What is the equation of the slant asymptote of the rational function?
f(x)=10x3−15x2+x−15x2−2
Responses
y=x−3
y equals x minus 3
y=2x−115
y equals 2 x minus fraction 11 over 5
y=2x−3
y equals 2 x minus 3
y=x−115
y equals x minus fraction 11 over 5
Answers
Using division of polynomials, the equation of the slant asymptote of the rational function is given by:
y = 2x - 3.
How to find the slant asymptote of a rational function?Suppose a rational function given by a division of two functions, as follows:
r(x) = f(x)/g(x).
The slant asymptote of the function is nothing more than the quotient of functions f(x) and g(x), that is, the division of functions f(x) and g(x).
For this problem, the function is:
r(x) = (10x³ - 15x² + x - 1)/(5x² - 1).
Hence:
f(x) = 10x³ - 15x² + x - 1.g(x) = 5x² - 1.Using a calculator, the division of these two functions is:
y = 2x - 3 + (3x - 4)/(5x² - 1)
3x - 4 is the remainder, but we consider only the quotient, hence the equation of the slant asymptote of the rational function is given by:
y = 2x - 3.
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Related Questions
Which type of data cannot be sorted?
Answers
Answer:
credit card an bank information
medical history
medical history
how much is this quarter
Answers
Unfortunately it is still only 25c
If the temperature on the ground is 63F, then the air temperature x miles high is given by T=63−29x. Determine the altitudes at which the air temperature is less than 4.4F.
Answers
The temperature is less that 4.4 °F for altitudes greater than 2.021 miles high.
In which altitudes do we get a certain range of temperatures?
Herein we find that the temperature, in grades Fahrenheit, decreases linearly inasmuch as the altitude, in miles, increases. In accordance with the statement, we solve for T in the following inequality:
63 - 29 · x < 4.4
63 - 4.4 < 29 · x
58.6 < 29 · x
29 · x > 58.6
x > 2.021 mi
The temperature is less that 4.4 °F for altitudes greater than 2.021 miles high.
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How would you write 125/6^−4using a positive exponent?
Answers
Answer: 162000
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
162000
[tex]\displaystyle\\Answer:\ (\frac{6}{125})^4[/tex]
Step-by-step explanation:
[tex]\displaystyle\\(\frac{125}{6} )^{-4}=\\\\(\frac{6}{125})^{-(-4)}= \\\\(\frac{6}{125})^4[/tex]
100 points!
what is/are the function(s) graphed in the photo provided?
Answers
The interval(s) over which the function is decreasing is (-∞, -2) U (-2, -1) U (-1, 1) U (5, +∞)
What is graph?According to the given graph
the increasing points:
[1, 5]
and the decreasing are:
(-∞, -2) U (-2, -1) U (-1, 1) U (5, +∞)
The correct and complete question is:
Use the graph to answer the question. 1. Find the interval(s) over which the function is decreasing. (1 point)
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Question 1
The point (6, y) lies on the line
y = -8x + 2. Find y
Answers
Answer:
y=-50
Step-by-step explanation:
x=6
substitute x and u will find the answer
What is the correct classification for each given angle? Drag and drop the answer into the box to match each angle. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. ∠RQU ∠SQU ∠RQT Ray R Q and Ray Q T are connected at point Q 90 degrees apart from each other. Line VQS extends diagonally down to the up right at point Q and forms an interior angle labeled as 19 degrees and 71 degrees. Ray QU extends down to the right of the QT and forms an interior angle labeled as 18 degrees.
Answers
∠RQU is an obtuse angle.
∠SQU is an acute angle.
∠RQT is an right angle.
How to Classify Angles?A right angle equals 90 degrees.An acute angle is less than 90 degrees.An obtuse angle is less than 180 degrees but greater than 90 degrees.A straight angle equals 180 degrees.m∠RQU = 19 + 71 + 18 = 108°.
Therefore, ∠RQU is an obtuse angle.
m∠SQU = 71 + 18 = 89°
Therefore, ∠SQU is an acute angle.
m∠RQT = 71 + 19 = 90°
Therefore, ∠RQT is an right angle.
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Please help me with this question.
Answers
Answer:14m
Step-by-step explanation:
3 1/2 x 4= 14
Simplify -100 square rooted
Answers
Answer:
√-100 = 10 i
Step-by-step explanation:
√-100 = √100 × √-1
The square root of 100 is 10. Furthermore, the square root of negative 1 is an imaginary insignificant number (iota) which can be transliterated as i. That's it. Now, we have our answer to the square root of negative 100.
The table represents a funtion. which value is an output of the function?
A) -6
B) -2
C) 4
D) 7
Answers
Answer:
B
Step-by-step explanation:
f(x) = function
you can see -6, 4 and seven are the values of x, which is not a function. and -2 is value of f(x) which is a function
The midpoint of AB is M(0, -3)M(0,−3). If the coordinates of AA are (6, -5)(6,−5), what are the coordinates of BB?
