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## Triangle PQR is transformed to similar triangle P’Q’R’. A coordinate grid is shown from negative 10 to 0 to positive 10 on both x- and y-axes at increments of 1. A triangle PQR has P at ordered pair 4, 4, Q at ordered pair 8, 4, R at ordered pair 4 and 8. A polygon P prime Q prime R prime has P prime at ordered pair 1,1, Q prime at ordered pair 2,1, R prime at ordered pair 1, 2. What is the scale factor of dilation?

The length of the legs, PQ and PR are 4 units.
The lengths of the legs, P’Q’ and P’R’ are 1 unit.
Since the legs (and triangle) got smaller we know that the scale factor is between 0 and 1.
So.. 4 * x = 1
divide both sides by 4
x = 1/4
The scale factor is 1/4

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## It is a fraction. it is greater than 0.5 and less than 0.9. its denominator is a square number.its numerator number is a prime number. what could be the mystery number be?

Option C – BD=76 cm

Step-by-step explanation:

Given : You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm.

To find : How long BD should it be?

Solution :

First we draw a rough diagram.

The given sides were AD = 44.8 cm, DC = 72 cm and AC = 84.8 cm.

According to properties of kite

Two disjoint pairs of consecutive sides are congruent.

DC=BC=72 cm

The diagonals are perpendicular.

So, AC ⊥ BD

Let O be the point where diagonal intersect let let the partition be x and y.

AC= AO+OC

AC=   …….[1]

Perpendicular bisect the diagonal BD into equal parts let it be z.

BD=BO+OD

BD=z+z

Applying Pythagorean theorem in ΔAOD

where H=AD=44.8 ,P= AO=x , B=OD=z

………[2]

Applying Pythagorean theorem in ΔCOD

where H=DC=72 ,P= OC=y , B=OD=z

…………[3]

Subtract [2] and [3]

……….[4]

Add equation [1] and [4], to get values of x and y

Substitute x in [1]

Substitute value of x in equation [2], to get z

We know, BD=z+z

BD= 38.06+38.06

BD= 76.12

Nearest to whole number BD=76 cm

Therefore, Option c – BD=76 cm is correct.

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## 1057 263 2960 357 which is not a prime number

Option C – BD=76 cm

Step-by-step explanation:

Given : You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm.

To find : How long BD should it be?

Solution :

First we draw a rough diagram.

The given sides were AD = 44.8 cm, DC = 72 cm and AC = 84.8 cm.

According to properties of kite

Two disjoint pairs of consecutive sides are congruent.

DC=BC=72 cm

The diagonals are perpendicular.

So, AC ⊥ BD

Let O be the point where diagonal intersect let let the partition be x and y.

AC= AO+OC

AC=   …….[1]

Perpendicular bisect the diagonal BD into equal parts let it be z.

BD=BO+OD

BD=z+z

Applying Pythagorean theorem in ΔAOD

where H=AD=44.8 ,P= AO=x , B=OD=z

………[2]

Applying Pythagorean theorem in ΔCOD

where H=DC=72 ,P= OC=y , B=OD=z

…………[3]

Subtract [2] and [3]

……….[4]

Add equation [1] and [4], to get values of x and y

Substitute x in [1]

Substitute value of x in equation [2], to get z

We know, BD=z+z

BD= 38.06+38.06

BD= 76.12

Nearest to whole number BD=76 cm

Therefore, Option c – BD=76 cm is correct.

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## We can show that triangle abc is congruent to triangle a prime b prime c prime by translation of

The triangle ABC is similar to triangle LMP. The order here is very important. The letters correspond to one another
A corresponds to L (first letters of each sequence)
B corresponds to M (second letters of each sequence)
C corresponds to P (third letters of each sequence)

In a similar fashion, the segments also correspond to one another.
AB corresponds to LM (first two letters of each sequence)
AC corresponds to LP (first and last letters of each sequence)
BC corresponds to MP (last two letters of each sequence)

————————————

AB corresponds to LM. AB is 4 units long. LM is 2 units long. So AB is twice as long as LM. This ratio (of 2:1) will be applied to every paired corresponding value.

