what is the value of the limit [tex]\lim_{x \to \5} \sqrt{x^{2}+4 }[/tex]

The equilateral triangle theorem states that in an equilateral triangle, all sides are equal in length and all angles are equal in measure (60 degrees).

The equilateral triangle theorem states that in an equilateral triangle, all sides are equal in length and all angles are equal in measure (60 degrees).

To prove this theorem, we can use the following steps:

1. Draw an equilateral triangle and label the sides as a, b, and c.

2. Use the definition of an equilateral triangle to state that all sides are equal in length, which means a = b = c.

3. Use the definition of an equilateral triangle to state that all angles are equal in measure, which means all angles are equal to 60 degrees.

4. Use the properties of a triangle to show that the sum of the interior angles of a triangle is 180 degrees.

5. Substitute the values for the sides and angles of the equilateral triangle into the formula for the sum of the interior angles of a triangle:

a + b + c = 180 degrees.

6. Simplify the equation by substituting the equal values of a, b, and c:

3a = 180 degrees.

7. Divide both sides of the equation by 3 to find the value of a:

a = 60 degrees.

8. Since a represents the measure of each angle in the equilateral triangle, this proves that the measure of each angle in an equilateral triangle is 60 degrees.

This proof demonstrates that the equilateral triangle theorem is true for all equilateral triangles.

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The distance between Katie and Helicopter will be 5.774 miles approximately.

We will solve this problem with the help of Trignometry. So, what is Trignometry?

A branch of mathematics called trigonometry examines correlations between triangles' side lengths and angles. Three crucial trigonometric functions—sine, cosine, and tangent—are represented by the abbreviations sin, cos, and tan.

In this problem, it is given that Katie is watching a helicopter flying at an altitude of 5 miles and the angle of elevation is π/3.

From Sin Cos Tan, you know that:

Sin = opposite/Hypotenuse

sin(π/3) = (5 miles)/Hypotenuse

Hypotenuse = (5 miles) / Sin(π/3) = 5/ ([tex]\sqrt[]{3}[/tex]/2) miles = 5.774 miles.

So, the distance between Katie to the Helicopter is about 5.774 miles.

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In this problem, it is given that Katie is watching a helicopter flying at an altitude of 5 miles and the angle of elevation is π/3.

From Sin Cos Tan, you know that:

Sin = opposite/Hypotenuse

sin(π/3) = (5 miles)/Hypotenuse

Hypotenuse = (5 miles) / Sin(π/3) = 5/ (/2) miles = 5.774 miles.

So, the distance between Katie to the Helicopter is about 5.774 miles.

The closure property of the whole number states that "Addition and multiplication of two whole numbers is always a whole number.

What is Property of Closure ?

A set has the closure property only under a particular operation which is if the result of the operation is always an element in the set.  When a set has the closure property under a particular operation, then we say that the set is “closed under the operation.”

a)The set of integers is closed under the operation of addition because the sum of any two integers is always another integer and is therefore in the set of integers.

b) The set of integers is not closed under the operation of division because when you divide one integer by another, you don’t always get another integer as the answer.  For example, 4 and 9 are both integers, but 4 ÷ 9 = 4/9.  4/9 is not an integer, so it is not in the set of integers!

Hence , the closure property of the whole number states that "Addition and multiplication of two whole numbers is always a whole number.

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A permit is a legal document that enables a person or a business to utilize a specific area for a project or other activity.

To obtain permission to use a specific location for a project, you may need to submit a request in writing or fill out a permission form. The exact document that you need to obtain permission will depend on the specific location and the requirements of the owner or manager of the location.

You may also need to provide information about your project, including the purpose, duration, and any potential impact on the location. Depending on the location and the nature of your project, you may also need to obtain other approvals or permits, such as building permits or environmental permits.

It is a good idea to research the requirements for using the specific location that you are interested in and to contact the appropriate authorities or individuals to find out what documents you need to obtain permission.

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The x-coordinate of the solution to this system of equations is x = -6.

