As per the given limit, the rigorous assertion of the function is a − δ < x < a + δ
In math term function is called as a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output
Here we have given that the distance between two points a and b on a number line is given by |a−b|.
And we need to find the rigorous assertion of the function.
Then the statement is written as
=> |f(x)−L|<ε
And it can be be interpreted as the distance between f(x) and L is less than ε.
Here we have another statement that is written as
=> 0<|x−a|<δ
And it ma be interpreted as the value of x≠a and the distance between x and a is less than δ.
Here we have also important to look at the following equivalences for absolute value that the statement |f(x)−L|<ε is equivalent to the statement L−ε<f(x)<L+ε.
And the statement 0<|x−a|<δ is also equivalent to the statement a−δ<x<a+δ here we know that x≠a.
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I DONT GET
can u help me
Answer:
the rate is 30:5
the unit rate is 6:1
Step-by-step explanation:
GIVE ME BRAINLY
CLICK THE CROWN BY MY ANWSER!
find the domain (15 points)
The domain of the relationship for this problem is given as follows:
Real values of x and y, except y ≠ 0 and x ≠ y.
How to obtain the domain of the relationship?The domain of a relationship is composed by the set of all possible input values assumed by the relationship.
The relationship for this problem is given as follows:
(4x - 4y)/(2xy + 2y²).
It is a fraction, hence the restriction is that the denominator cannot be zero.
Then the domain is obtained as follows:
2xy + 2y² ≠ 0.
2y(x + y) ≠ 0.
Hence the restrictions are given as follows:
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A new computer will load 17% faster than the old computer it took the old computer 22 seconds to load one graphic and nine seconds to load a paragraph of text if you're loading a document with two graphics and one paragraph how long will it take the new computer to load?
The new computer will take to loading a document with 2 graphics and 1 paragraph is 43.99 seconds.
How to calculate time taken using percentage?Time taken can be calculated using percentages by determining the percentage of time that has already passed, then calculating the remaining time based on the percentage of time remaining.
For example, if you are asked to calculate the time taken for a project that is 50% complete, you would first need to determine the total length of the project. Let's say it is a project with a timeline of two months.
Next, you would need to calculate the percentage of time that has already passed. In this case, since the project is 50% complete, 50% of the two months has already passed. This means that one month has passed.
Finally, you can determine the time taken by subtracting the time that has already passed from the total length of the project. In this case, the time taken would be one month, since one month has already passed and there is one month remaining until the project is completed.
The old computer would load 2 graphs and one paragraph in:
22 × 2 seconds + 9 seconds = 53 seconds
The new computer is 17% faster so:
53 - (17% × 53) = 43.99 seconds
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graph the equation y=2/3x-1 iready quiz graph linear equations
Answer: To graph the equation y = 2/3x - 1, we can start by finding some points that satisfy the equation.
We can pick any value for x and substitute it into the equation to find the corresponding y-value.
For example:
When x = 0, y = (2/3)(0) - 1 = -1
When x = 1, y = (2/3)(1) - 1 = -1/3
When x = 2, y = (2/3)(2) - 1 = 1/3
When x = 3, y = (2/3)(3) - 1 = 2/3
We can plot these points on a coordinate plane and then connect them with a straight line to graph the equation.
The graph will be a line that passes through the points (0, -1), (1, -1/3), (2, 1/3), and (3, 2/3).
Step-by-step explanation:
There are two different pathways around a circular lake. The circular pathway is inscribed inside of a square pathway. The circular pathway has an area of 768 square feet. How far would a person walk if she walked around the square pathway? Use 3 for pi.
The person walks 128 feet if she walked around the square pathway.
What are the 2D shapes?The plane forms that can be sketched on a flat (or plane) surface or a piece of paper are known as 2D shapes. Every 2D shape has different attributes, like area and perimeter. Some of the two-dimensional objects have sides and corners, while others have curved edges.
