A dilation maps (6, 10) to (3, 5) and the center of dilation is the origin. Given A(12, 4), determine
under the same dilation.

Answer:

  (x +4)²/25 +(y -3)²/16 = 1

Step-by-step explanation:

You want the equation of the ellipse with center (-4, 3) and semi-axes 5 and 4 in the x- and y-directions, respectively.

The standard form equation for an ellipse with center (h, k) and sem-axes 'a' and 'b' in the x- and y-directions, respectively, is ...

  (x -h)²/a² +(y -k)²/b² = 1

Using the given values, we find the equation to be ...

  (x +4)²/25 +(y -3)²/16 = 1

__

Additional comment

The longer of the two axes is the "major" axis, and its end points are the "vertices". For the purpose of an ellipse with center, vertices, and co-vertices specified, the equation is not affected by which axis is longer.

Effectively, this is the equation of a circle with different scale factors in the x- and y-directions.

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Using concepts of the normal and of the uniform distribution, it is found that the correct option is:

The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.

In an uniform distribution, all outcomes are equally as likely, thus they have the same height.

In the normal distribution,

The outcomes with the highest likelihood are those closest to the mean, thus they have the highest height.

This means that the mean of this distribution is 8.

The standard deviation cannot be a negative value,

So in this problem, it is 1.2,

Which means that the correct option is:

The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.

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The x-intercepts, in order from least to greatest, are (2.46, 0) and (5.54, 0).

Use the vertex form of a quadratic function, which is [tex]y = a(x-h)^2 + k,[/tex] where (h, k) is the vertex and "a" is the coefficient of the[tex]x^2[/tex]term. Since the vertex is at (4, 8 1/3), the quadratic function's equation is y = a(x-[tex]4)^2 + 8 1/3.[/tex]

Use the y-intercept to find the value of "a".

The y-intercept is (0,3), so when x=0, y=3.

Plugging these values into the equation above, we get: [tex]3 = a(0-4)^2 + 8 1/3[/tex].

Simplifying, we get 3 = 16a + 25/3, or 9/3 = 16a. Therefore, a = 9/48 or a = 3/16.

To obtain the complete equation, enter the value of "a" into the vertex form equation: [tex]y = (3/16)(x-4)^2 + 8 1/3.[/tex]

To find the x-intercepts, set y = 0 and solve for x.

The equation becomes: [tex]0 = (3/16)(x-4)^2 + 8 1/3[/tex].

Subtracting 8 1/3 from both sides, we get: [tex]-8 1/3 = (3/16)(x-4)^2[/tex]. Multiplying both sides by -1, we get: [tex]8 1/3 = (3/16)(x-4)^2.[/tex]

Take the square root of both sides to isolate[tex]x-4: \sqrt{(8 1/3) } = \sqrt{((3/16)(x-4)^2)}[/tex] Simplifying,

we get: [tex]\sqrt{(25/3)} = (3/4)(x-4).[/tex]

Solving for x, we get two solutions: [tex]x = 4 + 4\sqrt{(3)/3 } or x = 4 - 4\sqrt{(3)/3 }[/tex]

Sort the answers in order of best to worst. The x-intercepts are (2.46, 0) and (5.54, 0) because the first answer is around 5.54 and the second solution is roughly 2.46.

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The coordinates of vertex D in the parallelogram are (-7, -10).

We have,

To find the coordinates of vertex D of the parallelogram, we need to use the properties of a parallelogram.

One of these properties states that opposite sides of a parallelogram are parallel and have equal lengths.

Given that A = (8, 2), B = (6, -4), and C = (-5, -4), we can find the coordinates of D as follows:

Find the vector representing one of the sides of the parallelogram.

We can use the vector AB.

Vector AB = (x-coordinate of B - x-coordinate of A, y-coordinate of B - y-coordinate of A)

= (6 - 8, -4 - 2)

= (-2, -6)

Add this vector to point C to find the coordinates of D.

