Prove that limx→2 x/1+x= 1/2 using the definition of limit​

Answers

Answer 1
We have the limit as x→2 of x/1+x. Plug in the value of 2 for x.

We get,

2/(1+2) => 2/3

Related Questions

Please help I was sick and missed out on class thank you.

Answers

Answer: slope=-5 and y-intercept=1

Step-by-step explanation:

The equation given is in slope-intercept form. Slope-intercept for is y=mx+b, where m is slope and b is y-intercept.

This gives m=-5 and b=1.

11-(-2)x4 step by step pls my hm is due tmr

Answers

Answer:

Step-by-step explanation:

11 -(-2) x 4

11 + 2 x 4

11 +8

= 19

Compare.
2.2O 14/4
A. <
B. >
C. =

Answers

Answer:≤ sorry if it's wrong I'm not a fan of math

Step-by-step explanation:

Nathaniel is searching for a four-leaf clover in a field. He finds 2 four-leaf
clovers during the first 12 minutes of his search. If Nathaniel spends a total of
180 minutes searching in the field, predict the number of four leaf clovers
Nathaniel will find.

Answers

Answer:

30 clovers

Step-by-step explanation:

If Nathaniel find 2 four-leaf clovers in the first 12 minutes of his search, the rate at which he finds the four-leaf clovers is:

[tex]\implies \sf Rate=\dfrac{2\;clovers}{12\;minutes}=\dfrac{1}{6}\;clovers\;per\;minute[/tex]

To predict the number of four-leaf clovers Nathaniel will find in 180 minutes, multiply the found rate by 180 minutes:

[tex]\implies \sf \dfrac{1}{6} \times 180=30\;clovers[/tex]

Therefore, Nathaniel will find 30 clovers in 180 minutes based on the rate at which he found 2 clovers.

[tex] \sf \longmapsto \: Prediction \: of \: 4 \: leaf \: clovers=2/12×180

\: [/tex]

[tex] \sf \longmapsto \: Prediction \: of \: 4 \: leaf \: clovers=30clovers[/tex]

What do you say back to someone who said: “ Nobody understands how it is to be everyone’s go to and have no one to care for you. “?

Answers

Answer: just be positive

Step-by-step explanation:

Will mark brainliest (I also need to find the x and y intercepts)

Answers

Answer: downward, (4, -1), x = 4, no x-intercept, y-intercept: -6

Step-by-step explanation:
1. The parabla opens downwards because the y-values only decrease
2. The Vertex is the point with an x-value that creates a line of symmetry and can be noticed as it does not share the same x or y-value with any other point. If you look for it, you will notice that it's (4, -1).
3. As I explained above the x-value of the vertex creates a line of symmetry, therefore you can create the equation for the axis of symmetry by setting it equal to x.
4. X-intercepts are x-values that intersect with the x-axis so look for any points on the x-axis and if there are any, write them down. Y-intercepts are y-values that intersect with the y-axis, so look for any points on the y-axis and if there are any, write them down. If you checked, you should've realized that there are no x-intercepts and that the y-intercept is -6 and it's location is (0, -6).

A line has a slope of 3/8 and passes through the point (15.2,-7)

The equation of the line in point-slope form is???
ANSWERS↓↓

Answers

Considering the definition of a line, the correct answer is option A: the equation of the line in point-slope form is y + 7= 3/8(x- 15.2)

Linear equation

A linear equation o line can be expressed in the form y = mx + b

where

x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.

The point-slope form of an equation of a line is written as y-y₁=m(x-x₁)

where:

m is the slope.(x₁, y₁) are the coordinates of the point.Equation of a line in this case

In this case, you know:

A line has a slope of 3/8.The line passes through the point (15.2,-7).

The point-slope form of the line is written as:

y- (-7)= 3/8(x- 15.2)

y + 7= 3/8(x- 15.2)

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eva invest $120 at a rate of 3% per year compound interest. calculate the total amount eva has after 2 years

Answers

Answer:

Eva has $127.31 after 2 years.

Step-by-step explanation:

Here is the formula for compound interest

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where [tex]A[/tex] is the final amount, [tex]P[/tex] is the initial amount, [tex]r[/tex] is the interest rate as a decimal, [tex]n[/tex] is the number of times the interest applied per time period, and [tex]t[/tex] is the number of time periods.

