Which of the following is the solution to the system of equations?

y=2−xy=3x−1

The  total distance traveled by the "super ball" is 49 meters.

1. First bounce: The ball drops from 16 meters above the ground and rises to \(\(\frac{3}{4}\)\) of that height.

Distance traveled in the first bounce:

\(\[16 + \frac{3}{4} \times 16\]\)

2. Second bounce: The ball drops from the new height and rises to \(\frac{3}{4}\)\) of that height.

Distance traveled in the second bounce:

\(\[\left(\frac{3}{4} \times 16\right) + \frac{3}{4} \times \left(\frac{3}{4} \times 16\right)\]\)

3. Third bounce: The ball drops from the new height and rises to \(\(\frac{3}{4}\\) ) of that height.

Distance traveled in the third bounce:

\(\[\left(\frac{3}{4} \times \left(\frac{3}{4} \times 16\right)\right) + \frac{3}{4} \times \left(\frac{3}{4} \times \left(\frac{3}{4} \times 16\right)\right)\]\)

Now, the total distance traveled

\(\[ \text{Total distance traveled} = \left(16 + \frac{3}{4} \times 16\right) + \left(\frac{3}{4} \times 16 + \frac{3}{4} \times \left(\frac{3}{4} \times 16\right)\right)\)

                                         \(+ \left(\frac{3}{4} \times \left(\frac{3}{4} \times 16\right) + \frac{3}{4} \times \left(\frac{3}{4} \times \left(\frac{3}{4} \times 16\right)\right)\right) \]\)

\(\[\text{Total distance traveled} = 16 + 12 + 9 + \frac{27}{4} + \frac{81}{16}\]\)

\(\[\text{Total distance traveled} = 16 + 12 + 9 + \frac{27}{4} + \frac{81}{16}\)

                                       \(= 16 + 12 + 9 + \frac{108}{16} + \frac{81}{16} \]\)

\(\[\text{Total distance traveled} = 16 + 12 + 9 + \frac{108 + 81}{16}\)

                                    \(= 16 + 12 + 9 + \frac{189}{16} \]\)

Add the whole numbers and fractions separately:

\(\[\text{Total distance traveled} = 37 + \frac{189}{16}\]\)

Now, convert the improper fraction to a mixed fraction:

\(\[ \frac{189}{16} = 11\frac{13}{16} \]\)

Finally, add the whole number and the mixed fraction:

\(\[ \text{Total distance traveled} = 37 + 11\frac{13}{16} \]\)

So, the total distance traveled by the "super ball" is :

\(\[ \text{Total distance traveled} = 37 + 12 = 49 \text{ meters} \]\)

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The volume of a rectangular prism is lwh unit cube.

A rectangular prism can be defined as a 3-dimensional solid shape that has 6 faces, with its base as rectangles.

The volume of a rectangular prism is given by, the product of its dimensions.

Let us consider length, width and height of the rectangular prism be l, w, h respectively,

Then, the volume will be = length x width x height

= l x w x h

= lwh

And its unit will be unit cube because there are 3 dimensions in the prism which are being multiplied.

Hence, the volume of a rectangular prism is lwh unit cube.

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Answer:

If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B

If Marguerite rents for 1 week, it will cost her the same at either company

h(x) = 5x - 5

Step-by-step explanation:

Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. The following functions represent the rate structures of the two rental companies: x = the number of weeks Company A f(x) = 15(7x) Company B g(x) = 100x + 5 The function h(x) = f(x) – g(x) represents the difference between the two rate structures. Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply. If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B. If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B. If Marguerite rents for 1 week, it will cost her the same at either company. If Marguerite rents for 1 week, it will cost her more if she rents from Company A. h(x) = 5x – 5 h(x) = 5x + 5

Answer: Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. In one week there are 7 days, therefore in x weeks the cost of rentals are given below:

For company A: f(x) = 15(7x)

For company B: g(x) = 100x + 5  

h(x) = f(x) – g(x) represents the difference between the two rate structures.

h(x) = f(x) - g(x) = 15(7x) - (100x + 5)

h(x) = 105x - 100x - 5

h(x) = 5x - 5

If Marguerite rents for 2 weeks:

The cost for company A = 15(7x) = 15(7 × 2) = $210

The cost for company B = 100x + 5 = 100(2) + 5 = 200 + 5 = $205

If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B

If Marguerite rents for 1 weeks:

The cost for company A = 15(7x) = 15(7 × 1) = $105

The cost for company B = 100x + 5 = 100(1) + 5 = 100 + 5 = $105

If Marguerite rents for 1 week, it will cost her the same at either company

Answer:

If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.

h(x) = 5x + 5

those are the answers on edge

Step-by-step explanation:

The description corresponds to an observational study, which involves gathering data and information to draw conclusions without intervening in the process. Correct answer: letter D.

