Solve for x in the following triangle.​

Answer:

{n*(n+1) }    /2

Step-by-step explanation:

The clearest pattern is that the last digit is multiplied by the number after it and then the multiplication is divided by 2.

1 is multiplied by 2, then divided by 2.

2 is multiplied by 3, then divided by 2.

3 is multiplied by 4, then divided by 2.

So, the pattern is:

{n*(n+1) }/2.

Hope this helped!

Step-by-step explanation:

6 blocks ÷ 14 sudents =    6/14 =   3/7  of a block each

The required functions after transformations are y = -4(x+4)+5, y = (x-o)/14, y = -x+4

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

Given that, the equation for the parent linear value function, f(x)=x, that has been transformed by,

a) Reflecting across the -axis, vertical stretch by a scale factor 4, and a translation of 4 units up and 5 units left :-

Rule for reflection across x-axis = y = f(x) → y = -f(x)

After reflection,

f(x) = -x

And there is a vertical stretch by a scale factor 4, and a translation of 4 units up and 5 units left

f(x) = -4(x+4)+5

Therefore, the function will be f(x) = -4(x+4)+5

b) Vertical shrink by a scale factor of 14 and a horizontal shift O units right.

For vertical shrink = f(x)/14 = x/14

For horizontal shift = (x-o)/14

Therefore, the function will be f(x) = (x-o)/14

c) Reflection in the x-axis, a vertical shift of 4 units up and a horizontal shift 7 units left.

Rule for reflection across x-axis = y = f(x) → y = -f(x)

f(x) = -x

For a vertical shift of 4 units up and a horizontal shift 7 units left =

f(x) = (-x-7)+4

Hence, The required functions after transformations are y = -4(x+4)+5, y = (x-o)/14, y = -x+4

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There are 5 erasers to accompany the 20 pencils based on the given ratio.

If the ratio of pencils to erasers is 4:1, and there are 20 pencils, we can determine the number of erasers by setting up a proportion.

The proportion can be written as:

pencils/erasers = 4/1

Given that there are 20 pencils, we can substitute this value into the proportion:

20/erasers = 4/1

To solve for erasers, we can cross-multiply:

\(20*1=4*erasers\)

\(20 = 4*eraser\)

Since there is only 1 unit assigned to erasers, we multiply the unit value (5) by the number of eraser units (1) to find the total number of erasers, which is 5.

Dividing both sides by 4:

20/4 = erasers

5 = erasers

Therefore, there are 5 erasers.

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Answer:

Let's call the weight of the book that was removed "x".

The total weight of the twelve books can be represented as 12 times the average weight of 2.75 pounds:

12(2.75) = 33

After the book is removed, there are only 11 books left, and their total weight can be represented as 11 times the new average weight of 2.70 pounds:

11(2.70) = 29.7

We can set up an equation using these two expressions and the weight of the book that was removed:

33 - x = 29.7

Solving for x, we get:

x = 33 - 29.7

x = 3.3

Therefore, the weight of the book that was removed was 3.3 pounds.

Answer:

20

Step-by-step explanation:

4(4)+3(4)-2(4)=20

Answer:

5.78

Step-by-step explanation:

S=\(\frac{1}{2}\)(a+b)*h

a = 1.8

b = 5

h = 1.7

S = \(\frac{1}{2}\)(1.8+5)*1.7

S = (6.8*1.7)/2

S = 11.56/2

S = 5.78

In an expression using the logical operator And Also, as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false.

The And Also operator is a short-circuiting operator that is used to combine two or more Boolean expressions. It evaluates the left-hand expression first and then the right-hand expression only if the left-hand expression evaluates to true

. If the left-hand expression evaluates to false, then the right-hand expression is not evaluated at all. This helps to improve the performance of the code by avoiding unnecessary evaluations of expressions that would not change the outcome of the overall condition.

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In an expression using the logical operator And Also , as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false. Therefore option c. And Also correct.

This is because the AndAlso operator employs short-circuit evaluation, meaning it stops evaluating once it encounters

the first false condition since the overall result will definitely be false.

In an expression using AndAlso, if the first condition is false, the entire expression is evaluated as false without testing

any further conditions. This is also known as short-circuit evaluation.

