Answers
The asymptotes for the given function are y = 1 and x = 4 respectively.
What is an asymptote?An asymptote to any function can be defined as a line that touches the graph of the function as the coordinates of the graph approaches infinity.
[tex]\lim_{x \to \infty}[/tex]The given function is R(x) = (x² - 25)/(x² - 8x + 16)
Since, the given function is not defined at x² - 8x + 16 = 0.
The values of x can be found as below,
x² - 8x + 16 = 0
⇒ (x - 4)² = 0
⇒ x = 4
Now, [tex]\lim_{x \to \ 4}} R(x)[/tex] = [tex]\lim_{x \to \ 4}[/tex] (x² - 25)/(x² - 8x + 16)
= -9/0
= -∞
Hence, at x = 4 the function has a y asymptote.
Again, in order to find x asymptotes compute the following limit,
[tex]\lim_{x \to \infty} R(x)[/tex] = [tex]\lim_{x \to \infty}[/tex] (x² - 25)/(x² - 8x + 16)
Apply L' Hospital rule to get,
[tex]\lim_{x \to \infty}[/tex] (x² - 25)/(x² - 8x + 16) = [tex]\lim_{x \to \infty}[/tex] 2x/ (2x - 8)
⇒ [tex]\lim_{x \to \infty}[/tex] 2/2 = 1
Thus, the x asymptote of the function is at y = 1.
Hence, the horizontal and vertical asymptotes of the given function are y = 1 and x = 4 respectively.
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Related Questions
Nick has two pet rabbits.His Flemish giant rabbit weighs 5 times as much as his Holland lop rabbit,If nich's Flemish rabbit weighs 12 more pounds than his Holland lop rabbit,how much does his Flemish giant rabbit weight?
Answers
Answer:The Flemish giant rabbit weighs 32 pounds.
Step-by-step explanation:
If a and b are any real numbers such that 0 < a < 1 < b, which of the following must be true of the value of ab ?
O. 0 < ab < a
O. 0 < ab < 1
O. a < ab < 1
O a < ab < b
O. b < ab
Answers
Therefore , the solution of the given problem comes out to be that one statement is true other than else are false.
What is inequality?In mathematics, inequalities describe the connection between two variables that are not equal. Equal implies to be equal, not. The "not equal symbol ()" is typically used to indicate that two values are not equaivalent. But different inequalities are used to compare the data to see if one is more or less than the other.
Here,
0 < a<1<b
Multiply all terms by b since b>1
0 < ab < b < [tex]b^{2}[/tex]
Since
b > 1 , then ab > a so then ,
0 < a<ab < b < [tex]b^{2}[/tex]
Given that,
F. 0< ab<a, Never true
G. 0< ab<1, Not always true
H. a< ab<1, Not always true
J. a< ab<b, True
K. b< ab, Never true
Therefore , the solution of the given problem comes out to be that one statement is true other than else are false.
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What is 0.00862 rounded to 2 significant figures?
Answers
Answer:
0.0086
Step-by-step explanation:
PLEASE HELP WILL MAKR BRAINLIEST! Solve for y!!
Answers
Answer:
Below
Step-by-step explanation:
All of the angles are the same (their opposite sides are =)....it is an equilateral triangle
all of the angles sum to 180°
each angle is then 60°
5y+10 = 60
5y = 50
y = 10 °
Ma Baker's Pies charges $12 for a pumpkin pie and $14 for an apple pie. Last week, they sold a third as many pumpkin pies as apple pies, for a total of $5,400. How many pumpkin pies were sold last week?
20 POINTS!!!!
Answers
The Ancient Egyptians were the first to invent a dish close to what we know as a pie today. They had a honey filling covered in a crusty cake made from oats,
Who was the first American author of a recipe for pumpkin pie?This type of pie appears to have been made by some of the early colonists as well—but, by 1796, when Amelia Simmons' American Cookery, the first cookbook written by an American and published in America, appeared, pumpkin pie had evolved into a familiar form that we would recognize today.The cost of one apple pie = $6They stewed pumpkins or filled a hollowed out pumpkin shell with milk, honey and spices, and then baked it in hot ashes. Northeastern Native American tribes grew squash and pumpkins. The Native Americans brought pumpkins as gifts to the first settlers, and taught them the many uses for pumpkin.Types of squashes were first introduced to Europe in the form of Pumpkin seeds brought back from the Americas by Columbus himself. The introduction of pumpkins affected the way food was consumed in Europe. In both Italy and Spain, pumpkins were used in puddings and soups, making food much tastier and more enjoyable.And cost of one pumpkin pie = $8
Let the cost of one apple pie be $x
And cost of one pumpkin pie be $ y.