The x-coordinate of the solution to the following system of equations can be determined by solving the system of equations using the substitution method. The substitution method involves replacing the value of one of the variables with the other. This can be done by solving one of the equations for one of the variables and then substituting it into the other equation.  

In this case, we will solve the first equation for y:

2x = -4y

y = -2x

Substituting this expression for y into the second equation, we get:

5x - 6(-2x) = -6

5x + 12x = -6

17x = -6

x = -6/17

Therefore, the x-coordinate of the solution to this system of equations is x = -6.

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Answer:

x = 90 degree

y = 43 degree

Step-by-step explanation:

x is at the right angle, so it must be 90 degrees.

A triangle has a total of 180 degrees.

We know two angles, one is 90 degrees and one is 47 degrees

90 + 47 = 137 degrees

180 - 137 = 43 degrees

So, y = 43 degrees

There might be 200 votes cast overall. Given that a certain club has 50 members, 4 of those individuals are running for president, and every club member—including those running for president—votes for one of the four candidates, Understanding the provided conditions will help you get this.

We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events with a probability distribution.

given

There are 50 members in one club.

Each club member, including those vying for president, votes for one of the four candidates. There are four people standing for president.

We can write that based on the statements provided.

those who voted for these 4 members,

n = 50 Because the candidates have the option to vote for themselves or someone else,

There are x = 4 options available for each club member.

Thus, there are several distinct vote totals that could occur:

n ×4 = number of distinct votes possible

= 50 × 4

= 200

As a result, 200 votes are conceivably cast..

There might be 200 votes cast overall. Given that a certain club has 50 members.

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Answer:

Bonjour

h(x) = x² - 6x + 5 définie sur [0 ; 5 ]

1)

L' oiseau a commencé son vol à

h(0) =(0)² - 6(0) + 5 = 5 donc 5 mètres

3)

h(x) atteint son maximum pour x = -b/2a = 6 / 2 = 3

h(3) = 9 - 18 + 5 = -4 mètres

4)

(x-1)(x-5) = x² - 5x - x + 5 = h(x) ce qu'il fallait démontrer

5)

h(x) = 0 revient à

(x-1)(x-5) = 0 pour x = 1 et pour x = 5

L' oiseau est entré dans l'eau à 1 mètre et en est ressorti à 5 mètres

Bonne fin de journée

14-bit strings that contain exactly six 1's is 3003. the number of 14-bit strings that contain at least eleven 1's is 16384 - 16382 = 2. The number of 14-bit strings that contain at least one 1 is equal to the total number of 14-bit strings minus the number of 14-bit.

The number of 14-bit strings that contain exactly six 1's is equal to the number of ways to choose the positions for the 1's in the string. There are 14 positions in the string, and we need to choose 6 of them to be occupied by 1's. This can be done in 14 choose 6 ways, which is equal to 3003. The number of 14-bit strings that contain at least eleven 1's is equal to the total number of 14-bit strings minus the number of 14-bit strings that contain ten 1's or fewer. The total number of 14-bit strings is 2^14 = 16384, and the number of 14-bit strings that contain ten 1's or fewer is equal to the sum of the number of 14-bit strings that contain 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 1's. This sum is equal to 14 choose 0 + 14 choose 1 + 14 choose 2 + ... + 14 choose 10 = 1 + 14 + 91 + 364 + 1001 + 2002 + 3003 + 3432 + 3003 + 2002 + 1001 + 364 + 91 + 14 + 1 = 16382. Therefore, the number of 14-bit strings that contain at least eleven 1's is 16384 - 16382 = 2. The number of 14-bit strings that contain at least one 1 is equal to the total number of 14-bit strings minus the number of 14-bit

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AS per the given details, the system of linear inequalities for each ticket is  x + y ≥ 30, 7.5x + 12.5y ≤ 400

The term inequation is a claim that one quantity or algebraic expression has a value that is not equal to another.

