what theorems, properties, or strategies are common to the proof of the triangle proportionality theorem and the proof of converse of the triangle proportionality theorem?'

Answer:

x = 5

Step-by-step explanation:

                       x - 2(x +1) + 3(x -2) + 2(x - 6) = 0

x + (-2)*x  + (-2)*1 + 3*x +3*(-2) + 2*x + 2*(-6) = 0

                            x - 2x -2 + 3x - 6 + 2x - 12 = 0

                          x - 2x + 3x + 2x - 2 - 6 - 12 = 0

Combine like terms. Like terms have same variable with same power.

                                                          4x - 20 = 0

Add 20 to both sides.

                                                                 4x  = 20

Divide both sides by 4

                                                                   x = 20/4

                                                                   x = 5

Answer:

x = 5

Step-by-step explanation:

x  -2(x+1) + 3(x-2) + 2(x-6) =  0

here, we need to distribute the numbers on the outside of the parentheses to the inside numbers.

As you may know, when two numbers are in parentheses, they are to be multiplied--and it is the same idea here.

When we have a number, say 3, multiplied by parentheses, say (x - 2), we multiply all inside numbers by the outside number, which is called distributing.

We know that 3(x) = 3x, and that 3(-2) = -6, so we distribute

3(x  - 2)       to be        3x - 6

let's do that for all of our parentheses:
x  -2(x+1) + 3(x-2) + 2(x-6) =  0

-2( x  + 1 )

-2x   -  2

3(x  - 2)

3x   -  6

2( x  - 6)

2x  - 12

Now, let's rewrite our problem:

x  -2(x+1) + 3(x-2) + 2(x-6) =  0

x     - 2x  - 2    + 3x -6     + 2x - 12    = 0

First, we should combine like terms:

x - 2x  + 3x + 2x          - 2 - 6 - 12    = 0

(x - 2x = -x;  -x + 3x = 2x;  2x + 2x = 4x)

( - 2 - 6 = -8; -8 - 12 = -20

So, we are left with:

4x  -  20 = 0

At this point, we want to get x alone (so that we can find what "x" is)

4x - 20 = 0  

    + 20    + 20       ( add 20 to both sides of the equation to isolate x )  

   4x     =    20

  ÷ 4          ÷ 4           (divide both sides by 4 to find "1"x)

     x  =  5

So, we know that the value of x is 5, or x = 5

hope this helps! let me know if you need clarification on anything :)

Answer:

Step-by-step explanation:

Answer:37.68

Step-by-step explanation:

first we know the radius is 6 and to find the circumference of a circle you do 2πr and we can plug 3.14 into π and 6 for the radius to it would be 2*3.14*6=12*3.14=37.68

The percent increase in the number of followers is 50%

The first step is to calculate the increase

Given that the original number of followers was 300

After the video went viral, it increased to 450

So, we have

Increase= 450 - 300= 150

The percent increase can be calculated as follows

150/300 × 100%

So, we have

= 0.5 × 100%

Evaluate

= 50%

Hence the percent increase is 50%

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Answer:

What are you talking about .

Step-by-step explanation:

Answer:

105cm2

Step-by-step explanation:

area= area f rectangle + area of trapezium

        = (6x9)+( \(\frac{6+11}{2}\)x6)

         = 54+51

        = 105 cm2

Answer: 7

Step-by-step explanation: You can find the mean, or average, of a data set in two simple steps: Find the sum of the values by adding them all up. Divide the sum by the number of values in the data set.

Answer: 3 hours and 36 minutes

Step-by-step explanation:

720/400 = 1.8

1.8*2 = 3.6

3.6 hours = 3 hours and 36 minutes

The value of the test statistic used to test the claim is -2.00.

And, at a significance level of 0.05, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to support the claim that the mean GPA for Psychology students at the college is equal to 3.2.

Now, If a two-sided test of hypothesis is conducted at a 0.05 level of significance and the test statistic resulting from the analysis was 1.23, the potential type of statistical error is Type II error.

