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Answer:

(2,2)

Step-by-step explanation:

(5+-1/2,8+-4/2)

(-2,2)

The equation of the line through the points (−9,3) and (−6,−3) is y = -2x - 15.

To find the equation of the line through the points (−9,3) and (−6,−3), we use the point-slope formula given as

`y - y1 = m(x - x1)` where `m` is the slope of the line and `(x1, y1)` is the coordinates of a point on the line. The slope of the line can be found using the formula:

m = (y2 - y1) / (x2 - x1)Here, (x1, y1) = (−9,3) and (x2, y2) = (−6,−3)

Substitute the values in the formula, m = (-3 - 3) / (-6 + 9) = -6/3 = -2.Therefore, the slope of the line is -2.Now, we need to use one of the given points, say (−9,3), and the slope, m = -2, in the point-slope formula to find the equation of the line.y - y1 = m(x - x1)Here, (x1, y1) = (−9,3).

Substitute the values in the formula,y - 3 = -2(x - (-9))y - 3 = -2(x + 9)y - 3 = -2x - 18y = -2x - 18 + 3y = -2x - 15

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Step-by-step explanation:

See the missing reasons, in order from top to bottom:

Answer:

3\(x^{4}\)

Step-by-step explanation:

Using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{(m-n)}\)

Given

\(\frac{18x^8}{6x^4}\)

= \(\frac{18}{6}\) × \(\frac{x^8}{x^4}\)

= 3 × \(x^{(8-4)}\)

= 3\(x^{4}\)

The correct statement regarding the unit rate in this problem is given as follows:

Point (1,2) shows that the unit rate is of $2 per ounce.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The point of the graph is given as follows:

(1,2) -> x = 1, y = 2.

Hence the unit rate is given as follows:

k = y/x = 2/1 = 2.

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The value of the expression +, can be determined by performing matrix addition on the given matrices and then evaluating the resulting expression. Let's proceed with the calculations: Given matrices:

A = [[1, 2, 0], [3, 2 + c, -1], [2, 2 + c, 2 + c]]

B = [[0, 2 + c, -3], [3, c, -1], [0, 3, -1]]

Performing matrix addition on A and B, we add the corresponding elements:

A + B = [[1 + 0, 2 + (2 + c), 0 + (-3)],

[3 + 3, (2 + c) + c, -1 + (-1)],

[2 + 0, (2 + c) + 3, (2 + c) + (-1)]]

Simplifying further, we get:A + B = [[1, 4 + c, -3],

[6, 2 + 2c, -2],

[2, 5 + c, 1 + c]

Therefore, the value of + is equal to the matrix [[1, 4 + c, -3], [6, 2 + 2c, -2], [2, 5 + c, 1 + c]].

We can store this value in the string FG_sum using valid Python code formatting as follows:

FG_sum = "[[1, 4 + c, -3], [6, 2 + 2 * c, -2], [2, 5 + c, 1 + c]]"

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Answer:

Step-by-step explanation:

Increase

Increase = \(\dfrac{4}{5}-\dfrac{2}{5}=\dfrac{2}{5}\)

Increase percentage = 2/5 out of 2/5 * 100

                                    \(=\dfrac{2}{5}*\dfrac{5}{2}*100\)

                                     = 100 %

Answer:

x = 4, y = 3.

Step-by-step explanation:

2x - 2y = 2

2x + y = 11     Subtract:

-3y = -9

y = -9/-3

y = 3

Plug y = 3 in equation 1:

2x - 2(3) = 2

2x - 6 = 2

2x = 2 + 6 = 8

x = 4.

a.we get, `A = √(2α³/π)`.

b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

c.we can say that the variational principle is valid in this case.

(a) Let's find the normalization constant A.

We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization.  `∫⟨ψ|ψ⟩dx= 1`

Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`

Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`

Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`

Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,

`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`

We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.

Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`

Therefore, we get, `A = √(2α³/π)`.

Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.  

(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.

The first term represents the kinetic energy of the particle and the second term represents the potential energy.

We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`

The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.

Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.

