Rectangular flower bed needs a thin metal border all the way around. The sides are 4' x 3' long how many feet of border should be purchased? Find the perimeter

Answer:

0 and 4

Step-by-step explanation:

0+0=0

2+2=4

hope this helps

Answer:

1st one is 0, 2nd one is 4.

To find the derivative of the function y=(x^2+4)/(x^2-4)^5, we need to use the chain rule and the quotient rule.
First, we can simplify the function by factoring the numerator and denominator:
y = [(x^2+4)/(x^2-4)]^5
y = [(x^2-4+8)/(x^2-4)]^5
y = [(x^2-4)/(x^2-4) + 8/(x^2-4)]^5
y = [1 + 8/(x^2-4)]^5

Now, we can use the chain rule:
Let u = x^2-4
y = [1 + 8/u]^5
y' = 5[1 + 8/u]^4 * (8/u^2) * u'
y' = 40(x^2-4)^-2(1+8/(x^2-4))^4(x)

Therefore, the derivative of the function y=(x^2+4)/(x^2-4)^5 is:
y' = 40(x^2-4)^-2(1+8/(x^2-4))^4(x)

Step 1: Identify the outer function and the inner function.
Outer function: f(u) = u^5
Inner function: u = x^2 + 4/(x^2 - 4)

Step 2: Find the derivatives of the outer function and the inner function.
f'(u) = 5u^4 (derivative of the outer function)
du/dx = 2x - 4(x^2 - 4)^(-1)(2x) (derivative of the inner function)

Step 3: Apply the chain rule.
dy/dx = f'(u) * du/dx
dy/dx = 5u^4 * (2x - 4(x^2 - 4)^(-1)(2x))
dy/dx = 5(x^2 + 4/(x^2 - 4))^4 * (2x - 4(x^2 - 4)^(-1)(2x))

So, the derivative of the function y = (x^2 + 4/(x^2 - 4))^5 is:

dy/dx = 5(x^2 + 4/(x^2 - 4))^4 * (2x - 4(x^2 - 4)^(-1)(2x))

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Answer:

b

Step-by-step explanation:

math

The equation of the graph shown can be written in factored form as follows:

y = a(x - h)(x - k)(x - m)

To find the equation, we need to identify the x-intercepts and the minimum point of the graph.

From the description, we know that the graph starts at the top left and continues down through the x-axis at x = -4. This means that one of the factors is (x + 4).

Next, the graph reaches a minimum around y = -2.8. This indicates that the graph touches the x-axis at this point, so another factor is (x + 2).

Moving forward, the graph goes back down to another minimum around y = -0.4. Again, this means the graph touches the x-axis at this point. So we have another factor, (x + 1).

Now we have all the necessary factors: (x + 4), (x + 2), and (x + 1). To determine the coefficient "a," we can use the fact that the graph goes up after crossing the x-axis at x = -2. This suggests that "a" must be positive.

Therefore, the equation of the graph in factored form is:

y = a(x + 4)(x + 2)(x + 1)

Please note that without specific points, it is not possible to determine the exact value of "a" or the precise shape of the graph. The equation provided represents a general equation that satisfies the given conditions.

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Answer:

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

W is a subset of span(w), and span(w) is closed under vector addition, scalar multiplication, and contains the zero vector, we know that w must also have these properties. Therefore, w is a subspace of v.

To show that a subset w of a vector space v is a subspace of v if and only if span(w) = w, we need to prove both directions of the equivalence:

First, we'll assume that w is a subspace of v. In this case, we know that w is closed under vector addition and scalar multiplication, and that it contains the zero vector.

To show that span(w) = w, we need to prove two things:

span(w) is a subset of w: This is true by definition of span(w) - every vector in span(w) can be written as a linear combination of vectors in w, so it must be in w as well.

w is a subset of span(w): This is also true, because every vector in w is itself a linear combination of vectors in w (namely, itself with a coefficient of 1), so it is also in span(w).

Therefore, we have shown that span(w) = w.

Next, we'll assume that span(w) = w. In this case, we know that every vector in w can be written as a linear combination of vectors in w. We need to show that w is closed under vector addition and scalar multiplication, and that it contains the zero vector.

Let u, v be two vectors in w, and let c be a scalar. Then we can write:

\(u = a1w1 + a2w2 + ... + anwn\)

\(v = b1w1 + b2w2 + ... + bnwn\)

where w1, w2, ...,\(wn\) are vectors in w, and a1, a2, ..., an, b1, b2, ...,\(bn\)are scalars.

