square efgh underwent several transformations. a. what is the correct value of dilation d, being it is the value in which this square was transformed or dilated? b. explain how you calculated the value for d.

1)General solution is : y(x) = c1 cos(1.5x) + c2 sin(1.5x) - (1/17) cos(x) + (4/17) sin(x)

2)general solution of the given differential equation is:y(x) = c1 e^(4x) + c2 e^(-x) + t

1) The general solution of the given initial value problem can be found by solving the characteristic equation r2 + r + 4.25 = 0.

The roots of the equation are:r1,2 = (-1 ± √(1 - 4·4.25)) / (2) = (-1 ± 1.5i)

The general solution is given by:'

y(x) = c1 cos(1.5x) + c2 sin(1.5x) + y_p where y_p is the particular solution.

To find y_p, we can use the method of undetermined coefficients.

Let's assume that y_p = A cos(x) + B sin(x).y′′ + y′ + 4.25y = cos(x)y′

= - A sin(x) + B cos(x)y′′

= - A cos(x) - B sin(x)y′′ + y′ + 4.25y

= (-A + B + 4.25A cos(x) + 4.25B sin(x)) cos(x) + (-B - A + 4.25A sin(x) - 4.25B cos(x)) sin(x)

Comparing the coefficients of cos(x) and sin(x), we get:-A + B + 4.25A = 0-B - A - 4.25B = 1

Solving for A and B, we get: A = -1/17, B = 4/17

Therefore, the particular solution is:

y_p = (-1/17) cos(x) + (4/17) sin(x)

Finally, the general solution of the given initial value problem is:

y(x) = c1 cos(1.5x) + c2 sin(1.5x) - (1/17) cos(x) + (4/17) sin(x)

2) The given initial value problem can be solved by finding the roots of the characteristic equation r2 + 5r + 4 = 0.

The roots are:r1,2 = (-5 ± √(25 - 4·4)) / (2) = -1, -4

The general solution is given by:

y(x) = c1 e^(-x) + c2 e^(-4x) + y_p where y_p is the particular solution.

To find y_p, we can use the method of undetermined coefficients.

Let's assume that y_p = A e^(2t).y′′ + 5y′ + 4y = 3e^(2t)y′ = 2A e^(2t)y′′

= 4A e^(2t)y′′ + 5y′ + 4y

= (4A + 10A + 4A e^(2t)) e^(2t)

Comparing the coefficients of e^(2t), we get:4A + 10A = 3

Solving for A, we get: A = 3/14

Therefore, the particular solution is:y_p = (3/14) e^(2t)

Finally, the general solution of the given initial value problem is:

y(x) = c1 e^(-x) + c2 e^(-4x) + (3/14) e^(2t)3)

The characteristic equation of the given differential equation is r2 - 1 = 0.

The roots of the equation are:r1,2 = ±1

The general solution is given by:

y(x) = c1 e^(x) + c2 e^(-x) + y_pwhere y_p is the particular solution.

To find y_p, we can use the method of undetermined coefficients.

Let's assume that y_p = Ax + Be^(-x).y′′ − y

= x − e^(−x)y′ = A - Be^(-x)y′′

= - Be^(-x)y′′ − y

= (- Ax + B + e^(−x))(e^(-x))

Comparing the coefficients of x and e^(-x), we get:

-A + B = 0-1 - B = -1

Solving for A and B, we get: A = -1, B = -1

Therefore, the particular solution is:y_p = -x - e^(-x)

Finally, the general solution of the given differential equation is:y(x) = c1 e^(x) + c2 e^(-x) - x - e^(-x)4)

The characteristic equation of the given differential equation is r2 - 3r - 4 = 0.

The roots of the equation are:r1,2 = (-(-3) ± √((-3)2 - 4·1·(-4))) / (2·1) = 4, -1

The general solution is given by:y(x) = c1 e^(4x) + c2 e^(-x) + y_pwhere y_p is the particular solution.

To find y_p, we can use the method of undetermined coefficients.