Also, the right angle is at angle M for triangle LMP. The right angle will be at angle B for triangle ABC (since B corresponds to M). The answer will have an x coordinate of 7. So the answer is either choice B or choice C.

If we move 4 units down from point B, we land on (7,-10). That isn’t listed as an answer choice. Let’s try moving 4 units up from point B. We land on (7,-2). This is an answer choice

So the final answer is choice C) (7,-2)

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## What is the prime factorization of 162?

First, let’s factor  3x²-8x+2

Looking at wee can see that the first term is  and the last term is  where the coefficients are 3 and 2 respectively.

Now multiply the first coefficient 3 and the last coefficient 2 to get 6. Now what two numbers multiply to 6 and add to the middle coefficient -8? Let’s list all of the factors of 6:

Factors of 6:
1,2,3,6

-1,-2,-3,-6 …List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 6

1*6
2*3
(-1)*(-6)
(-2)*(-3)

note: remember two negative numbers multiplied together make a positive number

Now, which of these pairs add to -8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -8

First Number Second Number   Sum 1                            6                      1+6=7 2                           3                      2+3=5 -1                         -6                       -1+(-6)=-7 -2                        -3                       -2+(-3)=-5

None of these pairs of factors add to -8.

So the expression 3x²-8x+2 cannot be factored.

So (x – 2) is NOT a factor of  3x²-8x+2
So the statement is false

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## How long has theresa may been prime minister?

1- The correct answer is B. The Treaty of Versailles’ war-guilt clause angered many Germans and set the stage for future conflict.

2- The correct answer is D. During the 1920s, factories didn’t scale back production due to poor economy, as it was a prosper age.

3- The correct answer is C. The Russian Revolution was not a direct cause of the Great Depression.

4- The correct answer is A. An argument against free trade is that it increases the prices for many products.

5- The correct answer is A. A goal of the Great Leap Forward in China was to increase industrial activity.

Explanation:

1- The Treaty of Versailles was subject to multiple criticisms. The frustrations and imbalances that gave birth, had an important role in the decades that followed. Adolf Hitler opposed, since his political ascension began, the Treaty of Versailles, which made all the consequences of the war on the shoulders of Germany. In fact, according to article 231, Germany is considered to be responsible for the war. The British economist John Maynard Keynes, who participated in the negotiations, considered it a “Carthaginian peace”.

2- In the United States, the 1920s was a time of prosperity and economic improvement for the American society, called “roaring twenties”.

This prosperity benefited the whole society and caused the economy to continue growing at a rate that had not been registered before, generating a speculative bubble. But this prosperity would last a short period that would end on October 24, 1929, known as the Black Thursday, and with the arrival of the Crash of 29 that would culminate finally with the advent of the Great Depression.

3- The Russian Revolution had no interference in the economy of the United States. The change of course of a secondary economy in the international context did not affect American business in Europe.

4- An argument against free trade is that it increases the prices for many product, as it generates many goods to be sold abroad at very profitable prices, so the remnants must be matched to be sold in the domestic market.

5- The Great Leap Forward was a campaign of economic, social and political measures implemented in the People’s Republic of China between 1958 and 1961, during the presidency of Mao Zedong, with the aim of transforming the traditional Chinese agrarian economy through rapid industrialization and collectivization.

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## HELP PLEASE ASAP! 1. War breaks out near Country A and B, limiting trade with nearby nations. Country A has a single resource economy and Country B has a diversified economy. Which country is more at risk for economic problems? Country A is more at risk because it has many types of products that it must find new trade partners to buy. Country A is more at risk because it has fewer types of goods to attract new trade partners. Country B is more at risk because it has fewer types of goods to attract new trade partners. Country B is more at risk because it does not have natural resources. 2. Which of the following best describes a disadvantage of a representative democracy compared to a direct democracy? Elections are unnecessary because birth and political party determine the officials. Elected officials may not always act in the best interests of those they represent. People are able to vote directly on issues that they care about. Decision-making is often slower because more people are involved in making the decisions. 3. Which statement about officials found in various forms of government is least accurate? A confederation would likely have several states with powerful state senators. A parliamentary government would likely have a prime minister elected by the legislature. A unitary government would likely have several states with powerful state senators. A federation would likely have a president elected by the people.

