Solve for x.

3 + 4(x-2) = 12

-2x + 6y = 13

5x + 2y = 3(4y-2)

2x - 4(x+2y) = 20

8x-5y=20

Synergy is obtained when the value created by two divisions operated separately and independently is greater than the value that would be created by two divisions cooperating. The given statement is False.

The statement is false. Synergy is a term used to describe the benefits that can be achieved when two or more parts of a business work together to create more value than they could on their own. In other words, when two divisions cooperate and work together, the combined value they create is greater than the value that would be created if they worked independently and separately.

For example, if a company has a marketing division and a sales division, these two divisions could work independently to achieve their goals. However, if they work together and share information, resources, and expertise, they can create more value by developing more effective marketing strategies that lead to increased sales. In this case, the combined value of the marketing and sales divisions working together is greater than the value they could create if they worked independently.

Therefore, it is incorrect to say that synergy is obtained when two divisions operate separately and independently to create greater value than they would if they cooperated.

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Answer:

total perimeter = 98.26 ft

Step-by-step explanation:

circular perimeter = (18)(3.14)(0.5) = 28.26 ft

rectangular perimeter =26 + 26 + 18 = 70 ft

total perimeter = 28.26 + 70 = 98.26 ft

The two step equation for the scenario that your cousin is in where they pay for their textbooks is:

7x + 20 = 230

x = (230 - 20) / 7

The cost of the textbooks would be $30.

The total amount paid by your cousin in order to be able to cover a book for their 7 classes and the fee for art class is $ 230.

Assuming that the cost of each book from his 7 classes is denoted as x, then the expression would be:

= 7 x number of classes

= 7x

This amount is then added to the cost of the art class which is $ 20 so it becomes:

= 7x + 20

The two step equation is therefore:

7x + 20 = 230

x = (230 - 20) / 7

The cost of the textbooks is:

x = (230 - 20) / 7

x = $ 30

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While the conditions described above may increase the likelihood of Excel's Nonlinear Solver finding the global maximum of a profit function, there are no guarantees. The function may have multiple local maxima, or the solver may encounter convergence issues, even under ideal conditions.

Excel's Nonlinear Solver is a tool used to find the optimal solution for a function by iteratively adjusting its parameters. It is not guaranteed to identify the global maximum of a profit function under any conditions. However, there are some conditions that can increase the likelihood of finding the global maximum.

I. When profits demonstrate decreasing marginal returns:

If the profit function has decreasing marginal returns, it means that the additional profit gained from each additional unit of input decreases as the input level increases. In this case, the profit function will have a diminishing slope, and the solver is more likely to converge to a global maximum. However, this is not a guarantee, as there may be multiple local maxima.

II. When profits demonstrate increasing marginal returns:

If the profit function has increasing marginal returns, it means that the additional profit gained from each additional unit of input increases as the input level increases. In this case, the profit function will have an increasing slope, and the solver is less likely to converge to a global maximum. The solver may converge to a local maximum instead.

III. When the profit function has two or fewer discontinuities:

If the profit function has discontinuities, it can cause problems for the solver. If the solver encounters a discontinuity, it may not be able to converge to a solution. Therefore, the fewer the discontinuities, the more likely the solver is to find the global maximum.

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Answer: x = 20

Step-by-step explanation:

Hey there! If you have any questions feel free to let me know in the comments below.

Step 1: Subtract 36 from both sides.

3x = 96 - 36

Step 2: Simplify 96 - 36  to  60.

3x = 60

Step 3: Divide both sides by 3.

x = 60/3

Step 4: Simplify 60/3 to 20.

x = 20

Answer:

Step-by-step explanation:

here you go mate

step 1

3*x+36=96  equation

step 2

3*x+36(-36)=96(-36)  subtract -36 from the sides

∨ this is the number we are gonna divide with in step 3 to get our results

3x=60

step 3

3x/3=60/3  Divide by 3

answer

x=20

The number of touchdowns are 4, field goals are 2 and safeties are 2 for the given system of equation.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A collection of equations fulfilled by the same set of variables is called a system of linear equations." Finding the values of the variables employed in a system of equations entails solving the set of equations. By keeping the equations balanced on both sides, we compute the values of the unknown variables. Finding the value of the variable that makes the condition of all the provided equations true is the primary goal when solving an equation system.

Let us suppose touchdowns = x.

Let us suppose field goals = y.

Let us suppose safeties = z.