Answers
Step-by-step explanation:
Mid point of AB is (0, -3)
Coordinate of A is (6, -5)
By using mid point formula, if P(x, y) and Q (x′, y′), then mid point of P= (x + x′)/2 , (y + y′)/2
So, ( 0, -3)= 6+x/2, -5+y/2
0=6+x/2
0=6+x, x = -6
and, -3= -5+y/2, -6= -5+y....
y = -1
so the coordinate is (-6, -1)
To find the midpoint of two points, we can use the following formula:
[tex]midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two endpointsSolving the QuestionWe're given:
AA = (6, -5)AB = (0, -3)BB = [tex](x_2,y_2)[/tex]Plug the information into the formula:
[tex]midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})\\\\(0,-3)=(\dfrac{6+x_2}{2},\dfrac{-5+y_2}{2})[/tex]
If [tex]\dfrac{6+x_2}{2}[/tex] must equal 0, then [tex]x_2[/tex] must be -6.
If [tex]\dfrac{-5+y_2}{2}[/tex] must equal -3, then [tex]-5+y_2[/tex] must equal -6, making [tex]y_2[/tex] equal to -1.
Therefore, BB is (-6,-1).
Answer(-6, -1)
Here are 4 triangles that have been transformed by a different transformation. Which transformation is a reflection? Can someone please help me with this
Answers
Answer:
choice 1 or A the first one
Step-by-step explanation:
Evaluate 5x, for x=9
Answers
Answer: 45
Step-by-step explanation:
1. Replace x with 9 in term. Replacing x with 9 turns the term 5x into 5(9).
2. Multiply. 5 times 9 = 45.
This means that if x is equal to nine, then 5x is equal to 45/
Find a degree 3 polynomial with real coefficients having zeros 2 and 4 i and a lead coefficient of 1. Write P in expanded form. Be sure to write the full equation, including P ( x ) =
Answers
The degree of the polynomial is a f(x)=x^3-2x^2+16x-32.
According to the statement
We have to find that the degree of the polynomial.
So, For this purpose, we know that the
The degree of a polynomial is the highest power of the variable in a polynomial expression.
From the given information:
with real coefficients having zeros 2 and 4 i and a lead coefficient of 1.
Then
We know that the complex zeros always occur in pairs.
zeros are 2,4i,-4i
f(x)=(x-2)(x-4i)(x+4i)
f(x)=(x-2)((x)^2-(4i)^2)
f(x)=(x-2)(x^2-16i^2)
f(x)=(x-2)(x^2+16)
f(x)=x^3-2x^2+16x-32.
So, The degree of the polynomial is a f(x)=x^3-2x^2+16x-32.
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The balance sheet of Pacific Ocean Resort reports total assets of $720,000 and $870,000 at the beginning and end of the year,
respectively. The return on assets for the year is 21%.
Calculate Pacific Ocean's net income for the year.
Net income
Answers
Based on the return on assets of 21%, the net income of Pacific Ocean Resort for year is $166,950
What is return on assets?
The return on assets for the company is determined as the net income divided by the average total assets of Pacific Ocean Resort , bearing in mind that the average total assets is sum of the beginning and ending assets divided by 2
return on assets=net income/average total assets
return on assets=21%
net income=unknown
average total assets=($720,000+$870,000)/2
average total assets=$795,000
21%=net income/$795,000
net income=$795,000*21%
net income=$166,950
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PERSEVERE The sum of 4 consecutive odd integers is equal to zero.
a. Write an equation to model the sentence. Let n = the first odd integer.
b. Solve the equation to find the numbers. Write the numbers from least to greatest. Check your solution.
n =
The numbers are _________ ,__________, and __________
Answers
1. The equation that models the sentence is 4n + 12 = 0.
2. The numbers from least to greatest are -3, -1, 1, 3.
What are integers?Integers are whole numbers. An integer a number without a fraction or decimal component. Integers can either be positive, negative or zero. An odd number is a number that cannot be divided perfectly into two halves. An example of odd numbers are -11, 21.
Consecutive odd numbers are whole numbers that follow each other on the number line. Consecutive odd numbers increase by 2. Examples of consecutive odd numbers are 7, 9, 11.
If 4 consecutive odd integers are: n, (n +2) (n + 4) , (n + 6)
n + n + 2 n + 4 + n + 6 = 0
4n + 12 = 0
4n = -12
n = -12 / 4
n = -3
The numbers are -3, -1, 1 , 3
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Austin mowed 8 lawns in 3 hours. At that rate, how long will it take him to mow 12 lawns?
Answers
Answer: 32 hours
Step-by-step explanation:
brain
You have a puzzle with 36 pieces. Using the number of puzzle pieces on an edge, please describe the
domain (possible side lengths) and range (possible area).