We are given

[tex]P=120\\r=0.03\\n=1\\t=2[/tex]

Substitute our numbers into the equation

[tex]A=120(1+\frac{0.03}{1})^{1*2}[/tex]

[tex]A=120(1.03)^{2}[/tex]

[tex]A=120*1.03^{2}[/tex]

[tex]A=120*1.0609[/tex]

[tex]A=127.308[/tex]

find the order pairs for y=-5x-4

Answers

Answer:

(0,-4),(1,1)(2,6)

Step-by-step explanation:

A women went to Shopping.First she spent 4/5th of all money she had in her purse, and then she lost 2/3 of what was remaining. Now she has 10$ left. How much money did she spent?

Answers

The amount of money that was spent is $120.

How to illustrate the fraction?

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

In this case, the women went to Shopping and first she spent 4/5th of all money she had in her purse, and then she lost 2/3 of what was remaining.

The fraction of money left will be:

= 1 - 4/5 - (2/3 × 1/5)

= 1 - 4/5 - 2/15

= 1/15

Since she had $10 left the original amount will be:

= $10 ÷ 1/15

= $10 × 15

= $150

The amount spent will be:

= 4/5 × $150

= $120

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The time t in seconds that it takes a car to accelerate to ask mph can be described by T=0.001×0.7 32X^2 +15.417X +603.738 how fast in miles per hour is the car going after 8.55 seconds

Answers

The miles per hour that the car is going after 8.55 seconds is 610.79 miles per hour.

How to calculate the time taken?

From the information Illustrated, it should be noted that the t in seconds that it takes a car to accelerate to ask mph can be described by T = 0.001 × 0.732X² + 15.417X + 603.738.

In this case, it is important to note that x in the function simply represents the seconds.

Therefore, based on the information, the miles per hour is the car going after 8.55 seconds will be:

T = 0.001 × 0.732X² + 15.417X + 603.738.

T = 0.001 × 0.732(8.55)² + 15.417(8.55) + 603.738

T = 0.001 × 53.511 × 131.815 + 603.738

T = 610.79

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The four approved methods of document destruction are

Answers

Answer:

1area

2 water

3 food

4 house

Answer:

shredding, incineration, pulping, and pulverization.

Step-by-step explanation:

Shredding: This involves cutting paper into small pieces using a shredding machine. The shreds are usually too small to be reconstructed, making it an effective method for destroying sensitive documents.

Incineration: This involves burning paper to ash using high heat. Incineration is a fast and efficient way to destroy large volumes of documents, but it is not always practical or environmentally friendly.

Pulping: This involves breaking down paper using water and chemicals to create a slurry that can be recycled or disposed of. This method is effective for destroying large volumes of paper, but it is not suitable for destroying documents with sensitive information.

Pulverization: This involves grinding paper into a fine powder using a pulverization machine. The powder is then disposed of or recycled. This method is effective for destroying documents with sensitive information, but it is not practical for destroying large volumes of paper.

The function f(x)= square root of x is translated using the rule (x,y) (x-7,y+2) to create f(x)what is the domain of f(x)?

Answers

The value inside the square root should be greater than or equal to zero. Then the domain of the function will be [7, ∞).

What is a function?

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The domain means all the possible values of x and the range means all the possible values of y.

The function is given below.

f(x) = √x

The function after the transformation, then we have

f(x) = √(x - 7) + 2

The value inside the square root should be greater than or equal to zero. Then the domain of the function will be given as,

x - 7 ≥ 0

x ≥ 7

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Find the area of a regular 12-sided polygon inscribed in a circle of radius
8 cm.

Answers

area of n sided polygon  inscribed in a circle is

A = (1/2)nr²sin(360/n)    (r = radius of circle)

A = (1/2)12*8²*sin30

   = 1/2*12*64*1/2

A  = 192  square unit

Simplify (3x^2y^5)^3

Answers

the answer is b, 27x^6y^15
Answer:  Choice B

Work Shown:

[tex]\left(3\text{x}^2\text{y}^5\right)^3\\\\\left(3\right)^3\left(\text{x}^2\right)^3\left(\text{y}^5\right)^3\\\\27\text{x}^{2*3}\text{y}^{5*3}\\\\27\text{x}^{6}\text{y}^{15}\\\\[/tex]

Explanation:

The outer exponent 3 is "distributed", so to speak, to each term inside the parenthesis. This isn't the actual distribution rule. But we can think of it as such. This is what's happening in the second step.

So we'll cube the coefficient 3 to get 3^3 = 27, and we'll cube x^2 to get x^6, and finally cube y^5 to get y^15.