Given that, they score point 8 times, thus:

x + y + z = 8

The total points scored are 38 thus,

7x + 3y + 2z = 38

Also,

x = (y + z)

Substituting the value of y + z in equation 1 we have:

x + x = 8

2x = 8

x = 4

Substitute the value of x in second equation:

7(4) + 3y + 2z = 38

28 + 3y + 2z = 38

3y + 2z = 10

Now, using x = (y + z). we have:

4 - z = y

Substitute the value of y:

3y + 2z = 10

3(4 - z) + 2z = 10

12 - 3z + 2z = 10

-z = -2

z = 2

Substitute the value of x and z:

x = (y + z)

4 = y + 2

y = 2

Hence, the number of touchdowns are 4, field goals are 2 and safeties are 2 for the given system of equation.

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Answer: (7,10)

Step-by-step explanation:

x = 5

Step-by-step explanation:

Answer: the perimeter of the garden is 24 and the area of the garden is 32

Step-by-step explanation:

Perimeter: 4 + 4 + 8 + 8 = 24

Area: 4 x 8 = 32

A) Function is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

b)  The local minimum value of f is; 5608/2197 at x = -42/13, and the local maximum value of f is 139/8 at x = 7/2.

(a) To determine the intervals on which f is increasing or decreasing, we need to determine the critical points and then check the sign of the derivative on the intervals between them.

f(x)=8x³-42x-48x + 4

f'(x) = 24x² - 90

Setting f'(x) = 0, we get

24x² - 90 = 0

24x² = 90

x =±  √3.75

So, the critical points are;

x = -1 and x = 7/2.

We can test the sign of f'(x) on the intervals as; (-∞, -1), (-1, 7/2), and (7/2, ∞).

f'(-2) = 72 > 0, so f is increasing on (-∞, -1).

f'(-1/2) = -25 < 0, so f is decreasing on (-1, 7/2).

f'(4) = 72 > 0, so f is increasing on (7/2, ∞).

Therefore, f is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

(b) To determine the local maximum and minimum values of f, we need to look at the critical points and the endpoints of the interval (-1, 7/2).

f(-1) = -49

f(7/2) = 139/8

f(-42/13) = 5608/2197

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Every time the same instrument is used for a measurement, it produces consistent results, which denotes: -reliability.

The degree to which a measurement tool produces consistent, repeatable estimates of what is believed to be a true score at the core.

The same set of people receives the same instrument again. The correlation between the results on the two instruments is what defines dependability. The scores ought to be comparable if the outcomes remain constant over time. How long to wait between the two administrations is the key to test-retest reliability.

Reliability is defined as the probability that a given item will perform its intended function with no failures for a given period of time under a given set of conditions.

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your answer shall be 1.2

Answer:

none of the above

Step-by-step explanation:

but I'm not sure

The potential areas for Franklin's garden are 144ft², 36ft² and 196ft² hence options (b), (e), and (f) are correct.

To find the potential areas for Franklin's square garden, we need to find the perfect squares that can be expressed as the product of two identical whole numbers. These perfect squares will represent the areas of the square gardens with whole number side lengths,

a) 20 ft² = 2 x 2 x 5 = (2 x 2) x 5 = 4 x 5, not a perfect square

b) 144 ft² = 12 x 12 = (12 x 12), a perfect square

c) 1,000 ft² = 10 x 10 x 10 = (10 x 10) x 10 = 100 x 10, not a perfect square

d) 300 ft² = 10 x 10 x 3 = (10 x 10) x 3 = 100 x 3, not a perfect square

e) 36 ft² = 6 x 6 = (6 x 6), a perfect square

f) 196 ft² = 14 x 14 = (14 x 14), a perfect square

Therefore, the potential areas for Franklin's garden are 144 ft², 36 ft², and 196 ft². So, options (b), (e), and (f) are the potential areas for Franklin's square garden with whole number side lengths.

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On sectional charts, the graticules are the lines that separate each 30 minutes of latitude and each 30 minutes of longitude. One tick mark equals one minute of latitude or longitude. Moving northward increases latitude while moving westward increases longitude. The coordinates of the Garrison (Pvt) airport are 47° 40' 00" N and 101° 26' 00" W.

Direction is characterised as the course that something follows, the route that must be taken to get to a particular location, the direction in which something is beginning to take shape, or the direction you are facing. When you turn right instead of left, that is an illustration of direction.

Identifying whether a direction is clockwise or anticlockwise is a straightforward method for resolving direction problems. If we turn right, the direction will be entirely clockwise. Therefore, when starting from the correct point at North, every right movement will lead in the clockwise directions of East, South, and West.

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The sets that are equal are A = {1, 2, 3} and B = {2, 1, 3}

The order of elements does not matter when determining the equality of sets. Both sets A and B contain the same elements, namely 1, 2, and 3, even though their order is different. Therefore, we can say that A and B are equal sets.

The other sets mentioned, A = {1, 2} and B = {1}, A = {1, 2, 4} and B = {1, 2, 3}, and A = {1, 2} and B = {1, 2, 3}, are not equal because they have different elements. In the first case, set A has two elements, while set B has only one element.

