What are the domain and range of the function F(x)=x^2+5x+6/x+2

The ball traveled approximately \(26.27\) units in total.

To calculate the distance the ball traveled, we can use the distance formula between two points in a Cartesian coordinate system.

Distance = \(\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1} )^{2} }\)

Let's calculate the distance between Player A and Player B first:

Distance_AB =

\(\sqrt{((16-2)^{2}+(9-4)^{2}) }\)

\(= \sqrt{(14^{2}+5^{2} ) } \\= \sqrt{(196 +25)} \\= \sqrt{221} \\= 14.87\)

Now, let's calculate the distance between Player B and Player C:

Distance_BC =

\(\sqrt{ ((25 - 16)^2 + (16 - 9)^2)}\\= \sqrt{ (9^2 + 7^2)}\\= \sqrt{(81 + 49)}\\= \sqrt{130}\\=11.40\)

Finally, we can calculate the total distance traveled by adding the distances AB and BC:

Total distance = Distance_AB + Distance_BC

\(= 14.87 + 11.40 \\= 26.27\)

Starting from Player A at \((2, 4),\) it was thrown to Player B at \((16, 9),\) covering a distance of about \(14.87\) units. From Player B, the ball was then thrown to Player C at \((25, 16),\) covering an additional distance of approximately \(11.40\) units.

Combining these distances, the total distance the ball traveled was approximately \(26.27\) units.

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Answer:

13.6 is the distance of BC

Answer:

108g

Explanation:

Weight of the atom of an element = 1.792x10-22 (Given)

Let the atomic mass of the atom be = x

x ms of the element contains Avogadro number of atoms = 6 × 10^23 atoms

Weight of one mole of atoms = atomic weight  

Where one mole = 6.022 × 10^23 atoms  

Weight of one atom = x/(6 × 10^23)

= 1.8 × 10^-22

Thus, the atomic weight will be -

x = 6 × 10^23 × 1.8 × 10^-22​ = 107.9 = 108 g

/mole

Therefore, the atomic mass of the element is 108 g/mole.

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Answer:

Step-by-step explanation:

Ok:

1. This is a percent problem!

45/100*15=

675/100=

6.75

2. Subtract:

15-6.75=

8.25$

Answer: 8.25$

Answer:

2

Step-by-step explanation:

1+1

2

2 ones equals 2 in total.

You can also use a calculator to input:

1

+

1

press equal

and it should give you 2.

Hope this helps :)

What percent of 150 is 90? ANS ________ %

In this problem

150 represent 100%

so

Applying proportion

Find out what percentage represent 90

so

100/150=x/90

solve for x

x=(100/150)*90

x=60%

Answer:

Step-by-step explanation:

The solution of the liner equation 6k + 10.5 = 3k + 12 is k = 1/2.

Here, 6k + 10.5 = 3k + 12

         6k - 3k = 12 - 10.5

         3k = 1.5

          k = 1.5/3

          k = 1/2

Thus, The solution of the liner equation 6k + 10.5 = 3k + 12 is k = 1/2.

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Answer:

2560000 or 2.56*10^6

Step-by-step explanation:

\(\frac{((-4)^6)^2*(-5^2)^3}{(-4)^6*(-5)^2}\)

\(\frac{(-4)^1^2*(-5^6)}{(-4)^6*(-5)^2}\)

\(\frac{16777216*15625}{4096*25}\)

\(\frac{262144000000}{102400}\)

\(2560000\)

a) We have shown that for every positive integer k, 1/k = 1/(k+1) + 1/(k(k+1)). b) We have found integers a = 2, b = 3, and c = 6 such that 1 = 1/a + 1/b + 1/c. c) The every integer n ≥ 3, there exist n integers a₁, a₂, ..., aₙ such that 1 = 1/a₁ + 1/a₂ + ... + 1/aₙ.

(a) To prove that every positive integer k satisfies 1/k = 1/(k+1) + 1/(k(k+1)), we can start by manipulating the right-hand side of the equation:

1/(k+1) + 1/(k(k+1))

= (k/(k(k+1))) + 1/(k(k+1)) (finding a common denominator)

= (k + 1)/(k(k+1)) (combining the fractions with the same denominator)

= 1/k (canceling out the common factor of (k+1) in the numerator and denominator)

Thus, we have shown that for every positive integer k, 1/k = 1/(k+1) + 1/(k(k+1)).

(b) To prove that there exist integers a < b < c such that 1 = 1/a + 1/b + 1/c, we can choose specific values for a, b, and c. Let's choose a = 2, b = 3, and c = 6:

1/2 + 1/3 + 1/6

= 3/6 + 2/6 + 1/6

= 6/6

= 1

Therefore, we have found integers a = 2, b = 3, and c = 6 such that 1 = 1/a + 1/b + 1/c.

