Find the value of each variable show proofs

The statements are:

y=e" and y = ln x are inverses.

This is false. The inverse of y = e^x is y = ln x, and the inverse of y = ln x is y = e^x. So, the two functions y = e^x and y = ln x are inverses of each other, but y = e^x and y = e^ln x are not.

In een In(x) = log. (x)

This is false. The statement should be: e^ln(x) = x, which is true by the definition of logarithms.

ln e = 1

This is true. The natural logarithm of e is 1.

In (x) = log10 (x)

This is false. The statement should be: log10(x) = log(x) / log(10).

In e = 10

This is false. The natural logarithm of e is 1.

In(e) and en both equal x.

This is false. In(e) = 1, and e^n = x does not necessarily imply that In(e) = x.

Answer:

35

Step-by-step explanation:

DUDE JUST PLUG IN THE NUMBER.

[tex]x^4 -3x^3 + x -3\\(-2)^4 - 3(-2)^3 + (-2) -3\\16 + 24 -2 - 3\\35[/tex]

The antiderivative of 1x (or simply x) is (1/2)x² + C, where C is the constant of integration. In other words, the antiderivative of x is the function whose derivative is equal to x.

This is a basic result in calculus, and it is derived using the power rule of integration. The antiderivative of 1x (or simply x) is the function whose derivative is equal to x. This function is (1/2)x² + C, where C is the constant of integration. To find the antiderivative, one can use the power rule of integration, which states that the antiderivative of xⁿ is (1/(n+1))x⁽ⁿ⁺¹⁾ + C. In the case of x, n is equal to 1, so the antiderivative is (1/2)x² + C. The constant of integration represents the family of functions that have the same derivative, so it is added to the antiderivative to reflect this.

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As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given a scatter plot  in terms of the time the player spent practicing and the number of points he scored in the game.

A scatter plot uses dots to represent values for two different numeric variables.

The position of each dot on the horizontal and vertical axis indicates values for an individual data point.

As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association.

Hence, As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association

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The question that would be more appropriate for Enrique's survey of high school teachers is Among high school teachers, what is the most popular restaurant to eat dinner at in town?

Enrique's conclusion about adults liking to eat dinner at The Bistro more than other restaurants in town may not be accurate since his survey was only limited to high school teachers.

To make his conclusion more reliable, Enrique could have asked a more specific question that is relevant to high school teachers. Here are a few examples of more appropriate questions for Enrique's survey of high school teachers:

Among high school teachers, what is the most popular restaurant to eat dinner at in town?

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Answer:

The answer is C.

106.0 in^3

Answer:

106.0 in^3

Step-by-step explanation:

The answer is C. 1/10 of a centimeter.

The requried statement is mentioned in C where Table A represents y = 2.5x and table B represents y = 3x describe the relationships between x and y for each table. Option C is correct.

Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,

In Table A, y is 2.5 more than x, and in Table B, y is 3 more than x. Both tables represent additive relationships. the requried statement is mentioned in C where Table A represents y = 2.5x and table B represents y = 3x describing the relationships between x and y for each table. Option C is correct.

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Circle A and circle A' have the same circumference and the radii of circle A and circle A' have the same lengths. Therefore, options A and B are the correct answers.

Rotations are transformations that turn a shape around a fixed point. To rotate a shape we need: a centre of rotation. an angle of rotation (given in degrees) a direction of rotation – either clockwise or anti-clockwise.

Given that, circle A' is the result of rotating circle A by 180° about point P.

When we rotate any object its shape and size does not change, only its position changes.

Therefore, options A and B are the correct answers.

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The total volume in the 6 cups is  638.30 in^2

Remember that the volume of a cylinder of height H and radius R is:

V = pi*R^2*H

Here the diameter is 4.4 inches, then the radius is half of that:

R = 4.4in/2 = 2.2in

The height is 7 inches, then the volume of each cup is:

V = 3.14*(2.2in)^2*7in = 106.38 in^2

And in 6 cups the total volume will be:

volume = 6*106.38 in^2 = 638.30 in^2

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The work needed to pump the top half of the water out of the aquarium by raising it over the top of the aquarium is 34,300 J.

First we need to calculate the total amount of water that needs to be lifted and the height it needs to be lifted to.

The volume of water in the aquarium is given by:

V = 7 m * 1 m * 1 m = 7 m^3

Since we need to pump out the top half of the water, the volume of water that needs to be lifted is:

V = (1/2) * 7 m^3 = 3.5 m^3

The mass of the water can be calculated as:

m = V * density of water = 3.5 m^3 * 1000 kg/m^3 = 3500 kg

The height that the water needs to be lifted to is equal to the height of the aquarium, which is 1 m.