Coordinates of D = (x-coordinate of C + x-coordinate of AB, y-coordinate of C + y-coordinate of AB)

= (-5 - 2, -4 - 6)

= (-7, -10)

Therefore,

The coordinates of vertex D are (-7, -10).

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The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.

We know that,

In geometry, a cylinder is one of the basic 3d shapes with two parallel circular bases at a distance. A curving surface connects the two circular bases at a predetermined distance from the centre. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases. One real-world example of a cylinder is an LPG gas-cylinder.

The surface area of this cylinder is defined as the product of the radius of the base and the height of the cylinder.

The surface area of this cylinder = (2π x r)h

We have given a radius of the base is 8 cm and the height of the cylinder is 10 cm.

The surface area of this cylinder = (2π x r)h

= (2π x 8)10

= (50.24)10

= 502.4

Thus, The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.

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The complete question is attached below:

The equation of the line is y = x/7 - 1/7

The equation of a straight line is y=mx+c . Where m is the gradient or slope and c is the height at which the line crosses the y -axis, also known as the y -intercept.

The equation of a line can be expressed as;

y-y1 = m(x -x1)

where m is the slope

The slope = 1/7

x1 = 8 and y1 = 1

Therefore;

y -1 = 1/7( x -8)

7(y-1) = x-8

7y -7 = x-8

collecting like terms

7y = x - 8+7

7y = x -1

y = x/7 -1/7

The intercept is -1/7 and the slope is 1/7

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t = (6 + 3k)/(k - 2) is the formula for t in the equation k=2(t+3)/t-3.

The given equation is k=2(t+3)/t-3.

We need to isolate t on one side of the equation.

Let's start by cross-multiplying:

k(t - 3) = 2(t + 3)

Expanding the brackets:

kt - 3k = 2t + 6

Now, let's gather all the terms with t on one side and all the constant

terms on the other side:

kt - 2t = 6 + 3k

Factoring out t on the left side:

t(k - 2) = 6 + 3k

Finally, we can solve for t by dividing both sides of the equation by (k - 2):

t = (6 + 3k)/(k - 2)

Therefore, t is the subject of the formula, and it is given by t = (6 + 3k)/(k - 2).

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The complex number in standard form is written as:

Z =  1.99 + i*0.201, so the correct option is a

Remember that a complex number can be written in standard form as:

Z = a + b*i

And in polar form the notation is (R, θ):

[tex]Z = R*e^{i*\theta} = R*cos(\theta) + i*R*sin(\theta)[/tex]

Here we have the complex number:

Z = 2(cos(11pi/6) + i*sin(11pi/6))?

So here we just need to solve these expressions, we will get:

Z = 2*(0.995 + i*0.100)

Z =  1.99 + i*0.201

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Complete question:

"Convert the polar representation of this complex number into its standard form: z = 2(cos 11pi/6+ i sin 11pi/6)? "

Using the intersecting chord theorem, we can calculate the value of x as: 12

The intersecting chord theorem states that If two chords intersect in a circle , then the products of the measures of the segments of the chords are equal.

Applying the intersecting chord theorem to the two chords of the circle, we can say that:

3x = (9 * 4)

3x = 36

x = 36/3

x = 12

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Answer:

(a) 5 ft^2

Step-by-step explanation:

The formula for area of a triangle is given by the formula,

A = 1/2bh, where

Thus, we can plug in 5 for b and 2 for h in the formula to find the area of the triangle in square feet:

A = 1/2(5)(2)

A = (5/2)(2)

A = 10/2

A = 5

Thus, the area of a triangle whose base is 5 ft and whose height is 2 ft is 5 ft^2

The percentage of people with blood pressure below 133 is 78.81%.

First, we need to calculate the Z-score for the value 133 using the formula:

Z = (X - μ) / σ

where X is the value (133), μ is the mean (121), and σ is the standard deviation (15).

