Suppose that S and T are points on the number line. If ST = 10 and S lies at -4, where could be located? If there are several locations , separate them with commas .

The function G(x) is obtained by taking the parent function f(x) and applying a vertical and horizontal translation.

The parent function f(x) = x^2 represents a basic quadratic function. The function G(x) = (x + 2)^2 + 4 is obtained by transforming the parent function f(x). Let's break down the transformation:

Horizontal Translation: The term (x + 2) in G(x) represents a horizontal shift of the graph of f(x) to the left by 2 units. This means that the entire graph is shifted 2 units to the left compared to the parent function.

Vertical Translation: The term +4 in G(x) represents a vertical shift of the graph of f(x) upward by 4 units. This means that the entire graph is shifted 4 units up compared to the parent function.

These transformations modify the shape and position of the graph of the parent function. The combination of the horizontal and vertical translations results in a shifted and raised version of the original quadratic graph, giving us the function G(x).

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Answer:

589.05

Step-by-step explanation:

Answer:

∠ 1 = ∠ 3 = 63° , ∠ 2 = 117°

Step-by-step explanation:

∠ 2 and 117° are vertically opposite angles and are congruent , then

∠ 2 = 117°

∠ 1 and 117° are adjacent angles on a straight line and sum to 180°

∠ 1 + 117° = 180° ( subtract 117° from both sides )

∠ 1 = 63°

∠ 1 and ∠ 3 are vertically opposite angles and are congruent , then

∠ 3 = 63°

Answer:

d x – 3 = 4

e 4x + 1 = 29

hope it helps

Answer:

D

Step-by-step explanation:

x - 3 = 4

reciprocate the 3 it will be +3, so the solution will be

x= 4+3

4+3=7

therefore the equation 4+3=7 states that the x is equal to 7

The perimeter, in miles, of the rectangle formed by connecting the points representing the cabana, beach, water slide, and roller coaster will be 22 miles.

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.

Given, a coordinate system where 1 unit = 1 mile

Lets,

First, calculate the linear distance between adjacent points as displayed in the graph.

Distance between car to cabana = 4 units = 4 miles

Distance between cabana to beach = 6 units = 6 miles

Distance between beach to water slide = 5 units = 5 miles

Distance between water slide to roller coaster = 6 units = 6 miles

Distance between roller coaster to cabana =5 units = 5 miles

Thus,

1) the perimeter, in miles, of the rectangle formed by connecting the points representing the cabana, beach, water slide, and roller coaster:

Perimeter = 6 + 5 + 6 + 5

Perimeter = 22 miles

2) the total distance in miles from the car to the cabana and then from the cabana to the beach:

Distance = 4 + 6

Distance = 10 miles

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The Laplace transform of f(t) can be computed when f(t) = { t if 0 < t < 1, 1 if t > 1.

The Laplace transform of f(t) can be computed using the following equation:

\(\large F(s)=\int_{0}^{\infty}e^{-st}f(t)dt\)

Using the given function f(t) = { t if 0 < t < 1, 1 if t > 1.

Hence we have \(\large F(s)=\int_{0}^{\infty}e^{-st}f(t)dt =\int_{0}^{1}e^{-st}t\ dt+\int_{1}^{\infty}e^{-st}\ dt\)

Applying Laplace transform on f(t),

we get \(\large L(f(t))= \int_{0}^{1}e^{-st}t\ dt+\int_{1}^{\infty}e^{-st}\ dt\)

For the first integral \(\large \int_{0}^{1}e^{-st}t\ dt\)

The integration by parts formula is given by \(\large \int u \ dv = uv - \int v \ du\)

Taking,

\(u = t,\\\\ du = 1,\ \\dv = e^{-st} \\ v = -\frac{1}{s}e^{-st\)

we have

\(\large \int_{0}^{1}e^{-st}t\ dt=-\frac{t}{s}e^{-st}\Bigg|_{0}^{1}+\frac{1}{s}\int_{0}^{1}e^{-st}\ dt=-\frac{1}{s}\Bigg[e^{-s}-(1)\Bigg]+\frac{1}{s^2}(1-e^{-s})\)

The second integral,

\(\large \int_{1}^{\infty}e^{-st}\ dt=\frac{1}{s}\Bigg[0- e^{-s}\Bigg]=\frac{1}{s}e^{-s}\)

Thus, the Laplace transform of f(t) is given by,

\(\large L(f(t))= \int_{0}^{1}e^{-st}t\ dt+\int_{1}^{\infty}e^{-st}\ dt =\frac{1}{s^2}(1-e^{-s})-\frac{1}{s}e^{-s}\)

Therefore, \(\large F(s) = L(f(t)) = \frac{1}{s^2}(1-e^{-s})-\frac{1}{s}e^{-s}\),

when f(t) = { t if 0 < t < 1, 1 if t > 1.

