Recall that lim f(x) = L means: For all € > 0 there is a 6 > 0 such that for all x satisfying 0 < Ix ~ cl < & we have that |f(x) - Ll < € What if the limit does not equal L? Think about what the means in €, 6 language. Consider the following phrases: 1.€ > 0 2.6 > 0 3.0 < Ix - cl < 6 4. Wf(x) - Ll > e 5. but 6. such that for all 7. there is some 8. there is some x such that Order these statements so that they form rigorous assertion that lim flx) + L and enter their reference numbers in the appropriate sequence in these boxes:

The solution to the system is (7.5, 1)

From 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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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:

(i) 0

(ii) inifinity(very large value)

(iii) undefined

(iv) positive value

(v) negative value

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

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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The linear function that gives the number of matchsticks required to make the nth pattern is given as follows:

M(n) = 15n.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

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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Answer: Lisa will receive 475 Euros.

Step-by-step explanation: 500x0.95 = 475.

Answer:

Step-by-step explanation:

2

The person walks 128 feet if she walked around the square pathway.

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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Answer:

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]

The solution is g(ƒ(-2)) = 9.

What is meant by 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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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!

Answer:

60

Step-by-step explanation:

54/90% =60

The values of the variables namely x, y and z of the given triangle are;

x = 12, y = 9√13, z = 6√13

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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Answer:

uh 6

Step-by-step explanation:

10??????????????????????????6????

The interquartile range?

I believe it is 65.

You have a 39.6% chance of winning according to the binomial distribution, it has been discovered.

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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​

The new computer will take to loading a document with 2 graphics and 1 paragraph is 43.99 seconds.

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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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:

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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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:

Answer:

4.5

Step-by-step explanation:

4.5 times 2 = 9

9 divided by 2 =4.5

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)

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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The distance of EH is 4.1866 meters.

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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The measure of the exterior angle x of the polygon is equal to 76°

The 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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Answer:

111

Please mark brainliest

Step-by-step explanation:

The domain of the relationship for this problem is given as follows:

Real values of x and y, except y ≠ 0 and x ≠ y.

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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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

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!

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:

The measure of the angle ABC and angle CBD are 48 and 42 degrees

As 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