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Answer: The converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.

Step-by-step explanation:

What does it mean converse in geometry?

The converse of a statement is formed by switching the hypothesis and the conclusion. The converse of "If two lines don't intersect, then they are parallel" is "If two lines are parallel, then they don't intersect." The converse of "if p, then q" is "if q, then p."

So, in the figure below, if we can choose n║m, then ∠1≅∠2

Since  n║m , by the corresponding Angles Postulate,

∠1≅∠2.

Therefore, by the definition of congruent angles,

m∠1=m∠2

Since ∠1 and ∠2 form a linear pair, they are supplementary, so

m∠1+m∠2=180°.

Therefore, the converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.

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The decimal form of the number of filed goals Emily made is 0.32

Total number of attempts Emily made = 25

Total number of field goals = 8

We need to represent the filed goals in decimal

What is decimal?

A decimal is a number that includes a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.

feild goals is 8 out of 25

so, it is 8/25

= 0.32

Therefore, the decimal form of the number of filed goals Emily made is 0.32

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The derivative of y with respect to x (dy/dx) is (6x - y sin(x)) / (8y - cos(x)) using implicit differentiation on the equation y cos(x) = 3x² - 4y².

To find dy/dx using implicit differentiation for the given equation y cos(x) = 3x² + 4y², follow these steps:
1. Differentiate both sides of the equation with respect to x.
  (dy/dx)(y cos(x)) = (d/dx)(3x² + 4y²)
2. Apply the product rule for differentiation to y cos(x).
  (dy/dx)(y) * cos(x) + y(-sin(x)) = 6x + 8y(dy/dx)
3. Solve for dy/dx.
dy/dx * cos(x) - 8y(dy/dx) = 6x - y sin(x)
dy/dx * (cos(x) - 8y) = 6x - y sin(x)
dy/dx = (6x - y sin(x)) / (cos(x) - 8y)
So, the derivative dy/dx is given by:
dy/dx = (6x - y sin(x)) / (cos(x) - 8y)

To find dy/dx by implicit differentiation, we need to take the derivative of both sides of the equation with respect to x using the chain rule.
Starting with the given equation:
y cos(x) = 3x² - 4y²

We can rewrite it as:
y cos(x) - 3x² + 4y² = 0
Now, taking the derivative of both sides with respect to x:
d/dx[y cos(x)] - d/dx[3x²] + d/dx[4y²] = d/dx[0]
Using the chain rule on the left-hand side:
dy/dx cos(x) - y sin(x) + 8y dy/dx - 6x = 0
Rearranging and solving for dy/dx:
dy/dx = (6x - y sin(x)) / (8y - cos(x))
So, the derivative of y with respect to x (dy/dx) is (6x - y sin(x)) / (8y - cos(x)) using implicit differentiation on the equation y cos(x) = 3x² - 4y².

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Answer:

Table 1: 1.404, Table 2: 1.661

Step-by-step explanation:

Because f(x) and g(x) are inverses,

If f(x) = y,

then x = g(y)

Answer:

The answer is

not equivalent

equivalent

Answer:

y = 2x

Step-by-step explanation:

I just posted the same thing from the new post

15

5 t = 30$

1t = 30/5

= 6$ per ticket

then, 90$/6 = 15 tickets

The solution to the given system of equations is (2, 0) and (-6, -2).

The given equations are -x + y = 4, y = x² - 4, and x + 2.

The solution to the given equations is (2, 0) and (-6, -2).

To find the solution, first substitute the value of y in equation -x + y = 4 from equation y = x² - 4 as follows:y = x² - 4 (-x + y = 4)⇒ -x + x² - 4 = 4⇒ x² - x - 8 = 0

Solving the above quadratic equation, we get x = 2, -4

Substitute each value of x in the given equations to find the corresponding value of y.

The two solutions are (2, 0) and (-6, -2).

Thus, the solution to the given system of equations is (2, 0) and (-6, -2).