(c) To prove that for every integer n ≥ 3, there exist n integers a₁, a₂, ..., aₙ such that 1 = 1/a₁ + 1/a₂ + ... + 1/aₙ, we can use the following construction:

Choose a₁ = 2, a₂ = 3, and a₃ = 6 as shown in part (b) above.

Now, for the remaining integers a₄, a₅, ..., aₙ, we can choose them to be equal to the least common multiple (LCM) of a₁, a₂, ..., aₙ₋₁. This guarantees that each term 1/aₖ, where k > 3, will have the same denominator and can be added to the other terms.

Since the LCM is a multiple of each of the previous integers, it is guaranteed that the sum of the reciprocals will be equal to 1.

Therefore, for every integer n ≥ 3, there exist n integers a₁, a₂, ..., aₙ such that 1 = 1/a₁ + 1/a₂ + ... + 1/aₙ.

The complete question is:

(a) Prove that every positive integer k satisfies 1/k=1/(k+1) + 1/ (k(k+1)).

(b) Prove that there exist integers a <b<c such that 1 = 1/a + 1/b + 1/c.

(c) Prove that for every integer n ≥ 3 there exist n integers \(a_1,a_2,.....,a_n\) such that \(1=1/a_1+1/a_2+.....1/a_n\)

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The minimum standard deviation required for the nominal value to be within the 99.9% confidence interval for the resistance population mean can be calculated using the concept of confidence intervals and the z-score.

In a confidence interval, the margin of error is determined by the z-score, which corresponds to the desired level of confidence. For a 99.9% confidence interval, the z-score is approximately 3.29.

To calculate the minimum standard deviation, we need to find the margin of error and then solve for the standard deviation. The margin of error is determined by multiplying the z-score by the standard deviation and dividing it by the square root of the sample size.

Since we have 100 resistors and the mean resistance is 99.9Ω, the sample size is 100 and the sample mean is 99.9Ω. The margin of error can be calculated as (z * standard deviation) / sqrt(n).

To have the nominal value within the 99.9% confidence interval, the margin of error should be less than or equal to 0.1Ω (half of the desired confidence interval). By substituting the values, we can solve for the minimum standard deviation.

Once the minimum standard deviation is determined, it ensures that the nominal value falls within the 99.9% confidence interval for the resistance population mean.

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The probability that if a random person is chosen from the group of lawyers, the person will be a liar is 38/45, or 0.84.

As a fraction: The probability is given as 38/45, which means that out of 45 people chosen randomly from the group of lawyers, 38 of them are expected to be liars.

As a decimal: To express the probability as a decimal, we divide the numerator (38) by the denominator (45):

38 ÷ 45 ≈ 0.8444444444444444

Rounded to two decimal places, this would be approximately 0.84.

As a percentage: To express the probability as a percentage, we multiply the decimal form by 100:

0.8444444444444444 * 100 ≈ 84.44%

Rounded to two decimal places, this would also be approximately 84.44%.

So, the probability that if a random person is chosen from the group of lawyers, the person will be a liar can be expressed as 38/45 as a fraction, approximately 0.84 as a decimal, or approximately 84.44% as a percentage.

This can be expressed as a fraction, decimal, or percentage, whichever is more helpful.

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Taylor series for x^3tan^-1x^2 at x0 = 0 can be found by using the power series operations. The Taylor series for x^3tan^-1x^2 at x0 = 0 is:

x^3tan^-1x^2 = x^3(x^2 - (x^2)^3/3 + (x^2)^5/5 - ...)

To find the Taylor series, we need to express the function as a sum of terms with powers of (x - x0). We can start by using the power series for tan^-1x:

tan^-1x = x - x^3/3 + x^5/5 - ...

Then, we substitute x^2 for x and multiply by x^3 to get:

x^3tan^-1x^2 = x^3(x^2 - (x^2)^3/3 + (x^2)^5/5 - ...)

This gives us the Taylor series for x^3tan^-1x^2 at x0 = 0.

We can simplify the expression by expanding the powers of x:

x^3tan^-1x^2 = x^5 - x^7/3 + x^9/5 - ...

This means that the function can be approximated by the sum of these terms, which become more accurate as we include more terms. The Taylor series can be useful for approximating functions and making calculations easier, especially when using computers to perform calculations.

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The radius of the circle is r = 3.78 cm for the given circle.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

Given that the angle of the sector of the circle is 1.2 radians the area of the sector is 54 cm².

The radius of the circle will be calculated as:-

Area = Angle x πr²

54 = 1.2 x πr²

r² = ( 54 ) / ( 1.2 x π )

r² = 14.32

r = √14.32

r = 3.78 cm

Therefore, the radius of the circle is 3.78 cm.

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In part (a), if the sum of entries in each row of an n x n matrix A is equal to a common constant s, then s is an eigenvalue of A.