According to given problem,
For Lisa : sold 8 apple pies and 4 pumpkin pies for a total of $80
8x + 4y = 80 ------------(1)
For Shreya : sold 8 apple pies and 3 pumpkin pies for a total of $72
8x + 3y = 72 ---------------(2)
Solving equation (1) and (2), to get x and y.
Subtract equation (2) from equation (1)
i.e 8x + 4y - (8x +3y) = 80 - 72
or 8x - 8x + 4y - 3y = 8
or y = 8
And x = 6 { 8x + 4×8 = 80 or x = (80 - 32)/8 = 48/8 = 6 }
Hence, the cost of one apple pie = x = $6
And cost of one pumpkin pie = y =$8
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a car and a motorcycle leave at noon from the same location, heading in the same direction. the average speed of the car is mph slower than twice the speed of the motorcycle. in two hours, the car is miles ahead of the motorcycle. find the speed of both the car and the motorcycle, in miles per hour.
Answers
The speed of car is 50 miles per hour and the speed of the motorcycle is 40 miles per hour.
Let M = speed of the motorcycle.
Hence, speed of the car = 2M - 30.
Distance covered = Time taken x Speed.
Hence in 2 hours,
Distance covered by motorcycle = 2M
Distance covered by car = 2(2M-30).
Given, the car is 20 miles ahead of the motorcycle.
Hence,
2(2M-30) = 2M + 20
4M-60 = 2M + 20
2M = 80
M = 40
2M-30 = 2(40)-30 = 80-30 = 50
Therefore, speed of motorcycle is 40 miles per hour and speed of car is 50 miles per hour.
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In an exhibition, the cost of tickets for an adult is ₹5 more than thrice the cost of ticket for a child. Which equation relates the cost, , of adult ticket in terms of the cost, , of child ticket?
Answers
In an exhibition, the cost of tickets for an adult is 5 more than thrice the cost o f ticket for a child.
What is equation?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
Equation relates the cost, y, of adult ticket in terms of the cost, x, of child ticket.
Cost of Adult ticket = y
cost of child ticket = x
cost of tickets for an adult is 5 more than thrice the cost o f ticket for a child.
=> cost of tickets for an adult = 5 + 3 (cost o f ticket for a child.)
=> y = 5 + 3x
=> y = 3x + 5
Equation is y = 3x + 5
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Try it #3
Pls help!
Answers
Find the biggest common factor between the ratio's two terms to write the ratio in its simplest form. The largest number that equally divides both numbers is known as the greatest common factor of two numbers.
How do you express a ratio in its simplest form?1 : 1/2 = 2 : 1
Add whole numbers to the values.
Create a fraction with the full number 1 as the denominator.
Next, we have:
1 : 1/2 = 1/1 : 1/2
Remove the denominators from fractions to convert them to integers.
We discover the Least Common Denominator and rewrite our two fractions as necessary using the common denominator because our two fractions have unlike denominators.
1 1/3 : 4 4/7 = 7 : 24
There are now:
1 1/3 : 4 4/7 = 4/3 : 32/7
Remove the denominators from fractions to convert them to integers.
We discover the Least Common Denominator and rewrite our two fractions as necessary using the common denominator because our two fractions have unlike denominators.
0.360 : 0.153 = 40 : 17
Add whole numbers to the values.
By multiplying both sides by 103 = 1000 to remove all three decimal places, you can convert any decimal values to integers.
Next, we have:
0.360 : 0.153 = 360 : 153
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Which equation is linear?
-3
O y = 2+4
O y = 4x³ - 10
Oy= 3x (x - 2)
0y = 2-5
4
Answers
x + 3, 2x+ 5, 65x + 57
Quadratic equation with x^2
Cubic with x^3.
Now you can identify the equation easily, remember option c is not linear
3x(x-2) = 3x^2 - 6x it is quadratic
suppose the random variable, x, is distributed normal with mean 4 and standard deviation 1.37. suppose the probability that x is less than the value x is equal to 0.8907, that is, p(x0.8907. what is x?
Answers
Since the probability is less than equal to 0.8907, then the value of x is 0.9750.
Given, the random variable is from of a normal distribution with
μ = 4 and σ = 1.37
.where, μ is the mean value and σ is the standard deviation.
According to the Question:
P(X≤8.907) = P( X−μ/σ ≤ 0.8907 - 4.00/ 1.37)
= P ( Z ≤ -29196.43)
Using Z-table we get a value of x which is 0.9750
So,
P(X ≤ 0.8907) = 97.50%
According to the calculations, the required value of x is 97.50%.