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The correct answer is 1.6. By solving the proportion, we determined that the value of k that satisfies the given equation is approximately 1.6.

To find the unknown value, k, in the proportion (k)/(1.2) = (4)/(3), we can cross-multiply and solve for k.

cross-multiplying the proportion, we have:

3k = 4 * 1.2

Multiplying the numbers:

3k = 4.8

To isolate k, we divide both sides of the equation by 3:

k = 4.8 / 3

Evaluating the division, we find:

k ≈ 1.6

Therefore, the correct answer is 1.6. By solving the proportion, we determined that the value of k that satisfies the given equation is approximately 1.6.

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After answering the question provided, we can predict that the result will be as in the triangle by Pythagorean theorem = \(\sqrt{12^2 - 4^2}\) => N = \(\sqrt{144 - 16}\) => n = \(\sqrt{132}\)

A triangle is a polygon because it includes four or so additional parts. It features a simple rectangular shape. A rectangle having edges A, B, and C is referred to as a triangle. When the sides are actually not collinear, Euclidean geometry yields a single plane and cube. If a triangle contains three parts and three angles, it is a polygon. The intersections of a triangle's three sides are referred to as its corners. The sum of a triangle's sides is 180 degrees.

by Pythagorean theorem

n = \(\sqrt{12^2 - 4^2}\)

N = \(\sqrt{144 - 16}\)

n = \(\sqrt{132}\)

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Answer:

200 questions

Step-by-step explanation:

Given data

Let the total questions be x

so that

21% of x= 42 questions

let us solve for x

21/100*x= 42

0.21*x= 42

0.21x= 42

Divide both sides by 0.21

x= 42/0.21

x= 200 questions

Hence the questions are 200 questions

Answer:

slope = 4

Step-by-step explanation:

.................

The value of r'(1) and s'(4) is 0 that can be interpreted with the help of the graph that is given in the question.

Derivative in mathematics, the rate of change of a characteristic with recognize to a variable. Derivatives are essential to the answer of troubles in calculus and differential equations. The essence of calculus is the by-product. The by-product is the immediately price of extrade of a characteristic with recognize to certainly considered one among its variables. This is equal to locating the slope of the tangent line to the characteristic at a point

\(r(x) = f(g(x))\)therefore the derivative of r is given by \(r'(x) = f'g(x)\times g'(x)\)

\(r'(1) = f'(g(1))\times g'(1)\) from the graphs

r'(1) = f'4 \times g'1 = (5/4) \times(0) = 0

Similarly s'(1) = g'(f(1))\times f'(1) from the graphs

 f(1)=1.5, f'(1)

=\dfrac{ (3-0)}{(0-2)}

= -3/2 , g'(3/2) = 0

s'(4) = g'(3/2) \times f'(4) = 0(-1.5) = 0

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Complete question:

let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. find r'(1) and s'(4).

The area of the shaded region is  \(60 mm^2\)  .

The area of a double figure is a measurement of the area it encompasses. Inches or square metres are examples of squares, which are the most common unit of measurement.

The area of a figure is calculated by multiplying the length of one side by the height of the other. For illustration, the area of a rectangle is calculated by dividing its length by its breadth.

We must deduct the area of the triangle that isn't shaded from the area of the rectangle in order to determine the size of the shaded area.

Area  \(= length \times width = 12 mm \times 6 mm = 72 mm^2\)

The area of the triangle is

Area  \(= 1/2 \times base \times height\)

The rectangle's width, which is 6 mm, corresponds to the triangle's base. By deducting the longer side's length from the shorter side's length, we can determine the height, which is:

\(10 mm - 6 mm = 4 mm\)

Therefore, the area of the triangle is:

\(Area = 1/2 \times 6 mm \times 4 mm = 12 mm^2\)

We deduct the triangle's area from the rectangle's area to obtain the area of the darkened area.

Shaded area  \(= 72 mm^2 - 12 mm^2 = 60 mm^2\)

Therefore, The faded region's area is  \(60 mm^2\) .

