Assinala o numero de molas necessarias para pendurar 18 guardanapos uns a seguir aos outros de modo que 2 guardanapos partilhem a mesma mola

The coordinates of the image of the point (-7, 5) are (7, -5).

We are given point P. The coordinates of the point P are (-7, 5). We perform a transformation on the given point. We rotate the given point about the origin counter-clockwise. The angle of rotation is 180°. We need to find the coordinates of the image of the point after rotation.

Let the new coordinates of the image of the point after rotation be denoted by (X, Y). If the coordinates of the original point are (x, y), then the relations between the coordinates of the point and the image are given below.

X = x*cosθ - y*sinθ

X = (-7)*cos(180°) - (5)*sin(180°)

X = (-7)*(-1) - (5)*(0)

X = 7

Y = x*sinθ + y*cosθ

Y = (-7)*sin(180°) + (5)*cos(180°)

Y = (-7)*(0) + (5)*(-1)

Y = -5

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Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

X^2+ 2x+35

Step-by-step explanation:

Use pemdas. Multiply the parentheses. Multiply. Collect like terms. Remove the parentheses.

Answer:

4\(x^{2}\)+9x+23

Step-by-step explanation:

The total variable cost per unit is $5.40. The total fixed costs are $1,800.

Jennifer intends to create T-shirts for basketball lovers in the hypothetical situation. Various cost components and sales data are sent to us.

Direct material, direct labour, variable overhead, and variable selling commission make up the total variable cost per unit, which comes to $5.40 for each T-shirt.

Included in the $1,800 total fixed costs are fixed selling and administrative expenditures as well as fixed factory overhead.

The selling price is deducted from the unit's $22 total variable cost to determine the contribution margin.

The contribution margin ratio is the contribution margin per unit, stated as a percentage, divided by the selling price. It is estimated to be 55%.

The point at which total revenue and total costs are equal is known as the break-even point for T-shirts. It is 82 T-shirts in this instance.

The entire variable cost per unit divided by the selling price, stated as a percentage, is the variable cost ratio. It is estimated to be 45%.

The amount of money required to pay all expenses and arrive at break-even is known as the break-even in sales dollars. It totals $3,273.

Thus, the business must sell 8,837 T-shirts in order to reach its target income of $3,060.

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coco ggcd ya tv xxx TN can

Matt has 6 dimes coins and 24 nickel coins.

The solution to this math problem is as follows:

Let the number of dimes be x Matt has 4 times as many nickels as dimes therefore the number of nickels is 4x. The combined value of the coins is 180 cents. We know that a nickel is worth 5 cents and a dime is worth 10 cents. Therefore we can write an equation:10x + 5(4x) = 180

Simplifying,10x + 20x = 180

30x = 180

x = 6

Therefore there are 6 dimes and 4 * 6 = 24 nickels.

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The slopes of perpendicular lines are negative reciprocals is proved.

An equation of a straight line is given by

y = mx +c

It is given that

Line PQ is rotated 90° counterclockwise to form line P’Q’. The lines are perpendicular.

Line PQ contains the points (a, b) and (c, d). Line P’Q’ contains the points (–b, a) and (–d, c).

The slopes of lines PQ and P’Q’ can be determined using the formula

\(\rm m = \dfrac{ v _2 - v _1 }{ x _2 -x _1 }\)

The product of these slopes is -1 .

This product shows that the slopes are negative reciprocals

Therefore , The slopes of perpendicular lines are negative reciprocals is proved,

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The probability of both rice and carrots being served with dinner is 23.4%.

The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.

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The linearized equation for the non-linear equation z = x² + 4xy + 6xy² in the region defined by 8 ≤ x ≤ 10, 2 ≤ y ≤ 4 is given by :

z ≈ 244 + 20(x - 8) + 128(y - 2).

When using the linearized equation to calculate the value of z at x = 8, y = 2, the error is 0.

