Using the theory vectors, find all possible fourth corners to parallelograms that have vertices (1,1), (4,2), and (1,3)

The solutions that match the given differential equation are a)y=0 and b)y=2x.

The differential equation is a homogeneous linear differential equation with constant coefficients, which can be written in the form of y" + p(x)y' + q(x)y = 0. The general solution to this type of equation is y = c1e^(rx) + c2e^(rx) where r is the root of the characteristic equation r^2 + p(x)r + q(x) = 0.

In this case, the equation is of the form xy'' - y' = 0. By dividing both sides by x, we get y'' - (1/x)y' = 0, which is a homogeneous linear differential equation with constant coefficients. The characteristic equation is r^2 - (1/x)r = 0. The roots of this equation are r1 = 0 and r2 = 1/x.

Therefore, the general solution to this differential equation is y = c1 + c2x.

y=0 is a solution of the differential equation since it satisfies the equation when plugged in.

y=2x is also a solution of the differential equation since it also satisfies the equation when plugged in.

y=2x^2 and y=2 are not solutions of the differential equation because when plugged into the equation they don't satisfy it.

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There were 0-5 Listeners when the song was released.

The approximate number of listeners who had heard the song after the hour 5 was 15- below 50

The number of listeners was about 29,458 after hour 5842.62/

Alternative forms

Y= 4,637(1.26)ˣ

292131/50,5842,31/50,5.84262 =10³

5842.62

Including polynomial components, such as squared or cubed predictors, is the most popular technique to fit curves to data using linear regression. Typically, the model order is determined by the number of bends required in your line. Each exponent increment causes one additional bend in the curved fitting line.

Curve of Best Fit: a scatter plot curve that best approximates the trend. If the data looks to be quadratic, we use quadratic regression to get the equation for the best-fit curve. We do a cubic regression if it looks to be cubic.

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The best name for this shape is rectangle. There are two sets of parallel sides and two pairs of equal opposite sides in every rectangle.

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Answer:

5/10 - 1/10 = 4/10

a = 4/10

4/10 + 1/10 = 5/10

Step-by-step explanation:

Hope it helps! =D

The numbers that correctly complete this table are 53.83 years and 2.12%

The formula that can be used is:

Doubling time = 70 (constant)/ population growth

Doubling time =70 / 1.3

Doubling time = 53.84 years

The same formula can be applied:

33 = 70 (constant)/ population growth

population growth = 70 /33

population growth = 2.12 %

Based on this, the correct numbers to complete the table are 53.83 years and 2.12%.

Note: Here is the missing table:

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The decision rule given is x1 + x3 – 10 ≥ 0, which can be rearranged to x1 + x3 ≥ 10. This forms a line in the R2 space, and any point on or above this line will be classified as 1, while any point below this line will be classified as 0.

To draw the decision boundary, we can plot the line x1 + x3 = 10 on a graph with the x1 and x3 axes. The region above the line, where x1 + x3 ≥ 10, would be shaded to indicate that it is where the classifier predicts 1.

It is important to note that the classifier predicts 1 if x1 + x3 – 10 ≥ 0, but in the explanation above I have used x1 + x3 = 10 to draw the decision boundary, this is because x1 + x3 – 10 ≥ 0 is equivalent to x1 + x3 ≥ 10.

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The linear relationship is a proportional relationship because the ratios between each pair of values are equivalent and the graph passes through the point (0,0).

What is proportional relationship?

Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them. This parameter is referred to as the "constant of proportionality".

We are given points as (2,14.5), (4,29), (6,43.5) and the origin (0,0).

We know that in a proportional relationship the ratios are equal i.e.

[tex]\frac{y_{1} }{x_{1}} = \frac{y_{2} }{x_{2} } = \frac{y_{n} }{x_{n} }[/tex]

So,

⇒ 14.5/2 = 29/4 = 43.5/6 = 7.25

Since, the ratios are same, therefore the linear relationship is a proportional relationship.

