Consider the following expression. 3x+5y+2 Select all of the true statements below.

Therefore in each composite function we get different domains and ranges which is given below.

(1) f(x) = x+2 , g(x) = 3x - 1

(f + g)(x) = f(x) + g(x)

              =  x+2 + 3x - 1

             = 4x +1

Domain = (-∞ , ∞) and range = (-∞ , ∞)

(f - g )(x) = f(x) - g(x)

                =  x+2 -3x +1

               = -2x + 3

Domain = (-∞ , ∞) and range = (-∞ , ∞)

(f.g)(x) = f (x) g(x)

          = (x+2)( 3x - 1)

           = 3x²- x + 6x - 2

           = 3x²+ 5x -2

Domain = (-∞ , ∞) and range = [-49/12 ,∞)

(f/g)(x) = f(x)/g(x)

           = x+2/3x-1

Domain = (-∞ , 1/3) ∪ (1/3 ,∞) and range = (-∞ , 1/3) ∪ (1/3 ,∞)

(2) f(x) = x² - 5 and g(x) = -x +8

   (f + g)(x) = f(x) + g(x)

                 = x² - 5 -x +8

                 = x² - x +3

Domain = (-∞ , ∞) and range = [11/4 ,∞)

(f - g )(x) = f(x) - g(x)

              =  x² - 5 +x -8

              =  x² + x - 13

Domain = (-∞ , ∞) and range = [-53/4 ,∞)

(f.g)(x) = f (x) g(x)

          = ( x² - 5 )(- x +8)

          = -x³ + 8x² + 5x - 40

Domain = (-∞ , ∞) and range = (-∞ , ∞)

(f/g)(x) = f(x) / g(x)

          = x² - 5 / -x +8

Domain = (-∞ , 8) ∪ (8 ,∞) and range = (-∞ , -16 - 2√59 ) ∪ (-16 + 2√59  ,∞)

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Answer:

the shape has ,9 edges,,,

Answer:

To determine the speed, we can use the formula:

speed = distance / time

where distance is measured in feet and time is measured in minutes.

In this case, the distance is 264 feet and the time is 3 minutes. Plugging these values into the formula, we get:

speed = 264 feet / 3 minutes

simplifying, we get:

speed = 88 feet/minute

Therefore, the equipment is traveling at a speed of 88 feet per minute.

Answer:

Market price of set = 25.14

Step-by-step explanation:

Given:

Discount percentage = 20%

Service charge = 10%

GST = 7%

Amount pays = 23.54

FInd:

Market price of set

Computation:

Assume;

Market price of set = a

Market price of set after discount = a(1-20%)

Market price of set after discount = 0.80a

Market price of set after discount + (Market price of set after discount)(Service charge) + (Market price of set after discount)(GST) = Amount pays

0.80a + (0.80a)(10%) + (0.80a)(7%) = 23.54

0.80a + 0.08a + 0.056a = 23.54

0.936a = 23.54

a = 25.14

Market price of set = 25.14

Answer:

\( {x}^{2} - 6x + 11 = 0 \\ x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} \\ x = \frac{6± \sqrt{ - 8} }{2} \\ x = \frac{6±2i \sqrt{2} }{2} \\ x = 3±i \sqrt{2} \)

Answer:

\(x=3\pm\sqrt{2}i\)

Step-by-step explanation:

\(x^2-6x+11=0\)

\(x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}\)

\(x=\frac{-(-6)\pm\sqrt{(-6)^2-4(1)(11)} }{2(1)}\)

\(x=\frac{6\pm\sqrt{36-44} }{2}\)

\(x=\frac{6\pm\sqrt{-8} }{2}\)

\(x=\frac{6\pm2\sqrt{2}i }{2}\)

\(x=3\pm\sqrt{2}i\)

Answer:

the triangle is a scalene

Step-by-step explanation:

a triangle with sides unequal is known as a scalene

Answer: S and T.

Step-by-step explanation:

I watched a video on how to do this just to answer, so it might not be right LOL. But since the angles are the same if you draw them from each other they both show the angles are equal which means the lines are parallel.

Ileana  have to invest for 8 years :

Simple interest is a simple and straightforward formula for figuring out how much interest will be charged on a loan. Simple interest is calculated by dividing the daily interest rate by the principle and the number of days between payments.

The principal amount must be multiplied by the time, interest rate, and time period in order to calculate simple interest. Simple Interest = Principal x Interest Rate x Time is the written formula.

Principal amount = $15,500

interest = $5,084

Time = ?