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Answer:

x = 3 , y = 8

Step-by-step explanation:

Consider the figure to be a parallelogram.

• opposite sides of a parallelogram are congruent

then

8x = 5x + 9 ( subtract 5x from both sides )

3x = 9 ( divide both sides by 3 )

x = 3

and

7y - 16 = 5y ( subtract 5y from both sides )

2y - 16 = 0 ( add 16 to both sides )

2y = 16 ( divide both sides by 2 )

y = 8

By using the concept of relative velocity, the person will travel 14.5 km over the next 3 hours.

To solve the problem, we will use the concept of relative velocity and we can break it into two parts: the time taken to reach point B and the time taken to travel for the next 3 hours.

Let's start with the time taken to reach point B. We know that the person is moving at a constant speed of 5 km/h and it takes 30 minutes to pass point B. Since speed is distance over time, we can use the formula \($distance = speed \times time$\) to find the distance traveled to reach point B:

\(\[distance_{AB} = 5 \times \frac{1}{2} = 2.5 \text{ km}\]\)

Next, let's calculate the distance the person will travel over the next 3 hours. We know that the person is now moving at a speed of 4 km/h. Again, using the formula \($distance = speed \times time$\), we can find the distance traveled over 3 hours:

\(\[distance_{next3hours} = 4 \times 3 = 12 \text{ km}\]\)

Adding the distance traveled to reach point B and the distance traveled over the next 3 hours:

\(\[total\_distance = distance_{AB} + distance_{next3hours} = 2.5 + 12 = 14.5 \text{ km}\]\)

Therefore, the person will travel 14.5 km over the next 3 hours.

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a)  The combination of units that results in the minimum cost to supply a load of 200MW is Combination 1, with Unit 1 generating 130MW, Unit 2 generating 39MW, and Unit 3 generating 31MW. b) the optimal dispatch remains the same as before, which is Combination 1: Unit 1 generating 130MW

a) To determine how the units should be dispatched to supply a load of 200MW at minimum cost, we need to compare the costs of operating each unit within their respective output limits.

Unit 1 cost calculation:

At minimum output (50MW):

Cost = 5000 + 215P + 0.5P^2

      = 5000 + 215(50) + 0.5(50^2)

      = 5000 + 10750 + 0.5(2500)

      = 5000 + 10750 + 1250

      = 17000 + 1250

      = 18250 [C]

At maximum output (130MW):

Cost = 5000 + 215P + 0.5P^2

      = 5000 + 215(130) + 0.5(130^2)

      = 5000 + 27950 + 0.5(16900)

      = 5000 + 27950 + 8450

      = 32950 + 8450

      = 41400 [C]

Unit 2 cost calculation:

At minimum output (39MW):

Cost = 5000 + 270P + 1.0P^2

      = 5000 + 270(39) + 1.0(39^2)

      = 5000 + 10530 + 1.0(1521)

      = 5000 + 10530 + 1521

     = 16051 [C]

At maximum output (128MW):

Cost = 5000 + 270P + 1.0P^2

      = 5000 + 270(128) + 1.0(128^2)

      = 5000 + 34560 + 1.0(16384)

      = 5000 + 34560 + 16384

      = 55944 [C]

Unit 3 cost calculation:

At minimum output (40MW):

Cost = 9000 + 160P + 0.7P^2

      = 9000 + 160(40) + 0.7(40^2)

      = 9000 + 6400 + 0.7(1600)

      = 9000 + 6400 + 1120

      = 16520 [C]

At maximum output (149MW):

Cost = 9000 + 160P + 0.7P^2

      = 9000 + 160(149) + 0.7(149^2)

      = 9000 + 23840 + 0.7(22201)

      = 9000 + 23840 + 15540.7

      = 48380.7 [C]

To supply a load of 200MW at minimum cost, we need to determine the combination of units that results in the lowest total cost.

To find the optimal dispatch, we'll compare the costs of different combinations:

Combination 1: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 31MW

Total cost = Cost(Unit 1) + Cost(Unit 2) + Cost(Unit 3)

               = 41400 + 16051 + 16520

               = 73971 [C]

Combination 2: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 40MW

Total cost = Cost(Unit 1) + Cost(Unit

2) + Cost(Unit 3)

               = 41400 + 16051 + 16520

               = 73971 [C]

Combination 3: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 41MW

Total cost = Cost(Unit 1) + Cost(Unit 2) + Cost(Unit 3)

               = 41400 + 16051 + 18307.7

               = 75758.7 [C]

Based on these calculations, the combination of units that results in the minimum cost to supply a load of 200MW is Combination 1, with Unit 1 generating 130MW, Unit 2 generating 39MW, and Unit 3 generating 31MW.

b) If the company has the opportunity to buy energy on the spot market at the price of 300 d/MWh and 220 c/MWh, respectively.