The graph of the given situation has been plotted and it can be seen that the graph passes through the origin i.e. (0,0)

Hence, the linear relationship is a proportional relationship because the ratios between each pair of values are equivalent and the graph passes through the point (0,0).

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Translations between points B and B' and points S and S' are result of using translation vector T(x, y) = (- 3, - 1).

In this problem we find the case of two points being translated by rigid transformation formula. Translations are defined by following equations:

P'(x, y) = P(x, y) + T(x, y)

Where:

First, derive translation vector from translation formula:

T(x, y) = B'(x, y) - B(x, y)

T(x, y) = (- 9, - 2) - (- 6, - 1)

T(x, y) = (- 3, - 1)

Second, check that point S' is the image of point S:

S'(x, y) = S(x, y) + T(x, y)

S'(x, y) = (5, 1) + (- 3, - 1)

S'(x, y) = (2, 0)

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The value of tan(Y) = 0.75.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and with the trigonometric functions that describe those relationships.

Since triangle XYZ is a right triangle, we can use the trigonometric ratios of sine, cosine, and tangent to find the value of tan(Y). We can use the Pythagorean theorem to find the lengths of the sides XZ and YZ.

XZ = √(X^2 + Z^2) = √(4^2 + 3^2) = 5

YZ = XZ * sin(Y) = 5 * sin(Y)

Since we know the value of XZ and YZ, we can use the tangent function to find the value of tan(Y):

tan(Y) = YZ / XZ = sin(Y) / cos(Y) = YZ / 5 = 3 / 4 = 0.75

So, the value of tan(Y) = 0.75.

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By solving a subtraction, we can write the difference between the lengths as:

|x + 7|

Here we want to find the difference between the two lenghts below:

L₁ = (7x + 2)

L₂ = (6x - 5)

The difference between these can be written as the absolute value of the subtraction, then we will get:

| L₁ - L₂|

We use the absolute value because we don't know which one is the larger value.

Replacing the expressions we will get:

| (7x + 2) - (6x - 5)|

|7x + 2 - 6x + 5|

| x + 7|

That is the difference.

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Elementary row operations are always applied to an augmented matrix after the solution has been found. So the option D is correct.

Elementary row operations:

1. It is possible to convert a system of linear equations into an equivalent system, or into a new system of equations that has the same solutions as the original system, using these straightforward techniques.

2. In order to convert a matrix to row echelon form, Gaussian elimination is used.

3. Simple row operations on an augmented matrix never alter the underlying linear system's solution set.

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Answer:

-9x + -3

Step-by-step explanation:

1. Primeiro, vamos penteinar SO prazoos que possuem um mesmamã variável, ou seja, -5x e -4x:

-5x - 4x

2.  Agora, vamos penteinar SO prazoos que possuem o mesmo coeficiente, ou seja, 1 e -4:

-5x - 4x + 1 -

4 3.  Por fim, vamos penteinar SO prazoos que possuem o mesmo coeficiente, ou seja, -4 e 1:

-5x - 4x + -4 + 1

Answer:

Uma expressão está e sua forma mais simples quando não há mais nenhuma simplificação possível. Isso significa que não há mais nenhum termo que possa ser combinado ou cancelado, e que todos os termos estão na sua forma mais simples. Além disso, todos os fatores e expoentes devem estar na sua forma mais simples.

If two rooms in a tiny house share a wall the area of the living room is 54. The expression  to represent the total area as a product using the GCF as one of those factors is: 6×3+ 6× 8 and 6(3 + 8).

Living room area = 54 square feet

Area of the bedroom  = 42 square feet

Total area of the two rooms = 54 + 42

Total area of the two rooms = 66 square feet

So, the expressions that represent the total area of the two rooms  is: 6×3+ 6× 8 and 6(3 + 8).

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Answer:

54+42=6(9+7)

Step-by-step explanation:

The value of the variable x = π³ - π/π

Algebraic expressions are described as mathematical expressions that are comprised of variables, factors, constants, terms and coefficients.