1.1. To linearize the equation in the given region, we need to find the partial derivatives of z with respect to x and y:

∂z/∂x = 2x + 4y

∂z/∂y = 4x + 6xy

At the point (x₀, y₀) = (8, 2), we substitute these values:

∂z/∂x = 2(8) + 4(2) = 16 + 8 = 24

∂z/∂y = 4(8) + 6(8)(2) = 32 + 96 = 128

The linearized equation is given by:

z ≈ z₀ + ∂z/∂x * (x - x₀) + ∂z/∂y * (y - y₀)

Substituting the values, we get:

z ≈ z₀ + 24 * (x - 8) + 128 * (y - 2)

1.2. To find the error when using the linearized equation to calculate the value of z at x = 8, y = 2, we substitute these values:

z ≈ z₀ + 24 * (8 - 8) + 128 * (2 - 2)

= z₀

Therefore, the linearized equation gives the exact value of z at x = 8, y = 2, and the error is 0.

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Answer:

Step-by-step explanation:

Hello, please consider the following.

\(h(x)=5/2x+4 \\\\x=(h^{-1}o})(x)=(hoh^{-1})(x)=h(h^{-1}(x))=\dfrac{5}{2h^{-1}(x)+4}\\\\<=> 2h^{-1}(x)+4=\dfrac{5}{x}\\\\<=> h^{-1}=\dfrac{\dfrac{5}{x}-4}{2}\\\\<=>h^{-1}=\dfrac{5-4x}{2x}\)

Thank you.

Eventually, the differential equation's general solution is:

y = y_h + y_p

y = c1e^(-2x) + c2e^(-x) - (1/6)e^(-x) + (2/3)

In the context of differential equations, the homogeneous solution of a differential equation is a solution that satisfies the equation when the right-hand side is equal to zero.

To find the particular solution of y'' + 3y' + 2y = 4e^x using the variation of parameters method, we first find the homogeneous solution of the differential equation by setting the right-hand side to zero:

y'' + 3y' + 2y = 0

The characteristic equation is r^2 + 3r + 2 = 0, which factors as (r + 2)(r + 1) = 0. Therefore, the solutions are y_h = c1e^(-2x) + c2e^(-x), where c1 and c2 are constants.

Next, we find the Wronskian of the homogeneous solution:

W(y1, y2) = |e^(-2x) e^(-x) | = e^(-3x)

To find the particular solution, we assume that it has the form y_p = u1(x)e^(-2x) + u2(x)e^(-x), where u1(x) and u2(x) are unknown functions to be determined.

We then find y_p' and y_p'':

\(y_p' = u1'(x)e^(-2x) + u2'(x)e^(-x) - 2u1(x)e^(-2x) - u2(x)e^(-x)y_p'' = u1''(x)e^(-2x) + u2''(x)e^(-x) - 4u1'(x)e^(-2x) - 2u2'(x)e^(-x) + 4u1(x)e^(-2x) + u2(x)e^(-x)u1''(x)e^(-2x) + u2''(x)e^(-x) + u1'(x)e^(-2x) + u2'(x)e^(-x) - 4u1'(x)e^(-2x) - 2u2'(x)e^(-x) + 4u1(x)e^(-2x) + u2(x)e^(-x) = 4e^x\)

Simplifying and grouping terms, we get:

\(u1''(x)e^(-2x) - 3u1'(x)e^(-2x) + u2''(x)e^(-x) - u2'(x)e^(-x) = 4e^x\)

To solve for u1(x) and u2(x), we use the method of undetermined coefficients and assume that they are both linear combinations of the exponential function and its derivative:

u1(x) = A(x)e^x

u2(x) = B(x)e^(2x)

Substituting these expressions into the previous equation and solving for A(x) and B(x), we get:

A(x) = -e^x/6

B(x) = 2e^x/3

Therefore, the particular solution is:

\(y_p = (-e^x/6)e^(-2x) + (2e^x/3)e^(-x)y_p = (-1/6)e^(-x) + (2/3)\)

Eventually, the differential equation's general solution is:

y = y_h + y_p

y = c1e^(-2x) + c2e^(-x) - (1/6)e^(-x) + (2/3)

Therefore, the particular solution of the given differential equation y′′+3y′+2y=4ex is

\(y(x)=c_1e^{-x} + c_2e^{-2x} - 4 + 2e^{x}.\)

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The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Step-by-step explanation:

let age of samantha be 3x and age of jason be x.(since samantha is three times as old as jason)

Now,

3x+x=56 (sum of their ages is 56)

or 4x=56

or x=56/4

or x=14

therefore age of samantha=3x=3×14=42

age of jason = x = 14

The age of Samantha will be 42 years and that of Jason will be 14 years.