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A rectangular room has an area of 352 square feet. The length of the room is 6
feet more than the width of the room. Find the length and width of the room, in feet,
and separate them with a comma.
Answers
Solving a system of equations we can see that the length is 22 feet and the width is 16 feet.
How to find the length and the width?
For a rectangle of length L and width W, the area is given by the formula:
A = L*W
Here we know that the rectangular room has an area of 352 square feet, and we also know that the length of the room is 6 feet mroe than the width of the room, then we can write a system of equations:
352 = L*W
L = W + 6
To solve that system, we can substitute the second equation in the first one, we will get:
352 = (W + 6)* W
352 = W^2 + 6W
W^2 + 6W - 352 = 0
So we have a quadratic equation, the solutions give:
[tex]W = \frac{-6 \pm \sqrt{6^2 - 4*1*(-352)} }{2} \\\\W = \frac{-6 \pm 38 }{2}[/tex]
We take the positive value as the with, so:
W = (-6 + 38)/2
W = 16
And the length is 6 feet longer than that, so:
L = 16 + 6 = 22
Then the length is 22 feet, and the width is 16 feet.
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suppose that a product is designed to function for 10,000 hours with a 3% chance of failure. find the average number of failures per hour and the mttf.
Answers
A product is designed to function for 10,000 hours with a 3% chance of failure , then Average number of failures per hour = 0.03/10000 = 0.000003 and MTTF = 1/0.000003 = 333,333 hours
Given,
Chance Product is designed to function for 10,000 hours
of failure is 3%
To find,
Average number of failures per hour
MTTF
Solution,
Average number of failures per hour = Chance of failure/Total hours of function
= 3%/10000
= 0.03/10000
= 0.000003
MTTF = 1/Average number of failures per hour
= 1/0.000003
= 333,333 hours
The product is designed to function for 10,000 hours with a 3% chance of failure. This means that the average number of failures per hour is 0.000003 and the Mean Time To Failure (MTTF) is 333,333 hours. This means that, on average, the product should last 333,333 hours before it fails.
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Water is flowing into a tank at a rate of R(t) where t is measured in seconds. Is there ever a time where the R'(t) = 0? If so, what time interval does t occur in? Justify your answer using the Mean Value Theorem. t R(t) 0 70 1 72 2 78 3 80 4 83 5 78 6 82
Answers
On solving the provided question, we can say that - by equation, total amount of water removed was = 1.R(0) + 2.R(1) + 3.R(3) = 1(1340) + 2(1190) + 3(950) + 2(740) = 8050 liters
What is equation?An equation is a mathematical formula that expresses equality by joining two expressions together with the equal symbol =. A formula that claims two formulae are equal is the definition of an equation in algebra in its most basic form. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. An equal sign is a part of all mathematical formulas, including equations. Often, algebra is used in equations. In mathematics, algebra is employed when we don't know the precise quantity to calculate.
R'(2) = R(3) - R(1) /3-1 = 950-1190/2 = /120L/hr
total amount of water removed was = 1.R(0) + 2.R(1) + 3.R(3) = 1(1340) + 2(1190) + 3(950) + 2(740) = 8050 liters
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yes Are these polygons congruent? 1.5 cm 4 cm 3 cm no 2 cm
Answers
This is because in order to be congruent, the sides need to be the same lengths
When solving an equation, Tina gets to the last of line of her work and is left with "7=7." What does this mean?
A
The solution is 7.
B
There is infinite solutions.
C
There is only one solution.
D
There is no solution.
Answers
The last line of a solution is 7 = 7. It means there is infinite solutions.
What are types of solution of linear equation?
The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all feasible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.
The set of linear equations can have one of three different sorts of solutions. As follows:
1) unique solution
2) No solution
3) Infinite solutions
Given that the last line after solving an equation is 7 = 7.
Since the LHS and RHS of the equation is same thus it has infinite many solution.
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A cereal box says that now it contains 20% more originally it came with 18.5 ounces of cereal how much cereal does the box come with now
Answers
Answer:
Step-by-step explanation:
Step-by-step explanation: the original weight of a cereals is ounces. Now according to question, new weight of cereals is more of original weight of cereals. Therefore, New weight of cereals will be formulated as Hence, the new weight of cereals is ounces.
k3-4j=12,wen k =8,j=2
Answers
With the Application of Arithmetic operators the value of given equation is 492.
what is Arithmetic operators?
an operator that works with groups and numbers in arithmetic. The prefix and the binary plus (+) and minus (-) symbols are the only arithmetic operators in AHDL that are supported for Boolean expressions.
solution:
sub k =8,j=2 in equation k^3-4j = 12
Therefore, (8)^3 - 4 (2) = 12
512 - 8 - 12 = 0
492 is the value.
