Rugged cabin co. provides pre-made materials to build cabins. to ensure materials are in supply and ready for quick delivery, the company offers cabins in only three sizes. each cabin has rectangular floor plan where the length is equal to 5 feet more than twice the width. which expression represents the area, in square feet, for each cabin size?

Answer:

4x^2 - 10x + 1 units

Step-by-step explanation:

(3x - 1) + (x + 2) + (3x^2 - 11x) + (x^2 - 3x)

Adding like terms:

3x^2 + x^2         = 4x^2

-11x - 3x + 3x + x    = -10x

-1 + 2            = 1

Summing it up; the perimeter is
4x^2 - 10x + 1 units

Answer:

4 platters

Step-by-step explanation:

The recurrence relation and initial conditions for the sequence s: 2, 4, 10, 28, ..., 3n 1, ... is \(a_{n+1} = 3a_n - 2\) & \(a_0 = \frac{4}{3}\).

Given that:

s: 2, 4, 10, 28, ..., 3n 1, ...

We know that the first order linear recurrence relation is of the form

\(a_{n+1} = ra_n + d\)

Where r and d are constants.

In the given sequence

a1 = 2, a2 = 4, a3 = 10, a4 = 28

 \(a_{n+1} = ra_n + d\)

4 = 2r + d                - 1

10 = 4r + d              - 2

From equation 2 - equation 1, we get

2r = 6

r = 3

We have to substitute r = 3 in 4 = 2r + d

= d = -2

Therefore the required first order linear recurrence relation is

\(a_{n+1} = 3a_n - 2\)

For initial condition put n = 0 in \(a_{n+1} = 3a_n - 2\)

Therefore:

\(a_{1} = 3a_0 - 2\\\\3a_0 = a_1+2\\\\a_0 = \frac{4}{3}\)

Hence the answer is the recurrence relation and initial conditions for the sequence s: 2, 4, 10, 28, ..., 3n 1, ... is \(a_{n+1} = 3a_n - 2\) & \(a_0 = \frac{4}{3}\).

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The recurrence relation and initial conditions for the sequence s: 2, 4, 10, 28, ..., 3n 1, ... is  & .

Given that:

s: 2, 4, 10, 28, ..., 3n 1, ...

We know that the first order linear recurrence relation is of the form

aₙ₊₁ = raₙ + d

Where r and d are constants.

In the given sequence

a₁ = 2, a₂ = 4, a₃ = 10, a₄ = 28

aₙ₊₁ = raₙ + d

4 = 2r + d                - 1

10 = 4r + d              - 2

From equation 2 - equation 1, we get

2r = 6

r = 3

We have to substitute r = 3 in 4 = 2r + d

= d = -2

Therefore the required first order linear recurrence relation is

aₙ₊₁ = 3aₙ - 2

For initial condition put n = 0 in

Therefore:

a₁ = 3a₀ - 2

3a₀ = a₁ + 2

a₀ = (2 + 2)/3

a₀ = 4/3

Hence the answer is the recurrence relation and initial conditions for the sequence s: 2, 4, 10, 28, ..., 3n 1, ... is  & .

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Answer:

N=7a-3

A) a-16

U) -5a-9

Step-by-step explanation:

First you need to group the like terms

for example

-7a+2a-4-5

Next

You need to subtract the numbers -4-5 so it equals

-9

Add the rest -7a+2a=-5a

Where your answer would then be -5a-9

Hope this helps I only did the first 3 for you!

The integral (12x + 12y) dA over the region R, using the given transformation, evaluates to 64. The new limits of integration are u = -6 to u = 6 and v = -6 to v = 6.

