-2x+y=-7
how do you do this problem

Answer:

200

Step-by-step explanation:

From this information 15% = 30 and we need to find 100%:

Hope this helps!

The wingspan of the real aeroplane is equal to 68.25 cm.

In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures such as aeroplanes, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

Mathematically, the scale factor of a geometric figure can be calculated by dividing the dimension of the image by the dimension of the pre-image (original figure):

Scale factor = 13/4

Scale factor = 3.25

For the wingspan of the real aeroplane, we have:

Real Wingspan = 3.25 × 21

Real Wingspan = 68.25 cm.

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Lateral Surface Area of triangle prism = (2a + c) x h

We need to determine the area of all the rectangular sides of a triangular prism in order to calculate its lateral surface area. In this instance, there are two isosceles triangles and one rectangle.

The following formula can be used to determine the triangular prism's lateral surface area:

Lateral Surface Area = Perimeter of Base x Height

The sum of the lengths of each side of a triangular prism forms the base's perimeter.

Since the base is an isosceles triangle in this case, the perimeter can be calculated by dividing the length of the third side by twice the length of one of the equal sides.

We should expect that the foundation of the three-sided crystal has sides of length a, b, and c. We can expect to be that an and b are the equivalent sides, and c is the third side.

Perimeter of Base = 2a + c

The height of the triangular prism is the perpendicular distance between the two parallel bases, which is the length of the rectangular face of the prism. Let's assume that the height of the triangular prism is h.

Now, the lateral surface area of the triangular prism can be found by multiplying the perimeter of the base by the height of the prism:

Lateral Surface Area = Perimeter of Base x Height

Lateral Surface Area = (2a + c) x h

Therefore, to calculate the lateral surface area of the triangular prism, we need to know the length of the sides of the base, c and the height of the prism, h. Once we have these values, we can use the formula to find the lateral surface area.

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All values of x in the interval [0, 2] that satisfy the equation are \(\frac{\pi }{2} ,3\frac{\pi }{2}\).

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions. For instance, an équation is defined as having one or more variables in French.

The first step in resolving a variable equation is to identify the values of the variables that lead to the equality being true. The variables that must be changed in order to solve the equation are referred to as the unknowns, and the values of the unknowns that satisfy the equality are referred to as the equation's solutions.

Calculations:

16cos(x +8sin(2x)=0

Divide by 8

2cos(x)+sin(2x)=0

Identity:

sin(2x)=2sin(x)cos(x)

2cos(x)+2sin(x)cos(x)=0

Factor:

2cos(x)(1+sin(x))=0

2cos(x)=0

cos(x)=0=x=\(\frac{\pi }{2}\),3\(\frac{\pi }{2}\)

(1+sin(x))=0

sin(x)=−1=x=3\(\frac{\pi }{2}\)

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Answer:

15. (8x^3 + 27)(x + 1)

17. (x^2 + 3)(x + 2)

Step-by-step explanation:

8x^3(x + 1) + 27(x + 1)

x^2(x + 2) + 3(x + 2)

The method for finding and classifying critical points of a function involves finding the first derivative of the function and setting it equal to zero to find the critical points. Then, the second derivative test is used to classify the critical points as local maxima, local minima, or saddle points.

The given function is not provided in the question. Therefore, we cannot find and classify the critical points of the function. However, I can provide the general method for finding and classifying critical points of a function.

Finding the critical points: To find the critical points of a function, we need to find the values of x where the first derivative of the function is equal to zero or does not exist. These points are called critical points. Mathematically, we can express this as follows:

f′(x) = 0 or f′(x) does not exist

Classifying the critical points: Once we have found the critical points of the function, we can classify them using the second derivative test. This test involves finding the second derivative of the function at the critical points and determining its sign.

If the second derivative is positive, then the critical point is a local minimum. If the second derivative is negative, then the critical point is a local maximum. If the second derivative is zero or undefined, then the critical point is a saddle point.

Mathematically, we can express this as follows:

f′′(x) > 0, then (x, f(x)) is a local minimum.
f′′(x) < 0, then (x, f(x)) is a local maximum.
f′′(x) = 0 or does not exist, then (x, f(x)) is a saddle point.