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The area of the new rectangle will be 25 times that of the original

A rectangle is a 2D shape that has 4 sides and equal interior angles

If rectangle has a width of 2.45 feet and a length of 6.5 feet, then;

Width = 2.45 feet

Length = 6.5feet

A = 2.45 * 6.5

A = 15.925 square feet

If each side of the rectangle is increased by a factor of 5, hence;

W1 = 5(2.45) = 12.25feet

L1 = 5(6.5) = 32.5 feet

Determine the area of the new rectangle

A = 12.25 * 32.5

A = 398.125 square feet

Ratio of the area

A1/A = 398.125/15.925

A1 = 25A

Hence the area of the new rectangle will be 25 times that of the original

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Answer:

12) 0.29

14) 7.68

15) 10.86

Step-by-step explanation:

Answer: 0.83

Step-by-step explanation:

14.5/17.5 = 0.828571429

We stop at the 2nd decimal placement after 0.82 but because the following number 8 > 0 we round up the hundredths place which gives us 0.83

Answer:

\(23\)

Step-by-step explanation:

\(g+\frac{h}{7}\)

First, divide 36 by 7:

Add 14 and 9:

________________________

Answer:

x=-2

Step-by-step explanation:

Answer:x=24

Step-by-step explanation: took the test

The angle of elevation from Phillip to the space shuttle is 1.64°, calculated using the Pythagorean theorem and the square root of both sides.

Given that Phillip is watching a space shuttle launch from an observation spot 66 miles away and the space shuttle is at a height of 1.9 miles. The angle of elevation from Phillip to the space shuttle can be found using the following formula: tan θ = opposite/adjacent Where θ is the angle of elevation, opposite is the height of the shuttle, and adjacent is the distance between the shuttle and the observation spot. Using the Pythagorean theorem, we can find the hypotenuse as follows:hypotenuse² = opposite² + adjacent²Substituting the given values, we get:hypotenuse² = 1.9² + 66²= 3.61 + 4,356= 4,359.61Taking the square root of both sides, we get: hypotenuse ≈ 66.083 miles Substituting the given values in the first formula to find the angle of elevation, we get: tan θ = 1.9/66.083θ

tan⁻¹(1.9/66.083)θ ≈ 1.64°Therefore, the angle of elevation from Phillip to the space shuttle is approximately 1.64°.

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Answer:

$7

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The terms syllabic, melismatic, and neumatic are all related to the number of notes in relation to each syllable of a text. Syllabic means that each syllable of the text is sung to one note.

This is the simplest type of setting for text to music. In contrast, melismatic means that each syllable of the text is sung to many notes, creating a more intricate and ornamental melody. Neumatic is somewhere in between syllabic and melismatic, where each syllable is sung to a few notes, but not as many as in a melismatic setting.

Syllabic, melismatic, and neumatic all describe the relationship between the number of notes and each syllable of a text.

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The aggregate forwarding rate of peer i is equal to ri * (N - 1), which depends on the values of ui, us, and UP.

The aggregate forwarding rate of peer i is equal to ri * (N - 1). This is because each peer is forwarding the bits it receives to each of the other (N-1) peers at the rate of ri. Therefore, the aggregate forwarding rate of peer i is equal to ri multiplied by (N-1), which is equal to (u:/UP)* us * (N - 1). Whether the aggregate forwarding rate is bigger or smaller than the maximum upload rate ui depends on the values of ui, us, and UP. If ui is larger than (u:/UP)* us * (N - 1), then the aggregate forwarding rate is smaller than the maximum upload rate ui. On the other hand, if ui is smaller than (u:/UP)* us * (N - 1), then the aggregate forwarding rate is bigger than the maximum upload rate ui.

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this is the answer

(x+x+10)*2=4x+20

Answer:

27/12 KG

Step-by-step explanation:

On Sunday, Sheldon bought 4 1/2 kg of plant food. He used 1 2/3 kg on his strawberry plants and used 1/4 kg on his tomato plants. How many kilograms of plant food did Sheldon have left?