These algebraic expressions are also comprised of arithmetic operations, such as;

From the information, we have that;

y = π³

y = πx + π

Substitute the values, we get;

π³ =  πx + π

collect like terms

π³ - π = πx

Divide both sides by the coefficient of x

x = π³ - π/π

Thus, the value is x = π³ - π/π

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The probabilities for each type of blood are given as follows:

A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.

The total number of people is given as follows:

22 + 20 + 6 + 2 = 50.

6 people have type B, hence the probability is given as follows:

6/50 = 0.12 = 12%.

2 people have type AB, hence the probability is given as follows:

2/50 = 0.04 = 4%.

8 people have either type B or type AB, hence the probability is given as follows:

8/50 = 0.16 = 16%.

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Answer: 7

Step-by-step explanation:

First, we need to prime factorize the number 189,

189 = 3 × 3 × 3 × 7 × m

From the factors we can see that there is no pair of same numbers for 7, so if we replace m with 7, we can get a perfect square.

Hence the answer is 7

The perimeter of the rectangle WXYZ is 96 cm.

Here we see that

WXYZ is a rectangle (given)

Therefore,

∠WZY = 90 = ∠WZS

Since JS is parallel to PZ and JP is parallel to SZ, we get

JPSZ as a rectangle. Similarly, PKWQ, SYMR, and XQRL are rectangles.

JS = PZ

or, JS = PW + WZ

or, JS = KQ + WZ

or, WZ = JS - KQ

or, WZ = 52 - 25

or, WZ = 27

The side of the rhombus PS is a diagonal of rectangle JSPZ

Therefore length of the diagonal PS = √(JP² + JS²)

= √(52² + 39²)

= 65 cm

Hence for PWKQ,

PK = √(PQ² - KQ²)

= √(65² - 25²)

= 60 cm

For triangles ΔPWQ and ΔSYR,

the corresponding sides are parallel to each other. Hence we can say that

PW/YR = WQ/SY = PQ/RS

Therefore,

60/SY = 65/65            [Since they are the sides of a rhombus]

or, SY = 60 cm

Now, SY = SZ + ZY

or, SY = JP + ZY               [Opposite sides of a rectangle are equal]

or, ZY = 60 - 39

or, ZY = 21

Hence the perimeter of WXYZ

2(length + width)

= 2(27 + 21)

= 96 cm

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Complete Question

Rhombus PQRS is inscribed in a rectangle JKLM, as shown. Segments PZ and XR are parallel to JM. Segments QW and YS are parallel to JK. If JP = 39 cm, JS = 52 cm, and KQ = 25 cm, what is the perimeter of rectangle WXYZ?

A power function is a type of function with a variable in the form of an exponent. An exponential function is a type of function that contains a variable in the form of an exponent.

The most common example of this is y = xn, where n is the exponent and x is the independent variable. For example, y = (π)x is a power function with an exponent of x and an independent variable of π.

Exponential Function: An exponential function is a type of function that contains a variable in the form of an exponent. The most common example of this is y = bx, where b is the base and x is the independent variable. For example, y = xy is an exponential function with a base of x and an independent variable of y.

Polynomial: A polynomial is a type of function that has a degree, which is the highest exponent of its variables. For example, y = x2 (2-x3) is a polynomial with a degree of 2 since the highest exponent of its variables is 2.

Trigonometric: A trigonometric function is a type of function that involves trigonometric ratios. The most common example of this is y = tan t â cos t, which uses the trigonometric ratios of tangent and cosine.

Algebraic Function: An algebraic function is a type of function that can be expressed as a combination of polynomials. The most common example of this is y = s / 1+s, which is a combination of polynomials with a numerator of s and a denominator of 1+s.