I used the rule [tex](a^b)^c = a^{b*c}[/tex] for the third step.

what is the percent of change for your grade if originally you got 5 questions right and you checked your work and ended up with 15 questions right

Answers

Answer:

To calculate the percent of change for your grade, you will need to know your original grade and your revised grade. If you originally got 5 questions right and you checked your work and ended up with 15 questions right, you can calculate the percent of change as follows:

Subtract your original score from your revised score to find the difference: 15 - 5 = 10

Divide the difference by your original score and multiply by 100 to express the change as a percentage: (10 / 5) x 100 = 200%

This means that your grade increased by 200%.

Step-by-step explanation:

Which graph represents the solution to 1/7 m < - 1/22


Answers

The graph representing the solution will be of the form a line tending towards left from the point -7/22.

What is Linear Inequalities?

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Here the given inequality is less than inequality.

1/7 m < -1/22

Dividing both sides by 1/7, we get,

m < -1/22 ÷ 1/7

m < -1/22 × 7/1

m < -7/22

Hence the graph of the solution will be of the form a straight line tending leftwards from -7/22.

Hence the graph of the given inequality is a straight line tending leftwards from -7/22.

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how many full cases and additional items are needed to fulfill the order 56 items ordered 6 items per case

Answers

There are 9 full cases and 2 additional items are needed to fulfill the order 56 items ordered 6 items per case.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

56 items ordered for 6 items per case.

Now, After divide the quotient shows the number of full case and remainder shows the additional items.

Hence, We get;

 6 ) 56 ( 9

      54

   ---------

        2

Thus, There are 9 full cases and 2 additional items are needed to fulfill the order 56 items ordered 6 items per case.

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d= c/n solve for n, I've been trying to solve this by multiplying by n but i want to solve for n so that's wrong thank you guys :D

Answers

Answer:

You started correctly....

Step-by-step explanation:

d = c/n      Multiply both sides by 'n'

dn = c        now divide both sides of the equation by 'd'

n = c/d       Done.

If an 8-foot pole casts a 6-foot shadow at the same time a nearby tree casts
a 33-foot shadow, how tall is the tree (in feet)?

Answers

Answer:

The tree is 44 feet

Step-by-step explanation:

[tex]\frac{8}{6}[/tex] is equivalent to [tex]\frac{4}{3}[/tex] (divide the numerator and denominator by 2)

[tex]\frac{4}{3}[/tex] = [tex]\frac{x}{33}[/tex]

3 x 1  = 33, so 4 x 11 = 44

The tree is 48 feet tall. This can be determined by using the ratio of the shadows. The ratio of the pole's shadow to the tree's shadow is 33. This means that for every 6 feet the pole casts, the tree casts 33 feet. Therefore, if the pole is 8 feet tall, the tree must be 48 feet tall (8 x 6 = 48).

Lesson 17

Using the info given, solve for the missing value of the right triangle. Round each angle to the nearest degree, each length to the nearest tenth, & each trigonometric value to four decimal places, if necessary.
Hypotenuse = 14.5 meters
Opposite side = 6.3 meters
θ = ?

Answers

The measure of the angle (θ) is equivalent to sin⁻¹(6.3/14.5).

What is Pythagoras theorem?

The Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. Mathematically, it can be written as -

(hypotenuse)² = (base)² + (perpendicular)²

Given is a right angle triangle with hypotenuse as 14.5 meters and

opposite side as 6.3 meters.

We can write sine of the angle (θ) as -

sin(θ) = P/H

sin(θ) = Opposite side/Hypotenuse

sin(θ) = 6.3/14.5

(θ) = sin⁻¹(6.3/14.5)

Therefore, the measure of the angle (θ) is equivalent to sin⁻¹(6.3/14.5).

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A pre-paid cell phone company charges $10.35 as a monthly access fee and $0.08 per minute of calling time.

Express the monthly cost C in terms of minutes of call time ?

What will the monthly cost be if you make 280 minutes of calls this month?

Answers

Answer: $32.75

Step-by-step explanation:

If each call costs $0.08 and you make 280 minutes worth of calls this month you'll have made $22.04 worth of phone calls plus the monthly access fee ($10.35) if you add both those fees you'll be left with a bill of $32.75.

I hope this answer helped you. :)

Answer:

$32.75

Step-by-step explanation:

10.35 + (0.08×280)

Is this a polynomial? 3x^-2-5

Answers

On solving the provided question, we can say that - the value of the following polynomial will be 3x^2 = 5 => x^2 = 5/3

what are polynomials?