Once we have found and classified the critical points of the function, we can then enter the list of ordered pairs (x, y) where the max/min/saddle occurs for each classification. If there are no points for a classification, we enter "dne" (does not exist).

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To increase the injection rate q, we can increase the injection well pressure (piw), decrease the production well pressure (ppw), or decrease the distance between the injection and production well (d) any changes in these variables should be carefully evaluated and monitored to avoid any adverse effects on the reservoir performance.

How injection rate varies with different scenario?

The dimensionless productivity index for the well in the given equation can be calculated by dividing the flow rate (q) by the pressure difference (Pw-Ppw) and the distance between the wells (d).
The dimensionless productivity index = q / (Pw-Ppw)d

In order to increase the injection rate q, we can change the three controllable variables piw, ppw and d.

To increase the injection rate q, we can increase the injection well pressure (piw), decrease the production well pressure (ppw), or decrease the distance between the injection and production well (d).

However, there may be some restrictions on varying these variables freely. For example, increasing the injection well pressure beyond a certain limit may cause formation damage or fracture the reservoir rock. Similarly, decreasing the production well pressure too much may result in water coning or gas breakthrough.

Moreover, decreasing the distance between the wells may not be feasible due to the geological or physical constraints of the reservoir.

Therefore, any changes in these variables should be carefully evaluated and monitored to avoid any adverse effects on the reservoir performance.

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Answer:

domain will be ( -∞, ∞)

Step-by-step explanation:

The given functions are f(x) = x² - 1 and g(x) = 2x - 3

We have to find domain of (fog)(x)

We will find the function (fg)(x) first.

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

         = (2x - 3)²

         = 4x² + 9 - 12x - 1

        = 4x² - 12x + 8

       = 4 (x² - 3x + 2)

The given function is defined for all values of x.

Therefore, domain will be ( -∞, ∞)

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Answer:

a

Step-by-step explanation:

An ordered pair is a solution of an equation in two variables if replacing the variables by the coordinates of the ordered pair results in a true statement.

In mathematics, an equation in two variables represents a relationship between two quantities. An ordered pair consists of two values, typically denoted as (x, y), that represent the coordinates of a point in a two-dimensional plane.

When these values are substituted into the equation, if the equation holds true, then the ordered pair is considered a solution or a solution set to the equation. This means that the relationship described by the equation is satisfied by the values of the ordered pair. In other words, the equation is true when evaluated with the values of the ordered pair.

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Isabella made a pyramid-shaped paper gift box with a square base in her origami class and correct answer is option b) 97 square centimeters.

To calculate the amount of paper Isabella used to make the gift box, we need to find the total surface area of the four triangular sides.

Each triangular side has a base length of 5 centimeters and a slant height of 9.7 centimeters. The formula for the area of a triangle is given by:

Area = (1/2) * base * height

Substituting the values into the formula, we have:

Area = (1/2) * 5 * 9.7

Area = 24.25 square centimeters

Since there are four triangular sides, we multiply the area of one triangular side by four to get the total surface area of the triangular sides:

Total Surface Area = 24.25 * 4

Total Surface Area = 97 square centimeters

Therefore, Isabella used 97 square centimeters of paper to make the gift box.

Hence, the correct answer is 97 square centimeters.

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Best Fit Line

Given a series of points that represent some measures in the real world, for example, the heights vs the age of a group of children, when we plot it on a rectangular grid, we get a scatter plot, not necessarily aligned as to form a specific graph.

Sometimes is vital to have a known function that best represents the whole dataset, so we can make predictions.

The best fit line is widely used to do that. We can recognize the best fit line because it usually goes through the maximum number of points and the sum of the distances to each one of them is minimum.

From the three graphs given in the question, it's evident the first line is totally outside the set of points, so it does not do a good job representing the dataset.

The second graph approximates much better to a best-fit line but we can still see the trend of the line does not follow the trend of the dotted path.

Finally, the third graph looks very adequate to represent the scattered points because it keeps always close to them and follows their trend.

False. In cubic closest packing (CCP) or face-centered cubic (FCC) structure, the unit cell is not body-centered cubic (BCC). The unit cell in CCP/FCC is composed of a cube with lattice points at the corners and an additional lattice point at the center of each face.