Here we have given that Cian is buying movie tickets for a group. He wants to have at least 30 tickets and spend no more than $400. Adult tickets cost $12. 50 and child tickets cost $7. 50.

And we need to find the system of inequalities can be used to find the number of each type of ticket can could buy.

According to the given information, here we are given that,

The adult tickets cost $12.50 and the child tickets cost $7.50.

Let us consider the number of adult tickets be y and the number of child tickets be x.

Here we also given that, that Cian wants to spend no more than $400.

So, the system of inequations is written as

=> x + y  ≥ 30,

And the other inequality is written as,

=> 7.5x + 12.5y ≤ 400

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The two formulas for area of a triangle of sides a, b, c and height h for base b are

A = √(s×(s - a)×(s - b)×(s - c)) and

A = 1/2 × b × h

By Heron's formula area of a triangle of sides a, b, c and perimeter s = (a + b + c), the area of the triangle is

A = √(s×(s - a)×(s - b)×(s - c))

Also we know area of a triangle of base b and height h is given by the formula

A = 1/2 × b × h

So there are the two formulas for area of a triangle.

--The question is incomplete, answering to the question--

"What are the 2 formulas for area of triangle?"

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To find the slope from a table, you need to find the difference in the y-values (the dependent variable) between two points and divide it by the difference in the x-values (the independent variable) between those same two points.

This is known as the slope formula:

Here is an example of finding the slope from a table:

Suppose we have the following table:

x y

3 7

4 9

To find the slope between these two points, we can use the slope formula as follows:

slope = (9 - 7)/(4 - 3) = 2/1 = 2

So the slope between these two points is 2.

It's important to note that the slope is a measure of the slope of the line that passes through the two points. If you want to find the slope of the line that is the best fit for a larger set of data, you will need to use a different method, such as linear regression.

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The number of students that failed the examination in the class is 64

information from the problem

there are 160 students in a class

60% of students passed in examination

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

if 60% of the students passed the examination then the percentage that failed is solved by subtraction from 100. This is done by

= 100 - 60

= 40%

The number of failed students is solved by converting the 40% to a factor by diving by 100 such that 40% = 40 / 100 = 0.04

= 0.4 * 160

= 64

The total number of failed students is 64

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The statement is true that is root 2 over 2 is equal to 1 over root 2 is true we can write as √2/2=1/√2.

Given that,

We have to find is root 2 over 2 is equal to 1 over root 2.

We know that,

A number can be squared, but it can also be divided into its square root. The value we get from multiplying a number by itself yields its square value, whereas the value we get from finding a number that, when squared, yields the original value of the number yields its square root value.

Now,

Root 2 over 2 is equal to 1 over root 2 can write as

√2/2=1/√2

Taking multiplying √2 on both side.

√2/2×√2=1/√2×√2

(√2×√2)/2=(1×√2)/√2

2/2=√2/√2

1=1

Therefore, The statement is true that is root 2 over 2 is equal to 1 over root 2 is true we can write as √2/2=1/√2.

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The binomial factors of x²-16 is (x+4) and (x-4).

Binomial refers to an algebraic expression that only has two terms. A polynomial with two terms, it. It is referred to as a sum or difference between two or more monomials as well. It is a polynomial's most straightforward form.

Having two terms makes a polynomial a binomial. Binomials include, for instance, x 2 x -2 x2 and x 6 x -6 x6. This article will go over multiplying these binomials.

An integer that may be derived by evaluating a homogeneous polynomial with two terms is known as a binomial number in mathematics, more specifically in number theory.

Here, x²-16=0

Rewrite 16 as 42, and the expression will be equal to 0 if any of the factors on the left side of the equation are equal to 0.

x+4=0 and locate x.

Once x=-4 x-4=0 and x=4 are found.

As a result, the final solution is x = 4, 4 and all choices that lead to (x + 4) (x 4) = 0 are true.

Hence, The binomial factors of x²-16 is (x+4) and (x-4).

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Epidemiological process is used to determine the who had contacted with the measles and to identify those with immunity and assesses the probability of containing the measles .