It is given that Samantha is three times as old as Jason and the sum

of their ages is 56 years.

We have to find out age of both of them.

What will be the value of x , if 3x + 8x = 55?

The value of x will be 11x = 55 or x = 55 ÷ 11 or x = 5.

As per the question ;

Samantha is three times as old as Jason.

Sum of their ages = 56 years

Let's assume age of Jason be x.

⇒ The age of Samantha will be 3 times of x

i.e., 3x.

∵ Sum of ages of both of them = 56 years

⇒ x + 3x = 56

⇒ 4x = 56

⇒ x = 56 ÷ 4

⇒ x = 14

So , age of Jason will be 14 years.

Age of Samantha = 3x

= 3 × 14

= 42 years

Thus , the age of Samantha will be 42 years and that of Jason will be 14 years.

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The inverse of the function is 3+\(\sqrt[3]{x\x-2}\).

What is inverse of the function?

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1. One should not confuse (-1) with exponent or reciprocal here.

Given, f(x) = (x − 3)³ + 2

replace f(x) with y

y = (x − 3)³ + 2

y-2 = (x − 3)³

∛y-2 = x-3

∛y-2 +3 = x

Put y =x

we get

∛x-2 +3 =y

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Answer:

59%

Step-by-step explanation:

19/32= 59.375 so rounded would be 59 :)

Answer:

59%

Step-by-step explanation:

32 shots is the total, so it's 100%

100% = 32 shots

1% = 32 ÷ 100 = 0.32

19 ÷ 0.32 = 59.375

59.375 estimated to 59

The inequality "w < 30" describes the weeks for which Halimah will put money in the bank instead of buying an oud. It means she must save for less than 30 weeks to have less than $300 saved.

Let's assume the number of weeks Halimah saves money is represented by the variable "w".

Halimah saves $10 per week, so the total amount of money she saves after "w" weeks is:

Total amount saved = $10 x w

According to the problem, Halimah will put the money in the bank instead of buying an oud if she saves less than $300. Therefore, the inequality that describes the number of weeks for which Halimah will put money in the bank is:

$10 x w < $300

Simplifying the inequality:

w < 30

Therefore, the inequality that describes the number of weeks for which Halimah will put money in the bank is "w < 30".

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Complete question:

Halimah saves $10 per week for w weeks to buy an oud. If she saves less than $300, she will put the money in the bank instead of buying an oud.

What inequality describes the number of weeks for which Halimah will put money in the bank?

Answer:

the soda is less

Step-by-step explanation:

if you divide both the soda and the waters ounces by their price than you will get 0.15 for the soda and 0.16 for the water showing that its 1 cent more expensive than the soda

Distance travel by Drew = 1,315.21 feet (Approx)

Distance is a measure of how far apart two objects or locations are using numbers. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage. Sometimes, the symbol |AB| is used to represent the distance between two points.

Given:

Total block in north = 3

Total block in west = 3

1 block = 310 feet

Find:

Distance travel by Drew

Computation:

Total distance in north = 3 × 310 = 930 feet

Total distance in west = 3 × 310 = 930 feet

Distance travel by Drew = Total distance in

north? + Total distance in west?

Distance travel by Drew = v9302 + 9302

Distance travel by Drew:

= V864,900 + 864,900

Distance travel by Drew = V1,729,800

Distance travel by Drew = 1,315.21 feet (Approx)

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\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)

Answer:

answer b

Step-by-step explanation:

Step-by-step explanation:

That means the 96 is  75% of your grade

   96 (.75) + 75 (.25) = 90.75  final grade

Answer:

Maggie is 13years old

Step-by-step explanation:

Let the age of Maggie be = x

Let her brothers age be = y

Given:

Brother is 7 years younger than twice her age , y = 2x - 7  --------- ( 1 )

[ Twice her age = 2x

7 years younger than twice her age = 2x - 7 ]

Sum of their ages , x + y = 32 -------- ( 2 )