Z = (133 - 121) / 15

Z = 12 / 15

Z = 0.8

Next, we can use a standard normal distribution table or a calculator to find the area under the curve to the left of the Z-score 0.8.

Looking up the Z-score of 0.8 in the standard normal distribution table, we find that the area to the left of 0.8 is 0.7881.

Therefore, the percentage of people with blood pressure below 133 is 78.81%.

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The solution of expression ∫ (0 to 10) (x + 1) dx is,

⇒ 60

We have to given that,

Expression to solve,

⇒ ∫ (0 to 10) (x + 1) dx

Now, We can simplify as,

⇒ ∫ (0 to 10) (x + 1) dx

⇒ ∫ (0 to 10) (x) dx + ∫ (0 to 10) dx  

⇒ (x² / 2)₀¹⁰ + ((x)¹⁰₀

⇒ 1/2 (10² - 0) + (10 - 0)

⇒ 1/2 × 100 + 10

⇒ 50 + 10

⇒ 60

Therefore, The solution of expression ∫ (0 to 10) (x + 1) dx is,

⇒ 60

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Answer:

[tex]m = \frac{1 - ( - 3)}{0 - ( - 4)} = \frac{4}{4} = 1[/tex]

The standard deviation of the random variable x is 1.1145

Since the Probability distribution of a random variable is the collection of value and its probability pair for values of that considered random variable.

The probability of a value of x is never neg.

The sum of the probabilities is always 1.

The sum of all values of P(X = x) equals 1, which is, considering n values

There are no negative values of P(X = x).

Since we are given the probability distribution as below, we will go and calculate the mean and standard deviation using the formula:

E(X)= ∑xP(X=x)

Standard deviation = √Variance(x)

Var(x) = E(x²) - [E(x)]²

X           0          1            2        3        4          5

p(x=x)   0.032   0.152   0.316  0.316  0.152  0.032

First we have to find E(x)

E(x) = (0x0.032) + (1x0.152) + (2x0.316) + (3x0.316) + (0.152) + (5x0.032)

The mean E(x) = 2.5

To find variance, we use Var(x) = E(x²) - [E(x)]²

But we have to calculate E(x²) first, since we already have found E(x)

So,

E(x²) = (0²x0.032) + (1²x0.152) + (2²x0.316) + (3²x0.316) + (4²x0.152) + (5²x0.032)

therefore, E(x²) = 7.492

Now we have all the values we can find the variance:

Var(x) = E(x²) - [E(x)]²

=7.492 - [2.5]²

= 1.242

With variance now we can find the standard deviation;

S.D = √Var(x)

= √1.242

= 1.1145

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Answer: 0 , 5

Step-by-step explanation:

Imagine a plane taking off, first it drives to gain speed then flies, thats what you can use for coordinates.

X is the driving and Y is the flight.

The X is at 0, and the Y is at 5.

The value of angle L is 61°

Exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

If angle A and B are interior angles and angle C is the exterior angle, what this theorem is saying is that;

A+B = C

Similarly,

angle L and angle E are the interior angles and 113 is the exterior angle, therefore;

113 = L + 52

L = 113 -52

L = 61°

Therefore angle L is 61°

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The value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3

When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.

(2x - 13) + 123 = 180° {supplementary angles}

2x - 13 + 123 = 180°

2x + 110 = 180

2x = 180 - 110 {collect like terms}

2x = 70

x = 70/2 {divide through by 2}

x = 35

Therefore, the value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3

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Thanks to the other user

To find the decimal equivalent of 2/5, you can divide the numerator (2) by the denominator (5):

2 ÷ 5 = 0.4

Therefore, the decimal equivalent to 2/5 is 0.4.

The equation of the plane pi is: -6x-7y-9z=0.

To find the equation of the plane that contains the given line L and the origin as well, we first need to find two vectors that lie on the plane. One vector can be the direction vector of the line L, which is (2i - j + 3k). Now to find the second vector, we can take the vector from the origin to any point on the line L, and this vector will lie on the plane.