The term "Epidemiology" is the study of the determinants, occurrence, and distribution of health and disease in a defined population. Infection is the replication of organisms in host tissue, which may cause disease. A carrier is an individual with no overt disease who harbors infectious organisms. Dissemination is the spread of the organism in the environment. Epidemiology process utilizes an organized approach to problem solving by:

(1) confirming the existence of an epidemic and verifying the diagnosis.

(2) developing a case definition and collating data on cases.

(3) analyzing data by time, place, and person.

(4) developing a hypothesis.

(5) conducting further studies if necessary.

(6) developing and implementing control and prevention measures.

(7) preparing and distributing a public report.

(8) evaluating control and preventive measures.

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Answer:

[tex]y=2x+11[/tex]

Step-by-step explanation:

[tex]m=\frac{3-(-1)}{-4-(-6)}=2 \\ \\ y+1=2(x+6) \\ \\ y+1=2x+12 \\ \\ y=2x+11[/tex]

The required average of Will's bowling average after 8 games is 126.

Given the information, Willis’s bowling average after 5 games was 120. In his next 3 games, Willis scored 118,124, and 142.

The average of the values is the ratio of the total sum of values to the number of values.

here,
An average of 8 games is given as,
As an average of 5 games is 120, taking this average as 1 term
Now,
Average = 120 + 118 + 124 + 142 / 4 = 504 / 4
Average = 126

Thus, Will's required bowling average after eight games is 126.

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Equation of the line that passes through (2, 0) and is parallel and perpendicular to the line shown is y = - x + 5

What is perpendicular?

Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular symbol,, can be used to graphically depict the condition of perpendicularity. It can be defined between two planes, two lines, or two planes and another line.

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x - 3 ← is in slope intercept form

with slope m = 1

Given a line with slope m then the slope of a line perpendicular to it is

= -  = -  = - 1, thus

y = - x + c ← is the partial equation of line j

To find c substitute (2, 0) into the partial equation

0 = - 2 + c ⇒ c = 0 + 2 = 2

y = - x + 2 ← equation of line j

Parallel lines have equal slopes, thus

y = - x + c ← is the partial equation of line k

To find c substitute (- 1, 6) into the partial equation

6 = 1 + c ⇒ c = 6 - 1 = 5

y = - x + 5 ← equation of line k

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The chi-squared statistic can be used to determine whether there is a significant association between the two variables.

What is chi-squared statistic?

When the sample sizes are large, a chi-squared test is a statistical hypothesis test used in the study of contingency tables. To put it another way, the main purpose of this test is to determine whether two category factors have independent effects on the test statistic.

To test whether people who kiss more than ten times a day wear brighter colors to work than those who do not, the appropriate test statistic to use would be the chi-squared statistic.

The chi-squared statistic is a measure of the difference between observed and expected frequencies in a contingency table.

Once we have the contingency table, we can calculate the chi-squared statistic using the following formula:

     [tex]chi-squared = ((observed - expected)^2 / expected)[/tex]

In this case, the null hypothesis is that there is no association between kissing more than ten times a day and wearing bright colors to work. To calculate the expected frequency of each cell, we need to use the formula:

    expected = (row total * column total) / sample size)

Plugging in the values from our contingency table, we can calculate the chi-squared statistic as follows:

     [tex]chi-squared = (10 - 15)^2 / 15 + (20 - 15)^2 / 15\\\\= 25 / 15 + 25 / 15\\\\= 2[/tex]

The chi-squared statistic can be used to determine whether there is a significant association between the two variables.

Refer following diagram.

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To achieve the goal you have to make the annual sales of home entertainment equipment $3. 45 million

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

The annual sales of home entertainment equipment in your area are $23 million.

You want to capture 15% of the market.

let x be the $x million sales to capture 15% of the market.

So,

$23 million  ----- 100%

$x million  ------- 15%

by doing cross multiplication we get,

x = (23 * 15) /100

x =  $3. 45 million

hence, to achieve the goal you have to make the annual sales of home entertainment equipment $3. 45 million.