The term "cubic closest packing" refers to the arrangement of atoms or spheres in a cubic lattice where the spheres touch each other along their faces.

This arrangement is achieved by stacking layers of spheres in an ABCABC... pattern. Each sphere is in contact with 12 surrounding spheres, resulting in a coordination number of 12.

On the other hand, the body-centered cubic (BCC) structure has a different arrangement. In BCC, the unit cell consists of a cube with lattice points at the corners and an additional lattice point at the center of the cube. Each atom or sphere in BCC is in contact with eight neighboring atoms.

Therefore, the statement that the unit cell in cubic closest packing is body-centered cubic is false. The correct unit cell for cubic closest packing or face-centered cubic packing is the face-centered cubic (FCC) structure.

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Answer: 35 the digits both together = 8

Reverse it and add 2.

53+2 =55

55- 35 = 20

The required answer is 35 :)

Step-by-step explanation:

7/10 of one can; since 7 is less than 10 it would only be a fraction of the can.

( hope this helps! x )

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The statement that truly represent the diagram is

y = w and Δ ABC ~ Δ CDE

The two triangles depicted are similar triangles and similar triangle is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Examining the figure shows that pair of congruent angles are

angle  y = angle  w (alternate angles)

angle D = angle B (right triangle)

angle x = angle z (alternate angles)

similar triangles is represented by ~ and only the first option match the description

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Answer:

c=155h-64

Step-by-step explanation:

you mulitply the cost of the classes by the amount of hours, then you deduct the scholarship gift(64) from the total and get your total cost of the semester

Answer:

See below for proof.

\(S_{500}=125250\)

Step-by-step explanation:

Given arithmetic series:

Therefore:

\(S_n=1+2+3+...+(n-2)+(n-1)+n\)

\(S_n=1+(1+1)+(1+2)+...+(1+n-3)+(1+n-2)+(1+n-1)\)

\(S_n=1+(1+1)+(1+2(1))+...+(1+(n-3)(1))+(1+(n-2)(1))+(1+(n-1)(1))\)

Let:

Therefore:

\(S_n=a+(a+d)+(a+2d)+...+(a+(n-3)d)+(a+(n-2)d)+(a+(n-1)d)\)

Reverse the order:

\(S_n=(a+(n-1)d)+(a+(n-2)d)+(a+(n-3)d)+...+(a+2d)+(a+d)+a\)

Add the two expressions for Sₙ:

\(2S_n=(2a+(n-1)d)+(2a+(n-1)d)+(2a+(n-1)d)+...+(2a+(n-1)d)\)

Therefore, the term (2a + (n – 1)d) has been repeated n times:

\(2S_n=n(2a+(n-1)d)\)

Divide both sides by 2:

\(S_n=\dfrac{1}{2}n(2a+(n-1)d)\)

\(S_n=\dfrac{1}{2}n(a+a+(n-1)d)\)

Replace  a with  a₁  (first term) and a + (n – 1)d  with  aₙ (last term):

\(S_n=\dfrac{1}{2}n(a_1+a_n)\)

To find the sum of the series 1 + 2 + 3 + ... + 500, substitute the following values into the formula:

Therefore:

\(\implies S_{500}=\dfrac{1}{2}(500)(1+500)\)

\(\implies S_{500}=250(501)\)

\(\implies S_{500}=125250\)

Using Definition 1 of the Laplace transform, we have determined the Laplace transforms of the given functions as mentioned above.

Definition 1 of the Laplace transform states that for a function f(t) defined for t ≥ 0, its Laplace transform F(s) is given by F(s) = L{f(t)} = ∫[0,∞] e^(-st) f(t) dt. Using this definition, we can determine the Laplace transforms of the given functions:

1. The Laplace transform of t is given by L{t} = 1/s².

2. The Laplace transform of t² is given by L{t²} = 2/s³.

3. The Laplace transform of e^(6t) is given by L{e^(6t)} = 1/(s - 6).

4. The Laplace transform of te^(3t) requires applying the property of the Laplace transform for the derivative of a function. The Laplace transform of te^(3t) is given by L{te^(3t)} = -d/ds (1/(s - 3)²).

5. The Laplace transform of cos(2t) requires using the trigonometric property of the Laplace transform. The Laplace transform of cos(2t) is given by L{cos(2t)} = s/(s² + 4).