A polynomial is a mathematical statement made up of coefficients and uncertainty that exclusively uses additions, subtractions, multiplications, and positive integer powers of variables. A single indeterminate x polynomial is represented by the expression x2 4x + 7. A polynomial is an expression in mathematics that consists of variables (sometimes referred to as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression made up of coefficients and variables. The only operations that an expression can contain are addition, subtraction, multiplication, and non-negative integer exponents. These expressions are known as polynomials.

here,

[tex]3x^{-2}-5[/tex]

3x^2 = 5

x^2 = 5/3

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Simplify. Negative square root of 16y^2 if y<0

Answers

Answer:

The square root means that IF you square the square root, you will get the original number. Thus, 16 squared = 256 and y^2 squared = (y^2)(y^2) = y^4

Step-by-step explanation:

PLEASE HELP

Consider the two circles shown


To show that circle P is similar to circle Q, circle P is translated t units to the right. The image is then dilated about it’s center by a scale factor of s.


What are the values of t and s

Answers

Answer:

t is 13

scale factor is 7/4

a restaurant offers 7 appetizers and 9 main courses. In how many ways can a person order a two-course meal

Answers

Hint: try listing them and mixing and matching to find ur answer

Pls help me out here

Answers

All of the equations that are true include the following:

B. 56 + 70 = 14(4 + 5).

C. 28 + 49 = 7(4 + 7).

What is the distributive property of multiplication?

In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

How to determine the true equation?

In order to determine the true equation, we would apply the distributive property of multiplication and then check whether or not the right-hand side is equal to the left-hand side.

By applying the distributive property of multiplication to the given mathematical expression, we have the following:

32 + 96 = 8(4 + 14)

32 + 96 = 32 + 112 (False).

56 + 70 = 14(4 + 5).

56 + 70 = 56 + 70 (True).

28 + 49 = 7(4 + 7).

28 + 49 = 28 + 49 (True).

27 + 36 = 3(9 + 13)

27 + 36 = 27 + 39 (False).

25 + 35 = 5(5 + 6)

25 + 35 = 25 + 30 (False).

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A railroad crossing arm that is 20 feet long is stuck with an angle of elevation of 35". Find x and y in the illustration below.
Round to the nearest tenth as needed.
Note: The red line is NOT needed to solve this problem.
20 ft
35
yft
Select the correct response
Ox-32.9 feet; y=12.0 feet
x-11.5 feet, y-16.4 feet
x-12.0 feet, y-32.9 feet
x=16.4 feet, y=11.5 feet
< Previous

Answers

The angle of elevation of a 20-foot railroad crossing arm is fixed at 35 degrees. As necessary, round up to the next tenth. 20 ft, 35 ft, x -11.5 feet, y- 16.4 feet .

What is angle of elevation ?

Between the horizontal line and the line of sight, an angle called the angle of elevation is created. The angle of elevation formula tan =QR/PR can be used to calculate the building's height (QR). Therefore, the building has 8 units of height. When it lies between the line of sight and the horizontal line, the angle of elevation is generated. The angle created, known as the angle of elevation, occurs when the line of sight is above the horizontal line. However, in the depression angle, the line of sight is downward and parallel to the ground.

When we multiply in algebra, we come before a variable with a number. In the same way, xy means to multiply variable x by variable y, while 7xy means to multiply variable x by variable y and then to multiply the entire expression by seven. Due to the complexity of how train-based questions are frequently presented, it is always advisable to read the question thoroughly before responding. After reading the question, try to use a formula in it; this may lead to a direct solution and save you time.

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which is a solution to (x-2)(x+10)=13

Answers

Answer:

answers 3

Step-by-step explanation:

took more thinking than it should've tbh (3-2=1) (3+10=13) 1x13=13

on Monday in December, it was -8 degrees Celsius in Harbin China and -2 degrees Celsius and Beijing China on Tuesday and Beijing it was 5 degrees colder than it was the day before what was the new temperature?

Answers

The required temperature in Beijing China is -7°C on Tuesday.

As mentioned in the numeral,

On Monday in December
The temperature in Harbin China is  -8°C,

Now,
The Temperature in Beijing china is -2°C
According to the condition, the temperature on the next day in Beijing is 5° degrees colder than it was yesterday since the temperature is becoming colder implying that the temperature is getting decreased by -5°C.

The temperature on Tuesday is given as,
T = -2°C - 5°C  [subtracting -5 because the temperature is decreased]
T = - 7°C

Thus, the required temperature in Beijing China is -7°C on Tuesday.

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