To determine the new dispatch, we compare the costs of operating the units with the market prices:

Unit 1 cost with spot market price: 300 d/MWh

Cost = 5000 + 215P + 0.5P^2

      = 5000 + 215(300) + 0.5(300^2)

      = 5000 + 64500 + 0.5(90000)

      = 5000 + 64500 + 45000

      = 114500 [C]

Unit 2 cost with spot market price: 220 c/MWh

Cost = 5000 + 270P + 1.0P^2

      = 5000 + 270(220) + 1.0(220^2)

      = 5000 + 59400 + 1.0(48400)

      = 5000 + 59400 + 48400

      = 112800 [C]

Unit 3 cost with spot market price: 220 c/MWh

Cost = 9000 + 160P + 0.7P^2

      = 9000 + 160(220) + 0.7(220^2)

      = 9000 + 35200 + 0.7(48400)

      = 9000 + 35200 + 33880

      = 78080 [C]

To determine the new optimal dispatch, we compare the costs considering the spot market prices:

Combination 1: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 31MW

Total cost = Cost(Unit 1) + Cost(Unit 2) + Cost(Unit 3)

               = 114500 + 112800 + 78080

               = 305380 [C]

Combination 2: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 40MW

Total cost = Cost(Unit 1) + Cost(Unit 2) + Cost(Unit 3)

               = 114500 + 112800 + 78080

               = 305380 [C]

Combination 3: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 41MW

Total cost = Cost(Unit 1) + Cost(Unit 2) + Cost(Unit 3)

               = 114500 + 112800 + 79912

               = 307212 [C]

Based on these calculations, even with the spot market prices, the optimal dispatch remains the same as before, which is Combination 1: Unit 1 generating 130MW.

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If a section of a highway is constructed with a 23% grade, the angle that the highway will make with a horizontal line will be: 13°.

Using the SOH CAH TOA formula, the angle that the highway will make with the horizontal line can be gotten by finding the tangent which is the

vertical/horizontal

Horizontal = 100 ft

Angle of inclination = 0.23

For the 23% grade, we will have

tan⁻1 of 0.23 = 12.9527°

= 13.0°

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Answer:O perpendicular

Step-by-step explanation:

Answer:

39 years old

Step-by-step explanation:

50 - 11 = 39 years old

Answer:

39 years old

Step-by-step explanation:

The total possible ways of arranging 30 students in two groups of sizes 4 and 6 respectively are 6309453150, which is obtained by using the prerequisite knowledge of combinations.

What is the combination?

A combination is a mathematical procedure that deduces the number of feasible selections in a collection of articles in which the order of the selection does not matter. In combinations, you can choose any items in any order. Its formula is given by C(n,r) = n! / (n - r)! r!)

Calculation of the total possible ways of arranging two focus groups of students with sizes 4 and 6 respectively

Given a group of 30 students

Two focus groups are to be arranged in sizes 4 and 6 respectively

Total number of possible ways to arrange the two focus groups = C(30,4) × C(26,6)

Using the formula for combination, we get,

T.F.O = [30! / (26! 4!)] × [26! / (20! 6!)]

T.F.O = 27405 × 230230

         = 6309453150

Hence, the required possible ways to arrange two groups are given by 6309453150.

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Answer:

70, 84, and 116

Step-by-step explanation:

(x) + (x + 14) + (2x - 24) + 90 = 360

4x - 10 + 90 = 360

4x = 280

x = 70

x + 14 = 84

2x - 24 = 116

Answer:

\(y = \boxed0\)

Step-by-step explanation:

we are given a sin function

\( \displaystyle h(x) = - 4 \sin(x -\pi /4) \)

we want to figure out the midline of the function graphically The midline of a sinusoidal function is the horizontal line that passes exactly in the midline of its extreme value however since we a function recall that,

\( \displaystyle f(x) = a \sin(bx -c) + d\)

where the midline is

to figure out the midline rewrite the function

\( \displaystyle h(x) = - 4 \sin(x -\pi /4) + 0\)

therefore the midline is

\(y = \boxed0\)

Answer:

sorry i dont understand

Step-by-step explanation:

will figure out...