Given two pathways,
circular and square, and the circular pathway is inscribed inside of a square pathway,
area of circular pathway = 768 square feet
area of circle = π/4*d²
where d is the diameter
768 = π/4*d²
768*4 = πd² (π = 3)
3072/3 = d²
d = √1024
d = 32 feet
since the circle is inscribed in a square the length of a side of square is equal to the diameter of the circle,
d = a = 32 feet
to find the perimeter of the square path,
perimeter of square = 4a
perimeter of square = 4*32
perimeter of square = 128 feet
Hence the person has to cover 128 feet if she walked around the square pathway.
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Solve the system by substitution {2x−3y=12 −12y+8x=48
If there is one solution, type the answer as an ordered pair. If there is no solution, type ∅. If there are infinitely many solutions, type ∞.
The solution to the system is (7.5, 1)
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
2x−3y=12
−12y+8x=48
divide the first equation by 2
So, we have
x - 1.5y = 6
This gives
x = 6y + 1.5
By substitution, the second equation becomes
-12y + 8 (6y + 1.5) = 48
So, we have
-12y + 48y + 12 = 48
Evaluate
36y = 36
Divide by 36
y = 1
So, we have
x = 6 + 1.5
x = 7.5
Hence, the solution is (7.5, 1)
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How many cords of wood could you fit in a room that is 4 yards long 4 yards wide and two yards High answer to the nearest hundredth
Answer: To find the number of cords of wood that can fit in a room, we need to find the volume of the room and then divide that by the volume of a cord of wood.
A cord of wood is a unit of measurement that is equal to 128 cubic feet.
The volume of the room can be found by multiplying the length by the width by the height:
V = 4 x 4 x 2 = 32 cubic yards
To convert cubic yards to cubic feet, we can use the conversion factor of 1 cubic yard = 27 cubic feet.
So, the volume of the room in cubic feet is:
V = 32 x 27 = 864 cubic feet
To find the number of cords of wood that can fit in the room, we divide the volume of the room by the volume of a cord of wood:
cords = 864 / 128
cords ≈ 6.75
So, you could fit approximately 6.75 cords of wood in a room that is 4 yards long, 4 yards wide, and 2 yards high, to the nearest hundredth.
Step-by-step explanation:
A situation in which solutions exist so that both parties are trying to find a mutually acceptable solution to a complex conflict is known as which of the following?
A) mutual gains
B) win-lose
C) zero-sum
D) win-win
E) None of the above.
D) Win-win is a situation in which both parties come away with a positive outcome.
Win-win is a situation in which both parties come away with a positive outcome. It is the ideal solution to a complex conflict, as it ensures that both parties benefit in some way. Win-win solutions involve a collaborative approach to problem solving, where each party works together to find a mutually beneficial solution. This can involve compromise, trade-offs, and creative negotiation.
For example, two companies may be in competition for the same contract. Rather than viewing each other as adversaries, they could work together to create a win-win solution that meets their respective needs. This could involve a collaborative approach to the project, or a mutually beneficial pricing arrangement.
Win-win solutions also require an understanding of each party's needs, interests, and values. It is important to identify the underlying interests that each party has, and use them to create a solution that meets everyone's needs. By taking the time to understand each other's perspectives, it is possible to create a solution that is beneficial to both parties. In this way, win-win solutions provide an opportunity to develop a constructive relationship that can be beneficial in the long term.
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f(x) = 3x and g(x) = x − 1, find (gof)(− 2)
The solution is g(ƒ(-2)) = 9.
What is meant by solution?
