Describe the pythagorean theorem and how you'd solve 5²+b²=13².​

Answer:

A. -4

Step-by-step explanation:

Perpendicular lines have negative slopes

so you would have to flip the fraction and change the sign

so 1/4x = -4/1x or -4x

It would grow by approximately 1.6668 inches to 1.2504 inches

In Lixue's garden, the green pepper plants grew 5 inches in 3-4 months. To find out how many feet they can grow in one month, we can use the given information.

Let's start by converting the inches to feet. Since there are 12 inches in a foot, we divide 5 inches by 12 to get the equivalent in feet: 5 inches ÷ 12 = 0.4167 feet (rounded to four decimal places).

Now, we need to determine how much they can grow in one month. Since the plants grew 0.4167 feet in 3-4 months, we divide this amount by the number of months to find their average monthly growth.

If we assume that the plants grew 0.4167 feet in 3 months, their monthly growth rate would be 0.4167 feet ÷ 3 months = 0.1389 feet per month (rounded to four decimal places).

If we assume that the plants grew 0.4167 feet in 4 months, their monthly growth rate would be 0.4167 feet ÷ 4 months = 0.1042 feet per month (rounded to four decimal places).

Therefore, based on the given information, the green pepper plants can grow approximately 0.1389 feet to 0.1042 feet in one month, depending on whether we consider a 3-month or 4-month timeframe.

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a. The probability of exactly two thefts occurring in a minute is approximately 0.139.

b. The probability of no thefts occurring in a minute is approximately 0.026.

c. The probability of three or fewer thefts occurring in a minute is approximately 0.398.

a. The probability of exactly two thefts occurring in a minute can be calculated using the Poisson probability distribution. With an average rate of 3.6 thefts per minute, the probability is given by:

P(X = 2) = (e^(-λ) * λ^2) / 2!

where λ is the average rate of thefts per minute.

Plugging in the values, we have:

P(X = 2) = (e^(-3.6) * 3.6^2) / 2! ≈ 0.139

Therefore, the probability of exactly two thefts occurring in a minute is approximately 0.139.

b. The probability of no thefts occurring in a minute can be calculated using the Poisson probability distribution as well. The formula is:

P(X = 0) = e^(-λ)

Substituting the average rate of thefts per minute

P(X = 0) = e^(-3.6) ≈ 0.026

Thus, the probability of no thefts occurring in a minute is approximately 0.026.

c. The probability of three or fewer thefts occurring in a minute can be calculated by summing the probabilities of having 0, 1, 2, and 3 thefts. Using the Poisson probability distribution, we can calculate each individual probability and sum them up:

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Substituting the values, we get:

P(X ≤ 3) ≈ 0.026 + 0.094 + 0.139 + P(X = 3)

We can calculate P(X = 3) using the Poisson formula as before:

P(X = 3) = (e^(-3.6) * 3.6^3) / 3!

Substituting the value:

P(X = 3) ≈ 0.139

Therefore:

P(X ≤ 3) ≈ 0.026 + 0.094 + 0.139 + 0.139 ≈ 0.398

Hence, the probability of three or fewer thefts occurring in a minute is approximately 0.398.

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Step-by-step explanation:

f(x) = 2x - 1

f(10) = 2(10) - 1

= 20 - 1 = 19

Answer: 70 in.

Step-by-step explanation:

So we know that the perimeter of a rectangle =2(Length*Breadth)

Given =

Area of the rectangle = 35 \(in.^{2}\)

Length = 7 in.

Area of a rectangle = Length*Breadth

35 = 7*Breadth

\(\frac{35}{7}\) = Breadth

5 = Breadth

Now we can find out the perimeter of the rectangle =

= 2(Length*Breadth)

= 2(7*5)

= 2*35

= 70 in.

The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed

The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.

To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.

On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.

So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.

Therefore, the correct answer is: The total number of tasks Terrence completed.

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Answer:

The correct solution is "10.92 meters".

Step-by-step explanation:

The given values are:

Center of the mirror,

= 1.22 meters

Base,

= 7.32 meters

Samantha's eye,

= 1.82 meters

Let the height of the building will be "x".

Now,

The height of the building will be:

⇒ \(\frac{1.82}{x} =\frac{1.22}{7.32}\)

By applying cross-multiplication, we get

⇒    \(x=\frac{1.82\times 7.32}{1.22}\)

⇒       \(=\frac{13.322}{1.22}\)

⇒       \(=10.92 \ meters\)

Answer:

12:15*300

Step-by-step explanation:

calculate how much he get per dollar

12:15

now * 300

Answer:

when we add two negative numbers the result will always be a negative number, on adding negative numbers the direction of the move will always be to the left side

hope this helps!