The work needed to lift the water can be calculated using the formula:

W = m * g * h

where

So, the work needed is:

W = 3500 kg * 9.8 m/s^2 * 1 m = 34,300 J (joules)

Therefore, the work needed to pump the top half of the water out of the aquarium by raising it over the top of the aquarium is 34,300 J.

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Answer:

2,295 cm2

Step-by-step explanation:

Answer:

  (b)  2295 cm²

Step-by-step explanation:

You want the area of icing on a cake 13 cm high and 17 cm in radius.

The area of the top is ...

  A = πr²

The area of the side is ...

  A = 2πrh

Then the total area of icing on the cake is ...

  πr² +2πrh = πr(r +2h)

  = 3.14(17 cm)(17 cm + 2·13 cm) = 2295.34 cm²

The area of icing needed for the cake is about 2295 cm².

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The statement that correctly compares the two anthills is "the second anthill is one and one-third times as many ants as the first anthill."

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

First = 982

Second = 1 1/3 * First

This means that "the second anthill is one and one-third times as many ants as the first anthill."

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The measure of the angle B in the triangle is 51.34 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The triangle above is a right angle triangle. A triangle is right triangle because one of its angles is 90 degrees.

The angle of a right triangle can be found using trigonometric ratios as follows:

tan B = opposite / adjacent

tan B = 25 / 20

B = tan⁻¹ 5 / 4

B = tan⁻¹ 1.25

B = 51.3401917459

Therefore,

B = 51.34 degrees

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The Cartesian equation 2xy = 1 has the following polar equation r²·sen2θ = 1.

To convert the Cartesian equation 2xy = 1 into polar equation form, we need to use the relationships between Cartesian coordinates and polar coordinates. The relationships are as follows:

Substituting these relations in the Cartesian equation, we proceed to solve:

2 (r·cosθ)(r·sinθ) = 1

2r²·cosθ·sinθ = 1

r²·(2cosθ·sinθ) = 1

r²·sen2θ = 1

In conclusion, the polar equation has the following form: r²·sen2θ = 1.

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Answer:

[tex]x=\pm\,9i[/tex]

Step-by-step explanation:

[tex]x^2=-81\\x=\pm\,9i[/tex]

Answer:

the answer you are looking for here is 3/7

Answer:

3/7

Step-by-step explanation:

6/7 ×1/2 = 6×1 × 7×2 = 6/14 ÷ 2 = 3/7

Step-by-step explanation:

[tex]y = a(x - h) {}^{2} + k[/tex]

Answer: 1,422

Step-by-step explanation:

The ratio of trombones to all the brass section members is 3:7.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Number of Trumpets = 4

Number of Trombones= 3

Total = 4 + 3= 7

So, the ratio of trombones to all the brass section members

= Number of Trombones/ Total

= 3 /7

= 3:7

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Because of the SSS postulate for proving triangles congruent, you can say that triangles DEG and FEG are congruent. Corresponding parts of congruent triangles are congruent (CPCTC) means that angles DEG and FEG are congruent, which means their measures are equal. So 3y + 4 = 5y - 10.

4 = 2y - 10

14 = 2y

7 = y

The measure of angle DEF is 50 degrees

The amount the the home buyer saves in total by choosing Loan A is  most closest to $11,427. The Option B is correct.

In order to compare the total cost of each loan, we need to consider both the monthly payment and the discount points.

For Loan A, we have Loan amount: $390,000, Loan term: 15 years, Discount points: 4 and Monthly payment: $3,509.71. For Loan B, we have Loan amount: $390,000, Loan term: 15 years Discount points: 0 and  Monthly payment: $3,659.86.

The total cost of Loan A is the sum of the discounted upfront cost (discount points) and the total of all monthly payments over the life of the loan:

= (4% of $390,000) + ($3,509.71 x 180)

= $15,600 + $631,948.80

= $647,548.80

The total cost of Loan B is the total of all monthly payments over the life of the loan:

= ($3,659.86 x 180)

= $658,574.80

Now, the amount saved by choosing Loan A over Loan B is the difference between their total costs which equals:

= Total cost of Loan B - Total cost of Loan A

= $658,574.80 - $647,548.80

= $11,026

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Answer: 1/4

Step-by-step explanation:

To find the product of two fractions, you simply multiply the numerators together and multiply the denominators together. That is:

(5/8) x (6/15) = (5 x 6) / (8 x 15)

Simplifying the numerator and denominator by dividing both by their greatest common factor, which is 2, we get:

(5 x 6) / (8 x 15) = 30 / 120

Further simplifying the fraction by dividing both the numerator and denominator by their greatest common factor, which is 30, we get:

30 / 120 = 1 / 4

Therefore, the product of 5/8 and 6/15 is 1/4.