In part (b), if the sum of entries in each column of an n x n matrix A is equal to a common constant t, then t is an eigenvalue of A.

Problem (a):

To show s is an eigen vlaue

Define an eigenvector, which is a non-zero vector v such that,

Av = λv,

where λ is the eigenvalue.

Now, consider the given n x n matrix A.

We know that the sum of the entries in each row is equal to s.

We can use this information to find an eigenvector with eigenvalue s.

Let v = [1, 1, ..., 1]T,

Where T denotes the transposition of a matrix.

This means that v is a column vector with n entries, all of which are 1.

Now, calculate Av:

Av = [s, s, ..., s]T

We can see that Av is a multiple of v,

Where the scalar multiple is s.

Therefore, we have,

⇒ Av = s.v

This shows that v is an eigenvector of A with eigenvalue s.

Hence, we have shown that s is an eigenvalue of A by finding an eigenvector.

Problem (b):

Defining an eigenvector, which is a non-zero vector v such that Av = λv, where λ is the eigenvalue.

Now, consider the given n x n matrix A.

We know that the sum of the entries in each column is equal to t. We can use this information to find an eigenvector with eigenvalue t.

We can start by considering the transpose of A, denoted by AT, which is also an n x n matrix.

The sum of the entries in each row of AT is equal to t, since the sum of the entries in each column of A is equal to t.

Now, let v = [1, 1, ..., 1]T,

where T denotes the transpose of a matrix. This means that v is a column vector with n entries, all of which are 1.

Now, calculate ATv,

ATv = [t, t, ..., t]T

We can see that ATv is a multiple of v, where the scalar multiple is t. Therefore, we have,

ATv = t.v

This shows that v is an eigenvector of AT with eigenvalue t.

But we know that the eigenvalues of A and AT are the same since they have the same characteristic polynomial.

Therefore, t is an eigenvalue of A with eigenvector v.

Hence, we have shown that t is an eigenvalue of A by finding an eigenvector.

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The complete question is attached below:

The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.

An equation is an expression that shows the relationship between two or more variables and numbers.

The graph of a quadratic equation has the shape of a parabola. The standard quadratic equation has the form:

y = ax² + bx + c

The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.

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Answer:

The correct answer is A:3

Step-by-step explanation:

Answer: $34

$26.5

Step-by-step explanation:

Membership cost per month = $25

Price of a slice of pizza for members= $1.50

How much would Aaliyah have

to pay the pizza shop if she bought 6 slices of pizza this month

Total cost of Aaliyah on 6 slices of pizza = membership cost per month + prices of 6 discounted pizza

= $25 + $1.50(6)

= $25 + $9

= $34

What would be the

monthly cost for a slices of pizza

Monthly cost of Aaliyah a slices of pizza = membership cost per month + price of 1 discounted pizza

= $25 + $1.5

= $26.5

The 10 expressions in Math are:

Math is a subject that can be intimidating to many, but it is a fundamental part of life that is necessary to understand. It is important to have a basic grasp of different expressions in order to be successful in math. This essay will explore the ten expressions of math and provide insight into their importance.

The first expression is the sum. This is the answer you get when adding two or more numbers together. For example, if you have the numbers 5, 7, and 8, the sum would be 20. Sums can also be used to find the total amount of a group of objects.

The second expression is the difference. This is the answer you get when subtracting two or more numbers. For example, if you have the numbers 8 and 5, the difference would be 3. Differences can also be used to find the difference between two amounts.

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The people living in the north America are involved in different economic activities like animal husbandry, industries, services, farming, fishing etcc …

the red triangle is the building

the black triangle is the house

x is the height of the building

we have a problem of Tales triangles semblants so we can use this equalities

the height of the building is 110.5 feet

Answer:

78

Step-by-step explanation:

Since the base angles are congruent, then the triangle is isosceles and

AB = BC , that is

5x - 19 = 2x + 11 ( subtract 2x from both sides )

3x - 19 = 11 ( add 19 to both sides )

3x = 30 ( divide both sides by 3 )

x = 10

Then

AB = BC = 2x + 11 = 2(10) + 11 = 20 + 11 = 31

Thus

perimeter = 31 + 31 + 16 = 78

Answer: 78

Step-by-step explanation:

Hey there!

-5s = -13

DIVIDE -5 to BOTH SIDES

-5s/-5 = -13/-5

CANCEL out: -5/-5 because it give you 1

KEEP: -13/-5 because it help solve for the s-value

NEW EQUATION: s = -13/-5

SIMPLIFY IT!
s = 13/5

Therefore, your answer is: s = 13/5

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

Isolate the term of s from one side of the equation.

First, you have to divide by -5 from both sides.

→ -5s/-5=-13/-5

Solve.

Divide the numbers from left to right.

