Maths-
General
Easy

Question

# After the first raffle drawing 497 tickets remain. After the second raffle drawing, 494 tickets remain. Assuming that the pattern continues, write an explicit formula for arithmetic sequence to represent the number of raffle tickets that remain after each drawing. How many tickets remain in the bag after the seventh raffle drawing?

Hint:

## The correct answer is: a_n=479.

General
Maths-

### Use long division to rewrite each rational function, What are the asymptotes of  f ? 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 + 4= 0
x = -4
The vertical asymptote of the rational function is x= -4
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= -4 and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = =2

### Use long division to rewrite each rational function, What are the asymptotes of  f ? 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 + 4= 0
x = -4
The vertical asymptote of the rational function is x= -4
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= -4 and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = =2
General
Maths-

### In a trail map, the equation y =  represents the Tamiami Trail. Choose the equation for a perpendicular trail.

• We have been given the trail map equation of y-axis in the question.
• We have to choose the equation for a perpendicular trail from the given four options.
Step 1 of 1:
We have given an equation
We have to find equation of line which is perpendicular to given line
Its slope is equal to given line.
So, it is parallel not perpendicular.

### In a trail map, the equation y =  represents the Tamiami Trail. Choose the equation for a perpendicular trail.

Maths-General
• We have been given the trail map equation of y-axis in the question.
• We have to choose the equation for a perpendicular trail from the given four options.
Step 1 of 1:
We have given an equation
We have to find equation of line which is perpendicular to given line
Its slope is equal to given line.
So, it is parallel not perpendicular.
General
Maths-

### A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Graph the sequence for the first 5 rows.

• A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it
• We have to find the graph of the sequence for the first 5 rows
Step 1 of 1:
Here it will be an AP, with first term 14 and common difference 2.
So, The explicit formula will be

Now the graph will be

### A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Graph the sequence for the first 5 rows.

Maths-General
• A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it
• We have to find the graph of the sequence for the first 5 rows
Step 1 of 1:
Here it will be an AP, with first term 14 and common difference 2.
So, The explicit formula will be

Now the graph will be

General
Maths-

### Juanita is trying to determine the vertical and horizontal asymptotes for the graph of  the function  . Describe and correct the error Juanita made in determining the vertical and horizontal 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 – x - 12= 0
x2 – 4x + 3x - 12= 0
x(x - 4) + 3(x - 4) = 0
(x - 4)(x + 3)
x = -3 and x =4
The vertical asymptote of the rational function is x= -3 and x= 4
horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = =1
Juanita has taken the horizontal asymptote as y = -4 is an error in her calculation.

### Juanita is trying to determine the vertical and horizontal asymptotes for the graph of  the function  . Describe and correct the error Juanita made in determining the vertical and horizontal 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 – x - 12= 0
x2 – 4x + 3x - 12= 0
x(x - 4) + 3(x - 4) = 0
(x - 4)(x + 3)
x = -3 and x =4
The vertical asymptote of the rational function is x= -3 and x= 4
horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = =1
Juanita has taken the horizontal asymptote as y = -4 is an error in her calculation.
General
Maths-

### A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Write an explicit  formula to represent the number of chairs in the nth row.

• A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it
• We have to find the explicit formula to represent the number of chairs in the nth row.
Step 1 of 1:
Here it will be an AP, with first term 14 and common difference 2.
So, The explicit formula will be

### A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Write an explicit  formula to represent the number of chairs in the nth row.

Maths-General
• A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it
• We have to find the explicit formula to represent the number of chairs in the nth row.
Step 1 of 1:
Here it will be an AP, with first term 14 and common difference 2.
So, The explicit formula will be

General
Maths-

### A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Write a recursive formula to represent the number of chairs in the nth row.

• A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it
• We have to find the recursive formula to represent the number of chairs in the nth row.
Step 1 of 1:
Here it will be an AP, with common difference 2.
So, The recursive formula will be

### A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Write a recursive formula to represent the number of chairs in the nth row.