Answer:

To multiply two fractions, you simply multiply their numerators (top numbers) and denominators (bottom numbers), respectively.

So, 5/8 x 6/15 = (5 x 6) / (8 x 15) = 30 / 120

To reduce this fraction to its simplest form, we can divide both the numerator and denominator by their greatest common factor, which is 30.

30 / 120 = (30 ÷ 30) / (120 ÷ 30) = 1/4

Therefore, the product of 5/8 x 6/15 is 1/4

The values of the variable are:

x is 45.

y is 18.

z is 18.

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

From the figure,

Sin 45 = z / (18√2)

Sin 45 = 1 /√2

So,

1/√2 =z / 18√2

z = 18

Cos 45 = y / (18√2)

1/√2 = y/18√2

y = 18

Tan x = y / z

Tan x = 18/18

Tan x = 1

x = [tex]tan^{-1}[/tex]1
x = [tex]tan^{-1}[/tex] tan 45

x = 45

Thus,

x is 45.

y is 18.

z is 18.

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The average speed with the given distance and time is 119/40 miles per hour.

Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.

Given that, number of miles jogged = [tex]3\frac{2}{5}[/tex] = 17/5 miles and the time taken = 7/8 hours

Here, average speed = 17/5 ÷ 7/8

= 119/40 miles per hour

Therefore, the average speed is 119/40 miles per hour.

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The square root function involves the square root symbol √ which is  mostly read as "square root of", the rule says that the square root of a number 'x' is a number 'y' such that y² = x.

We know that the square root of a number can be either positive or negative, but while defining the square root function, we restrict its range to be the set of all positive real numbers and hence making all square roots possible to be positive.

If the range for the square root of a number is set to be positive as well as negative it wont be a function that is why there is a restriction to the range of this set allowing only positive real numbers.

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2/10 Net 30 represents credit given to the buyer for the sale of goods or services. 2/10 net 30 means that the customer gets a 2% discount if the outstanding balance is paid within 10 days. Otherwise, full payment is due within 30 days.

2/10 Net 30:

The terms and conditions of the transaction are set forth in the purchase order and the corresponding invoice. These terms include terms of credit between the seller (also known as the payee) and the buyer (also known as the payer). A typical net credit period of 30 means the balance must be paid within 30 days of the invoice date. 2/10 Net 30 (also known as 2 10 Net 30) means that if a buyer pays within the first 10 days, their balance will be reduced by 2%. So "2" is the discount amount (2%) and "10" is the due date (10 days).

For example, if your company purchased $500 worth of goods or services on June 1st, you have entered into a loan agreement with the seller. If your company pays the net amount between June 1st and June 10th, you get a 2% discount, bringing the total amount to $490.

This example 2/10 net 30 step by step.

Day Start counting days from the invoice date.

Quick Formula: 100% Discount % x Invoice Amount.

100% - 2% = 98% x $500 = $490.

Formula:

(immediate discount) x (invoice amount) = less payment

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Interval of increase and decrease refers to a period of time in which a quantity rises or falls. For example, a stock market index may have an interval of increase and decrease over a certain period, such as a month or a year.

Interval of increase and decrease is a term used to describe a period during which a certain quantity either increases or decreases. This phenomenon is commonly seen in financial markets, such as the stock market, where indices may go up and down over a certain period of time. This interval of increase and decrease can be measured using different measures such as time, percentage growth, and movement. This interval helps investors and analysts to determine how the stock market is performing and if there are any changes in the market. It also helps them to predict future trends and make better investment decisions. During this interval, it is important to monitor the stock market and any changes that may occur. This helps to ensure that investments are made with the best possible outcome.

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If the triangles are similar but no congruent, then the triangles have different size, thus the only correct option is the dilation (first option).

We know that two figures are congruent if the figures have the same shape and size, while two figures are similar only if have the same shape (but the figures can have different size).

Here we know that the triangles are similar but no congruent, so the triangles must have different size. From the given transformations, the only one that changes the size is the first option, a dilation.

And for example, if we apply a dilation AND the other transformations, then we still will get a similar figure, but if we apply a reflection/rotation/translation alones, we will get a congruent triangle.

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