Let us now take t=0, and find the point on the line L:

r = 3i + 3j - k + 0(2i - j + 3k)

= 3i + 3j - k

So, the vector from the origin to this point is simply (3i + 3j - k). We can just take (3i + 3j - k) as our second vector.

Now, we can find the normal vector of the plane by taking the cross-product of two vectors that we just found, we get:

n = (2i - j + 3k) * (3i + 3j - k)

= -6i - 7j - 9k

Therefore, the equation of the plane pi is: -6x-7y-9z=0.

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The required angles are,

∠BAC = 73 degree

∠BCA = 17 degree

∠DCF = 17 degree

∠CDF = 80 degree

∠CFD = 95 degree

Since we can see that,

In triangle ABC

The angle B is right angled

Since we know that,

Sum of interior angles of triangle = 180 degree

Therefore, in triangle ABC

⇒ (9x -8 ) + (2x-1) + 90 = 180

⇒ 11x  = 99

⇒    x  = 9

Thus,

Angle BAC =  9x - 8

                   = 9x9 - 8

                   = 73 degree

Angle BCA = 2x - 1

                   = 2x9 - 1

                    =  17 degree

Now in triangle, CDF,

Angle C is alternate angle for both the triangles,

Therefore,

Interior angle C of triangle CDF = angle DCF = 17 degree

Angle CDF = 9y  - 1

                   = 9x9 - 1

                   = 80 degree

Angle CFD = 11y + 4

                   = 11x9 - 4

                   = 95 degree

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In a rectangle, the value of x is,

⇒ x = 5

We have to given that;

ABCD is a rectangle.

And, AC = 5x + 2

BD = x + 22

Since, We know that;

Diagonal of a rectangle are equal in length.

Hence, We get;

AC = BD

(5x + 2) = (x + 22)

5x - x = 22 - 2

4x = 20

x = 20/4

x = 5

Thus, the value of x is,

⇒ x = 5

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All the expressions after completing the square each equation are,

⇒ (x - 1/2)² = 5/4

⇒ (x - 5/2)² + 3/4 = 0

⇒ (2x + 3/2)² = 57/4

Given that;

Expressions are,

⇒ 2x² - 2x + 7 = 5

⇒ -2x² + 10x = 14

⇒ 4x² + 6x = 12

Now, We can completing the square each equation as;

⇒ 2x² - 2x + 7 = 5

⇒ x² - x + 7/2 = 5/2

⇒ x² - x + 1/4 - 1/4 + 7/2 = 5/2

⇒ (x - 1/2)² = 1 + 1/4

⇒ (x - 1/2)² = 5/4

⇒ -2x² + 10x = 14

⇒ - x² + 5x = 7

⇒ x² - 5x = - 7

⇒ x² - 5x + 25/4 - 25/4 = - 7

⇒ (x - 5/2)² = - 7 + 25/4

⇒ (x - 5/2)² = - 3/4

⇒ (x - 5/2)² + 3/4 = 0

⇒ 4x² + 6x = 12

⇒ (2x)² + 2×2x×3/2 + 9/4 -9/4 = 12

⇒ (2x + 3/2)² = 12 + 9/4

⇒ (2x + 3/2)² = 57/4

Thus, All the expressions after completing the square each equation are,

⇒ (x - 1/2)² = 5/4

⇒ (x - 5/2)² + 3/4 = 0

⇒ (2x + 3/2)² = 57/4

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Based on the information provided, it seems that you have a rectangular grid with a shaded area, and the grid contains  option D.  48 square units.

To calculate the area of the shaded part, we would need to know the dimensions of the rectangle as well as the specific location and size of the shaded region within it.