Rate = 4.1% simple interest

to find the simple interest :

                                         I = \(\frac{(p*t*r)}{100}\)

       Then:

         Time = \(\frac{I*100}{P*R}\)

                  = \(\frac{(5084*100)}{(15500*4.1)}\)

                  = \(\frac{508400}{63,550}\)

                  = 8 years

Ileana  have to invest for 8 years

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Answer:

∠WRM = 62

Step-by-step explanation:

∠WRM = ∠WRK + ∠KRM

5x - 13 = 2x - 5 + 37          {Combine like terms}

5x - 13 = 2x  + 32             {Add 13 to both sides}

      5x = 2x + 32 + 13

     5x = 2x + 45         {Subtract 2x from both sides}

5x - 2x = 45

        3x = 45             {Divide both sides by 3}

         x = 45/3

x  = 15

∠WRM = 5x - 13

           = 5*15 - 13

         = 75 - 13

∠WRM = 62

m∠WRM = 5x - 13

m∠KRW = 2x - 5

m∠KRM = 37°

As m∠KRW and m∠KRM are forming m∠WRM , their sum will be equal to the measure of m∠WRM .

Which means :-

\(2x - 5 + 37 = 5x - 13\)

\( - 5 + 37 = 5x - 13 - 2x\)

\( - 5 + 37 = 3x - 13\)

\(32 = 3x - 13\)

\(3x = 32 + 13\)

\(3x = 45\)

\(x = \frac{45}{3} \)

\(\color{olive}\implies\color{hotpink}x = 15\)

m∠KRW :-

\( = 2 \times 15 - 5\)

\( = 30 - 5\)

\(\color{olive}\implies \: \color{hotpink}m∠KRW= 25°\)

\(\color{olive}\implies \: \color{hotpink}m∠KRM = 37°\)

m∠WRM :-

\( = 5 \times 15 - 13\)

\( = 75 - 13\)

\(\color{olive}\implies \:\color{hotpink} m∠WRM = 62° \)

As the sum of m∠KRW and m∠KRM add upto the measure of m∠WRM (25 + 37 = 62) we have found out the correct measure of the angles .

Therefore , the measure of :-

\(\color{olive}\implies \:\color{hotpink} m∠WRM = 62° \)

Answer:

-26-8i does this help?

Step-by-step explanation:

I took what was in the parenthesis and put them together coming out with -10 and -4i. Then I took what was next and started putting the variables together and the numbers together.

The space meet his requested dimensions and the dimensions are 784 m².

For given question,

The blueprints show a square space measuring 0.028 km on each side.

Ian requested that the new office be at least 600 m².

First we find the dimensions in square meter.

We know that 1 km = 1000 m

⇒ 0.028 km = 28 m

Now we find the area of the square space.

⇒ A = 28²

⇒ A = 28 × 28

⇒ A = 784 m²

The area of the space is 784 square meter.

Since 784 > 600, the space meet his requested dimensions.

Therefore,  the space meet his requested dimensions and the dimensions are 784 m².  

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(a) If f(x) is a convex function with x ∈ ℝⁿ, then all local minima of f(x) are also global minima. In other words, if there exists a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo, then f(x) ≥ f(xo) for all x ∈ ℝⁿ.

(b) A graph of a non-convex function can be visualized to understand why the statement in part (a) is not true. It will show a scenario where a local minimum is not a global minimum.

(a) To prove that all local minima of a convex function are also global minima, we can utilize the property of convexity. Suppose there is a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo. We assume that xo is a local minimum. Now, consider any arbitrary point x in ℝⁿ. We can express x as a convex combination of xo and another point y in the neighborhood, using the convexity property: x = λxo + (1 - λ)y, where λ is a scalar between 0 and 1. Using this expression, we can apply the convexity property of f(x) to get f(x) ≤ λf(xo) + (1 - λ)f(y). Since f(x) ≥ f(xo) for all x in the neighborhood, we have f(y) ≥ f(xo). Therefore, f(x) ≤ λf(xo) + (1 - λ)f(y) ≤ λf(xo) + (1 - λ)f(xo) = f(xo). This inequality holds for all λ between 0 and 1, implying that f(x) ≥ f(xo) for all x ∈ ℝⁿ, making xo a global minimum.

(b) A graph of a non-convex function can demonstrate a scenario where the statement in part (a) is not true. In such a graph, there may exist multiple local minima, but one or more of these local minima are not global minima. The non-convex nature of the function allows for the presence of multiple valleys and peaks, where one of the valleys may contain a local minimum that is not the overall lowest point on the graph. This occurs because the function may have other regions where the values are lower than the local minimum in consideration. By visually observing the graph, it becomes apparent that there are points outside the neighbourhood of the local minimum that have lower function values, violating the condition for a global minimum.

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Answer:

25

Step-by-step explanation:

10+7+8=25 this is because her cat weighs 8 pounds and her dog weighs 10 pounds more so that's 18 lb. after words it says Cameron's dog weighs 7 pounds less than bills so you do 18+7 and that equals 25

The consumption bundle that will not be the consumer's choice, given the assumptions of choosing the optimal bundle, is option B) 30 snacks and 12 meals. To determine the optimal consumption bundle, we need to consider the consumer's budget constraint and maximize their utility.