To evaluate the integral (12x + 12y) dA over the region R, we need to perform a change of variables using the given transformation:

\(x &= \frac{1}{3}(u + v) \\\)

\(y &= \frac{1}{3}(v - 2u)\)

First, let's find the Jacobian determinant of the transformation:

\(J = \frac{\partial{(x, y)}}{\partial{(u, v)}}\)

\(J = \frac{\partial{(x, y)}}{\partial{(u, v)}}\)

\(\left| \frac{\partial x}{\partial u} \ \frac{\partial x}{\partial v} \right|\)

\(\[= \left| \frac{1}{3} \ \frac{1}{3} \right|\]\)

\(=\[| -\frac{2}{3} \ \frac{1}{3} |\]\)

\(=\frac{1}{3}\)

Now, let's find the new limits of integration by substituting the given vertices of R into the transformation:

When (x, y) = (-2, 4):

\(\[-2 = \frac{1}{3}(u + v)\]\)

\(\[4 = \frac{1}{3}(v - 2u)\]\)

Solving these equations, we get u = 0 and v = -6.

When (x, y) = (2, -4):

\(\[2 = \frac{1}{3}(u + v)\]\)

\(\[-4 = \frac{1}{3}(v - 2u)\]\)

Solving these equations, we get u = 0 and v = 6.

When (x, y) = (3, -3):

\(\[\begin{aligned}3 &= \frac{1}{3}(u + v) \\\\-3 &= \frac{1}{3}(v - 2u)\end{aligned}\]\)

Solving these equations, we get u = 6 and v = 0.

When (x, y) = (-1, 5):

\(\[\begin{aligned}-1 &= \frac{1}{3}(u + v) \\5 &= \frac{1}{3}(v - 2u)\end{aligned}\]\)

Solving these equations, we get u = -6 and v = 0.

Therefore, the new limits of integration for the integral are u = -6 to u = 6 and v = -6 to v = 6.

Now, we can rewrite the integral using the new variables:

\([\int_{-6}^{6} \int_{-6}^{6} (12x + 12y) , da = \frac{1}{3} \int_{-6}^{6} \int_{-6}^{6} \left( 12(u + v) + 12(v - 2u) \right) , dudv]\)

\(\[= \frac{4}{9} \int_{-6}^{6} \int_{-6}^{6} \left( 4u + 4v + 4v - 8u \right) \, dudv\]\)

\(\[= \frac{4}{9} \int_{-6}^{6} \int_{-6}^{6} \left( -4u + 8v \right) \, dudv\]\)

Integrating with respect to u first, we have:

\(\[= \frac{4}{9} \int_{-6}^{6} \left( -\frac{4u^2}{2} + 8uv \right) \, du\]\)

\(\[= \frac{4}{9} \int_{-6}^{6} \left( -2u^2 + 48v \right) \, du\]\)

\(\[= \frac{4}{9}\) (864)

= 64

Therefore, the value of the integral (12x + 12y) dA over the region R is 64.

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The phrase "number of values for which a certain condition holds" is referred to as multiplicity. The phrase, for instance, can be used to describe the magnitude of the totient valence function or the frequency with which a given polynomial equation has a root at a specific location.

Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,

f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,

and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.

This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.

Hence ,Multiplicity means the quality or state of being multiple or various. and

the number of components in a system (such as a multiplet or a group of energy levels)

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Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,

f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,

and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

Answer:Shake hands when you meet someone.Make direct eye contact with the person you are speaking with.Unless the movie theater is crowded, do not sit right next to someone.Do not stand close enough to a stranger to touch arms or hips.Cover your coughs.

Step-by-step explanation:trust me

Answer:

A) 80 degrees

Step-by-step explanation:

100-20=80

Using the surface area of the sphere, it is found that the radius of the bearing that Helen needs to buy is of 6 millimeters.

The surface area of a sphere of radius r is given by:

\(S_A = 4\pi r^2\)

In this problem, we have that:

\(S_A = 452.16\)

Hence:

\(4\pi r^2 = 452.16\)

\(r = \sqrt{\frac{452.16}{4\pi}}\)

r = 6.

The radius of the bearing that Helen needs to buy is of 6 millimeters.

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Answer: 6

Step-by-step explanation: NOT NEEDED

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

Answer:

volume of the cylinder = 18,480

Step-by-step explanation:

volume of a cylinder =

\(v = \pi {r}^{2} h\)

where radius = 14cm

height = 30cm

therefore the volume

\(v = \frac{22}{7} \times {14}^{2} \times 30 \\ v = 22 \times 14 \times 2 \times 30 \\ v = 18480\)

The opposite of being short $4.28 would be having $4.28 or more. That is a surplus or extra of $4.28.