If you can provide more details about the dimensions of the rectangular grid and the shaded region, I would be happy to help you calculate the area of the shaded part. Once we have that information, we can apply the formula for calculating the area of a rectangle,

which is Area = length × width. The result will give us the area of the shaded part in square units.

The area in square units, of the shaded part of the rectangle It has 48. Therefore the correct option  D

The Question was Incomplete, Find the full content below :

The grid shown below is in the shape of a rectangle. What is the area, in square units, of the shaded part of the rectangle? a 14 b 24 c 28 d 48

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The area of the given figure with rectangle and triangle is 27.5 square centimeters.

The given figure has a rectangle and two triangles.

The area of the rectangle is length times width

Length = 5 cm

Width = 4 cm

Area of rectangle = 5×4

=20 square centimeters

Area of triangle =1/2 base ×height

=1/2×2.5×3

=3.75  square centimeters

As there are two triangles, 2(3.75)=7.5   square centimeters

Total area = 20+7.5

=27.5 square centimeters

Hence, the area of the given figure with rectangle and triangle is 27.5 square centimeters.

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The triangles are not similar

Given data ,

Let the first triangle be ΔJKL

Let the second triangle be ΔMNP

Now , the corresponding sides are

JK / JL ≠ NM / MP

where the corresponding sides of similar triangles are not in the same ratio

And , the common angle to both the triangles is ∠J = ∠M

So , ∠J = ∠M and JK / JL ≠ NM / MP

Hence , the triangles are not similar

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In accounting, the accounting equation is a fundamental principle that describes the relationship between a company's assets, liabilities, and equity. This equation is represented as Assets = Liabilities + Equity. Every financial transaction that a company undertakes has an impact on at least two of the components of the accounting equation.

Transaction Analysis:

a. The company completed consulting work for a client and immediately collected $5,600 cash earned.

This transaction increases both cash and revenue. There is no impact on liabilities or equity.

Accounts Affected:

Cash: +$5,600

Revenue: +$5,600

b. The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.

This transaction does not impact any account initially. Revenue will increase when payment is received.

Accounts Affected:

Accounts Receivable: +$4,100

Revenue: +$0

c. The company paid an assistant $1,450 cash as wages for the period.

This transaction decreases cash and increases expenses. There is no impact on liabilities or equity.

Accounts Affected:

Cash: -$1,450

Expenses: +$1,450

d. The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b.

This transaction increases cash and decreases accounts receivable. There is no impact on liabilities or equity.

Accounts Affected:

Cash: +$2,050

Accounts Receivable: -$2,050

e. The company paid $720 cash for this period's cleaning services.

This transaction decreases cash and increases expenses. There is no impact on liabilities or equity.

Accounts Affected:

Cash: -$720

Expenses: +$720

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Complete Question

The following transactions were completed by the company

a. The company completed consulting work for a client and immediately collected $5,600 cash earned.

b. The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.

c. The company paid an assistant $1,450 cash as wages for the period.

d. The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b

e. The company paid $720 cash for this period's cleaning services  Required: Enter the impact of each transaction on individual items of the accounting equation. (Enter decreases to account balances with a minus sign.)

Answer:

12

Step-by-step explanation:

206

5x10 12x13=206 it may be incorrect but i not sure if it is incorrect

Answer:

Step-by-step explanation:

The numerical value of the given log expression is -73.

From definitions of logarithms, we know that :

[tex]log(a*b) = log(a) + log(b)\\log(a / b) = log(a) - log(b)[/tex]

[tex]log(a^n) = n*log(a)[/tex]

Therefore,

[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = \frac{4}{3}*log(b) - 8*log(a) - 5*log(c)[/tex]

substituting the given values

[tex]log(a) = 10\\log(b) = 9\\log(c) = 1\\[/tex]

we get the value of the given expression

[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = \frac{4}{3}*9 - 8*10 - 5*1[/tex]

[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = 12 - 80 - 5[/tex]

[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = -73[/tex]

Therefore the numerical value of the given log expression is -73.

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