Root Function: A root function is a type of function that involves a root of a polynomial. The most common example of this is y = sqrt(x3 â 1) / 1+ 3sqrt(x), which uses the root of the polynomial x3 â 1 in the numerator and 3sqrt(x) in the denominator.

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Vector v and w have lengths of 11 and contain elements of 21, 10, 32, 2, -3, 4, 5, 6, 7, 4, -22 and -18, 72, 11, -9, 10, 2, 34, -5, 18, 9, 2 respectively. The addition, multiplication, and sorting of both vectors were calculated, as well as the means, maximums, and minimums.

a) The lengths of the vectors v and w are both 11.

b) Vector v contains the elements 21, 10, 32, 2, -3, 4, 5, 6, 7, 4, -22 and vector w contains the elements -18, 72, 11, -9, 10, 2, 34, -5, 18, 9, 2.

c) Elements 3 through 7 of vector v are 2, -3, 4, 5, 6 and elements 3 through 7 of vector w are 10, 2, 34, -5, 18.

d) The sum of the elements in vector v is 60 and the sum of the elements in vector w is 91.

e) The mean of vector v is 5.454545454545455 and the mean of vector w is 8.272727272727273.

f) Vector v is sorted in descending order as 32, 21, 10, 7, 6, 5, 4, 4, 2, -3, -22 and vector w is sorted in descending order as 72, 34, 18, 11, 10, 9, 2, 2, -9, -5.

g) The addition of vectors v and w is 53, 82, 28, 2, 7, 13, 6, 8, -7, 4, -20.

h) The multiplication of vectors v and w is -378, 720, 352, -18.

i) Elements in vector v that are greater than zero are 21, 10, 32, 2, 4, 5, 6, 7, 4.

j) Elements in vector w that are less than zero are -18, -9, -5.

k) Vector v multiplied by 6 is 126, 60, 192, 12, -18, 24, 30, 36, 42, 24, -132.

l) The maximum of vector v is 32 and the minimum of vector v is -22. The maximum of vector w is 72 and the minimum of vector w is -9.

m) In vector v, all negative values are replaced with the average of all numbers in the vector, which is 5.454545454545455. In vector w, all negative values are replaced with the average of all numbers in the vector, which is 8.272727272727273.

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The public increased the amount of currency it held and that banks increased the reserve-deposit ratio is $0.66 million.

Now, According to the question:

December 1921

-Currency held by public: $4.59

-Reserve Deposit ratio: 0.095

-Bank reserves: $3.11

-Money supply: $37.3

December 1932

-Currency held by public: $4.82

-Reserve Deposit ratio: 0.109

-Bank reserves: $3.18

-Money supply: $34.0

We know that:

Bank deposits = (Bank reserves)/(Desired reserve-deposit ratio).

The Fed injected $0.30 billion (the public held $0.23 billion as currency and reserves increased by $0.07 billion was held as reserves). However, the money supply still fell by $3.3 billion.

It would have taken an additional 0.109 × $3.3 billion = $0.36 billion in reserves to support $3.3 in additional deposits.

So the answer is $0.30 billion + $0.36 billion = $0.66 billion.

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The given question is incomplete, complete question is :

Based on the information in the table, what quantity of reserves would the Federal Reserve have had to inject into the economy in 1932 to prevent the money supply from falling, given that the public increased the amount of currency it held and that banks increased the reserve-deposit ratio?

December 1921

-Currency held by public: $4.59

-Reserve Deposit ratio: 0.095

-Bank reserves: $3.11

-Money supply: $37.3

December 1932

-Currency held by public: $4.82

-Reserve Deposit ratio: 0.109

-Bank reserves: $3.18

-Money supply: $34.0

The sample used in the study is b) the 4200 Florida residents surveyed. surveyed. To obtain the answer following steps are :
1. Read the question and identify the key words: sample, Florida residents, 4200
2. Consider the given options and eliminate those that don't match
3. Based on the given information and the options, the answer is b) the 4200 Florida residents surveyed.