In the second case, set A contains the element 4, which is not present in set B.

In the third case, set A has two elements, while set B has three elements, including the element 3, which is not present in set A.

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Answer:

5r + 2p + 6

Step-by-step explanation:

= 4r + 9 + r + 2p - 3

= 4r + r + 2p + 9 - 3

= 5r + 2p + 6

The correct choice is option B that is the expression 4r + 9 + r + 2p - 3 is equivalent to 5r + 2p + 6.

What do you mean by algebraic expressions ?

Algebraic expression is an equation which consists of variables and the arithmetic operations such as division , multiplication , etc.

It is given that the expression is 4r + 9 + r + 2p - 3. We need to find out the correct answer from the given options.

Here there are two variables which are r and p. So , we need to add firstly terms with variable r and then term with variable p and then the constants. Let's simplify the expression as follows :

4r + 9 + r + 2p - 3

Add terms with variable r :

5r + 9 + 2p - 3

Now , we need to add the constants and we get the simplified expression as  :

5r + 2p + 6

Therefore , the correct choice is option B that is the expression 4r + 9 + r + 2p - 3 is equivalent to 5r + 2p + 6.

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The value of X = 25.

Solution:

The two equations are

(i) the first condition is difference of x and y is 14

x - y = 14 ---------equation 1

(ii) the second condition of the given data is value of x is 3 times more than two times of y value.

x - 2y = 3 --------equation 2

From equation 2, we have to separate two variables x and y,

x = 3 + 2y  --------equation 3

We have to Substitute equation 3 in equation 1

3 + 2y - y = 14

3 + y = 14

y = 14 - 3

y = 11

Substitute y = 11 in equation 1........

x - 11 = 14

x = 14 + 11

x = 25

So, the value of x is 25 and y is 11.

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Answer:

Step-by-step explanation:

Given the difference of x and y is 14, and the difference of x and 2y is 3, you want two equations, their graph, and the value of x.

The difference of 'a' and 'b' is (a -b). Here, the two differences are expressed as the equations ...

The attachment shows a graph of these equations. Their point of intersection is (25, 11), meaning the value of x is 25.

The graph of the first equation is easily drawn by recognizing the x- and y-intercepts are 14 and -14, respectively.

The graph of the second equation will go through the x-intercept point of (3, 0) and the y-intercept point of (0, -3/2). It is probably easier to graph this by hand by considering the x-intercept point and the slope of 1/2.

Since we're only interested in the value of x, it is convenient to eliminate the variable y. We can to that by subtracting the second equation from twice the first:

  2(x -y) -(x -2y) = 2(14) -(3)

  x = 25 . . . . . . . . . simplify

Answer:

OG slope is 1, perpendicular slope is -1

Step-by-step explanation:

rise over run is 1/1, perpendicular slopes are the reciprocoal, or opposite slope, so -1

The series of transformations that correctly maps parallelogram ABCD to parallelogram QRST is Reflect parallelogram ABCD across the x-axis and dilate the result by a scale factor of two centered at the orgigin

A quadrilateral of parallel opposite sides with equal lengths is the two-dimensional geometric shape widely known as a "parallelogram". As such, this four-sided figure has characteristic equal-measured opposites regarding their angles.

Though differing in size and form, parallelograms always possess these notable attributes. Meanwhile, sub-types have emerged from said category, which includes squares, rhombuses, and rectangles – each having additional outstanding qualities to define its uniqueness.

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The total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

In the given power system depicted in Figure 1, there are three units that are always running. Each unit has specific characteristics regarding their minimum power output (Pmin), maximum power output (Pmax), and incremental cost (Ci). Let's discuss the characteristics of each unit and calculate the total cost of power generation for a given load demand.

Unit 1:

Pmin = 200 MW

Pmax = 500 MW

Ci = $50/MWh

Unit 2:

Pmin = 150 MW

Pmax = 400 MW

Ci = $40/MWh

Unit 3:

Pmin = 100 MW

Pmax = 300 MW

Ci = $30/MWh

To calculate the total cost of power generation for a given load demand, we need to determine the optimal power output for each unit. We start by considering the units with the lowest incremental cost first.

Suppose the load demand is D MW. We allocate the load demand to the units as follows:

Step 1: Check if Unit 1 can meet the load demand within its power range. If yes, allocate the load demand to Unit 1 and calculate the cost:

Cost1 = Ci * P1, where P1 is the power output of Unit 1.

Step 2: If there is still remaining load demand, allocate it to Unit 2:

Cost2 = Ci * P2, where P2 is the power output of Unit 2.

Step 3: If there is still remaining load demand, allocate it to Unit 3:

Cost3 = Ci * P3, where P3 is the power output of Unit 3.

