertical asymptote of the rational function is x=−3 and x=-4
This function has no x -intercept at (4,0) and y -intercept at (0,7) . 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 x = -4.

How do you find vertical and horizontal asymptotes of a rational function? What are the vertical asymptotes for 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 +7x + 12 = 0
x2 + 3x + 4x + 12 = 0
x(x + 3) + 4 (x + 3) = 0
(x + 3)(x + 4)=0
x= -3  or  x = -4
The vertical asymptote of the rational function is x=−3 and x=-4
This function has no x -intercept at (4,0) and y -intercept at (0,7) . 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 x = -4.
General
Maths-

Tell whether the given sequence is an arithmetic sequence. 15,13,11,9,....

• We have given a sequence 15,13,11,9,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 15,13,11,9,...
The difference in first two terms is

Now the difference in next two terms is

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

Tell whether the given sequence is an arithmetic sequence. 15,13,11,9,....

Maths-General
• We have given a sequence 15,13,11,9,...
• We have to find weather the given sequence is AP or not.
Step 1 of 1:
We have given sequence 15,13,11,9,...
The difference in first two terms is

Now the difference in next two terms is

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

General
Maths-

Write an explicit formula for the arithmetic sequence.an = 12 - 5n

• We have given an explicit formula an = 12 - 5n
• We have to find the recursive formula
Step 1 of 1:
We have given a explicit formula an = 12 - 5n

Now,

So, The recursive formula is .

Write an explicit formula for the arithmetic sequence.an = 12 - 5n

Maths-General
• We have given an explicit formula an = 12 - 5n
• We have to find the recursive formula
Step 1 of 1:
We have given a explicit formula an = 12 - 5n

Now,

So, The recursive formula is .

General
Maths-

Write an explicit formula for the arithmetic sequence.an = 8 + 3n

• We have given an explicit formula an = 8 + 3n
• We have to find the recursive formula
Step 1 of 1:
We have given a explicit formula an = 8 + 3n

Now,

So, The recursive formula is .

Write an explicit formula for the arithmetic sequence.an = 8 + 3n

Maths-General
• We have given an explicit formula an = 8 + 3n
• We have to find the recursive formula
Step 1 of 1:
We have given a explicit formula an = 8 + 3n

Now,

So, The recursive formula is .

General
Maths-

Use long Division to rewrite each rational function. Find the asymptotes of  and sketch the graph.

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 - 6= 0
x = 6
The vertical asymptote of the rational function is x= 6
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= 6 and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = =1

Use long Division to rewrite each rational function. Find the asymptotes of  and sketch the graph.

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 - 6= 0
x = 6
The vertical asymptote of the rational function is x= 6
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= 6 and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = =1
General
Maths-

Write an explicit formula for the arithmetic sequence.

• We have given  and
• We have to find the explicit formula for this AP.
Step 1 of 1:
We know that the common difference d is also equal to
Now in given question we have
Ie,

And a1 = -1
So, The explicit formula will be

Write an explicit formula for the arithmetic sequence.

Maths-General
• We have given  and
• We have to find the explicit formula for this AP.
Step 1 of 1:
We know that the common difference d is also equal to
Now in given question we have
Ie,

And a1 = -1
So, The explicit formula will be

General
Maths-

Write an explicit formula for the arithmetic sequence.

• We have given an = an - 1 - 3 and a1 = 10
• We have to find the explicit formula for this AP.
Step 1 of 1:
We know that the common difference d is also equal to
Now in given question we have
Ie,

And a1 = 10
So, The explicit formula will be

Write an explicit formula for the arithmetic sequence.

Maths-General
• We have given an = an - 1 - 3 and a1 = 10
• We have to find the explicit formula for this AP.
Step 1 of 1:
We know that the common difference d is also equal to
Now in given question we have
Ie,

And a1 = 10
So, The explicit formula will be

General
Maths-

Use long Division to rewrite each rational function. Find the asymptotes of  and sketch the graph.

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) = =3

Use long Division to rewrite each rational function. Find the asymptotes of  and sketch the graph.