Then, we have:

\(u + v = (a1+b1)*w1 + (a2+b2)*w2 + ... + (an+bn)*wn\)

which is a linear combination of vectors in w, so u + v is in w.

Also, we have:

\(cu = c(a1w1 + a2w2 + ... + anwn) = (ca1)w1 + (ca2)w2 + ... + (can)*wn\)

which is also a linear combination of vectors in w, so c*u is in w.

Finally, since w is a subset of span(w), and span(w) is closed under vector addition, scalar multiplication, and contains the zero vector, we know that w must also have these properties. Therefore, w is a subspace of v.

Therefore, we have shown both directions of the equivalence, and proved that a subset w of a vector space v is a subspace of v if and only if span(w) = w.

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Answer:

Calculator Use. Convert improper fractions to mixed numbers in simplest form. This calculator also simplifies proper fractions by reducing to lowest terms hope this helps

Answer:

b

Step-by-step explanation:

Answer:

Henry's cousin went to an audition.

Step-by-step explanation:

Answer:

this is no answer

The solution of the given inequalities is y>-3 and y>4 respectively.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given inequalities are -3y > 9 and 2y - 6 > 2.

-3y > 9

y > -9 / 3

y > -3

The second inequality will be calculated as,

2y - 6 > 2

2y > 2 + 6

2y > 8

y > 4

Therefore, the solution of the given inequalities is y>-3 and y>4 respectively.

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1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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Answer:

x = 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Geometry

Step-by-step explanation:

Step 1: Set up Equation

(7x - 1) + 80 + (6x - 3) = 180

Step 2: Solve for x

Answer: x = 8

Step-by-step explanation:

Hoped this helped

any nonzero vector in R^3 can be an eigenvector of T with eigenvalue λ = -1. For example, the vector (1, 0, 0) is an eigenvector of T with eigenvalue λ = -1, since T sends it to its negative (-1, 0, 0). Similarly, (0, 1, 0) and (0, 0, 1) are also eigenvectors of T with eigenvalue λ = -1.

To find the matrix for the linear transformation T that reflects all vectors in R^3 through the xy plane, we first need to determine how T affects the standard basis vectors.

T sends the vector (1, 0, 0) to (-1, 0, 0), since reflecting across the xy-plane negates the z-coordinate. Similarly, T sends (0, 1, 0) to (0, -1, 0), and (0, 0, 1) to (0, 0, -1). Therefore, the matrix for T with respect to the standard basis is:

[T] = [ -1  0  0 ]

     [  0 -1  0 ]

     [  0  0 -1 ]

To find the eigenvalues and eigenvectors of T, we can solve the characteristic equation:

det([T] - λ[I]) = 0

where I is the 3x3 identity matrix. Substituting the matrix for T and expanding the determinant, we get:

det([T] - λ[I]) = det([ -1-λ   0     0   ])

                 det([  0    -1-λ   0   ])

                 det([  0     0   -1-λ ])

               = (-1-λ)(-1-λ)(-1-λ)

               = -(λ+1)^3

Therefore, the only eigenvalue of T is λ = -1, and we need to find its eigenvectors. To do this, we need to solve the system of equations:

([T] - (-1)[I])v = 0

Substituting the matrix for T and the eigenvalue λ = -1, we get:

[   0    0    0 ][x]   [0]

[   0    0    0 ][y] = [0]

[   0    0    0 ][z]   [0]

This system of equations has a rank of 0, which means that there are infinitely many solutions.

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Assuming y[-1] = 0, we can solve this equation recursively for n ≥ 0.

To find the unit-pulse response h[n] for the given discrete-time systems, we can solve for y[n] when the input x[n] is a unit pulse.

For the system y[n+1] + 0.5y[n] = x[n+1]:

We can substitute x[n] = δ[n], where δ[n] is the unit pulse.

y[n+1] + 0.5y[n] = δ[n+1]

Next, we can express y[n+1] in terms of y[n] and solve the equation.

y[n+1] = -0.5y[n] + δ[n+1]

Since the initial condition is not provided, we assume y[-1] = 0.

For n = 0, the equation becomes:

y[1] = -0.5y[0] + δ[1]

For n = 1, the equation becomes:

y[2] = -0.5y[1] + δ[2]

By substituting the value of y[1] from the previous equation, we can continue this process recursively to find y[n] for n ≥ 0.