Therefore, we can say that the variational principle is valid in this case.

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Answer:

There are 4 teams coach Matt could have

Each team consist of

4 Fifth graders per team and

9 Sixth graders per team

Step-by-step explanation:

Fifth graders = 16

Sixth graders = 36

Find the highest common factor of 16 and 36

16 = 1, 2, 4, 8, 16

36 = 1, 2, 3, 4, 6, 9, 12, 18, 36

The highest common factor of 16 and 36 is 4

Therefore,

There are 4 teams coach Matt could have

Fifth graders per team = 16 / 4

= 4 Fifth graders per team

Sixth graders per team = 36 / 4

= 9 Sixth graders per team

Answer:

4 5th graders and 9 6th graders

The expression that only uses multiplication and that is equivalent to x reduced by 1/8 of x is: x * (1 - 1/8).

An expression in mathematics is a combination of numbers, variables, and operations that represent a value or set of values.

The expression calculates the reduction of x by 1/8 of x by subtracting 1/8 of x from x, which is x * 1/8. By subtracting this from x, the expression calculates x reduced by 1/8 of x. The expression that only uses multiplication and that is equivalent to x reduced by 1/8 of x is:

x * (1 - 1/8).

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The perimeter of the figure is the sum of the lengths of all its sides. To calculate it, we need to find the perimeter of the rectangle and the circumference of the quarter circle and then add them together.

To find the perimeter of the rectangle, we need to sum up the lengths of all its sides. Let's assume the length of the rectangle is 'l' and the width is 'w'. Therefore, the perimeter of the rectangle is 2(l + w).

For the quarter circle, we need to find the circumference. The formula for the circumference of a circle is 2πr, where π is approximately 3.14 and 'r' is the radius. In this case, the radius is equal to half of the width of the rectangle. So the circumference of the quarter circle is 0.5πw.

To find the total perimeter, we add the perimeter of the rectangle and the circumference of the quarter circle:

Perimeter = 2(l + w) + 0.5πw

Now, you can substitute the given values for 'l' and 'w' to find the perimeter. Remember to use the approximation 3.14 for π.

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Answer:

p = 22/5

Step-by-step explanation:

50p+5=225

Subtract 5 from each side

50p+5-5=225-5

50p = 220

Divide by 50

50p/50 = 220/50

p = 22/5

Answer:

50p+5=225

(50p+5) + (-5) =225 + (-5)

50p + 5 - 5 = 225 - 5

50p = 220

(fraction: 50p/50 = fraction: 220/50)

Sorry but you need to finish it because i cant do exponits sorry...

Step-by-step explanation:

for the ones with the 1.43, it'll be written as an improper fraction. Let me know if you have questions,I've started it for you now try the rest

0.333 is apoximently 1/3

0.666 is aproximently 2/3

i couldnt find out the others tho s0rry

\Hoped that helped:P

Answer:

The GCF of 42 and 55 is 1.

Step-by-step explanation:

sorry it took me a while to write in my book

42 AND 55 ARE A PAIR OF CO-PRIME NUMBERS

CO PRIME:a pair of numbers which have the only common factor as 1 is called as co prime

Answer:

the gcf is 1

Step-by-step explanation:

Gabriel will have to make 25 trips to work in order to cycle a total of 50 kilometers, based on the unit rate of 2 kilometers per trip.

To solve this problem using unit rates, we can determine the rate at which Gabriel cycles by dividing the total distance cycled by the number of trips made.

In this case, Gabriel cycled a total of 16 kilometers by making 8 trips, resulting in a unit rate of 2 kilometers per trip (16 km ÷ 8 trips = 2 km/trip). To find out how many trips Gabriel needs to make to cycle 50 kilometers, we can use the same unit rate: 50 km ÷ 2 km/trip = 25 trips.

Therefore, Gabriel will need to make 25 trips to work to cycle a total of 50 kilometers.


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The limit of the sequence cn that diverges by using the appropriate Limit Laws or theorems  is ln(2/3).

A limit is a fundamental concept in calculus that describes the behavior of a function as its input values approach a certain value, often infinity or negative infinity.