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) = =3
General
Maths-

The cost to rent a bike is 28 for the first day plus 2 for each day after that. Write an explicit formula for the rental cost for n days. What is the cost of renting a bike for 8 days?

• We have given a cost of rent of bike 28 for the first day plus2 for each day after that.
• We have to write an explicit formula for the rental cost for n days and cost of renting bike for 8 days.
Step 1 of 2:
We have given first day cost is 28 and for each more day 2 will be charged
Here

a1 = 28

d = 2
We know that general formula is an = a1 + (n - 1)d
So,

Step 2 of 2:
Now, Cost of renting for 8 days will be

The cost to rent a bike is 28 for the first day plus 2 for each day after that. Write an explicit formula for the rental cost for n days. What is the cost of renting a bike for 8 days?

Maths-General
• We have given a cost of rent of bike 28 for the first day plus2 for each day after that.
• We have to write an explicit formula for the rental cost for n days and cost of renting bike for 8 days.
Step 1 of 2:
We have given first day cost is 28 and for each more day 2 will be charged
Here

a1 = 28

d = 2
We know that general formula is an = a1 + (n - 1)d
So,

Step 2 of 2:
Now, Cost of renting for 8 days will be

General
Maths-

The daily attendance at an amusement park after day x is given by the functionf(x) =.      On Approximately which day will the attendance be 1125 people ?

We have given the equation of the daily attendance at an amusement park after day x
F(x) =
We have to find on which day attendance will be 1125
y = f(x) = 1125

x = -1.001   or x= 0.999

The daily attendance at an amusement park after day x is given by the functionf(x) =.      On Approximately which day will the attendance be 1125 people ?

Maths-General
We have given the equation of the daily attendance at an amusement park after day x
F(x) =
We have to find on which day attendance will be 1125
y = f(x) = 1125

x = -1.001   or x= 0.999
General
Maths-

Graph each function and identify the horizontal and vertical asymptotes

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 .
4x2 -25 = 0
4x2 = 25
x2 =
x =  and    x =
The vertical asymptote of the rational function is x=−1.
This function has no x -intercept at (4,0) and y -intercept at (0,7) . 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) = = 0.75.

Graph each function and identify the horizontal and vertical asymptotes

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 .
4x2 -25 = 0
4x2 = 25
x2 =
x =  and    x =
The vertical asymptote of the rational function is x=−1.
This function has no x -intercept at (4,0) and y -intercept at (0,7) . 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) = = 0.75.
General
Maths-

Graph each function and identify the horizontal and vertical asymptotes

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 + 1= 0
x2 +x + x + 1= 0
x(x + 1) + 1 (x + 1) = 0
(x + 1) (x + 1) = 0
x + 1 = 0   or    x + 1 = 0
x = -1
The vertical asymptote of the rational function is x=−1.
This function has no x -intercept  and y -intercept at (0,7) . 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 degree of the numerator is greater than the denominator, then there is no horizontal asymptote.

Graph each function and identify the horizontal and vertical asymptotes

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 + 1= 0
x2 +x + x + 1= 0
x(x + 1) + 1 (x + 1) = 0
(x + 1) (x + 1) = 0
x + 1 = 0   or    x + 1 = 0
x = -1
The vertical asymptote of the rational function is x=−1.
This function has no x -intercept  and y -intercept at (0,7) . 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 degree of the numerator is greater than the denominator, then there is no horizontal asymptote.
General
Maths-

Write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of y = 2x + 3

• We have to write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of 𝑦 = 2𝑥 + 3.
Step 1 of 1:
We have to find a line passes through a point (4, 5) and perpendicular to a line 𝑦 = 2𝑥 + 3.
Since product of two perpendicular lines is equal to -1.
So,

Therefore the equation of the line will be

Write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of y = 2x + 3

Maths-General
• We have to write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of 𝑦 = 2𝑥 + 3.
Step 1 of 1:
We have to find a line passes through a point (4, 5) and perpendicular to a line 𝑦 = 2𝑥 + 3.
Since product of two perpendicular lines is equal to -1.
So,

Therefore the equation of the line will be