An experiment would involve manipulating the variables to see the effect of the manipulation. In this case, it would involve changing the caffeine consumption and observing the effect on heart arrhythmias.

In order to better understand the relationship between heart arrhythmias and caffeine consumption, researchers need to consider a variety of factors, including the amount of caffeine consumed, the timing of consumption, and any potential underlying medical conditions that could be influencing the results.

Furthermore, researchers need to ensure that the study population is large enough and diverse enough to accurately reflect the general population. Additionally, researchers need to consider potential confounding variables, such as lifestyle factors, medications, and other dietary components that could be influencing the results.

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Answer:

Explanation:

We want to write 47 in base 3

To do this, we follow the steps below:

47/3 = 15 Remainder 2

15/3 = 5 Remainder 0

5/3 = 1 Remainder 2

1/3 = 0 Remainder 1

Now, to base 3, we write the remainders, starting from the last one to the first one.

The next greater odd integer for an odd integer x is x + 2, which is option B.

If x is an odd integer, we know that it can be represented as 2n + 1, where n is an integer. To find the next greater odd integer, we add 2 to x, giving us x + 2, which is option B. Therefore, B must be the next greater odd integer.

Option A, 2x, is not necessarily odd because if x is an odd integer, 2x will be an even integer.

Option C, x + 3, is also an odd integer, but it is not necessarily the next greater odd integer.

Option D, x², is not necessarily odd because if x is an odd integer, x² will be an odd integer.

Option E, 2x + 1, is also an odd integer, but it is not necessarily the next greater odd integer.

In summary, the next greater odd integer for an odd integer x is x + 2, which is option B.

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A. The gauge is showing 3/8 fraction of the fuel tank and B. 30 Liters must be added o the fuel tank to fill it.

A) Each division in the Fuel gauge represent the fraction ,

So,

To find what fraction the gauge shows multiply 6 by 1/16.

= 6 x 1/16

= 6/16

= 3/8

B) We know that,

The tank has 3/8 of its total capacity.

So,

to fill the tank must be added 1-3/8 Liters.

= 5/8 L

Therefore,

Multiplying 5/8 by 48

= 5/8 x 48

= 30 Liters.

So, 30 Liters of fuel must be added to the tank to completely fill it.

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Complete question - (a) What fraction does the Gauge show?

(b) The fuel tank holds 48 litres when it is full. How many Litres must be added to fill the tank?

Answer:

B & D

Step-by-step explanation:

You can use PEMDAS (exponets go first)

7x7x7x7x7x7=7^6 times 7=7^1

42

7^12=7x7x7x7x7x7x7=13841287201 divided by 7x7=49

13841287201/49=282475249

Answer:

y=9

Step-by-step explanation:

\(y + 4 = 13 \\ y = 13 - 4 \\ y = 9\)

A unit rate's component is always 1. To find the unit rate, divide the fraction by the fraction such that the denominator is equal to one.

The meaning of math units:

Of mathematics, a unit can be thought of as the right side point in a number or the number one. In this instance, the unit number in the number 6713 is 3. A unit is also a term that may be used to describe the common measurement units.

The dimensions of a unit:

The area of a unit as depicted on the subdivision or annexation map that created the unit is referred to as its size. The lot, tract, or parcel size divided by the number of dwellings is the unit size for two-family and multiple-family homes on a single unit.

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These records or lists must be retained and available for inspection for a certain period of time which is for minimum 3 years.

According to the Internal Revenue Service (IRS) guidelines, paid preparers must retain the records or lists containing the taxpayer's name, identification number, and tax year for a minimum of three years from the date of the return's filing. This retention period allows for the records to be available in case of any inquiries, audits, or investigations by the IRS.

During this retention period, the records or lists should be kept in a safe and secure manner, ensuring their accessibility if requested by the IRS or any authorized personnel. It is important to note that the three-year retention period starts from the date the return was filed, not the date of the preparer's signature.

Complying with the retention requirement is essential for paid preparers to demonstrate their adherence to IRS regulations and maintain transparency in tax filing processes. By retaining the records or lists for the specified period, paid preparers can fulfill their obligations and provide necessary documentation when needed.

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A temperature change of 20°C corresponds to a Fahrenheit temperature change of 36°F. The Fahrenheit scale has a different conversion formula than the Celsius scale, resulting in a larger change in degrees for the same temperature difference.

To convert from Celsius to Fahrenheit, we use the formula: F = (C * 9/5) + 32, where F represents the temperature in Fahrenheit and C represents the temperature in Celsius.