Answer:

yes

Step-by-step explanation:

The solution to the systems of equations graphically is (2, 4)

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

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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Answer:

Answer: B. The law says you must write a new living will each time you re admitted to the hospital.

Explanation:

The law does not require that you make a new will whenever you are admitted to the hospital. Any existing will that has fulfilled the provisions of the law are biding unless the person decides to change the will of their own volition.

There is therefore no need to make a new will every time if there is already one in existence and the person is satisfied with it. The Registered Nurse should therefore correct this statement by the Licensed Practical Nurse.

Answer:

31° , 62° , 113° , 154°

Step-by-step explanation:

sum the 4 angles and equate to 360

y + 2y + 3y + 20 + 4y + 30 = 360 , that is

10y + 50 = 360 ( subtract 50 from both sides )

10y = 310 ( divide both sides by 10 )

y = 31

2y = 2(31) = 62

3y + 20 = 3(31) + 20 = 93 + 20 = 113

4y + 30 = 4(31) + 30 = 124 + 30 = 154

the 4 angles are 31° , 62° , 113° , 154°

Answer:

A)

i) 17 => 14 => 11

ii) 3 => 17 => 87

B)

=> 6+5(n-1)

The principal P that must be invested at an interest rate of 15%, compounded continuously, so that $1,300,000 will be available for retirement in 20 years is approximately $64,658.61.

STEP 1: State the quantities given in the problem.

A = $1,300,000 (the desired amount available for retirement)

r = 15% (the interest rate)

t = 20 years (the time period)

STEP 2: Substitute the values of A, r, and t into the compound interest formula A = Pe^(rt).

We can rewrite the formula as follows:

A = Pe^(rt)

Substituting the given values:

$1,300,000 = Pe^(0.15 * 20)

STEP 3: Divide to isolate P.

To isolate P, we divide both sides of the equation by e^(0.15 * 20):

P = $1,300,000 / e^(0.15 * 20)

STEP 4: Simplify to find P.

Using a calculator, we can evaluate the exponential term e^(0.15 * 20):

e^(0.15 * 20) ≈ 2.718^(0.15 * 20) ≈ 2.718^3 ≈ 20.0855

Now we can substitute this value back into the equation for P:

P = $1,300,000 / 20.0855

Calculating this division gives us the value of P:

P ≈ $64,658.61

Note: In continuous compounding, the formula A = Pe^(rt) represents the amount A accumulated over time t with an initial principal P and an interest rate r compounded continuously. The constant e is the base of the natural logarithm and approximately equal to 2.71828.

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The system of equations to represent the total cost, y, when x additional pieces are purchased with a basic cat tree at each store are;

y = 50x + 100    ------(eq 1)

y = 75x + 50    ------(eq 2)

A) Let the total cost of the cat tree be y

Let each additional piece added be x.

Since basic tree is $100 and each additional platform costs $50, then we can say that;

y = 50x + 100    ------(eq 1)

Now, their basic cat tree starts at $50 and each additional piece costs $75. Thus;

y = 75x + 50    ------(eq 2)

B) Subtract eq 1 from eq 2 to gte;

25x - 50 = 0

25x = 50

x = 50/25

x = 2

y = 75(2) - 50

y = $100

C) The Store that would be cheaper depending on the add - ons is Puuur Place because as x increases, it's y-value increases at a lesser rate than that of Meow.

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Answer:

Avoid histograms with small bin widths that group data into lots of bins. A histogram constructed with small bin widths will show the distribution as a “pancake.” so no it does not help us see the pattern in the data.

Step-by-step explanation:

Answer:

25.12 in

Step-by-step explanation:

In the given circle

the height of the cylinder is h = (7/2)^(1/3) and the radius is r = y = (7/8)h.

To solve this problem, we can use the method of Lagrange multipliers.

Let's denote the height and radius of the cylinder by h and r, respectively. Then, the volume of the cylinder can be expressed as V = πr^2h.

We need to maximize V subject to the constraint that the cylinder is inscribed in the cone. The equation of the cone is given by x^2 + y^2 = (7/8)^2z^2, where (x,y,z) are the coordinates of a point on the cone. Since the cylinder is inscribed in the cone, its base will lie on the base of the cone, and its height will be equal to the height of the cone.

Using these constraints, we can write the Lagrangian as:

L = πr^2h + λ[(7/8)^2z^2 - x^2 - y^2]

Taking partial derivatives of L with respect to r, h, x, y, and λ, and setting them equal to zero, we get the following equations:

2πrh + λ(-2x) = 0
πr^2 + λ(-2y) = 0
λ(7/4)z = 0
x^2 + y^2 = (7/8)^2z^2
(x/8)^2 + (y/8)^2 = z^2 - h^2

The first two equations give us r/h = x/2y, and r = y. Substituting these into the third equation, we get λ = -4h^3/49.