Let's assume that y_p = At + B.y′′ − 3y′ − 4y = 4ty′ = Ay′′ = A4y′′ − 3y′ − 4y = 4t(A4 - 3A) + B(4) = 4t

Comparing the coefficients of t, we get: A = 1

Solving for B, we get: B = 0

Therefore, the particular solution is:y_p = t

Finally, the general solution of the given differential equation is:y(x) = c1 e^(4x) + c2 e^(-x) + t

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Answer:

8%

Step-by-step explanation:

To find the percent change, we first have to find the amount changed, which is (46000-42500) = 3500. Then, we find what percentage that is of the original amount. Remember that when calculating percentage change, it's important to calculate change with respect to the initial value.

To find the percentage, we can divide 3500 by 42500, and multiply that by 100, resulting in 8 being our nearest whole percent

The three (3) statements which are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   ....equation 1.

Where:

h and k represents the coordinates at the center of a circle.

r represents the radius of a circle.

From the information provided, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

Comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius, r = 3

Additionally, this line and the circle's center lies on the x-axis because the y-value is equal to zero (0).

(x – 0)² + (y - 0)² = 3²

x² + y² = 9.

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Answer:41,328

Step-by-step explanation:

18+7+11=36 36%

100-36=64 64%

25,200 x 164%=41,328

Answer:

$25,600

Step-by-step explanation:

===============================================

Explanation:

To isolate s, we need to undo the division. We'll multiply both sides by 3

14 = s/3

3*14 = 3*(s/3)

42 = s

s = 42

-------

As a check,

14 = s/3

14 = 42/3 .... replace s with 42

14 = 14

We get the same thing on both sides, so this confirms we have the correct value of s.

Answer:= 3.456 × 1011

Step-by-step explanation:

Answer:

Step-by-step explanation:

4:6 it is wrng

Answer:  280.28cm

See attached ppt file

Answer:

9/4 or 2.25

Step-by-step explanation:

9=4t

Move the 4

9/4=t in decimal its 2.25=t

Answer:  

B

Step-by-step explanation:

Latoya created a factor tree and wrote the prime factorization of 90 shown below.

A factor tree of 90. 90 branches to 9 and 10. 9 branches to 3 and 3. 10 branches to 2 and 5. The equation is 90 = 2 times 3 times 5.

What is Latoya’s error?

She should not have found the factors of 9.

She should have included an exponent of 2 on the 3.

She should have included 9 and 10 in the prime factorization.

She should have started the tree with 2 times 45.

Hope this helps!!!!!!

Answer:

B

Step-by-step explanation: make it brainleist plz

a) The maximum area of such a rectangle is 50 square units. b) The maximum area of such a rectangle is 36.

When graphed, a linear equation results in a straight line. Since each value of x results in just one value of y, this relationship is referred to as being one-to-one. When a quadratic equation is graphed, the result is a parabola that extends uphill or downward in the y direction, starting at a single point known as the vertex. Because there are two values for x for every value of y (aside from the y-value at the vertex point), the relationship between x and y is not one-to-one.

a) The given equation is 2y + 4x =40

Let the coordinates of the top right corner be (x,y).

Then, y = (40 -4x)/2

The area of the rectangle is given by A =xy

A= x x (40 -4x)/2

A = 20x-2x²

We have to find the maximum area of the rectangle.

Differentiate the expression for Area A with respect to x to get the slope of the curve

A’ = 20-4x

At the maximum area, A’=0

Therefore, 20 -4x =0

4x =20

X=5

Substituting x=5 in the equation of the line 2y + 4x =40

2y +20 =40

2y = 20

Y =20

Therefore, the coordinates of the top right corner of the rectangle are (5,10).

The maximum area of the rectangle is given by A = xy = 5 x 10 =50 sq.units

b) The maximum area of such a rectangle can be found by using the formula: A = lw,

where l is the length of the rectangle

w is the width of the rectangle

Since the base of the rectangle is on the x-axis and the upper left corner is on the line y=2x+6, the length of the rectangle is equal to the distance between y=2x+6 and the x-axis, which is 6. The width of the rectangle is equal to the distance between y=-2x+6 and the x-axis, which is also 6. Thus, the maximum area of such a rectangle is 36 square units.

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Answer: 65

Step-by-step explanation:

Answer:

\( \frac{1}{81} \)

Step-by-step explanation:

express that with a positive exponent using this:

\( {a}^{ - n} \frac{1}{ {a}^{n} } \)

so ..