In this case, the temperature change is given as 20°C. To find the corresponding Fahrenheit temperature change, we apply the conversion formula: F = (20 * 9/5) + 32 = 36 + 32 = 68°F.

Therefore, a temperature change of 20°C corresponds to a Fahrenheit temperature change of 68°F. Among the given answer choices, the closest option is 36°F.

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Answer:

the numbers are 18 and 71

Step-by-step explanation:

let x and y be the 2 numbers with x > y , then

4y = x + 1 ( subtract 1 from both sides )

4y - 1 = x → (1)

x - y = 53 → (2)

substitute x = 4y - 1 into (2)

4y - 1 - y = 53

3y - 1 = 53 ( add 1 to both sides )

3y = 54 ( divide both sides by 3 )

y = 18

and x = 4y - 1 = 4(18) - 1 = 72 - 1 = 71

the 2 numbers are 18 and 71

Answer:

Smaller number=18, Larger Number=71

Step-by-step explanation:

Let the smaller number be s

the larger number be l

4s=1+l

4s-l=1

l-s=53

(4s-l)+(l-s)=1+53

3s=54

s=18

l-s=53

l-18=53

l=71

The value of the missing angle is calculated as: ∠BGC = 76°

The parameters are given as:

∠AGB = 35°

∠AGE = 69°

From angle theorems, we know that the sum of angles on a straight line is 180°. If we split any straight line into smaller angles, all of these angles would then be summed up to make 180° which is the same as with a triangle. Angles in a straight line are a very useful problem solving tool for many geometric problems.

Thus:

∠AGB + ∠AGE + ∠BGC = 180°

Thus:

35 + 69 + ∠BGC = 180

∠BGC = 180 - (69 + 35)

∠BGC = 76°

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The smallest integer 160 needs to be multiplied by to give a square number is 15.

A perfect square is a number system that can be expressed as the

square of a given number from the same system.

The smallest integer 160 needs to be multiplied by to give a square number;

60 x 15= 900

Hence,

The square root of 900= 30

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If square based pyramid's perimeter is 18.5 ft and it's height is 7.6 ft, then volume of that pyramid is 54.4 cubic foot.

The "Volume" of a square pyramid is known as the space which is occupied by pyramid, and it is represented as : V = (1/3) × B × h, where V is volume, B is area of base, and h is height of pyramid,

The shape of "base-of-pyramid" is a square,

So, we find "base-area" by dividing perimeter by 4 and squaring it;

⇒ Perimeter of base of pyramid = 18.5 ft,

⇒ Length of "one-side" of base = 18.5/4 = 4.625 ft,

So, ⇒ Base area = (4.625 ft)² = 21.390625 sq ft,

Now, using the formula to find volume;

⇒ Volume = (1/3) × 21.390625 × 7.6 ,

⇒ Volume = 54.384375 cubic feet,

Rounding volume to "nearest-tenth" of a cubic foot,

We get,

⇒  Volume ≈ 54.4 ft³.

Therefore, Volume of pyramid is 54.4 ft³.

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The given question is incomplete, the complete question is

Find the volume of a pyramid with a square base, where the perimeter of the base is 18.5 ft and the height of the pyramid is 7.6 ft. Round your answer to the nearest tenth of a cubic foot.

The formula to determine the total cost of the monthly rental is R300 + (Number of minutes beyond 500 * R0.50)

The formula to calculate the total cost (in rands) for CALL PACKAGE 2 can be expressed as:

Total cost (in rands) = Monthly rental + (Number of minutes beyond the free minutes * Cost per minute)

In this case, the monthly rental for PACKAGE 2 is R300, and the first 500 minutes are free. Calls beyond the free minutes cost R0.50 per minute.

Therefore, the formula becomes:

Total cost (in rands) = R300 + (Number of minutes beyond 500 * R0.50)

This formula calculates the total cost by adding the monthly rental fee to the cost of the minutes used beyond the free minutes, which is calculated by multiplying the number of minutes beyond 500 by the cost per minute, R0.50.

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The given function [cos(7y) cos (3y) - sin (7y) sin (3y)] is equal to cos(10y) as per trigonometric identities.

"Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle."

Given, trigonometric function is: cos(7y) cos (3y) - sin (7y) sin (3y)

We know, cos(A + B) = cos(A) cos(B) - sin(A) sin(B)

Therefore, cos(7y) cos (3y) - sin (7y) sin (3y)

= cos(7y + 3y)

= cos(10y)

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Answer:

0

Step-by-step explanation:

1 x 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 x 0 = 0 Because of the Indentity Property

Answer:

the width is 4

Step-by-step explanation:

7 times 4= 28

or

28 divided by 7

The  trigonometry angle range -π ≤ α ≤ π in radians means angle α is

To answer the question, we need to know what a trigonometric angle range is

A trigonometric angle range is the range of values which the trigonometric angle can have

Since we need to find the meaning of the  trigonometry angle range -π ≤ α ≤π.