In contrast, the OrElse operator evaluates to true as soon as one of the compound conditions is true, without testing

any further conditions. The Nor and Xor operators are less commonly used and have different behavior.

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Finally ahmod will have 4 nickels and 10 dimes.

Ahmod has two times as many dimes as nickels.

They have a combined value of 100 cents.

Group all coins in sets by grouping each nickel with 2 dimes.

Each set, containing 1 nickel and 2 dimes, is worth 5 + 2*10 = 25 cents.

You will have 100/25 = 4 such groups

As we have 4 such groups at last ahmod will have 4 nickels and 10 dimes.

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Answer:

6

Step-by-step explanation:

, , , , ,, , , , , , , , ,sssss

if the family gives up two nights in the hotel, they could afford d) 5 meals

The family has a budget of $800 for meals and hotel accommodations. If they could afford eight nights in a hotel without buying any meals, we can determine the cost of one night at the hotel. To do this, we can divide the total budget by the number of nights:

$800 / 8 nights = $100 per night

Now, let's consider the scenario where the family gives up two nights in the hotel. This would free up $200 from their budget ($100 per night x 2 nights). We can then use this amount to determine how many meals the family can afford by dividing the available funds by the cost of one meal:

$200 / $40 per meal = 5 meals

Therefore, if the family gives up two nights in the hotel, they could afford 5 meals. The correct answer is d. 5.

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Answer:

The second line

Step-by-step explanation:

the one on the left is (2,2) the one on the right is (8,2)

Answer:

Step-by-step explanation:

Cost of toy =100

Selling price = 90

Loss = 100

Loss in percentage = 10/90*100

Loss in %= 11.11

Answer:

\(x\textdegree = 120\textdegree\)

Step-by-step explanation:

Because alternate exterior angles (of a transversal that intersects parallel lines) are congruent, the bottom left interior angle of the triangle is 55º.

Using this information, we can solve for the bottom right interior angle of the triangle (denoted θ) by setting the sum of the measures of the triangle's interior angles to 180º.

\(55\textdegree + 65\textdegree + \theta = 180\textdegree\)

↓ subtract 55º and 65º from both sides

\(\theta = (180-55-65)\textdegree\)

↓ simplify

\(\theta = 60\textdegree\)

Now that we have the measure of the triangle's bottom right interior angle, we can solve for xº because an interior angle of a triangle and its corresponding exterior angle are supplementary (their angle measures add to 180º).

\(\theta + x\textdegree = 180\textdegree\)

↓ plug in the solved value for θ

\(60\textdegree + x\textdegree = 180\textdegree\)

↓ subtract 60º from both sides

\(x\textdegree = (180 - 60)\textdegree\)

↓ simplify

\(x\textdegree = 120\textdegree\)

Answer: It will take 12 hours for the price of the jacket to decrease by $18

Step-by-step explanation: All you got to do for this problem is 18 divided by 1.50 to get $12.

Answer:

YES

Step-by-step explanation:

use pythagorean theorem

15^2 + 36^2 = 39^2

225 + 1296 = 1521

1521=1521

Answer:

Yes

Step-by-step explanation:

\(As\ we\ know\ that,\\The\ sides\ of\ a\ right\ triangle\ are\ pythagorean\ triplets\ in\ the\ form:\\a^2+b^2=c^2\\Here,\\39\ is\ the\ hypotenuse\ as\ it\ is\ the\ longest\ side.\\Hence,\\a^2+b^2=c^2\\Substituting\ a=15,b=36\ on\ the\ LHS,\\15^2+36^2\\=225+1296\\=1521\\On\ the\ RHS\ ,lets\ substitute\ c=39.\\Hence,\\c^2=39^2\\c^2=1521\\As\ LHS=RHS,\ The\ given\ triangle\ is\ a\ right\ triangle.\)

Tyler would have an average roll of 5 which is only the closest he can get to 1 without going over if he is using standard six-sided dice.

We have the scenario that if Tyler has rolled six 4s, the highest possible sum he can achieve is 24 (6 x 4).

Tyler should aim to roll the remaining dice as low as possible, for him get as close as possible to 1 without going over.