For the system y[n+1] + 1.5y[n] = x[n]:

Following the same procedure, we substitute x[n] = δ[n] into the equation:

y[n+1] + 1.5y[n] = δ[n]

Again, assuming y[-1] = 0, we can solve this equation recursively for n ≥ 0.

Note that finding a closed-form solution for the pattern of y[n] might not be straightforward, as it depends on the initial conditions and the specific values of the unit pulse at different time indices.

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Taner will only need to run 3 km this week to complete his 6 km running goal.

If we require a definition, we may start by saying that fractional numbers are numbers that symbolize one or possibly more portions of a unit that has been subdivided into equal parts.

Given that, Taner's overall running goal is 6 km (including last week and this week)

So,

Taner's 2-week goal is 6 kilometres.

Now,

Taner's goal for the week is 3 kilometres = (6/2).

As the Taner completed 3 km of running last week. Taner can achieve his objective this week by running just 3 miles.

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Design Brief: Electricity Price Reduction Device

The objective of this design project is to develop a cost-effective device that addresses the root cause of increasing electricity prices. The device should tackle factors such as inefficient energy distribution, high transmission losses, or excessive consumption.

It should be scalable and adaptable to various electricity infrastructures. The device must be safe, environmentally friendly, and comply with industry standards.

Cost efficiency and reliability are critical considerations. The design should enable easy installation and maintenance while maximizing energy efficiency.

Ultimately, the device aims to significantly reduce electricity costs, promoting affordability and sustainability for consumers and businesses alike.

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Answer:

19

Step-by-step explanation:

A' represents everything out A

B' represents everything out B

C' represents everything out C

So only the outside is left hope this helps

The given statement "The q-system of inventory submits inventory orders at random times" is true because it is based on the q-model's assumption that demand is random and that inventory is replenished when it falls to a certain level.

The q-system of inventory, also known as the q-model or the reorder point system, is a method of inventory control that sets a reorder point (q) at which inventory is replenished.

The system assumes that demand for inventory is random and that inventory is replenished when it falls to the q-level. Since demand is random, orders will be submitted at random times based on the inventory level, and not according to a predetermined schedule.

Therefore, the given statement is true because the q-system of inventory submits inventory orders at random times based on the random demand for inventory.

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Answer:

14.5

Step-by-step explanation:

The radius is half the diameter.

29/2=14.5

Step-by-step explanation:

6 notebooks = $d

1 notebook = $?

So

1 notebook price = $d ÷ 6

Answer:

Step-by-step explanation:

n represents the number of notebooks

d represents the cost of a notebook

n = d            one notebook = d dollars

9n = 9d        multiply both sides by 9

Given that each cube represents 1 cubic units, we need to count how many cubes are in the figure.

From the front view, we count 2 cubes.

From the back view, we count 5 cubes.

There are 5 + 2 = 7 cubes in total, so the volume of the figure is 7 cubic units.

Answer:

The shortest altitude is 6.72 cm

Step-by-step explanation:

Given that the side lengths are

24 cm, 25 cm, 7 cm

The area of a triangle =

\(A = \sqrt{s \cdot (s-a)\cdot (s-b)\cdot (s-c)}\)

Where;

s = Half the perimeter = (24 + 25 +  7)/2 = 28

A = √((28×(28 - 24)×(28 - 25)×(28 - 7)) = 84 cm²

We note that 84/7 = 12

Therefore, the triangle is a right triangle with hypotenuse = 25, and legs, 24 and 7, the height of the triangle = 7

To find the shortest altitude, we utilize the formula for the area of the triangle A = 1/2 base × Altitude

Altitude  = A/(1/2 ×base)

Therefore, the altitude is inversely proportional to the base, and to reduce the altitude, we increase the base as follows;

We set the base to 25 cm to get;

Area of the triangle A =  1/2 × base × Altitude

84 = 1/2 × 25 × Altitude

Altitude = 84/(1/2 × 25) = 6.72 cm

The shortest altitude = 6.72 cm.

Answer:

Step-by-step explanation:

Dont do it. Just take the detention

Among the options provided, option C is true: software programming does involve multiple roles. Option C

A. Basically the maintenance is very minimal not greater than 60% of overall development costs.

This statement is not necessarily true. While it is true that maintenance costs can vary depending on the specific software and its usage, it is not accurate to say that maintenance is always minimal and not greater than 60% of overall development costs.