We know that

Since α is in the range -π ≤ α ≤ π = -180° ≤ α ≤ 180°, this implies that the angle α is

So, the  trigonometry angle range -π ≤ α ≤ π in radians means that angle α is

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The product of Matrix XY is [2].

A matrix is an array of rows and columns containing numbers, symbols, or expressions that is rectangular in shape.

In linear algebra, matrices describe linear mappings and enable explicit computations. As a result, a significant portion of linear algebra involves the study of matrices, and the majority of the characteristics and operations of abstract linear algebra may be described in terms of matrices.

Given matrices X = [-1    0]

and  Y = \(\left[\begin{array}{ccc}-2\\-1\\\end{array}\right]\)

product of the matrix is done with the dot product of rows and column

[ a     b]\(\left[\begin{array}{ccc}c\\d\\\end{array}\right]\) = [ac + bd]

product of XY is [-1    0] \(\left[\begin{array}{ccc}-2\\-1\\\end{array}\right]\)  = [-1(-2)  + 0(-1)]

XY = [2]

Hence the measure of XY is [2].

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Using the distributive property we have that multiplying by some terms grouped in parenthesis is the same as multiplying each term.

On one hand:

2(x+3) = 2 · x + 2 · 3

= 2x + 6

On the other:

(x+4)​ = x + 4

Then

2(x+3) + (x+4)​ = 2x + 6 + x + 4

We combine like terms in the expression

2x + 6 + x + 4

terms with x: 2x and x

numbers: 6 and 4

adding them we have that:

terms with x: 2x + x = 3x

numbers: 6 + 4 = 10

Then

2x + 6 + x + 4

= 3x + 10

Answer: 2(x+3) + (x+4)​ = 3x + 10

Le Fang, Chunyuan Li, Jianfeng Gao, Wen Dong, and Changyou Chen developed implicit deep latent variable models

for text generation. Implicit deep latent variable models are a class of probabilistic models that can capture complex dependencies between variables in high-dimensional data such as images and text.

The models are characterized by the existence of latent variables that encode the underlying structure of the data. In text generation, the latent variables

represent the semantic meaning of the generated text. The models are trained on large corpora of text data and can generate new text samples that are coherent and semantically meaningful.The researchers proposed a novel approach to training implicit deep latent variable models that combines variational inference with adversarial training. This approach ensures that the generated text samples are of high quality and match the distribution of the real data. The models were evaluated on several text generation tasks, including sentence completion, language modeling, and machine translation. The results showed that the models outperformed existing state-of-the-art models

in terms of generating coherent and semantically meaningful text.The researchers also explored the use of implicit deep latent variable models for text classification and sentiment analysis. The models were able to capture the underlying structure of the data and achieve high accuracy on several benchmark datasets.

Overall, thethe area of the patio in square feet is 216 square feet.

the area of the patio in square feet is 216 square feet.the area of the

patio in square feet is 216 square feet.

the area of the patio in square feet is 216 square feet.

proposed models represent a significant advancement in the field of text generation and have the potential to be applied to a wide range of natural language processing tasks.

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Answer:

.70/100 ×120 is 84 .which is temporary so to find permanent u subtract 120 from 84 which is 36

Step-by-step explanation:

Answer:

jskdbsisjxbsisdidbebsiejebdbwjejdbebdbdjejejsiejejeb

Note that this prompt is designed to test ones knowledge on cosigners and loans. See the correct responses below.

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Answer:

$1605

Step-by-step explanation:

1500 ⋅ 0.07 = 105

Add 105 to 1500

$1605

Hope I helped :)

Please consider Brainliest :)

Answer:

25x²-60x+36

Step-by-step explanation:

(5x-6)²

Expand the brackets.

(5x-6)(5x-6)

5x(5x-6)-6(5x-6)

Multiply.

25x²-30x-30x+36

Add or subtract the like terms.

25x²-60x+36

Perfect squares trinomials are those expressions which are found by squaring binomial expressions. The expansion of the given binomial expression, (5x - 6)² is (25x² + 36 - 60x).

Perfect squares trinomials are those expressions which are found by squaring binomial expressions. A few examples of perfect squares trinomials are,

a² + b² + 2ab = (a + b)²

a² + b² - 2ab = (a - b)²

The expansion of the given binomial expression, (5x - 6)² can be done as,

(5x - 6)²

= (5x)² + 6² - 2(5x)(6)

= 25x² + 36 - 60x

Hence, The expansion of the given binomial expression, (5x - 6)² is (25x² + 36 - 60x).

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