Answers
Answer:there are 4 possible edges and issa 6x6 puzzle
Step-by-step explanation: clarify question or add screen shot?
Delilah is making a garden that she wants to be 5 feet longer than it is wide. Write
the equation that Delilah should use to determine the width of a garden that has an
area of 50 square feet.
How wide and how long does Delilah need to make her garden to achieve the desired speciation?
Width =
Answers
The equation is 50 = (5 + w)w and the width is 5 and the length is 10
Write the equation that Delilah should use to determine the width of a garden that has an area of 50 square feet.The given parameters are
Area = 50
Length = 5 + Width
This means that
l = 5 + w
The area is calculated as
A = lw
Substitute l = 5 + w in A = lw
A = (5 + w)w
Substitute A = 50 in A = (5 + w)w
50 = (5 + w)w
Hence, the equation is 50 = (5 + w)w
How wide and how long does Delilah need to make her garden to achieve the desired speciation?We have
50 = (5 + w)w
Express 50 as 10 * 5
So, we have
10 * 5 = (5 + w)w
This means that
5 + w = 10
w = 5
Solve 5 + w = 10
w = 5
Substitute w = 5 in l = 5 + w
l = 5 + 5
l = 10
Hence, the width is 5 and the length is 10
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simplify 4/x+4 + x/x-4
A.Hint: Find the common denominator and then add.
Answers
The simplification of the given equation is (x² + 8x - 16)/(x-4)(x+4) by the method of LCM.
What is defined as the LCM?LCM is an abbreviation for least common multiple. The smallest number which is a multiple of both numbers is the least common multiple of them.For, the given equation;
4/(x+4) + (x/x-4)
To find the common denominator, use LCM; multiply a first term by (x-4)/(x-4) and the 2nd term by (x+4)/(x+4):
= (x-4)×4/(x-4)(x+4) + x×(x+4)/(x-4)(x+4)
The following step is to disperse the 4 (x-4) and x (x+4);
So you now have;
= (4x-16 + x² + 4x)/(x-4)(x+4)
Further simplify.
= (x² + 8x - 16)/(x-4)(x+4)
As, (x² + 8x - 16) is further not factor-able. So, the simplified form of the given equation is; (x² + 8x - 16)/(x-4)(x+4).
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The following table shows the average total cost, measured as dollars expended per pupil, of operating a high school with the given enrollment. This table is based on a study of economies of scale in high school operations from the 1960s.
Enrollment 170 250 450 650
Average total cost 539 482 421 415
What would you estimate for the average cost per student at an enrollment of 750 students? $
Answers
Using linear regression, the estimate for the average cost per student at an enrollment of 750 students is of $373.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points are given as follows:
(170, 539), (250, 482), (450, 421), (650, 415).
Inserting these points into the calculator, the function is:
y = -0.24733x + 558.23703.
When x = 750:
y = -0.24733(750) + 558.23703 = 373.
The estimate for the average cost per student at an enrollment of 750 students is of $373.
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A rectangle has a height of b^3+b^2b
3
+b
2
b, cubed, plus, b, squared and a width of b^2+7b+4b
2
+7b+4b, squared, plus, 7, b, plus, 4.
Answers
The area of the rectangle is equal to b² · (b + 1) · (b + 0.628) · (b + 6.372).
What is the area of the rectangle?
The area of the rectangle is equal to the product of the height and the width, each of them represented by polynomials. In this question we must apply algebraic handling to simplify the product of the two polynomials:
A = h · w (1)
Where:
h - Heightw - WidthIf we know that h = b³ + b² and w = b² + 7 · b + 4, then the area of the rectangle is:
A = (b³ + b²) · (b² + 7 · b + 4)
A = b² · (b + 1) · (b + 0.628) · (b + 6.372)
The area of the rectangle is equal to b² · (b + 1) · (b + 0.628) · (b + 6.372).
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What is the value of x? URGENT
Answers
Step-by-step explanation:
If you check by inspection there are two sides which are equal. The triangle is considered an Isosceles Triangles where two sides amd angles are equal.
The two base angles are equal=x°
38°+x°+x°=180°
2(x°)=180°-38°
2x°=142°
x=71°
A taxi service charges you $1.25 plus $0.75 per mile
driven to the airport. The total cost of the trip to the
airport was $12.50. How many miles was the trip to the
airport?