Any mixture of one or more solutes that have been dissolved in a solvent is referred to as a solution. To create a homogenous mixture, a solute must dissolve in a solvent.To create a homogenous mixture, a solute must dissolve in a solvent.In chemistry, a solution is a homogeneous mixture of two or more compounds in their relative proportions. The composition of the solution can be continually changed up to the solubility limit.Although solutions of gases and solids are possible, the term "solution" is most frequently used to refer to the liquid condition of matter.A homogenous mixture of two or more components with particles smaller than 1 nm is referred to as a solution.{g∘f}(2) = g(f(-2))
g(-2) = -6
ƒ(-6) = 2x - 1
ƒ(-6) = -2(-6) - 1
ƒ(-6) = 13
ƒ(g(2)) = 13
{f∘g(-2) = f(g(-2))
ƒ(2) = 3
g(3) = -3x
g(3) = -3(-3)
g(3) = -9
g(ƒ(-2)) = 9
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The function below is defined by two equations. The equation in the first row gives the output for negative nu the domain. The equation in the second row gives the output for non-negative numbers in the domain. Find th indicated function values. f(x) = 8x+4 if x
The indicated function values for f(x) = 8x + 4 if x is:
(a) f(-4) = -13, (b) f(2) = 22
(c) f(0) = 8, (d) f (-100) + f(100) = 215
What is meant by function ?
A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x).
We must look at the value of x to determine which equation to take into account. In the first equation, we will substitute x if it is negative; in the second equation, we will substitute x if it is positive or null.
(a) x = -4 so x is negative.
We use the first equation f(x) = 5x + 7 and we have f(-4) = 5 × (-4) + 7 = -13
(b) x = 2 and is positive.
We use the second equation f(x) = 7x + 8.
The result is f(2) =7 × (2) + 8 = 22
(c) x = 0 In this case the function is defined by the second equation f(x) = 7x + 8. So f(0) =7 × (0) + 8 = 8
(d) We need to calculate the function values of each one and then make the sum.
With f(-100), x = -100 and is negative
We use the first equation f(x) = 5x + 7 and
we have f(-100) = 5 × (-100) + 7 = -493.
With f(00), x = 100 is positive so we use the second equation f(x) = 7x + 8 and get f(100) = 7 × 100 + 8 = 708
We add them to get the result: f(-100) + f(100) = -493 + 708 = 215
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The complete question is:
The function below is defined by two equations. The equation in the first row gives the output for negative numbers in the domain. The equation in the second row gives the output for non-negative numbers in the domain. Find the indicated function values.
f (x) = { 5x+7 if x < 0
{ 7x+8 if x ≥ 0
(a) f (- 4)
(b) f (2)
(c) f (0)
(d) f (-100) + f(100)
If m
and mzABD = (4x + 14)°. Find the
measurements of CBD and
The measure of the angle ABC and angle CBD are 48 and 42 degrees
How to determine the measure of the anglesAs a general rule:
Complementary angles add up to 90 degrees
This means that
we get: ∡ABC + ∡CBD = 90
3x + 6 + 4x - 14 = 90 ------ Substituting 3x + 6 and 4x - 14 for ∡s ABC and CBD
Evaluate the like terms
7x = 98
Divide both sides by 7
x = 14
So, we have
Measure of ∡ABC: 3 * 14 + 6 = 48
Measure of ∡CBD: 4 * 14 - 14 = 42
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Complete question
Find the measure of each angle
angle ABC and angle CBD are complementary angles, m angle ABC=(3x+6)degrees, and m angle CBD=(4x-14)degrees
2. Write an equation to represent f(e)
Absolute Value Functions
The absolute value function for f(e) is given as follows:
f(e) = |e|
The piece-wise definition of the function is given as follows:
f(e) = e, e >= 0.f(e) = -e, e < 0.What is the absolute value of a number?The absolute value of a number is the number without the signal, representing the difference between the number and zero.
This means that the elevation function gives just elevation, without considering if the elevation is positive or negative, and thus the function is defined as follows:
f(e) = |e|
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How do i solve for the value of s
Solve for
r
-48 - r = -39
Answer:
[tex]r=-9[/tex]Step-by-step explanation:
[tex]-48 - r = -39[/tex]
[tex]-48+-r=-39[/tex]
[tex]-r-48=-39[/tex]
[tex]-r-48+48=-39+48[/tex]
[tex]-r=9[/tex]
[tex]\cfrac{-r}{-1}=\cfrac{9}{-1}[/tex]
[tex]r=-9[/tex]
what is theregular price ,r,of a museum ticket before the discount? enter the amount in the table
Answer:
60
Step-by-step explanation:
54/90% =60
Manny drives 2 times the hours that Tabria does. Manny and Tabria drive for a total of 9 hours. How
long did each person drive?