Maths-General
• A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it
• We have to find the recursive formula to represent the number of chairs in the nth row.
Step 1 of 1:
Here it will be an AP, with common difference 2.
So, The recursive formula will be

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

Slope of both lines are  respectively
Since slope are not equal then both are not parallel.
Product of both slope is
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

Slope of both lines are  respectively
Since slope are not equal then both are not parallel.
Product of both slope is
So, both are not perpendicular also.
So,
Both are nor parallel neither perpendicular.

General
Maths-

### Casey opened a saving account with a 50 deposit. For every month after the first month she deposits 25. Write an explicit rule to represent the amount of money being deposited in her account. How much money will Casey have in her account after 24 months?

• We have given Casey opened a saving account with \$50 deposit. For every month after the first month she deposits \$25.
• We have to find the explicit rule to represent the amount of money and total amount after 24 months.
Step 1 of 2:
In the first month \$50 deposited and after that every month \$25 will deposits.
So, This will form an AP.
So, The explicit form will be

Step 2 of 2:
After 24 months the amount will be

### Casey opened a saving account with a 50 deposit. For every month after the first month she deposits 25. Write an explicit rule to represent the amount of money being deposited in her account. How much money will Casey have in her account after 24 months?

Maths-General
• We have given Casey opened a saving account with \$50 deposit. For every month after the first month she deposits \$25.
• We have to find the explicit rule to represent the amount of money and total amount after 24 months.
Step 1 of 2:
In the first month \$50 deposited and after that every month \$25 will deposits.
So, This will form an AP.
So, The explicit form will be

Step 2 of 2:
After 24 months the amount will be

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 = 4
y = 4
One line is parallel to y-axis and another line is parallel to x-axis
So, Both are 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

x = 4
y = 4
One line is parallel to y-axis and another line is parallel to x-axis
So, Both are perpendicular.

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 =

y = -3
Slope of both lines are 0,0 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

y =

y = -3
Slope of both lines are 0,0 respectively
Since slope are equal then both are parallel.

General
Maths-

### What is the horizontal asymptote of the 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 .
• 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 horizontal asymptote.
For the given function both the polynomials have the same degree, divide the coefficients of the leading terms.
y = a / d

### What is the horizontal asymptote of the 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 .
• 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 horizontal asymptote.
For the given function both the polynomials have the same degree, divide the coefficients of the leading terms.
y = a / d
General
Maths-

### Are graphs of the equations parallel, perpendicular or neither?y = 2x + 1; 2x - y = 3

• 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 = 2x + 1
2x - y = 3
Slope of both lines are 2, 2 respectively
Since slope are equal then both are parallel.

### Are graphs of the equations parallel, perpendicular or neither?y = 2x + 1; 2x - y = 3

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 = 2x + 1
2x - y = 3
Slope of both lines are 2, 2 respectively
Since slope are equal then both are parallel.

General
Maths-

### A Trainer mixed water with an electrolyte solution. Container is having 12 gal of 25%  electrolyte solution. The Concentration of electrolytes can be modelled by  , 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 + 12= 0
x = -12
The vertical asymptote of the rational function is x= -12
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= -4 and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = =2

### A Trainer mixed water with an electrolyte solution. Container is having 12 gal of 25%  electrolyte solution. The Concentration of electrolytes can be modelled by  , 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 + 12= 0
x = -12
The vertical asymptote of the rational function is x= -12
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= -4 and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = =2
General
Maths-

### Find the 12th term. -8, -5.5 , -3, -0.5, 2.0,....

• We have given a sequence -8, -5.5, -3, -0.5, 2.0,...
• We have to find weather the given sequence is AP or not
Step 1 of 1:
We have given a sequence -8, -5.5, -3, -0.5, 2.0,...
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 3.5.
So, The recursive formula is

### Find the 12th term. -8, -5.5 , -3, -0.5, 2.0,....

Maths-General
• We have given a sequence -8, -5.5, -3, -0.5, 2.0,...
• We have to find weather the given sequence is AP or not
Step 1 of 1:
We have given a sequence -8, -5.5, -3, -0.5, 2.0,...
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 3.5.
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 (4, 3) and perpendicular to a line 4x - 5y = 30
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 (4, 3) and perpendicular to a line 4x - 5y = 30
Since product of two perpendicular lines is equal to -1.
So,

Therefore the equation of the line will be