More specifically, the limit of a function f(x) as x approaches a number is the value that f(x) gets arbitrarily close to as x gets arbitrarily close to a. We denote the limit of f(x) as x approaches a by the notation:

\(\lim_{x \to \ a} f(x)\)

To determine the limit of the sequence c_n = ln((4n-7)/(6n+4)) as n approaches infinity, we can use algebraic manipulation and the properties of limits as follows:

\(cn = ln((4n-7)/(6n+4))\\= ln(4n/6n × (1-7/(4n))/(1+4/(6n)))\\= ln(2/3 × (1-7/(4n))/(1+2/(3n)))\\= ln(2/3) + ln((1-7/(4n))/(1+2/(3n)))\)

As n approaches infinity, the fraction (1-7/(4n))/(1+2/(3n)) approaches 1 since the denominator becomes much larger than the numerator. Therefore, we have:

\(\lim_{n \to \infty} (1-7/(4n))/(1+2(3n)) = 1\)

By the continuity of the natural logarithm function, we can then take the limit inside the logarithm and obtain:

\(\lim_{n \to \infty} cn = ln(2/3) + ln(1) = ln(2/3)\)

Therefore, the limit of the sequence cn is ln(2/3).

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The value of expression 7 (y - 4) - 1 if, y = 11 is 48, so option C is correct.

At least two numbers or variables, one or more arithmetic operations, and a statement are all required components of a mathematical expression.

The term "expression" or "mathematical expression" refers to a finite collection of symbols that are well-formed in line with context-dependent criteria.

Given:

One less than seven times difference between a number and four,

The value of y = 11,

The above statement can be written as shown below,

7 (y - 4) - 1

Put the value of y as shown below,

7 (y - 4) - 1 = 7 (11 - 4) - 1

7 (y - 4) - 1 = 7 × 7 - 1

7 (y - 4) - 1 = 49 - 1

7 (y - 4) - 1 = 48

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Answer:

Step-by-step explanation:

We need to create an equation to represent how many air fresheners the teacher can buy.

Teacher has $10 and a $3 discount coupon which would give her an extra $3 to spend. Each air freshener is $3.50.

x = number of air fresheners

($10 + $3) / $3.50 = x        can be written as $13/$3.50 = x

We add $10 and $3 because that gives us the total amount she has to spend.

We divide by $3.50 because that is the cost of each air freshener. The result is the number of air fresheners she can buy.

In this case.

$13/$3.50 = x

3.71 = x   BUT we can't buy part of an air freshener, so she can purchase 3 air fresheners.

The probability that a fair coin comes up heads for the first time after an odd number of coin flips is 1/2. This means that there is an equal chance of getting heads or tails on any given flip, and the outcome of each flip is independent of previous flips.

When a fair coin is tossed, the probability of getting either heads or tails is 1/2. Let's consider the possible scenarios for getting heads for the first time after an odd number of flips. The first flip can either be heads (with probability 1/2) or tails (also with probability 1/2). If the first flip is tails, we are back to the starting point and have to repeat the process. In each subsequent round, the probability of getting heads for the first time after an odd number of flips remains the same, 1/2.

Therefore, the probability of getting heads for the first time after an odd number of flips is the sum of an infinite geometric series with a first term of 1/2 and a common ratio of 1/2. Using the formula for the sum of an infinite geometric series, which is a/(1-r), where a is the first term and r is the common ratio, we can calculate the probability as 1/2 divided by (1 - 1/2), which simplifies to 1/2. Hence, the probability is 1/2.

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Answer:

(-11/4, -1/2)

Step-by-step explanation:

Too much to explain

Answer:

right angle

Step-by-step explanation:

Answer:a,b, and d

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The equation 480t = 1200 can be used to find the number of hours an aircraft takes to reach a destination that is 1200 miles away.

The correct answer is option (C) 480t = 1200.

"An equation is a mathematical statement that is made up of two expressions connected by an equal sign."

speed = distance / time

For given question,

An aircraft flies at a speed of 480 miles per hour and takes t hours to reach its destination.