Surplus refers to an amount or quantity that is left over or in excess of what is needed or used. It can refer to various things, such as:

In finance, a surplus refers to an excess of revenue over expenses, or an excess of assets over liabilities. It means having more of something than is necessary or expected.

Therefore, the opposite of being short $4.28 would be having $4.28 or more. This is often referred to as having a surplus or extra of $4.28.

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Answer:

x = -1

Step-by-step explanation:

\(10 - 7x - 5 + 12x = 0\)

➡️ \(5 - 7x + 12x = 0\)

➡️ \(5 + 5x = 0\)

➡️ \(5 + 5x - 5 = 0 - 5\)

➡️ \(5x = 0 - 5\)

➡️ \(5x = - 5\)

➡️ \(5x \div 5 = - 5 \div 5\)

➡️ \(x = - 5 \div 5\)

➡️ \(x = - 1\)

Answer: B Lydia got fewer than 4 questions wrong on her math test.

The inequality < 4 means "less than 4," so the correct sentence that represents this inequality is C) Lydia got 4 or fewer questions wrong on her math test.

The correct answer is option a. $7,594.46.

To calculate the amount you would reduce the amount you owe in the first year, we can use the formula for the equal installment of a loan. The formula is:

Installment = Principal / Number of Installments + (Principal - Total Repaid) * Interest Rate

In this case, the principal is $45,000, the number of installments is 5, and the interest rate is 8.5%.

Let's calculate the amount you would reduce the amount you owe in the first year:

Installment = $45,000 / 5 + ($45,000 - $0) * 0.085Installment = $9,000 + $3,825

Installment = $12,825

Therefore, you would reduce the amount you owe by $12,825 in the first year.The correct answer is option a. $7,594.46.

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The probability is 0.3845.The probability of anything occurring is known as probability.

Explanation:

2/52 * 10/52  = 20/52 = 0.3845.

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\(\begin{align}\sf\:\text{LHS} &= \cos(A)\cos(60^\circ - A)\cos(60^\circ + A) \\&= \cos(A)\cos(60^\circ)\cos(60^\circ) - \cos(A)\sin(60^\circ)\sin(60^\circ) \\&= \frac{1}{2}\cos(A)\left(\frac{1}{2}\right)\left(\frac{1}{2}\right) - \frac{\sqrt{3}}{2}\cos(A)\left(\frac{\sqrt{3}}{2}\right)\left(\frac{\sqrt{3}}{2}\right) \\&= \frac{1}{8}\cos(A) - \frac{3}{8}\cos(A) \\ &= \frac{-2}{8}\cos(A) \\ &= -\frac{1}{4}\cos(A).\end{align} \\\)

Now, let's calculate the value of \(\sf\:\cos(3A) \\\):

\(\begin{align}\sf\:\text{RHS} &= \frac{1}{4}\cos(3A) \\&= \frac{1}{4}(4\cos^3(A) - 3\cos(A)) \\&= \cos^3(A) - \frac{3}{4}\cos(A).\end{align} \\\)

Comparing the \(\sf\:\text{LHS} \\\) and \(\text{RHS} \\\), we have:

\(\sf\:-\frac{1}{4}\cos(A) = \cos^3(A) - \frac{3}{4}\cos(A). \\\)

Adding \(\sf\:\frac{1}{4}\cos(A) \\\) to both sides, we get:

\(\sf\:0 = \cos^3(A) - \frac{2}{4}\cos(A). \\\)

Simplifying further:

\(\sf\:0 = \cos^3(A) - \frac{1}{2}\cos(A). \\\)

Factoring out a common factor of \(\sf\:\cos(A) \\\), we have:

\(\sf\:0 = \cos(A)(\cos^2(A) - \frac{1}{2}). \\\)

Using the identity \(\sf\:\cos^2(A) = 1 - \sin^2(A) \\\), we can rewrite the equation as:

\(\sf\:0 = \cos(A)(1 - \sin^2(A) - \frac{1}{2}). \\\)

Simplifying:

\(\sf\:0 = \cos(A)(1 - \frac{3}{2}\sin^2(A)). \\\)

Since \(\sf\:\cos(A) \\\) cannot be zero (as it would result in undefined values), we can divide both sides of the equation by \(\sf\:\cos(A) \\\):

\(\sf\:0 = 1 - \frac{3}{2}\sin^2(A). \\\)

Rearranging the terms:

\(\sf\:\sin^2(A) = \frac{2}{3}. \\\)

Taking the square root of both sides, we get:

\(\sf\:\sin(A) = \pm\sqrt{\frac{2}{3}}. \\\)

The solution \(\sf\:\sin(A) = \sqrt{\frac{2}{3}} \\\) corresponds to the range where \(\sf\:0° \leq A \leq 90° \\\). Therefore, the solution \(\sf\:\sin(A) = \sqrt{\frac{2}{3}} \\\) is valid.

Hence, we have proved that:

\(\sf\:\cos(A)\cos(60^\circ - A)\cos(60^\circ + A) = \frac{1}{4}\cos(3A). \\\)

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Given:

To Prove:

cosAcos(60°-A)cos(60°+A) = 1/4 cos3A

Solution:

Here are the steps in detail:

1. Expanding cosAcos(60°-A)cos(60°+A) using the product-to-sum identities:

=cosAcos(60°-A)cos(60°+A)

=(cosA)(cos(60°-A)cos(60°+A))

=(cosA)(1/2cos(60°-2A) + 1/2cos(60°+2A))

=(cosA)(1/2cos(-A) + 1/2cos(120°))

2. Substituting cos(60°-A) = cos(60°+A) = 1/2 into the expanded expression:

= cosA(1/2cos(-A) + 1/2cos(120°))

=cosA(1/2(1/2cosA) + 1/2(-1/2))

= cosA(1/4cosA - 1/4)

= (1/4)cosAcosA - (1/4)cosA

=(1/4)cos3A

3. Simplifying the resulting expression to obtain 1/4 cos3A:

=(1/4)cosAcosA - (1/4)cosA

=(1/4)cosA(cosA - 1)

=(1/4)cos3A

Therefore, we have proven that cosAcos(60°-A)cos(60°+A) = 1/4 cos3A. Hence Proved.

Answer:

remember to round numbers to 1 significant figure

Step-by-step explanation:

usually in an exam when you're asked to estimate the answer to a calculation, usually you round each number to 1 sf and then work on from there.

You like to watch movies at the local theater. You have two payment options. Your first option is to buy a discount card which will cost you $160, and then $20 for m movies, 20m + 160. Your second option will cost you $100, and then pay $40 for m movies, 40m + 100. After how many movies will the total costs of the two options be the same?

the answers is 3

The measure of {x} in the figure is 14.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Given is a parallelogram as shown in the image.

Opposite angles of a parallelogram are equal. So, we can write -

x + 50 = y

y - x = 50                                                                  .... Eq { 1 }

Sum of the angles of a quadrilateral are 360°. We can write -

2(x - 30) + (x + 50) + y = 360                                          .... Eq { 2 }

2x - 60 + x + 50 + y = 360

3x + y = 370

3x + 50 + x = 370

4x = 320

x = 80

y = 130

Therefore, the measure of {x} and {y} are 80 and 130 respectively.

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{Question in english -

Help please, I need to find the values, well, I'll settle for one...}

The angle  of EBF is  6w -28°.

It is required to find the angle  of EBF.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.

Given:

ABF = 8w - 6

ABE = 2(w + 11)

According to given question we have,

Angle EBF = ABF - ABE

Angle EBF = 8w - 6 - [2(w + 11)]

Angle EBF = 8w - 6 - [2w + 22]

Angle EBF = 8w - 6 - 2w - 22

Angle EBF = 6w -28°

Therefore, the angle  of EBF is  6w -28°.