Therefore the value of given equation is 492
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Complete Question:
What Is The Answer
k3 - 4j +12, when k=8, j=2
Which equation is represented by the graph below
Answers
Answer: pls show list of equations
Step-by-step explanation:
Given the equation f + 24 = −3, solve for f. NEED HELP ASAAPPPPPPPP I WILL GIVE BRAINLY IF THE QUESTION IS RIGHT!!
−72
−27
−21
8
Answers
Answer: -27
Step-by-step explanation:
To solve for x, we have to make f alone.
f+24=-3 [subtract both sides by 24]
f=-27
The answer is -27.
Answer: -27
Step-by-step explanation: f+24+-3 to find f subtract 24 from -3. which equals -27 it might not be the proper way but it works. :)
Need help and fast please and thank you.
y= 0.141(15) + 0.842 =
Answers
y = 2.115 + 0.842
= 2.957
no explanation
Please help asap ill give brainlest
Answers
The solutions to the equation word problems are as follows;
1) Amount jane will have is 50 + 2d
2) Amount Elis will have = 24 + 6d
3) The equation is; 50 + 2d = 24 + 6d
4) Amount each has saved = $63
How to solve Algebra Word Problems?We are given that;
Amount Jane has = $50
Amount Elis has = $24
Amount saved by Jane each day = $2
Amount saved by Elis each day = $6
1) After d days of saving, amount jane will have is;
A = 50 + 2d
2) After d days of saving, amount Elis will have is;
A = 24 + 6d
3) The equation that will be used to show when Joan and Elis would have saved same amount is;
50 + 2d = 24 + 6d
4) 50 + 2d = 24 + 6d
26 = 4d
d = 26/4
d = 6.5 days
Amount each has saved = 50 + 2(6.5) = $63
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write an equation in slope-intercept form for the line that passes through (9,12) and is parallel to y=4
Answers
An equation in slope-intercept form for the line that passes through (9,12) and is parallel to y=4 is y= 4x -24.
What is Parallel lines?
Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.
Parallel lines will have the same slope but different y-intercepts so again we can use the coordinates to determine the y intercept of the new equation.
So we know that the slope intercept formula is y=mx + b where m is the slope and b is the y-intercept so we will input the x and y coordinates to solve for b.
12 = 4(9) + b
12 = 36 + b
b = -24
The equation will be y= 4x -24.
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Calculate the surface area of a sphere with a diameter of 28
Answers
Answer:
The surface area of a sphere is 2461.76 units.
Step-by-step explanation:
Given;Diameter (d) of a sphere = 28 unitsTo Find;Area of SphereFormula;A = 4 π r²where,
π = 3.14 or 22/7
r = radius of sphere
Here, we know that
radius = diameter ÷ 2 = 28/2 = 14 units
So,
A = 4 π r²
A = 4 × 3.14 × (14)² units
A = 12.56 × 196 units
A = 2461.76 units
Thus, The surface area of a sphere is 2461.76 units.
Answer: the surface area of the sphere of diameter 28cm is 2464 cm²
Step-by-step explanation:
Given, diameter = 28 cm
hence, radius of the sphere = d/2 = 28/2 =14 cm
Therefore, the surface area of a sphere of radius (r) = 4пr²
where п= 22/7= 3.14
= 4×3.14×14×14
= 2464 cm²
solve for x. pls helppp
Answers
The value of x is 12 .
Given ,
angle DEH as exterior angle and angle E, C, D as interior angles .
What is the relation between interior & exterior angles of a triangle ?
Interior angle refer to all those angles that are inside a shape. On the other hand, the exterior angle is an angle that is made by the side of the shape and a line drawn out from an adjacent side.
Furthermore, the exterior angle is equal to the sum of the non-adjacent interior angles .
Calculations
angle DEH = angle C + angle D
9x + 22 = 5x + 10 + 60
9x - 5x = 70 - 22
4x = 48
x = 12
The value of x is 12 .
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Tommy is flying his kite one afternoon and notices that he has let out
the entire 130 ft of string. The angle his string makes with the ground
is 48°. How high, to the nearest foot, is his kite at this time?