Let d represents the distance(in miles) traveled by an aircraft in t hours with a speed of 480 miles per hour.

By using the formula of speed,

⇒ 480 = d/t

When destination is 1200 miles away.

This means d = 1200 miles.

⇒ 480 = 1200/t

⇒ 480t = 1200                      .....................(Multiplying both the sides by t)

This equation can be used to find the number of hours it takes the aircraft to reach a destination that is 1200 miles away.

Therefore, option (C) is the correct answer.

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Answer:

12

Step-by-step explanation:

7 times 3 is 21

and 4 times 3 is 12

Answer:

12

Step-by-step explanation:

first do 7 divided by 4 to find what 1 is worth. this answer is 1.75

now divide 21 by 1.75 to get 12

12 is your answer

hope this helped :)

Answer: x=1

Step-by-step explanation:

x-5=2x-6

x-5+6=2x-6+6

x+1=2x

x-x+1=2x-x

2x-x=1

x=1

Answer: x = 1

Step-by-step explanation:

fewer or less than means minus -

difference of x and 5 = x - 5

6 fewer = - 6

twice the number of x = 2x

x - 5 = 2x - 6

x = 2x - 6 + 5

x -2x = - 6 + 5

- x = - 1

x = 1

checking

1 - 5 = 2(1) - 6

4 = 2 - 6

4 = 4

The negative sign indicates that the power is flowing in the negative x-direction.

To solve this problem, we can use the relationships between the electric field (E), magnetic field (H), and power density (P) in electromagnetic waves.

Given:

Incident H field phasor: H = ay8e30x (A/m)

Relative electrical permittivity of the dielectric medium: εr = 4

Boundary surface area radius: r = 60 cm = 0.6 m

We'll go through each part of the problem step by step:

a) Electric field phasor:

The relationship between the electric field and magnetic field in a plane wave is E = (1/η) x H, where η is the intrinsic impedance of the medium.

The intrinsic impedance of a dielectric medium is given by η = η0/√εr, where η0 is the impedance of free space (approximately 377 Ω).

Substituting the values, we have:

η = η0/√εr = 377/√4 = 188.5 Ω

Thus, the electric field phasor is:

E = (1/η) x H = (1/188.5) x (ay8e30x) = (ay4.22e-2x) V/m

b) Average incident power density vector:

The average power density (P) of an electromagnetic wave is given by P = (1/2)Re(E x H*), where H* denotes the complex conjugate of H.

Taking the real part, we have:

P = (1/2)Re(E x H*) = (1/2)Re[(ay4.22e-2x) x (ay8e30x)*]

= (1/2)Re[(-32.16ae28x)] = -16.08e28x W/m²

The negative sign indicates that the power is flowing in the negative x-direction.

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The match of vector field f for  f(x, y) = y, x is graph II .

We can say that some points for the given function are F(1,2)= (2,1) F(2,1) =(1,2) F(0,1) = (1,0) F(2,3) = (3,2) F(0,2)=(2,0) .

That means arrow heads should start with these points and this is shown accordingly in graph II only.

Therefore ,

option A matches with figure 2

option B matches with figure 1

option C matches with figure 3

option D matches with figure 4

A vector field is a way to visualize them as represented by a number of small arrows each having a magnitude or a direction.

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Each factored version of a basic quadratic equation therefore contains two zeros. an equation with a degree 2 single variable. With x being the variable and a, b, and c being constants (a 0), it has the general form ax2 + bx + c = 0.

A quadratic equation is a second-order polynomial equation in one variable that goes like this: x ax2 + bx + c=0, where a 0. Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. The resolution could be simple or complicated.

given

1) y = \(x^{2} - 9x -36\)

= y = \(x^{2} -12x + 3x -36\\x(x+3)-12(x+3)\\(x+3)(x-12)\)

2) y =\(x^{2} +5x -24\\x^{2} +8x-3x -24\\x(x+8)-3(x+8)\\(x+8)(x-3)\)

so each simple quadratic equations to factored form has 2 zeros .

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