It is assumed that  Tyler is using standard six-sided dice, the lowest number he can roll on a single die is 1. So for him to get as close to 1 as possible, Tyler should roll six 1s on the remaining dice.

In conclusion, this would give Tyler a total of 30 (24 + 6) and an average roll of 5.

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Answer:

(f - g)(x) = 3x^5 - 2x^4 - x^2 + x - 11 in standard form.

Step-bystep-Explanation:

To find (f - g)(x), we need to subtract the function g(x) from the function f(x) by subtracting the corresponding terms.

Given:

f(x) = 3x^5 + 6x^2 - 5

g(x) = 2x^4 + 7x^2 - x + 16

To find (f - g)(x), we subtract each term of g(x) from the corresponding term of f(x):

(f - g)(x) = (3x^5 - 2x^4) + (6x^2 - 7x^2) + (-5 - (-x)) - 16

Simplifying this expression, we get:

(f - g)(x) = 3x^5 - 2x^4 + 6x^2 - 7x^2 + (5 + x) - 16

Combining like terms, we have:

(f - g)(x) = 3x^5 - 2x^4 - x^2 + x - 11

Therefore, (f - g)(x) = 3x^5 - 2x^4 - x^2 + x - 11 in standard form.

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The correct answer is:

**C) 0.28**

The sum of deviations refers to the sum of the differences between individual data points and the mean of the dataset. In any dataset, the sum of deviations from the mean will always equal 0.

This is because, when calculating the mean, you sum all the data points and then divide by the number of data points. The mean represents the "middle" or "balance" point of the dataset. When you add up the differences between each data point and the mean, the positive and negative deviations will cancel each other out, resulting in a sum of 0.

So, any non-zero value for the sum of deviations is impossible. In this case, 0.28 is the only non-zero value.

The Golden Rule Test suggests that the decision embodies the principles of empathy and fairness, treating others as one would want to be treated. The Publicity Test indicates that the decision has been well received and is aligned with public expectations.

- The Publicity Test is designed to assess whether the decision or action can withstand public scrutiny and be disclosed openly.

- I score this test an 8 because the decision or action in question has already been made public and received positive feedback from various stakeholders.

- The organization has been transparent in its communication, engaging with the public and addressing concerns promptly.

- The decision aligns with the organization's values and mission, which resonates positively with the public.

- The organization has effectively managed any potential negative publicity by proactively addressing criticisms and providing clear justifications for the decision.

- Overall, the Publicity Test indicates that the decision has been well received and is aligned with public expectations.

The Moral Mentor Test Score: 6

- The Moral Mentor Test evaluates the decision or action by considering whether it reflects the guidance of a wise and ethical mentor.

- I score this test a 6 because while the decision is generally ethical, there are some potential ethical dilemmas that need to be carefully addressed.

- The decision has considered the welfare of various stakeholders and adheres to legal and regulatory frameworks.

- However, there might be some moral complexities associated with certain aspects of the decision that need further evaluation.

- It is important for the organization to seek guidance from ethical experts and consider potential long-term consequences to ensure the decision aligns with the principles of a moral mentor.

- Overall, the Moral Mentor Test suggests that the decision is on the right track but requires careful ethical analysis and considerations.

The Admired Observer Test Score: 9

- The Admired Observer Test assesses whether the decision or action would be approved by an admired and objective observer.

- I score this test a 9 because the decision demonstrates a high level of integrity and is likely to be approved by an objective observer.

- The decision is aligned with industry best practices and follows ethical guidelines.

- It takes into account the interests of various stakeholders and aims to maximize positive outcomes for all parties involved.

- The decision is well-reasoned, considering both short-term and long-term implications.

- Overall, the Admired Observer Test indicates that the decision is commendable and likely to be seen as fair and ethical by an objective observer.

The Transparency Test Score: 7

- The Transparency Test evaluates whether the decision-making process is transparent and accountable.

- I score this test a 7 because while the decision-making process has been relatively transparent, there is room for improvement.

- The organization has provided some level of information and rationale behind the decision, but there may be areas where more transparency is required.

- It is essential for the organization to proactively communicate the decision, its underlying factors, and potential impacts to ensure stakeholders have a clear understanding.

- Increasing transparency can help build trust and mitigate any potential misunderstandings or mistrust.