41/2 - (12/3 + 1/4)

\(1\frac{2}{3} + \frac{1}{4}\)

\(1\frac{8 + 3}{12}\) = 1 11/12

\(4\frac{1}{2} - 1\frac{11}{12}\)

\(3\frac{6-11}{12}\) = 2 7/12

When filling a cylinder by weight, the scale set point should equal the desired weight of the contents.

Filling a cylinder by weight is a common practice in industries such as chemical and gas manufacturing. This method ensures accurate measurements and prevents overfilling or underfilling the cylinder. To fill a cylinder by weight, the empty cylinder is placed on a scale and tared to zero. The desired weight of the contents is then entered as the scale set point. The contents are added to the cylinder until the scale displays the set weight, at which point the filling process is complete. By setting the scale point to the desired weight, the operator can ensure that the cylinder is filled accurately and according to the specified requirements.

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Answer:

multiply both sides by 8

Step-by-step explanation:

I don't really know why I just know lol hope this helps

The distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

The time, t = π / 2 sec,

Calculate the distance by using the formula given below,

\(Distance = r\times time\)

So, for distance, a = 1 × π / 2 =  π / 2

for distance, b = 1 × π =  π

for distance, c = 1 × 3 π / 2 =  3 π / 2

Therefore, the distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

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Answer:

Step-by-step explanation:

Find 1% of $350:

Find 8% of $350:

Here are the steps

Lets do

\(\\ \tt\longmapsto 0.01(350)=3.50\)

Multiply with 8

\(\\ \tt\longmapsto 8(3.50)=24.00+4.00=28.00\$\)

The distance between the point P and the line ℓ is 24 / √(74) units.

To find the distance between a point P and a line ℓ, we need to use the coordinates of both the point and the line. In this case, we have the coordinates of the point P, which is (−1, 1), and two points on the line ℓ, which are (11, −1) and (−3, −11).

The first step is to find the equation of the line ℓ. We can use the two points on the line to find the slope of the line, which is:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points on the line. Substituting the given coordinates, we get:

m = (-11 - (-1)) / (-3 - 11) = -10 / (-14) = 5 / 7

Now we can use the point-slope form of the equation of a line to find the equation of line ℓ:

y - y₁ = m(x - x₁)

where (x₁, y₁) is any point on the line. We can choose either of the given points, let's choose (11, −1):

y - (-1) = (5 / 7)(x - 11)

Simplifying this equation, we get:

y = (5 / 7)x - 36 / 7

So, the equation of line ℓ is y = (5 / 7)x - 36 / 7.

Now we can use the formula for the distance between a point and a line:

distance = |ax + by + c| / √(a² + b²)

where a, b, and c are the coefficients of the equation of the line, and x and y are the coordinates of the point. In this case, the coefficients of the equation of line ℓ are a = 5 / 7, b = -1, and c = -36 / 7. Substituting the coordinates of the point P, we get:

distance = |(5 / 7)(-1) - 1 + (-36 / 7)| / √((5 / 7)² + (-1)²)

Simplifying this equation, we get:

distance = 24 / √(74)

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The total length of the tapes will be 21.762 inches solved using the concept of multiplication.

Given that paper is 8.06 inches long. each paper length is 8.06 inches long

we have some pieces of paper. She tapes 5.4 pieces together end-to-end what will the total length be?

here we will use the concept of multiplication.

Multiplication is a method of calculating the product of two or more numbers in mathematics. It is one of the most fundamental arithmetic operations that we use every day. Multiplication tables are the most common application.

The multiplication of two numbers in arithmetic represents the repeated addition of one number with respect to another. These can be whole numbers, natural numbers, integers, fractions, and so on. If m is multiplied by n, it means that m has been added to itself 'n' times or vice versa.

She tapes 2 pieces of paper together if we consider 1 paper then we can find the total length will be 8.06*5.4 = 43.524 now we have to divide by 2. final answer will be 43.524 /2 = 21.762.

So the Total length will be 21.762 inches.

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