Answer:
4.5
Step-by-step explanation:
4.5 times 2 = 9
9 divided by 2 =4.5
Solve 2 4/5x=−1 1/4 . Write your answer as a fraction in simplest form.
Answer: -56/55
Step-by-step explanation:
2 4/5x = -11/4
14/5x = -11/4
Cross multiply:
-55x = 14 * 4 = 56
x = -56/55
Please help to answer this qns.. 6th grade algebra
The linear function that gives the number of matchsticks required to make the nth pattern is given as follows:
M(n) = 15n.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.When a linear function represents a proportional relationship, it means that the intercept is of zero.
As for each pattern the number of sticks is increased by 15, the slope is of 15 and the equation is given as follows:
M(n) = 15n.
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Sample of 10 medical bills is selected, what is the probability that 0 medical bills will contain errors
You have a 39.6% chance of winning according to the binomial distribution, it has been discovered.
Calculate probability?Only two outcomes are conceivable for each trial. You either succeed or fail in hitting the target. The binomial distribution is used to answer this question because the likelihood that a target will be struck on any given trial is independent of all other trials.
It is determined by the number of unique combinations of x objects from a set of n elements and the likelihood of striking the objective, which is 63%, and is expressed as the probability of exactly x successes on n repeated trials with p probability.
hence, two throws
The likelihood is P(X = 2) since you must strike it twice to win.
0.396 = 39.6%
The complete question is,
Considering the circumstances, what is your likelihood of success: A plush animal is what you're attempting to win. To succeed, a target must be hit twice straight. It is 63% likely that you will succeed on your first attempt.
O 23.3% \sO 63%
O 106% \sO 39.6%.
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Find the quartile
49, 27,10,76, 91, 86, 40, 38, 15, 33, 12, 87, 60, 9, 80
Answer:
uh 6
Step-by-step explanation:
10??????????????????????????6????
The interquartile range?
I believe it is 65.
anyone help this is part 1
Explain weather there is a possible transformation of f in the form g(x) =f(x)+k, where k is a constant for which the graph y=g(x) will have no x-intercepts. Enter your answer and your justification in the space provided.
Answer:
Yes, a transformation of f in the form g(x) =f(x)+k can have no x-intercepts. This will occur if the constant k is added to the y-value of every point on the f(x) graph, resulting in the chart of g(x) being shifted upward by k units. If the original diagram of f(x) had no x-intercepts, then the graph of g(x) would also have no x-intercepts because the x-coordinate of each point on the graph of f(x) is unchanged by the transformation.
Step-by-step explanation:
what is the 35th term for 9, 3, 1, 1/3
Answer:
111
Please mark brainliest
Step-by-step explanation:
Lisa is traveling to Greece this summer and needs to exchange 500 US Dollars to Euros.
How many Euros will Lisa receive with the following exchange rate?
1 USD = 0.95 Euros
Answer: Lisa will receive 475 Euros.
Step-by-step explanation: 500x0.95 = 475.
Answer:
Step-by-step explanation:
2
In AUVW, UV ~ WU and m/W = 38°. Find mLU.
What is the perimeter of triangle “QTS”
Answer: 15 + x, or x + 15
Step-by-step explanation:
The perimeter of triangle QTS is represented as line segments QT + TS + QS. This means:
6 + 6 + ((3x - 1) + (4 - 2x))
You can first simplify 6 + 6, 6 + 6 = 12
12 + ((3x - 1) + (4 - 2x))
Next, focus on ((3x - 1) + (4 - 2x))
3x + (-1) + 4 + (-2x), addition is commutative, so use addition
3x + (-2x) + 4 + (-1)
(3x - 2x) + (4 - 1)
x + (4 - 1)
x + 3
The equation is now:
12 + x + 3
You can simplify this more by adding 12 + 3
15 + x
The answer is 15 + x or x + 15 because that is as simplified as the equation can be.