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Answer:

Value of a= 6

Value of b= 7.81

Step-by-step explanation:

We are given \(tan \theta=\frac{5}{6}\)

and \(cos \theta=\frac{a}{b}\)

We need to find values of a and b

We know that: \(tan \theta=\frac{Perpendicular}{Base}\)

While \(cos \theta = \frac{Base}{Hypotenuse}\)

So, a = Base and b= Hypotenuse

We know the value of base i,e \(tan \theta=\frac{Perpendicular}{Base}=\frac{5}{6}\)

We get Base=6, Perpendicular = 5

To find Hypotenuse we can use Pythagoras theorem

\((H)^2=(P)^2+(B)^2\\H^2=(5)^2+(6)^2\\H^2=25+36\\H^2=61\\H=\sqrt{61}\\H=7.81\)

The value of hypotenuse is 7.81

The value of Base is 6

So, \(cos \theta = \frac{Base}{Hypotenuse} =\frac{a}{b}= \frac{6}{7.81}\)

Value of a= 6

Value of b= 7.81

Answer:

1) Lowest temperature = -5.5 (Wednesday)

2) a. -62 is less than (colder than) -55 so the average temperature on Mars is warmer.

b. -62 < -55

3) No. -14 means that the number is 14 less than zero. -21 means that the number is 21 less than zero. Also, if you plot these numbers on a number line, -21 will be further to the left than -14. The further to the left a number is, the less it is. So, -21 is less than -14 and Anchorage is colder than Minneapolis.

The required point at which point is the object accelerating toward the right is Z.

A  force following up on a moving body at a point to the bearing of movement, having a tendency to cause the body to follow a round or ended way. The power of gravity following up on a satellite in circle is an illustration of a centripetal power; the rubbing of the tires of a vehicle making a turn comparatively gives centripetal  force on the vehicle.

The item in the guide is moving by round movement: consequently, there is a force (called centripetal force ) that pulls the item towards the center point of the circle.

As indicated by Newton's law motion,

F = ma

a power on the item relates to a speed increase, and this speed increase (called centripetal speed increase) has a similar course of the power. Thus, since the speed increase is towards the focal point of the circle also, the main place of the direction where the speed increase is towards the right is at point Z.

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Answer:

13

Step-by-step explanation:

13 is the right answer

Answer:

Down below

Step-by-step explanation:

\(Q=2u^2-5\\u=-3\\Q=(2*-3)^2-5\\Q=(-6)^2-5\\Q=36-5\\Q=31\)

Note: wasn't sure if it was \(2u^2\) or 2u*2. tell me and i will change it. this also may be wrong.

In this specific case, the initial term (a) is 5 and the common ratio (r) is -2

Henceforth, after determining what a and r are, we use the formula for the nth term. Which is:

\(a_n = a \times r^{n-1} \)

Therefore, the 14th term is :

\(\implies 5 \times { (- 2)}^{14 - 1} \\\implies 5 \times {( - 2)}^{13} \\ =\boxed { -40,960} \)

Hope it helps!

Answer:

Probability=

(number if outcomes favourable)/(total number of outcomes)

Therefore P(no red/green)=1-(8/21+6/21)

=1-(8+6)/21=1-14/21=(21×1-14)/21=(21-14)/21

=7/21=1/3 ans

Step-by-step explanation:

Answer:

purple because when its really dark it looks sick

Step-by-step explanation:

An expression represents the product of 3 and ((5/4)n+1.8) is 3.75n + 5.4

The correct answer is an option (D)

Consider the expression  ((5/4)n + 1.8)

First we write the fraction 5/4 in the decimal form.

5/4 = 1.25

So, the expression ((5/4)n + 1.8) becomes,

((5/4)n + 1.8)

=   (1.25 n + 1.8)                         ..........(1)

Now consider the product of 3 and ((5/4)n + 1.8)

3 ×  ((5/4)n + 1.8)

= 3 × ((1.25)n + 1.8)                          ............(from statement (1))

= (3 × (1.25 n)) + (3 × 1.8)

= (3 × 1.25)n + 5.4

= 3.75n + 5.4

Thus, 3 ×  ((5/4)n + 1.8) = 3.75n + 5.4

The correct answer is an option (D)

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Which expression represents the product of 3 and (5/4n + 1.8)? (SHOW WORK PLEASE)

A) 5.55n

B) 9.15n

C) 3.75n + 1.8

D) 3.75n + 5.4