\( {9}^{ - 2} = \frac{1}{ {9}^{2} } \)

now you have to evaluate the exponent/ power

so..

\( \frac{1}{ {9}^{2} } = \frac{1}{81} \)

why 81 ?

because the exponent of 9 is 2 so you have to multiple 9 by itself so

9x9=81

so the answer is

\( \frac{1}{ {81}^{} } \)

sorry for the bad english hehe

Answer: A - rotation of 270 degrees counterclockwise about the origin

Step-by-step explanation:

When a point is rotated 270 degrees counterclockwise, the points change from (x,y) to (-y,x). We can see this when (-4,-3) turns into (-3,4) which we find by doing (-3,-4(-1).

So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

The probability density function is:

f(x) = (1 / (e⁷- e³)) × eˣ

To determine the value of k that makes the function a probability density function (PDF) over the interval [3, 7], we need to ensure that the integral of the PDF over the entire interval is equal to 1.

The probability density function is given by:

f(x) = keˣ

To find k, we integrate the PDF over the interval [3, 7] and set it equal to 1:

1 = ∫[3,7] keˣ dx

Integrating keˣ with respect to x gives us:

1 = k ∫[3,7] eˣdx

To evaluate this integral, we can use the property that the integral of eˣ is eˣ + C, where C is a constant.

1 = k(e⁷- e³)

Now, we can solve for k:

k = 1 / (e⁷ - e³)

Therefore, the value of k that makes the function a probability density function over the interval [3, 7] is k = 1 / (e⁷ - e³).

The probability density function is:

f(x) = (1 / (e⁷- e³)) × eˣ

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The variable data refers to the list [10, 20, 30]. After the statement data[1] = 5, data evaluates to [10, 5, 30]. A list is one of the compound data types that Python provides. Lists can contain items of different types, but they are usually all the same type.

Lists are mutable sequences, meaning that their elements can be changed after they have been created. Lists can be defined in several ways, including by enclosing a comma-separated sequence of values in square brackets ([ ]).

The elements of a list can be accessed using indexing, with the first element having an index of 0. The second element has an index of 1, the third element has an index of 2, and so on. To change the value of an element in a list, you can use indexing with an assignment statement.

For example, the statement `data[1] = 5` changes the second element of the `data` list to 5. Therefore, after this statement, the `data` list will be `[10, 5, 30]`.

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The other factor of x² - 25 given that one of the factors is; (x - 5) is; (x + 5).

It follows from the task content that the other factor of x² - 25 is to be determined given that the first factor is ; (x - 5).

Recall from the difference of two squares theorem that;

Given an expression of the form; a² - b²; where a² and b² represent perfect squares:

the expression can be as; (a - b) (a + b).

Hence, since x² and 25 are perfect squares; it follows that the given expression can be written as;

(x - 5) (x + 5)

Ultimately, the other factor is; (x + 5).

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The WACC for Company A is approximately 0.564 or 56.4%.

To calculate the weighted average cost of capital (WACC) for Company A, we need to consider the cost of debt and the cost of equity, weighted by their respective proportions in the company's capital structure.

Given information:

Debt proportion (D/V) = 26%

Equity proportion (E/V) = 100% - 26% = 74%

Before-tax cost of debt (r_d) = 3.2%

Risk-free rate (r_f) = 1.1%

Market risk premium (RPM) = 6%

Beta (β) = 0.9

Marginal tax rate (T) = 30%

The formula to calculate WACC is as follows:

WACC = (D/V) * r_d * (1 - T) + (E/V) * r_e

To calculate the cost of equity (r_e), we can use the Capital Asset Pricing Model (CAPM):

r_e = r_f + β * RPM

Plugging in the given values:

r_e = 1.1% + 0.9 * 6% = 1.1% + 5.4% = 6.5%

Now, let's calculate WACC:

WACC = (0.26) * 3.2% * (1 - 0.30) + (0.74) * 6.5%

WACC = 0.0832 + 0.481

WACC ≈ 0.5642

Rounding to three decimal places, the WACC for Company A is approximately 0.564 or 56.4%.

Please note that the WACC represents the average rate of return required by both debt and equity investors to finance the company.