In conclusion, using Definition 1 of the Laplace transform, we have determined the Laplace transforms of the given functions as mentioned above.

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The system of linear equations has no solution when the constant k is equal to 2. It has infinitely many solutions when k is not equal to 2.

To determine the value(s) of k for which the system of equations has no solution, we can examine the coefficients of the variables.

In the given system, the coefficients of x, y, and z are 1, 1, and k²-5 respectively. For the system to have no solution, the coefficients of x, y, and z must be proportional across the equations.

However, in this case, the coefficient of x is 1, while the coefficient of y is 2. Therefore, the system can never satisfy both equations simultaneously. By comparing the equations, we see that the coefficient of x in the first equation is not equal to the coefficient of x in the second equation.

Thus, the system has no solution when k = 2.

To determine the value(s) of k for which the system has infinitely many solutions, we need to check if the equations are dependent or have consistent coefficients.

If the equations are dependent, it means they are multiples of each other or represent the same line in the three-dimensional space. To determine this condition, we can examine the ratio between the coefficients of x, y, and z in the equations.

In the given system, the ratio between the coefficients of x, y, and z is always 1:2:(k²-5). If this ratio remains the same for all equations, the system will have infinitely many solutions.

Thus, when k is not equal to 2, the system has infinitely many solutions.

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Answer:

Probability ≈ 0.0833

Step-by-step explanation:

Consider steps below;

\(Total Possible Outcomes - 9C6,\\\\9! / 6! ( 9 - 6 )!,\\1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 / ( 1 * 2 * 3 * 4 * 5 * 6)( 1 * 2 * 3 ),\\\\362,880 / 720 * 6 = Combinations - 84,\\\\\)

\(Number Of Outcomes - 7C6,\\\\7! / 6! ( 7 - 6 )!,\\1 * 2 * 3 * 4 * 5 * 6 *7/ ( 1 * 2 * 3 * 4 * 5 * 6 ) ( 1 ),\\\\Outcomes - 7\)

\(Conclusion ; Solution - 7 / 84 = ( About ) 0.0833\\Hope That Helps!\)

Solution; Probability ≈ 0.0833

The confidence interval of a f-up study was (2.56,5.1). Which of the following is true?The correct answer is that this is a statistically significant finding. A confidence interval (CI) is a range of values calculated from a given set of data or statistics that represents the plausible values of a population parameter.

A statistical significance test, on the other hand, is a hypothesis test that assesses whether or not the observed data is unlikely to have happened by chance alone. A statistical significance test is conducted to determine whether a finding is significant or simply due to chance. If a statistical significance test determines that the observed data is unlikely to have occurred by chance alone, it is considered statistically significant.

Therefore, since the given confidence interval does not include zero, this suggests that the findings are statistically significant. In other words, it implies that the population mean is either greater than 2.56 or less than 5.1. Therefore, it can be concluded that this is a statistically significant finding.

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Answer:

X = 50

Step-by-step explanation:

Both equations TOGETHER equal 180 degrees so you write the equation:

2x + 30 + x = 180

(combine X's. Subtract 30 from both sides):

3x = 150

(divide both sides by 3)

X = 50

Answer:

17°

Step-by-step explanation:

Complementary must add up to 90°

therefore, 90-73

Answer:

solution given:

x+73=90° complementary

x=90-73

x=17°

x=17°

The variables in the point-slope form of a line (x₁,y₁) is a given point on the line, m the slope of the line and (x,y) is any point on the line.

Given that the variables in the point-slope form of a line.

The general form of the equation of a line is y - y₁ = m (x-x₁) where  m is the slope of line, y₁ and x₁ is any point on the line

It is an equation of degree one x and y represent the coordinate of the point on the line represented in the coordinate plane

m = slope of the line

The general equation of a line is y = mx + c where

m = slope of line

(x₁ , y₁) = it is the given point on the line as data points are represented as (x₁,y₁) , (x₂,y₂) , (x₃,y₃) and so on

(x ,y) = it is any point line where x is any point on the x-axis and y is any point on y-axis

Hence, the variables in the point-slope form of a line where (x₁,y₁) is a given point on the line, m the slope of the line and (x,y) is any point on the line.

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