1- Country A is more at risk because it has fewer types of goods to attract new trade partners.

2- A disadvantage of a representative democracy compared to a direct democracy is that elected officials may not always act in the best interests of those they represent.

3- The least accurate statement is the one that says that a unitary government would likely have several states with powerful state senators.

Explanation:

1- If war breaks out near Country A and Country B, and Country A has a single resource economy while Country B has a diversified economy, Country A would be more at risk because as it only produces one resource, it would be more difficult for it to find new markets where to sell its production.

2- Representative democracy is often presented as the most efficient form of democracy possible in mass societies, arguing that it allows an effective decision by a sufficiently small number of people in the name of the greatest number. The efficiency of the service can be judged based on the metrics of profitability and efficiency over time. Representatives who vote on behalf of the people allow a monetary benefit, since the use of polling stations, vote counters, etc. is reduced. The government is generally responsible for paying the salaries of the representatives and would have to cover the substantial cost of a democracy. Representative democracy has been conceptually associated with historically instantiated by the political system known as “representative government,” which was born in the eighteenth century with the French and American revolutions. It is a system in which people choose their legislators (representatives), who are then responsible to them for their activity within the government.

3- A unitary government is a form of government where power is concentrated and there is a single center of power that extends its action throughout the territory of the respective nation through its agents and local authorities, delegates of that same central power. A unitary government is the opposite of a federal government.

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## What are the prime number under 10

Well first you have to make variables for each number.
1st – x
2nd – y
3rd – z

first sentence says twice first number so 2x. is means equals so =. eleven more than sum of the other two numbers. sum of other two numbers is (y + z) and eleven more than that is (y + z) + 11. So so this sentence says:
2x = (y + z) + 11

second sentence says sum of twice the first and three times third. twice first is 2x and three times third is 3z. their sum would be (2x + 3z). It it says is one more than second number. So = (y + 1). So so this means:
(2x + 3z) = (y + 1)

third sentence says second number (y) is is equal to sum of first and third (x + z). so;
y = (x + z)

now for the work.

We we can easily solve for a by subtracting the first 2 equations. the way to subtract 2 equations is by subtracting one left side of equal sign from the other equations left side and then doing the same with the right side.

So we will subtract the 1st and second equations we made.
So so left sides would be
2x – (2x + 3z)
2x – 2x – 3z
-3z

right side would be:
y + z + 11 – (y + 1)
y + z + 11 – y – 1
z + 10

now put the sides with an equal sign
-3z = z + 10
-4z = 10
z = -2.5

now we can plug in z into the equations and subtract second and third equations. But but we will subtract opposite sides. So so left minus right and right mi is left after we plug in z:
(2x + 3 (-2.5)) – (x + (-2.5))
2x – 7.5 – x + 2.5
x – 5

other one would be
(y + 1) – y
1

So so put an equal sign and get:
x – 5 = 1
x = 6

now plug x and x into 3rd equation
y = x + z
y = 6 + (-2.5)
y = 3.5

now we have values. You can check answer by plugging values into other 2 equations

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## A number is written with the following factorization: 2^2 X 3 X 5^4 X 8 X 11^2. Is this factorization a prime factorization? Explain why or why not. If it is not correct, give the correct prime factorization of the number.

We need to estimate the value of T'(8) and then we need to give the meaning of this value. Since we have a table and not an expression of a function our goal is to find the Average Rate of Change between two points.