Answer:

9b²-4

Step-by-step explanation:

(3b-2)(3b+2)

9b²+6b-6b-4

9b²+0-4

9b²-4

first to answer, pls brainliest.

The average value fave using the formula fave = (1 / (b - a)) ∫[a,b] 7 sin(4x) dx. The definite integral of f(x) over the interval [a, b] is:

∫[a,b] 7 sin(4x) dx = -7/4 [cos(4x)] [from a to b]

To find the average value fave of the function f(x) = 7 sin(4x) on the given interval, we need to calculate the definite integral of the function over the interval and then divide it by the length of the interval.

The given interval is specified as [−, ], where the lower and upper limits are missing. To proceed with the calculation, we need the specific values for the lower and upper limits of the interval. Please provide the missing values so that we can compute the average value of the function.

Once we have the interval limits, we can calculate the definite integral of f(x) = 7 sin(4x) over that interval. The integral of sin(4x) with respect to x is evaluated as -cos(4x) / 4. Therefore, the definite integral of f(x) over the interval [a, b] is:

∫[a,b] 7 sin(4x) dx = -7/4 [cos(4x)] [from a to b]

Next, we need to find the length of the interval, which is given by b - a.

Finally, we can compute the average value fave using the formula:

fave = (1 / (b - a)) ∫[a,b] 7 sin(4x) dx

By plugging in the specific values for a, b, and evaluating the definite integral, we can calculate the average value fave of the function f(x) over the given interval.

Please provide the missing values for the interval, and I'll be able to assist you in finding the average value fave in a more specific manner.

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Answer:

2p²-5p+3 is the final answer as they aren't any like terms to collect in order to simply the solution further.

Step-by-step explanation:

Wishing you a splendiferous day,

stay salty...

Answer: y=7x^2−42x+69

Step-by-step explanation:

Answer:

So then al you have to do is put 15 blocks

Step-by-step explanation:

An example of a linear function table is y=3x

A linear function is used to relate an independent variable and a dependent variable by introducing a rate of change(function) of which the independent variable is equated to find the dependent variable. Linear functions are those whose graph is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

for example:

y=3x hence is the dependent variable as it depends on the change of x and 3 is the rate of change which is a constant and is determined by the division of the values of y/x hence to make a table of y over x of which y is determined by the rate of change the unrelated variable x, 3.

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The eigenvalues are λ₁ = 3 and λ₂ = 1.(both positive)

Since both eigenvalues are positive, the critical point (-3, 2) is a local minimum.

To find the local maxima, local minima, and saddle points of the function f(x, y) = x² + xy + y² + 6x - 3y + 4, we need to compute the gradient and classify the critical points.

Step 1: Compute the gradient of f(x, y):

∇f(x, y) = (∂f/∂x, ∂f/∂y)

∂f/∂x = 2x + y + 6

∂f/∂y = x + 2y - 3

Step 2: Set the gradient equal to zero and solve for x and y:

2x + y + 6 = 0 ----(1)

x + 2y - 3 = 0 ----(2)

Solving equations (1) and (2), we find the critical point:

x = -3

y = 2

Step 3: Compute the Hessian matrix of f(x, y):

H = | ∂²f/∂x² ∂²f/∂x∂y |

| ∂²f/∂y∂x ∂²f/∂y² |

∂²f/∂x² = 2

∂²f/∂y² = 2

∂²f/∂x∂y = 1

Plugging in the values, we get:

H = | 2 1 |

| 1 2 |

Step 4: Determine the nature of the critical point:

To classify the critical point, we examine the eigenvalues of the Hessian matrix H. If both eigenvalues are positive, it is a local minimum; if both are negative, it is a local maximum; if one is positive and the other is negative, it is a saddle point.

The characteristic equation is given by:

| 2 - λ 1 |

| 1 2 - λ |

Det(H - λI) = (2 - λ)(2 - λ) - 1 = λ² - 4λ + 3 = (λ - 3)(λ - 1)

The eigenvalues are λ₁ = 3 and λ₂ = 1.

Since both eigenvalues are positive, the critical point (-3, 2) is a local minimum.

Therefore, the function f(x, y) = x² + xy + y² + 6x - 3y + 4 has a local minimum at (-3, 2).

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