- The Person in the Mirror Test assesses whether the decision or action aligns with the individual's values and principles.

- I score this test an 8 because the decision demonstrates alignment with the individual's values and principles.

- The decision-maker has considered the ethical implications and personal integrity while making the decision.

- The decision reflects a commitment to fairness, honesty, and accountability.

I score this test a 9 because the decision demonstrates a high level of empathy and fairness towards others.

- The decision considers the interests and well-being of various stakeholders, treating them with respect and dignity.

- It reflects a commitment to fairness, equality, and reciprocity in relationships.

- The organization has taken steps to ensure that the decision does not cause harm or disproportionately benefit any specific group.

- Overall, the Golden Rule Test suggests that the decision embodies the principles of empathy and fairness, treating others as one would want to be treated.

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The average person burns 575-775 calories per hour in a game of basketball. If they are shooting baskets, they will burn 325-450 calories per hour.

What is Calories?
Calories are a measure of energy. Two main definitions of "calorie" are frequently used due to historical factors. The amount of heat required to increase the temperature of one kilogramme of water by one degree Celsius was the original definition of the large calorie, food calorie, as well as kilogramme calorie (or one kelvin). The amount of heat required to produce the same increase in one gramme of water was known as the small calorie or gramme calorie. As a result, 1000 small calories are equal to 1 large calorie.

How many calories do basketball players burn?

Calories expended per minute equal (MET x body weight in kg x 3.5) / 200

Hence, the average person burns 575-775 calories per hour in a game of basketball. If they are shooting baskets, they will burn 325-450 calories per hour.

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Answer:

Subtract the amount of £1 coins from 50p coins:

256-172 = 84

84/3 coins = 28 people paid with 3 coins.

172 people paid using £1 coins

172 + 28 = 200 total people

percent who used 3 coins = 28/200 = 0.13 x 100 = 14% so the answer is 14%

The solution set to the original equation x^4 - 41x^2 + 180 = 0 is: x = ±3, ±2√5.

To solve the equation x^4 - 41x^2 + 180 = 0, we can make the substitution u = x^2. This substitution helps simplify the equation and allows us to solve for u.

Substituting u = x^2 into the equation x^4 - 41x^2 + 180 = 0, we get:

u^2 - 41u + 180 = 0.

Now we can solve this quadratic equation for u. Factoring the equation, we have:

(u - 9)(u - 20) = 0.

Setting each factor equal to zero, we get:

u - 9 = 0 or u - 20 = 0.

Solving for u in each equation, we have:

u = 9 or u = 20.

Now we need to substitute back x^2 for u to find the values of x.

For u = 9:

x^2 = 9,

Taking the square root of both sides, we have:

x = ±3.

For u = 20:

x^2 = 20,

Taking the square root of both sides, we have:

x = ±√20 = ±2√5.

Therefore, the solution set to the original equation x^4 - 41x^2 + 180 = 0 is:

x = ±3, ±2√5.

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Step-by-step explanation:

Refer to attachment.

Hope it helps.

Answer:

60

Step-by-step explanation:

your welcome

The area of the region is 44 square units

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

y = 2x - 5

The intervals where curve intersect is

[-1, 10]

For the surface area between around the region bounded by the curves, we have

Area = ∫[a, b] [f(x)] dx

This gives

\(Area = \int\limits^{10}_{-1} {2x - 5} \, dx\)

Integrate

\(Area = (x^2 - 5x)|\limits^{10}_{-1}\)

Expand

Area = (10² - 5(10)) - ((-1)² - 5(-1))

Evaluate

Area = 44

Hence, the surface area is 44 square units

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Answer:

1)a. y = x² + 4 is y = x² shifted up 4 units.

To graph y = x² + 4, start with these

points:

x y

-2 8

-1 5

0 4

1 5

2 8

Draw a smooth curve through these

points.

b. y = (x - 3)² is y = x² shifted 3 units to the

right.

To graph y = (x - 3)², start with these

points:

x y

0 9

1 4

2 1

3 0

4 1

5 4

6 9

Draw a smooth curve through these

points.

2)a. y = x² - 5

b. y = (x - 7)²

c. y = (x + 3)²

d. y = (x - 6)² + 4