19 miles
17 miles
13 miles
15 miles
11 miles
Answers
Determine the mass in (g) of 2.6x10-3 mol Na2So4
Answers
Answer:
0.36933g or 0.3693g in 2.6 x 10^-3 moles of Na2SO4
Step-by-step explanation:
Molar mass
Na = 22.99
S = 32.07
O = 16
Na(2) + S + O(4) =
22.99(2) + 32.07 + 16(4) =
45.98 + 32.07 + 64 = 142.05g
Na2SO4 = 142.05g
2.6 x 10^-3 moles = 0.0026 moles
0.0026 x 142.05 = 0.36933
The profit, in dollars, a company makes selling a new line of iPhones is given by the
equation P(x) = −0.03x^2 + 225x − 24000, where x is the number of iPhones sold.
a) Find the instantaneous rate of change of the profit at x = 1000 iPhones sold.
b) Interpret your result.
Answers
The instantaneous rate of change is the change in the concentration of rate that occurs at a particular point of time. The variation in the derivative values at a particular point denotes the instantaneous rate of change. The instantaneous rate of change at a point is the value of derivative function evaluated at that point.
P(x) = −0.03x^2 + 225x − 24000
To find the instantaneous rate of change we need to differentiate the equation with respect to x
P'(x) = -0.06x +225
at x =0
P'(0)= 225
now put x = 1000 because we need to know instantaneous rate of change of the profit at x = 1000 iPhones sold
P'(1000) = -0.06(1000) + 225
= -60 + 225
= 165
Hence, the instantaneous rate of change of the profit at x = 1000 iPhones sold is 165
This means that the increase in sales also increase the profit but at a decreasing rate or the marginal profit of iPhones increases with decreasing rates
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10) 2−(n+2) >-(7 + n) + 7
Answers
Answer:
This is a false statement so there is no solution.
Step-by-step explanation:
2-(n+2) > -(7 +n) + 7
2 -n -2 > -7 -n + 7
-n > -n This cannot be true, so there is not solution.
Answer:
No solutions
Step-by-step explanation:
2-(n+2) > -(7+n)+7 Distribute the -1 to both parentheses
2 - n - 2 > -7 - n + 7 Simplify values (2 - 2; -7 + 7)
-n > -n Add n to both sides
No solutions (There are no solutions because when the equation simplifies, there are no variables and values left)
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What is the minium value of the function g (x) = x^2 - 6x - 12?
Answers
The minimum value of the function is = -12
The function g(x) is defined for integers x such that if x is even, g(x) = x/2 and if x is odd, g(x) = x + 5.
given that , g(x)= x^2 - 6x - 12
asked to find minimum value
to get minimum value of g(x) put x=0
on putting x=0 ,the value of x^2 becomes 0
the value of 6x also becomes 0
so the equation g(0) becomes 0-0-12
g(0)= -12
on putting x=0 we get g(0) as -12 which is its minimum value
we get minimum value for g(x) when x=0
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Answer:
The function's minimum value is -12.
Step-by-step explanation:
Integers x are used to define the function g(x), and it is defined so that if x is even, g(x) = x/2 and if x is odd, g(x) = x + 5.
Considering, g(x)=x2 - 6x - 12
requested to determine the minimal value
Put x=0 to obtain the minimal value of g(x).
When x=0 is entered, the value of x2 is changed to 0.
6x's value is also reduced to 0.
so the equation g(0) becomes 0-0-12
g(0)= -12
on putting x=0 we get g(0) as -12 which is its minimum value
we get minimum value for g(x) when x=0
fifteen less than the product of twenty-three and 2.8
Answers
(23 * 2.8) - 15
23 * 2.8 = 64.4
64.4 - 15 = 49.4
Calculate and interpret the residual for the flower that had 2 tablespoons of sugar and looked fresh for 204 hours.
Answers
The Residual is -8.4 hours and the interpretation of the given residual is that the carnation stayed fresh for 8.4 hours less than expected based on how much sugar it received.
How to find the residual of a scatter plot?A residual plot is a type of scatter plot where the horizontal axis represents the independent variable, or input variable of the data, and the vertical axis represents the residual values.
Now, looking at the given residual plot and using a calculator online, we can say that the equation of the least squares regression line is;
y^ = 180.8 + 15.2x
Now, for 2 tablespoons of sugar , we have x = 2. Thus;
y^ = 180.8 + 15.2(2)
y^ = 212.4 hours
Residual for 204 hours is;
Residual = 204 - 212.4 = -8.4 hours
Thus, the interpretation of the given residual is that the carnation stayed fresh for 8.4 hours less than expected based on how much sugar it received.
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Complete question is;
Does adding sugar to the water in a vase help flowers stay fresh? To find out, two statistics students went to a flower shop and randomly selected 12 carnations. When they got home, the students prepared 12 identical vases with exactly the same amount of water in each vase. They put one tablespoon of sugarin 3 vases, two tablespoons of sugar in 3 vases, and three tablespoons of sugar in 3 vases.In the remaining 3 vases, they put no sugar. After the vases were prepared, the students randomly assigned 1 carnation to each vase and observed how many hours each flower continued to look fresh.
Calculate and interpret the residual for the flower that had 2 tablespoons of sugar and looked fresh for 204 hours.