Given that the price of snacks is $4 and the price of meals is $10, and the consumer has $240 remaining on their meal card, we can calculate the maximum number of snacks and meals that can be purchased within the budget constraint.

For option A) 5 snacks and 20 meals, the total cost would be $4 × 5 + $10 × 20 = $200. Since the consumer has $240 remaining, this bundle is feasible.

For option B) 30 snacks and 12 meals, the total cost would be $4 × 30 + $10 × 12 = $240. This bundle is on budget constraint, but it may not be the optimal choice since the consumer could potentially consume more meals for the same cost.

For option C) 20 snacks and 16 meals, the total cost would be $4 × 20 + $10 × 16 = $240. This bundle is also on budget constraint.

Since options A, C, and D are all feasible within the budget constraint, the only bundle that will not be the consumer's choice is option B) 30 snacks and 12 meals. The consumer could achieve a higher level of utility by reallocating some snacks to meals while staying within the budget constraint. Therefore, the correct answer is option B.

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Answer:

1.5 meters tall / 150cm

Step-by-step explanation:

1.6 meters - 10cm

= 160 cm - 10cm

= 150cm

9514 1404 393

Answer:

  no real solutions; k = ±i(2/3)√15

Step-by-step explanation:

If k is one of the roots, then substituting it for x will satisfy the equation:

  k -4k -20/k = 0

Multiplying by k gives ...

  -3k^2 -20 = 0

  k^2 = -20/3 = -6 2/3

There are no real values of k such that this is true.

__

If we allow k to be imaginary, then ...

  k = ±i√(20/3) = ±i(2/3)√15

Possible imaginary values of k are ±(2/3)√15.

Answer:

the first one in your life with my name in your company is in fact the

The expected total number of candies that Abi eats in a year can be calculated by multiplying the number of candies she eats per day by the number of days in a year.

For example, if Abi eats 3 candies per day, we can calculate her expected total number of candies in a year as follows:

Number of candies per day = 3
Number of days in a year = 365

Expected total number of candies = Number of candies per day × Number of days in a year
Expected total number of candies = 3 × 365
Expected total number of candies = 1095

Therefore, the expected total number of candies that Abi eats in a year is 1095.

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The exercise highlights that converting the dual problem into standard form and applying the primal simplex method does not yield the same algorithm as the dual simplex method. By considering a specific standard form problem and its dual, it is shown that the primal simplex method applied to the dual problem may require one or more changes of basis, unlike the dual simplex method where termination occurs immediately due to the specific structure of the problem.

In the given exercise, we have a standard form problem and its dual:

Primal Problem:

minimize 21x1 + 22x2

subject to x1 = 1

x1, x2 ≥ 0

Dual Problem:

maximize P1 + P2

subject to P1 < 1

P2 < 1

P1, P2 ≥ 0

Since there is only one possible basis in this case, the dual simplex method terminates immediately because of the specific structure of the problem.

However, if we convert the dual problem into standard form and apply the primal simplex method to it, one or more changes of basis may be required. This is because the primal simplex method operates differently from the dual simplex method and may encounter different pivot elements and entering/leaving variables during the iterations. These differences in the algorithm can lead to changes in the basis during the primal simplex method's execution.

Therefore, it is evident that converting the dual problem into standard form and applying the primal simplex method does not result in the same algorithm as the dual simplex method. The primal simplex method may require one or more changes of basis during its execution, unlike the dual simplex method, which terminates immediately in this specific problem due to the singular structure of the basis.

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Answer:

5 cm

Step-by-step explanation:

Opposite sides are equal in a rectangle.

So, Area of missing length = 16-11 = 5 cm

A cube has 6 sides. Divide the surface area by 6 to get the area of one side:

13 1/2 /6 = 2 1/4

The area of one side is S^2

To fins the length of the sides find the square root of the area:

Side = sqrt(2 1/4)

Side = 1 1/2 cm.

You didnt give the problem or explain anything all you said is what he has to pay i think you forgot to add something BUDDY careful next time =)

The concept that a message gives different meanings to different objects is called option (b) polymorphism.

Polymorphism is a fundamental concept in object-oriented programming (OOP) that allows different objects to respond to the same message or method invocation in different ways. In other words, it allows objects of different classes to be treated as if they were of the same class, as long as they implement the same method or message.

This can make code more flexible, reusable, and easier to maintain. Polymorphism is achieved through inheritance, interfaces, or overloading methods. For example, a "draw" method could be implemented differently for different shapes, such as circles, rectangles, or triangles.