This is because the sample used in the study was the 4200 Florida residents who were surveyed, and this sample was used to estimate the proportion of all Florida residents who were willing to spend more tax dollars on protecting the beaches from environmental disasters.

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To find the slope of the line given the points (0,2) and (1,0), we can use the formula: m = (y2 - y1) / (x2 - x1).

m = (0 - 2) / (1 - 0) = -2

Using point-slope form, we can write the equation of the line as:

y - 2 = -2 (x - 0)

y = -2x + 2

To get the inequality we just need to change the equation to the inequality by replacing the equal sign with the inequality sign.

So the linear inequality for the points (0,2) and (1,0) is:

y >= -2x + 2

At that level of output and price, profit is maximized when marginal revenue and the marginal cost of production are equal:

MR = *TR/*Q

MC = *C/*Q

Eq.  = MR = MC

where, MR = Marginal Revenue

MC = Marginal Cost

* = Change in

TR = Total Revenue

Q = Quantity

C = Cost

The marginal revenue rule states that by selecting the amount at which marginal revenue equals marginal cost, we can maximize the net benefit of any action. The activity's net benefit is maximum at this amount.

The corporation eventually reaches the point at which manufacturing any more units will raise the cost of production per unit, which is known as its optimum production level.

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The required point that divides the line into 5:1 is given by (-5,0)

Let M(x, y) be the point which divides line segment PQ internally in the ratio m : n. PA, MN and QR are drawn perpendicular to x- axis. PS and MB are drawn parallel to x – axis. This is known as section formula.

Given here: A line segment with end points  (−10,−10) to ( − 4 , 2 )

Now the coordinates of the point that divides a line in the ratio m:n is given by

x= mx₂+nx₁ /m+n

y=my₂+ny₁/m+n

Thus the co-ordinates are x=5×-4+1×-10 / 5+1

                                             =-30/6

                                             = -5

And y= 5×2+1×-10 / 6

         =0

Hence, The required point that divides the line into 5:1 is given by (-5,0)

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From the given table the greatest frequency is 40,

midpoint of greatest frequency =$2100.

Relative frequency is also referred to as the empirical probability, which is calculated by the division of each frequency by the total number of frequency in the sample.

We can answer the question creating the following table:

Class            Frequency       Rel. Frequency

$600-$800             3                  3/120=0.025

$800-$1000            7                  7/120=0.059

$1000-$1200          11                  11/120=0.092

$1200-$1400          22                22/120=0.183

$1400-$1600          40                40/120=0.333

$1600-$1800          24                24/120=0.2

$1800-$2000         9                  9/120=0.075

$2000-$2200        4                  4/120=0.033

Total                       120                      1

From the above table the greatest frequency is 40,

midpoint of greatest frequency =$2100.

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9 pounds of Chamomile tea needed  to make a mixture that costs $14.74 per pound

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

let:

x pounds of Chamomile tea needed

Therefore,

18.10X + 12.22(12) = 14.74(12 + x)

18.10X + 146.64 = 176.88 +  14.74x

3.36X = 30.24

X = 9 pounds

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Answer:

= 53/42

Step-by-step explanation:

10/12 is equivalent to: 70/84

3/7 is equivalnt to: 36/84

Then:

10/12 + 3/7 = 70/84 + 36/84

= (70 + 36) / 84

= 106 / 84

= 53 / 42

The measure of an exterior angle of the regular polygon shown in the figure is 60°.

The angle between a side of a polygon and an extended adjacent side is called its exterior angle.

Given is a polygon, since, it has six vertices, so we can say it is a regular hexagon,

We know that, the sum of interior angles of regular hexagon is 720°

Therefore, one interior angle = 720 / 6 = 120°

If we extend a side of the hexagon, (refer to figure attached in solution)

Then, the interior angle and an exterior angle "A" will make a linear pair,

Therefore,

120° + A = 180°

A = 60°

Hence, the measure of an exterior angle of the regular polygon shown in the figure is 60°.

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