Answers
If Tommy is flying his kite one afternoon and notices that he has let out
the entire 130 ft of string. The height , to the nearest foot, is his kite at this time is : 144 ft.
How to find the height?Given data:
String = 130 ft
Angle = 48°
Let h represent the height
Hence,
Tan48° = h/130
h= 130 tan48°
h = 130 (1.11061251483)
h = 144 ft
Therefore we can conclude that the height is 144ft.
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Identify the slope and y-intercept of each linear function's equation. X -3=4 slope = 1; y-intercept at -3 y=1-3x slope =-3; y-intercept at 1 y = 3x. - 1 slope =-1; y-intercept at 3 -x+3=y slope = 3; y-intercept at -1
Answers
Using slope-intercept form, the slope and y-intercept of the equation are 1 and - 7 respectively
Slope and Y-interceptThe slope-intercept formula is often used to calculate or identify the slope, the y-intercept, the x-intercept, or the equation of a straight line in the equation.
The slope of the line is defined as the rate of change of the y - axis to the change in the x - axis.
The formula is represented as;
m = Δy / Δx
where Δ represent the change
The y-intercept of a line is the point at which the line touches the y-axis of the graph.
With these information, we can write a slope-intercept form of a straight line which is given as;
y = mx + c
m = slopec = y-interceptIn the given question;
x - 3 = 4
Let's collect like terms
x - 3 - 4 = x - 7
The equation can be rewritten as y = x - 7
In this case, the slope is 1 and the y-intercept is - 7
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What is the equation of a line that passes through (8,-5) and is parallel to the graphed line?
Answers
Answer:D. y = 3/4x + 1
A real estate agent sold three apartment buildings. The first sold for $1,259,300, the second sold for $2,839,750, and the third sold for $1,935,200. What was the total cost for the three buildings?
Answers
Answer:
The total cost for the three buildings was $6,034,250.
Step-by-step explanation:
Given,
The first sold for $1,259,300,
the second sold for $2,839,750,
the third sold for $1,935,200.
We add these three sold cost of apartment buildings
$1,259,300 + $2,839,750 + $1,935,200 = $6,034,250.
To calculate the total cost of three things, you will need to add the individual costs of each item together.
1. Determine the cost of each item. Add together the cost of all three items. This total is the cost of the three items.
2. If the items are sold as a package, determine the cost of the package. This is the cost of the three items.
3. If the items are sold at a discounted rate, calculate the total cost of each item after the discount has been applied. Add together the costs of the three items after the discount has been applied. This total is the cost of the three items.
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simplify the expression. be sure to show or explain how you arrived at your answer (-6i)(4i)
Answers
Answer:
hi no ugh I pero Eresi me gusta la
By definition i^2=-1
Simplify
-24•(-1)
Solution
24
Can I get Brainly pls
Find the value of a if the line line y=-x+4 is tangent to the graph of f(x) = x^2 - 5x +a
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
If the line y=-x+4 is tangent to the graph of f(x) = x^2 - 5x + a, it means that the line and the graph of the function are just touching at a single point, and are not intersecting at any other points.
To find the value of a, we can start by setting the equation for the line and the equation for the function equal to each other:
y = -x + 4
f(x) = x^2 - 5x + a
Then, we can substitute the equation for the function into the equation for the line:
-x + 4 = x^2 - 5x + a
We can then solve this equation for a by moving all the terms to one side:
-x + 4 - x^2 + 5x = a
-x^2 + 6x - 4 = a
We can see that the left-hand side of this equation is a quadratic expression in x, and we know that a quadratic function is tangent to a line when the line is a horizontal tangent. This occurs when the derivative of the function is equal to the slope of the line.
The derivative of f(x) = x^2 - 5x + a is 2x - 5, so we can set this equal to the slope of the line, which is -1:
2x - 5 = -1
2x = -6
x = -3
Now that we know the value of x, we can substitute it back into the equation for the function to find the value of a:
f(-3) = (-3)^2 - 5(-3) + a
f(-3) = 9 + 15 + a
f(-3) = 24 + a
Since the line and the function are just touching at this point, the y-value of the function at x=-3 must be equal to the y-value of the line at x=-3. We can substitute these values into the equation for the line to find the value of a:
y = -(-3) + 4
y = 3 + 4
y = 7
Substituting this back into the equation for the function, we get:
f(-3) = 24 + a = 7
a = 7 - 24
a = -17
Therefore, the value of a is -17.
what do you mean by tangent?
A tangent is a line that touches a curve at a single point, but does not intersect the curve at any other points. In other words, it is a line that is just "skimming" the curve, rather than crossing it.
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