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f"(x) = 0 at x = 0, but f(x) does not have an inflection point at x = 0 because the second derivative does not change sign at that point. In fact, f(x) is a convex function for all values of x, meaning it curves upwards and has no inflection points.

An inflection point is a point on a curve where the concavity changes, meaning that the second derivative of the function changes sign. Specifically, if f(x) is a twice-differentiable function, then a point c is an inflection point if f''(c) = 0 and the sign of f''(x) changes when x passes through c.

However, it is possible for a function to not have an inflection point at a point where f''(x) = 0. This can occur when the sign of f''(x) does not change as x passes through the point, meaning that the concavity does not change.

One simple example of such a function is f(x) = x^4. This function has a second derivative of f''(x) = 12x^2, which equals zero at x = 0. However, the sign of f''(x) is always positive, meaning that the concavity is always upward and does not change at x = 0. Therefore, f(x) does not have an inflection point at x = 0 despite f''(0) = 0.

In general, any even-degree polynomial will have a second derivative that equals zero at the origin, but the concavity will not change at the origin if the leading coefficient is positive. Other examples of functions that do not have inflection points at points where f''(x) = 0 include functions with constant concavity, such as f(x) = x^2 or f(x) = sin(x).

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Answer:

x = 18

Step-by-step explanation:

1/2 x - 7 = 1/3 (x - 12)           Remove the brackets on the right

1/2x - 7 = 1/3 x - 12*1/3

1/2x - 7 = 1/3 x - 4               Subtract 1/3 x from both sides

1/2x - 1/3x - 7 = - 4             Combine like terms on the left

1/6x - 7 = - 4                       Add 7 to both sides

1/6 x = - 4  + 7                    Combine the right side

1/6 x = 3                             Multiply both sides by 6

6 * 1/6x = 3*6

x = 18

Answer:

Find the 100th term when the first term is -3 and the common difference is 4.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Find the 100th term when the first term is -3 and the common difference is 4. I took the test and got 100 percent.

The answer is OC. Minimum: -12.48; maximum: 64.48.

The minimum usual value - 20 and the maximum usual value y + 20 for the given values of n and p, n = 100; p = 0.26 are found below.

Minimum usual value = np - z * sqrt(np(1 - p)) = 100 × 0.26 - 1.645 × sqrt(100 × 0.26 × (1 - 0.26))= 26 - 1.645 × sqrt(100 × 0.26 × 0.74) = 26 - 1.645 × sqrt(19.1808) = 26 - 1.645 × 4.3810 = 26 - 7.2101 = 18.79 ≈ 18.80

Maximum usual value = np + z * sqrt(np(1 - p)) = 100 × 0.26 + 1.645 × sqrt(100 × 0.26 × (1 - 0.26))= 26 + 1.645 × sqrt(100 × 0.26 × 0.74) = 26 + 1.645 × sqrt(19.1808) = 26 + 7.2101 = 33.21 ≈ 33.22

Therefore, the minimum usual value - 20 is 18.80 - 20 = -1.20.The maximum usual value y + 20 is 33.22 + 20 = 53.22.

Hence, the answer is OC. Minimum: -12.48; maximum: 64.48.

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The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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Answer:

it should be y= -4x + 10

Step-by-step explanation:

hope this helps.

Answer:

x = 10

Step-by-step explanation:

First look at the big overall triangle.

It has a right angle and another angle of 44; therefore the missing angle is (since the sum of angles inside a triangle is 180)

180 - 90 - 44 = missing angle

missing angle (top) = 46; now the angle of a straight line is 180 and they give you 56° which  has a supplementary angle of 180 - 56 = 124°.

Now we know that the triangle that include the x has angles 46° (missing top angle), and supplementary angle of 124°.  Therefore

x = 180 - 46 - 124

x = 10

Answer:x=20

Step-by-step explanation:You would keep x by itself and you would add 17+3 which would equal 20.So therefore the answer would be x=20.

Answer:

  7

Step-by-step explanation:

You want the common difference of the arithmetic sequence that starts ...

  15, 22, 29, ...

The common difference is the difference between a term and the one before. It is "common" because the difference is the same for all successive term pairs.

  22 -15 = 7

  29 -22 = 7

The common difference is 7.

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