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Answer:

Step-by-step explanation:

HE SPENDS 1/3 on food and saves.

Answer: He spends more on food

Step-by-step explanation:

First you have to make the denominator in each fraction equivalent

3/4 to 1/8      so you have to multiply 4 by 2 to get eight so you do the same to the numerator 3x2=6 so 6/8>1/8

There are a few different contexts in which the concept of continuity arises, and the specific conditions that must be satisfied for something to be considered continuous can vary depending on the context. Here are three common sets of conditions that are often used to define continuity:

In mathematics, a function is generally considered to be continuous if it satisfies the following three conditions:

In physics, a physical quantity is generally considered to be continuous if it can vary smoothly and continuously over a range of values, rather than taking on only discrete values.

In computer science, a function is generally considered to be continuous if it satisfies the following three conditions:

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There are a few different contexts in which the concept of continuity arises, and the specific conditions that must be satisfied for something to be considered continuous can vary depending on the context. Here are three common sets of conditions that are often used to define continuity:

In mathematics, a function is generally considered to be continuous if it satisfies the following three conditions:

In physics, a physical quantity is generally considered to be continuous if it can vary smoothly and continuously over a range of values, rather than taking on only discrete values.

In computer science, a function is generally considered to be continuous if it satisfies the following three conditions:

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Answer:

-2

Step-by-step explanation:

plug both equations in desmos graphing calculator website

and you can see that the solution (where both equations intersect)

is (-2,6)

solutions are (x,y)

so the x coordinate of the solution is -2

Answer:

x=5/6

Step-by-step explanation:

5/6+1/6=1

Answer: x= 5/6

Step-by-step explanation:

x + 1/6 = 1

Change 1 to an improper fraction = 6/6

x + 1/6 = 6/6

1/6 - 1/6 = 0

6/6 - 1/6 =5/6

 x = 5/6

Following are the steps to solve multi-step equations:

1. Paraphrase

2. Constituents

3. Division and/or addition

4. Subtraction and addition

Therefore,

Following are the steps to solve multi-step equations:

1. Paraphrase

2. Constituents

3. Division and/or addition

4. Subtraction and addition

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The roots of the quadratic equation 3x² - 10x + 8 = 0 are x = 4/3  and x = 2  .

The Roots of the quadratic equation are defined as the numerical values that satisfy the equation .

The quadratic equations is 3x² - 10x + 8 = 0  ;

⇒ 3x² - 6x -4x + 8 = 0   ...by using split the middle term method ;

⇒ 3x(x - 2) -4(x - 2) [tex]=[/tex] 0

⇒ (3x-4)(x-2) = 0 ;

⇒ 3x - 4 = 0   and   x - 2 = 0 ;

On solving further , we get

x = 4/3 and x = 2  .

Therefore , the required roots are 4/3 and 2 .

The given question is incomplete , the complete question is

What is the roots of the quadratic equation 3x² - 10x + 8 = 0 ?

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1. 4y

2. 2b

3. 3r

4. -1c

5. 5/3d+3b

6. 3x+2y^3 -4y

7. -2x+3y

8. 1/3

9. 27

10. 4

11. 12

Step-by-step explanation:

that means we need to transform the equation, so that it is in the form of

b = ...

b - c + d/8 = a | add c to both sides

b + d/8 = a + c | subtract d/8 from both sides

b = a + c - d/8

that's it.

Answer:

2[tex]\sqrt{10}[/tex]

Step-by-step explanation:

[tex]\sqrt{5}[/tex] * [tex]\sqrt{8}[/tex] =

[tex]\sqrt{5*8}[/tex] =

[tex]\sqrt{40}[/tex] =

[tex]\sqrt{4*10}[/tex] =  ==> 4 has a square root: [tex]\sqrt{4}[/tex] = 2

2 * [tex]\sqrt{10}[/tex] = 2[tex]\sqrt{10}[/tex].