Therefore, the correct option is (b) polymorphism

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By using sum or difference formulas, cos(-a) can be written as - cos(a). Explanation: We know that cosine is an even function of x, therefore,\(cos(-x) = cos(x)\) .Then, by using the identity \(cos(a - b) = cos(a) cos(b) + sin(a) sin(b)\), we can say that:\(cos(a - a) = cos²(a) + sin²(a).\)

This simplifies to:\(cos(0) = cos²(a) + sin²(a)cos(0) = 1So, cos(a)² + sin(a)² = 1Or, cos²(a) = 1 - sin²\)(a)Similarly,\(cos(-a)² = 1 - sin²(-a)\) Since cosine is an even function, \(cos(-a) = cos(a)\) Therefore, \(cos(-a)² = cos²(a) = 1 - sin²(a)cos(-a) = ±sqrt(1 - sin²(a))'.\)

This is the general formula for cos(-a), which can be written as a combination of sine and cosine. Since cosine is an even function, the negative sign can be written inside the square root: \(cos(-a) = ±sqrt(1 - sin²(a)) = ±sqrt(sin²(a) - 1) = -cos\).

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Answer:

shape as that of the base of the solid

Step-by-step explanation:

A solid has a three dimensional shape. A three dimensional shape has both length, breadth and height. If the solid is being cut parallel to the base, a two dimensional shape (has length and width) is formed.

The shape of the two dimensional shape is the same as the shape of the base. Hence if solid is cut parallel to the bases, the shape formed would have the same shape as that of the solid base.

Answer:

y = 3x - 9

Step-by-step explanation:

First, find the slope using y2 - y1 / x2 - x1

36 - 21 = 15

15 - 10 = 5

15/5 = 3, so the slope (m) is 3.

Now, plug into point-slope form: y - y1 = m (x - x1)

y - 21 = 3 (x - 10)

Simplify

y - 21 = 3x - 30

y = 3x - 9

I hope this helps!!

Organizational culture is defined as the common beliefs, values, attitudes, customs, behaviors, and traditions that characterize a specific organization and determine the manner in which it functions. Organizational culture is set by the manager.

In a corporate or business environment, organizational culture can influence the daily operations of employees. It is the responsibility of managers to create a positive culture that emphasizes teamwork, respect, integrity, and accountability. The manager is an essential individual responsible for establishing and maintaining the organization's culture, which will ultimately define the employee's attitudes, behaviors, and productivity levels. He or she sets the tone for the workplace by creating an environment that fosters collaboration, innovation, and success. Employees need to feel connected to their workplace and colleagues to be motivated to do their best work. If a manager promotes a culture of fear, competition, or dishonesty, employees may become unmotivated or unproductive. An effective manager understands the importance of creating a positive workplace culture and works hard to establish and maintain it. Managers can establish a positive culture by encouraging open communication, providing regular feedback and recognition, fostering a sense of teamwork, creating opportunities for professional development, and setting high standards for performance. Managers must lead by example and demonstrate the behaviors and attitudes that they expect from their employees. They must hold themselves and others accountable for their actions, communicate expectations clearly, and provide support when needed. A positive organizational culture will enable an organization to attract and retain top talent, increase employee engagement, and promote collaboration and innovation.

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The value of k in the rational expression (5k - 2)/3k = 7 is - 2/17.

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

We also know that a fraction is written in the form of p/q, where q ≠ 0.

Given, A rational expression (5k - 2)/3k = 7.

Now, The denominator of the LHS will be multiplied to the numerator of RHS.

Therefore, 5k - 2 = 21k.

5k - 21k = 2.

- 17k = 2.

- k = 2/17.

k = - 2/17.

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Answer:

\(y = 2x - 3\)

Step-by-step explanation:

❗ The way I solved this problem doesn't involve me using point-slope form like the problem tells you to use❗

⭐ Perpendicular lines have a slope that is the opposite reciprocal of the slope of the line it is perpendicular to

⭐What does "opposite reciprocal" mean?

⭐What is slope-intercept form?

We can find the equation of the perpendicular line by:

1. Substituting the slope into the point-slope form equation:

⭐ Perpendicular lines have a slope that is the opposite reciprocal of the slope of the line it is perpendicular to

The slope of the line the perpendicular like is perpendicular to is \(\frac{-1}{2}\).

Therefore, the slope of the perpendicular line is \(2\)

Substitute the slope into the point-slope form equation.

\(y = 2x + b\)

Now, all we have to do is solve for b.

2. Substituting the given coordinate into the point-slope form equation:

We are given the coordinate (6,9).

\(y = 2x + b\)

\(9 = 2(6) + b\)

\(9 = 12 + b\)\(-3 = b\)

Substitute "b" into the point-slope form equation.

\(y = 2x + 3\)