I hope this helps!
Find x, y, and z. Express in simplest radical form.
Please help
The values of the variables namely x, y and z of the given triangle are;
x = 12, y = 9√13, z = 6√13
How to use Pythagoras Theorem?There are three sides of a right angle triangle namely; Opposite, Adjacent and Hypotenuse.
The formula for Pythagoras theorem is;
Hypotenuse² = Opposite² + Adjacent²
Thus;
y² = 27² + 18²
y = √(27² + 18²)
y = √1053
y = 9√13
Using concept of similar triangles, we can say that;
x/18 = 18/27
x = (18 * 18)/27
x = 12
Using Pythagoras theorem again;
z = √(12² + 18²)
z = √468
z = 6√13
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find the value of x and y
The measure of the exterior angle x of the polygon is equal to 76°
How to evaluate for the exterior angle xThe exterior angles of a polygon added together is equal to 360° so;
x + x + 60° + 64° + 36° + 48° = 360°
2x + 208° = 360°
2x = 360° - 208° {subtract 208° from both sides}
2x = 152°
x = 152°/2 {divide through by 2}
x = 76°
Therefore, the measure of the exterior angle x of the polygon is equal to 76°
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Suppose b is a constant and that f(x) is a function defined when x = b. Complete the following sentences.
1. If f(b) is large, then 1/f(b) is __
2. If f(b) is small, then 1/f(b) is __
3. If f(b) = 0 then
1/f(b) is __
4. if f(b) is positive, then
1/f(b) is __
5. If f(b) is negative, then 1/f(b) is __
(i) 0
(ii) inifinity(very large value)
(iii) undefined
(iv) positive value
(v) negative value
What is limiting value of a function?A limiting value of a function is a value that the function approaches as the input (or independent variable) approaches a certain value. It is also called the function's limit at that point. This concept is used in calculus to understand the behavior of functions and their derivatives.
so in all the cases we have to find the limiting value of f(x)
1. if the value of f(b) is very large the 1/f(b) is very small.
2. if f(b) is small then the value of 1/f(b) is very large
3. if f(b) is 0 then 1/f(b) is not defined.
4. if f(b) is positive then its reciprocal is also positive.
5. if f(b) is negative then its reciprocal is also negative.
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(I) 0
(ii) The infinite (very large value)
IIII, undefinable
(iv) A favorable value
(v) negative value
What does a function's limiting value mean?A function's limiting value is a point that the function approaches as the input (or independent variable) gets closer to a particular value. At that time, it is also known as the function's limit. Calculus makes use of this idea to comprehend how functions behave and how their derivatives work.
Therefore, we must always determine the limiting value of f. (x)
1. The value of 1/f(b) is very small if the value of f(b) is very large.
2. The value of 1/f(b) is very large if f(b) is tiny.
3. 1/f(b) is not defined if f(b) is 0.
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Circle E has a radius of 5.3 meters. FG is a chord and HE is a perpendicular bisector of FG. If FG = 6.5 meters, calculate the distance of EH.
The distance of EH is 4.1866 meters.
What is Circle?Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.
From the question, we have,
Radius of the circle = 5.3 meters
EF = EI = 5.3 meters
FG = 6.5 meters
Also, we have, HE is a perpendicular bisector of FG.
FH = HG = 6.5 / 2 = 3.25
We have to calculate EH.
We have, FH is the projection of EF in the vertical axis.
FH = EF sin (θ), where θ is the angle FEH.
3.25 = 5.3 sin (θ)
sin (θ) = 0.6132
θ = sin⁻¹ (0.6132)
θ = 37.82°
We have, EH is the projection of EF into the horizontal axis.
EH = EF cos (θ)
= 5.3 cos (37.82°)
= 5.3 × 0.7899
= 4.1866 meters
Hence the length of EH is 4.1866 meters.
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