For a nonlinear graph whose slope changes at each point, the average rate of change between any two points is the slope of the line through the two points. So:

1. Estimated value of T′(8).

T'(8) means the derivative of the function T(t) when t = 8 hours. So, we can estimate this value using the average rate of change:

2. The meaning of T′(8)

This means the average temperature after midnight in Phoenix on March 15, from t = 6 to t = 8 hours, that is, for each hour the temperature rises 5/2 degrees on the Fahrenheit scale. The points have been plotted in the Figure bellow.

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## Quadrilateral A’B’C’D’ is a dilation of quadrilateral ABCD about point P. Quadrilateral ABCD is shown. Side AB is labeled 5. Side BC is labeled 4. Side CD is labeled 10. Side DA is labeled 6. Quadrilateral A prime B prime C prime D prime is between quadrilateral ABCD and point P. Side A prime B prime is labeled 1 and one fourth. Side B prime C prime is labeled one. Side C prime D prime is labeled 2 and a half. Side D prime A prime is labeled 1 and a half. reduction enlargement

Answer:  The correct option is (A) reduction.

Step-by-step explanation:  Given that the quadrilateral A’B’C’D’ is a dilation of the quadrilateral ABCD.

As shown in the given figure, the lengths of the sides of quadrilateral ABCD are as follows:

AB = 5 units, BC = 4 units, CD = 10 units and DA = 6 units.

And, the lengths of the sides of quadrilateral A’B’C’D’ are as follows:

We know that the dilation will be an enlargement if the scale factor is greater than 1 and it will be a reduction if the scale factor is less than 1.

Now, the scale factor is given by

Since the scale factor is less than 1, so the dilation will be a reduction.

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## LIFE OR DEATH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Factor x^2 + 10x – 18. (x + 3)(x – 6) prime (x – 2)(x + 5) (x – 2)(x – 9)

LIFE OR DEATH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Factor x^2 + 10x – 18. (x + 3)(x – 6) prime (x – 2)(x + 5) (x – 2)(x – 9)

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## Write 12 as a product of prime factors?

Write 12 as a product of prime factors?

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## Most democracies have a government with three branches: executive, legislative, and judicial. In Canada, the legislative branch is the A) Senate B) president C) Parliament D) Prime Minister

A. To protect the interests of the United States

B. To preserve the lives of the hostages

Explanation:

The hostage crisis in Iran took place over a period of 444 days, during which a group of Iranian students took 66 diplomats and citizens of the United States of America (USA) hostage. The crisis began on November 4, 1979 and lasted until January 20, 1981.

Carter refused to yield to the demands, Khomeini used the situation to consolidate his power and nullify the challenges of the moderate wing of his government, headed by its president. The euphoria over the humiliation of the most powerful nation distracted the Iranian people from the economic difficulties of their country. Carter, in April 1980, broke diplomatic relations with Iran and imposed a trade embargo, except medicine and food. Iranian funds in the US they were frozen and accounted for to compensate the hostages when they were released and to pay the demands of US companies against Iran.

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## Yi and Sue play a game. They start with the number 42000. Yi divides by a prime number, then passes the quotient to Sue. Then Sue divides this quotient by a prime number and passes the result back to Yi, and they continue taking turns in this way. For example, Yi could start by dividing 42000 by 3. In this case, he would pass Sue the number 14000. Then Sue could divide by 7 and pass Yi the number 2000, and so on. The players are not allowed to produce a quotient that isn’t an integer. Eventually, someone is forced to produce a quotient of 1, and that player loses. For example, if a player receives the number 3, then the only prime number (s)he can possibly divide by is 3, and this forces that player to lose. Who must win this game

Naturally, any integer larger than 127 will return , and of course , so we restrict the possible solutions to .

Now,

is the same as saying there exists some integer such that

We have

which means that any that satisfies the modular equivalence must be a divisor of 120, of which there are 16: .

In the cases where the modulus is smaller than the remainder 7, we can see that the equivalence still holds. For instance,

(If we’re allowing , then I see no reason we shouldn’t also allow 2, 3, 4, 5, 6.)