Substituting all of these into the last equation, we get:

(x/8)^2 + (y/8)^2 = (49/64)h^2

We want to maximize the volume of the cylinder, which is given by V = πr^2h = πy^2h. Substituting r = y and λ = -4h^3/49 into this equation, we get:

V = -8πh^4/49

Thus, the volume of the cylinder is maximized when h = (7/2)^(1/3) and r = y = (7/8)h.

Therefore, the height of the cylinder is h = (7/2)^(1/3) and the radius is r = y = (7/8)h.
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Answer:

The length of the rectangle is 7x + 27

Step-by-step explanation:

Given;

area of the rectangle, A = 21x + 81 units²

width of the rectangle, w = 3 units

let the length of the rectangle, = L

Area of the rectangle = length x width

A = L x w

21x + 81 = 3L

L = ¹/₃(21x + 81)

L = 7x + 27

Therefore, the length of the rectangle is 7x + 27

Throughout my studies in media and current events, I have gained several major learnings that have shaped my understanding of the subject matter.

These include the importance of media literacy and critical thinking, the power and influence of social media, the role of bias in news reporting, the significance of ethical journalism, and the impact of media on shaping public opinion.

1. Media Literacy and Critical Thinking: One of the most crucial learnings is the importance of media literacy and critical thinking skills. It is essential to analyze and evaluate the information presented by media sources, considering their credibility, bias, and potential agenda. Developing these skills enables individuals to make informed judgments and avoid misinformation or manipulation.

2. Power and Influence of Social Media: Another significant learning is recognizing the power and influence of social media in shaping public opinion and disseminating news. Social media platforms have become prominent sources of information, but they also pose challenges such as the spread of fake news and echo chambers. Understanding the impact of social media is crucial for both media consumers and producers.

3. Role of Bias in News Reporting: Media bias is an important factor to consider when consuming news. I have learned that media outlets may have inherent biases, influenced by their ownership, political affiliations, or target audience. Recognizing these biases allows for a more balanced and critical understanding of news content, and encourages seeking diverse perspectives.

4. Significance of Ethical Journalism: Ethics play a fundamental role in responsible journalism. I have learned about the importance of principles such as accuracy, fairness, and accountability in reporting news. Ethical journalism promotes transparency and ensures the public's trust in the media, contributing to a well-informed society.

5. Impact of Media on Shaping Public Opinion: Lastly, I have learned that the media holds a significant role in shaping public opinion and influencing societal attitudes. Through various forms of media, such as news coverage, documentaries, or entertainment, narratives are constructed that can sway public perception on issues ranging from politics to social matters. Recognizing this influence is crucial for media consumers to engage critically with the information they receive and understand the potential impact it can have on society.

These five major learnings have provided me with a comprehensive understanding of media and current events, enabling me to navigate the vast landscape of information and make more informed judgments about the media I consume. They highlight the importance of media literacy, critical thinking, understanding bias, ethical journalism, and the impact media has on public opinion, ultimately contributing to a more well-rounded and discerning approach to media consumption.

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Answer:

-7

Step-by-step explanation:

(x-5)/2=-6

x-5=-12

x=-7

Answer:

x = -7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

(x - 5)/2 = -6

Step 2: Solve for x

The measure of the angles of the triangle are 84 degrees, 30 degrees and 66 degrees.

The sum of interior angle of a triangle is equal to 180 degrees.

Given the data in the question;

Let the first angle = 14x

Second angle = 5x

Third angle = 11x

Since the sum of interior angle of a triangle is equal to 180 degrees.

first angle + second angle + third angle = 180

14x + 5x + 11x = 180

Solve for x

30x = 180

x = 180/30

x = 6

Therefore, First angle = 14x = 14(6) = 84 degrees

Second angle = 5x = 5(6) = 30 degrees

Third angle = 11x = 11(6) = 66 degrees.

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f(x) = x is a simple linear function with a slope of 1, f(x) = 3 5 6 is a constant function, f(x) = 3-x is a linear function with a negative slope of -1,  f(x) = 1 is a constant function, f(x) = 2 is a constant function

A constant function is a mathematical function whose output value is the same for every input value

From the given parameters, f(x) = x is a simple linear function with a slope of 1, this implies  that for every unit increase in x, the value of y increases by 1.

Also,  f(x) = 3 5 6 is a constant function, where the value of y is always 3 5 6, regardless of the value of x.

In the same way,  f(x) = 3-x is a linear function with a negative slope of -1, which means that for every unit increase in x, the value of y decreases by 1. The fourth function f(x) = 1 is a constant function, where the value of y is always 1, regardless of the value of x.

The domain of the fifth function is 3 0, which means that x can take any value between 3 and 0.

The sixth function f(x) = 2 is a constant function, where the value of y is always 2, regardless of the value of x.

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