→ -13/-5=13/5

\(\Longrightarrow: \boxed{\sf{s=\dfrac{13}{5} }}\)

I hope this helps! Let me know if you have any questions.

Answer:

The endpoint of an angle  

x

lies in the 4th quadrant. Here is why.

First of all, let's recall a few definitions.

Recall the definition of a trigonometric function  

sec

(

x

)

:

sec

(

x

)

=

(by definition)  

=

1

cos

(

x

)

Recall the definition of a trigonometric function  

cot

(

x

)

:

cot

(

x

)

=

(by definition)  

=

cos

(

x

)

sin

(

x

)

Step-by-step explanation:

jhyjyujtyuyju

Answer:

42/11!

Step-by-step explanation:

So first, you need to make sure you have the formula which is V= Base X height. The base is the area of 1 circle, so you multiply the radius X radius X PI.

1/3 x 1/3 is 1/9. 22/7 is used as pi so multiply 1/9 by 22/7 and you get 22/63. Now you divide that by 4/3. When dividing fraction, you keep the first decimal (4/3) the same, turn the division symbol into a multiplication one, and flip the last fraction (so 22/63 is now 63/22!).

Now you just solve 4/3 x 63/22, which will give you 252/66. Now simplify that by dividing both numbers by 3 until you get the smallest answer, which is 42/11!

The height of the cylinder is approximately 42/11 inches. The answer is option C.

Here, we have,

we know that,

The formula for the volume of a cylinder is V = πr²h,

where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cylinder is 1 and one-third in^3 and the radius is one-third in. Substituting these values into the formula, we get:

1 and one-third = 4/3

V = π(1/3)²h = 4/3

Simplifying the equation, we get:

h = (4/3) / (π(1/3)²)

  = (4/3) / (π/9)

  = (4/3) * (9/π)

  = 12/π

Approximating π as 22/7, we get:

h ≈ (12/π)

  ≈ (12/(22/7))

  = 42/11 inches

Therefore, the height of the cylinder is approximately 42/11 inches. The answer is option C.

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To calculate the concentrations of all species present in a 0.72 M NH3 solution (Kb=1.8×10−5), we can use the principles of the equilibrium expression for the dissociation of NH3 in water.

NH3 (ammonia) is a weak base that reacts with water to form NH4+ (ammonium) and OH- (hydroxide) ions. The equilibrium expression for this reaction can be written as:

NH3 + H2O ⇌ NH4+ + OH-

Since the initial concentration of NH3 is 0.72 M, we can assume that x mol/L of NH3 will dissociate to form x mol/L of NH4+ and OH-. Therefore, the concentrations of NH4+ and OH- will also be x mol/L.

To calculate the value of x, we can use the Kb expression, which relates the equilibrium constant to the concentrations of the species. In this case, Kb = [NH4+][OH-]/[NH3]. Substituting the known values, we have:

1.8×10−5 = x * x / (0.72 - x)

Solving this equation will give us the value of x, which represents the concentration of NH4+ and OH-. Finally, we can express the concentrations of NH3, NH4+, and OH- using two significant figures, separated by commas, based on the calculated value of x.

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The relation does not relate y as a function of x because point (2,2) and (3,2) have the same y value. Hence, option 2 is the correct answer.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

We know that a function is a relationship between inputs where each input is related to exactly one output.

In the given graph (2,2) and (3,2) have the same y value that is two inputs have same output.

Hence, the relation does not relate y as a function of x because point (2,2) and (3,2) have the same y value and option 2 is the correct answer.

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Answer:

8.6

Step-by-step explanation:

Answer:

10 books

Step-by-step explanation:

To find how much it can hold, divide what it can support by what the stuff it is holding weighs.

(3+(3/4) ) / (3/8) = (15/4) / (3/8) = (15/4)*(8/3) = 120/12 = 10

Answer:

10 books!

Step-by-step explanation:

3 3/4 divided by 3/8 = 10.

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The grade point average received by hector is 3.75.

Your grade point average (GPA) is calculated by dividing the total number of credits you have earned in high school by the sum of all of your course grades. The majority of colleges and secondary schools use a 4.0 scale to report grades. A perfect score, or an A, is a 4.0.

The unit value for each course in which a student obtains one of the grades mentioned above is multiplied by the grade point total for that grade to determine the GPA. Then, divide the sum of these products by the sum of the units. The cumulative GPA is calculated by dividing the total grade points by the total number of units.

3 a and one is B received by Hector.

The A = 4.0, B = 3.0, C = 2.0, D = 1.0 is given by college

We have GPA= A+A+A+B/4

GPA=4+4+4+3/4

GPA= 15/4

GPA=3.75

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Complete question

Hector Ramirez received three A's and one B in his college courses. What is his grade point average? Assume each course is three credits. A = 4.0, B = 3.0, C = 2.0, D = 1.0