Finally, the total cost of power generation, Cost_total, is the sum of Cost1, Cost2, and Cost3:

Cost_total = Cost1 + Cost2 + Cost3

To find the optimal power output for each unit, we consider the load demand and compare it to the minimum and maximum power output limits for each unit. The power allocation is based on meeting the load demand while minimizing the overall cost of power generation.

In summary, given the characteristics of the three units in the power system (Pmin, Pmax, and Ci), the total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

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The most appropriate choice for HCF will be given by-

Number of identical bouquets that can be made out of 21 white tulips and 91 red tulips if no flowers are left out = 7

What is HCF?

HCF means highest common factor. HCF of two number a and b is the highest number that divides both a and b.

Number of white tulips = 21

Number of red tulips = 91

Number of identical bouquets that can be made out of 21 white tulips and 91 red tulips if no flowers are left out = HCF (21, 91)

Now,

\(21 = 3\times 7\\91 = 7\times 13\\\)                

HCF (21, 91) = 7

Number of identical bouquets that can be made out of 21 white tulips and 91 red tulips if no flowers are left out = 7

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none of the provided options (a. 602, b. 672, c. 652, d. 642) are correct.

determine the government expenditure due to the subsidy on consumers, we need to find the quantity at which the demand and supply curves intersect and then calculate the subsidy amount.

Given:

Demand: P = 40 - 5\(Q_{d}\)

Supply: P = 10 - 25\(Q_{s}\)

First, we need to set the demand equal to the supply to find the equilibrium quantity:

40 - 5\(Q_{d}\) = 10 - 25\(Q_{s}\)

Rearranging the equation:

5\(Q_{d}\) - 25\(Q_{s}\) = 30

Next, we need to consider the subsidy on consumers. A subsidy on consumers effectively lowers the price they pay, shifting the demand curve downward by the subsidy amount. In this case, the subsidy is $12. Therefore, the new demand curve becomes:

P = 40 - 5\(Q_{d}\) - 12

Simplifying:

P = 28 - 5\(Q_{d}\)

Now, we can set the new demand curve equal to the supply curve to find the new equilibrium quantity:

28 - 5\(Q_{d}\)Q_d = 10 - 25\(Q_{s}\)

Rearranging the equation:

5\(Q_{d}\) - 25\(Q_{s}\) = 18

Comparing this equation with the earlier equation (5\(Q_{d}\) - 25\(Q_{s}\) = 30), we can see that the subsidy has effectively reduced the quantity by 12 units. Therefore, the equilibrium quantity with the subsidy is 12 units lower than the equilibrium quantity without the subsidy.

Now, we need to calculate the subsidy amount, which is the product of the subsidy per unit and the equilibrium quantity:

Subsidy amount = Subsidy per unit * Equilibrium quantity

Subsidy amount = $12 * 12

Subsidy amount = $144

The government expenditure due to the subsidy on consumers is $144.

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Answer:

\((fof^{-1})(x)=x\)

Step-by-step explanation:

Composition of two functions f(x) and g(x) is represented by,

(fog)(x) = f[g(x)]

If a function is,

f(x) = (-6x - 8)² [where x ≤ \(-\frac{8}{6}\)]

Another function is the inverse of f(x),

\(f^{-1}(x)=-\frac{\sqrt{x}+8}{6}\)

Now composite function of these functions will be,

\((fof^{-1})(x)=f[f^{-1}(x)]\)

                  = \([-6(\frac{\sqrt{x}+8}{6})-8]^{2}\)

                  = \([-\sqrt{x}+8-8]^2\)

                  = \((-\sqrt{x})^2\)

                  = x

Therefore, \((fof^{-1})(x)=x\)

Answer:

(x+2)^2 + (y-4)^2 = 4^2

Step-by-step explanation:

A circle is x^2 + y^2 = 1 , where r = 1

The radius of that circle looks to appear to be r = 4.

x^2 + y^2 = 4^2

Transition that circle origin from (0,0) to (-2,4)

The origin is (-2,4) which mean h = -2 left and k = 4 up.

(x-h)^2 + (y-k)^2 = 4^2

(x-(-2))^2 + (y-4)^2 =4^2

Answer:

ss

Step-by-step explanation:

sas

The radius of the circle who center is at ( 5 , 2 ) and the point on the circle is ( -3 , 4 ) is given by r = 2√17 units

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be r

Let the center of the circle be A ( 5 , 2 )

Let the point on the circle be P ( -3 , 4 )

Now , standard form of a circle is

( x - h )² + ( y - k )² = r²

So , r² = ( 5 - ( -3 ) )² + ( 2 - 4 )²

On simplifying the equation , we get

r² = ( 8 )² + ( 2 )²

r² = 64 + 4

r² = 68

Taking square roots on both sides , we get

r = √68

r = 2√17

Hence , the radius of the circle is 2√17 units

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