Maintenance can be a significant portion of the total cost of software development, especially for complex systems or long-term projects. It involves activities such as bug fixing, updates, enhancements, and support, which can require substantial resources.

B. Indefinite lifespan.

This statement is generally not true. Software typically has a finite lifespan. The lifespan of software can vary depending on factors such as its purpose, technology advancements, user needs, and market demand.

Software may become obsolete or be replaced by newer versions or alternative solutions over time. However, some software may have longer lifespans if it continues to serve a critical purpose and undergoes regular updates and maintenance.

C. Involve multiple roles.

This statement is true. Software programming typically involves multiple roles. Developing software requires a collaborative effort and involves various roles such as software developers, software architects, quality assurance engineers, project managers, and stakeholders. Each role plays a crucial part in the software development lifecycle, contributing their expertise and responsibilities to ensure the successful creation and delivery of software applications.

Option C is correct.

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The probability of a person being randomly choosing having waiting time greater than 4.25 is 0.2917 or 29.17%.

To answer this question we need to know about-

Probability is the measure of the likelihood of an event to happen. The probability value ranges between 0 and 1.

When the probability value is 0, it means that the event is impossible to happen.

When the probability value is 1, it means that the event is certain to happen.

Uniform distribution is when the values of a probability distribution are spread uniformly across the interval, it is called a Uniform distribution

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes.

The probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is found as follows:

Let X = Waiting time of a randomly selected passenger P(X > 4.25) = ?

Now we have to use the uniform distribution formula to find the probability:

P(C< X >D)=C-D/B-A

where C = lower value of the selected interval

           D= upper value of the selected interval

           B= highest value of the selected interval

           A= lowest value of the selected interval

putting above values in the formula -

P(X > 4.25) = 6 - 4.25/6-0= 0.2917

Hence the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is 0.2917.

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The sag in the cable for problem 5/160 is approximately 24.4 meters.

To solve the problem of finding the sag in a cable, we can use the catenary equation. The equation is given by:

y = a cosh(x/a)

For problem 5/159, we were given a cable weighing 25 N/m and spanning a distance of 160 m. We can find the tension in the cable by using the formula:

T = wL/2

Substituting in our values, we get:

T = (25 N/m)(160 m)/2 = 2000 N

Now we can solve for a by using the formula:

a = T/(w*g)

where g is the acceleration due to gravity. Substituting in our values, we get:

a = (2000 N)/((25 N/m)*9.81 m/s^2) ≈ 8.13 m

Finally, we can find the sag at the midpoint of the cable (x = L/2) by plugging into the catenary equation:

y = a cosh(x/a) = (8.13 m) cosh(80 m/8.13 m) ≈ 24.6 m

Therefore, the sag in the cable is approximately 24.6 meters.

For problem 5/160, we are given a similar situation but with a shorter span of 159 meters. Using the same method as above, we find that:

T = (25 N/m)(159 m)/2 = 1987.5 N

a = (1987.5 N)/((25 N/m)*9.81 m/s^2) ≈ 8.06 m

y = a cosh(x/a) = (8.06 m) cosh(79.5 m/8.06 m) ≈ 24.4 m

Therefore, the value obtained is approximately 24.4 m.

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Answer:

Step-by-step explanation:

You will need to subtract the amount paid from the total amount

100 - 46.23

= 53.77

Ricardo will receive $53.77 in change. :)

Answer:

I would say the answer is A because its closest to the number 300

Step-by-step explanation:

i hope i helped if its wrong im sorry

Answer: 2.5, 5.4

Step-by-step explanation:

\(-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4\)

9514 1404 393

Answer:

  x = 25; ∠3 = ∠6 = 60°

Step-by-step explanation:

Angles 3 and 6 are alternate interior angles, so are congruent.

  2x +10 = 3x -15

  25 = x . . . . . . . . . . . add 15-2x

  2x +10 = 2(25) +10 = 60

The measures of angles 3 and 6 are 60°.

The contrapositive of the conditional statement is D. If the graph of two variables is not a linear function, then the two variables are not directly proportional.

"In the event that the graph of two variables fails to exhibit linearity, it can be inferred that the two variables are not directly proportional.

This contrapositive statement provides an alternative perspective on the relationship between variables and the nature of their corresponding graphs.

By examining the contrapositive, we employ an analytical approach that explores the logical implications arising from the negation of the original conditional statement. Consequently, if the graph of two variables deviates from the linear pattern, it leads us to the logical conclusion that the variables themselves are not directly proportional.

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