Substitute ( 1 ) in ( 2 ) :

x + ( 2x - 7 ) = 32

x + 2x - 7 = 32

3x = 32 + 7

3x = 39

x = 13

Maggie's age  = 13 years

Substitute x in ( 1 ) :

y = 2x - 7

  = 2 ( 13 ) - 7

  = 26 - 7

  = 19

Brother's age = 19 years

Step-by-step explanation:

Use Pythagorean theorem to find the base of the right triangle

221^2 = 195^2 + b^2

b = 104 km

triangle area = 1/2 base * height =  1/2 * 104 * 195 = 10140 km^2

Now multiply by the height to find volume

10140 km^2  * 15 km  = 152100 km^3

Given:

Vector R has an x-component of Rx = −20 N and a y-component of Ry = 10 N.

To find:

The direction of vector R.Solution:

We can use the following formula to calculate the direction of vector R:

\(\theta=\tan^{-1}\frac{R_y}{R_x}\)

Where\(\theta\) is the angle between the vector and the x-axis.

Substitute the given values of

\(R_x\)and \(R_y\).

\(\theta=\tan^{-1}\frac{R_y}{R_x}\)

\(\theta=\tan^{-1}\frac{10}{-20}\)

\(\theta=-26.57°\)

Therefore, the direction of vector R is -26.6°.

Answer: So, the answer is -26.6° in 100 words.

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Answer:

18.2

Step-by-step explanation:

divide 91 by 5

x x x x x. x x x x x x x x x x xx. x

Answer:

1,980

Step-by-step explanation:

using the formula

(n – 2) × 180°

= (13 – 2) × 180°

= 11 × 180

= 1,980

if we were asked to find the interior angle

we will use this formula

\(interior \: angle \: of \: a \: polygon = \frac{sum \: of \: interior \: angle}{number \: of \: sides} \)

= 1,980/13

= 152.3°

i hope all this helped

Answer:

12/7 = 1 5/7

Step-by-step explanation:

divide 12 by 7 to get 1 with a remainder of 5 and take the denominator and put it under the remainder 5/7 the answer is 1 5/7

In an organization, two popular training methodologies that can be utilized are on-the-job training and off-the-job training.

Let's examine each methodology along with their popular methods:

1. On-the-Job Training:

On-the-job training refers to the process of acquiring knowledge and skills while performing tasks and responsibilities directly related to one's job. It takes place within the actual work environment and provides hands-on experience. Some popular methods of on-the-job training include:

a. Job Shadowing: This method involves a new employee observing and working closely with an experienced employee, learning from their day-to-day activities and tasks.

b. Mentoring: In this method, a more experienced employee (mentor) guides and supports a less experienced employee (mentee) by providing advice, feedback, and sharing their expertise.

c. Coaching: Similar to mentoring, coaching involves a more experienced employee providing guidance and support to enhance the skills and performance of the employee being coached.

d. Apprenticeships: This method combines on-the-job training with classroom instruction. It allows individuals to learn a trade or skill through practical experience while working alongside skilled professionals.

2. Off-the-Job Training:

Off-the-job training refers to the process of learning and acquiring skills outside of the regular work environment. It usually takes place in a separate training facility or classroom setting. Some popular methods of off-the-job training include:

a. Workshops and Seminars: These are interactive sessions where participants learn new skills, gain knowledge, and exchange ideas on specific topics facilitated by subject-matter experts.

b. Conferences and Conventions: These events bring together professionals from a particular industry or field to attend presentations, panel discussions, and networking opportunities to learn about new trends and developments.

c. E-Learning and Online Courses: With advancements in technology, online platforms offer various courses and training programs that individuals can access remotely at their own pace and convenience.

d. Simulations and Role-Playing: These methods involve creating artificial scenarios or situations that closely resemble real work situations, allowing participants to practice and develop skills in a controlled environment.

e. Case Studies and Group Discussions: Participants analyze real-life scenarios and engage in group discussions to understand problem-solving techniques, decision-making processes, and best practices.

It's important to note that the selection of the training methodology and methods depends on the specific needs, goals, and resources of the organization, as well as the desired learning outcomes for the employees. A combination of both on-the-job and off-the-job training can often be beneficial for comprehensive skill development and knowledge acquisition.

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