A Type II error occurs when we fail to reject a false null hypothesis, meaning that we conclude there is no significant difference or effect when there actually is one.

To answer the second question, we can perform a one-sample t-test to test the claim that the mean GPA for Psychology students at a certain college is less than 3.2.

The hypotheses are:

H₀: μ = 3.2

Ha: μ < 3.2

where μ is the population mean GPA.

We can use the t-statistic formula to calculate the test statistic:

t = (x - μ) / (s / √n)

where, x is the sample mean GPA, s is the sample standard deviation, n is the sample size, and μ is the hypothesized population mean.

Substituting the given values, we get:

t = (3.1 - 3.2) / (0.35 / √49)

t = -0.10 / 0.05

t = -2.00

Therefore, the value of the test statistic used to test the claim is -2.00.

Since this is a one-tailed test with a significance level of 0.05, we compare the t-statistic to the critical t-value from a t-table with 48 degrees of freedom.

At a significance level of 0.05 and 48 degrees of freedom, the critical t-value is -1.677.

Since the calculated t-statistic (-2.00) is less than the critical t-value (-1.677), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean GPA for Psychology students at the college is less than 3.2.

To calculate the p-value of the test, we can perform a one-sample t-test using the formula:

t = (x - μ) / (s / √n)

where x is the sample mean GPA, μ is the hypothesized population mean GPA, s is the sample standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (3.1 - 3.2) / (0.35 / √49)

t = -0.10 / 0.05

t = -2.00

The degrees of freedom for this test is 49 - 1 = 48.

Using a t-distribution table or calculator, we can find the probability of getting a t-value as extreme as -2.00 or more extreme under the null hypothesis.

Since this is a two-sided test, we need to find the area in both tails beyond |t| = 2.00. The p-value is the sum of these two areas.

Looking up the t-distribution table with 48 degrees of freedom, we find that the area beyond -2.00 is 0.0257, and the area beyond 2.00 is also 0.0257. So the p-value is:

p-value = 0.0257 + 0.0257

p-value = 0.0514

Rounding to three decimal places, the p-value of the test is 0.051.

Therefore, at a significance level of 0.05, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to support the claim that the mean GPA for Psychology students at the college is equal to 3.2.

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Answer: To find the explicit formula for the geometric sequence with the recursive formula an = 2an-1 and a1 = 1/8, we can use the following steps:

First, we can write out the first few terms of the sequence using the recursive formula:

a1 = 1/8

a2 = 2a1 = 2/8 = 1/4

a3 = 2a2 = 2/4 = 1/2

a4 = 2a3 = 2/2 = 1

a5 = 2a4 = 2

We can see that the common ratio between any two consecutive terms is 2, so we can write:

a2/a1 = 2

a3/a2 = 2

a4/a3 = 2

a5/a4 = 2

In general, we can write the ratio of any two consecutive terms as:

an/an-1 = 2

We can use this to find an expression for an in terms of a1:

a2/a1 = 2

a2 = 2a1

a3/a2 = 2

a3 = 2a2 = 2(2a1) = 4a1

a4/a3 = 2

a4 = 2a3 = 2(4a1) = 8a1

a5/a4 = 2

a5 = 2a4 = 2(8a1) = 16a1

In general, we can write:

an = 2^(n-1) * a1

Substituting a1 = 1/8, we get:

an = 2^(n-1) * (1/8) = 1/(2^(8-n))

Therefore, the explicit formula for the geometric sequence is:

an = 1/(2^(8-n))

Step-by-step explanation:

The cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).

A spherical οr elliptical cοοrdinate system knοwn as the geοgraphic cοοrdinate system is used tο measure and transmit pοsitiοns οn Earth as latitude and lοngitude.

First, we can find the distance between pοints Y and q, which will be the same as the distance between pοints 5 and B since they are οppοsite sides οf the parallelοgram:

Distance Yq = \(\sqrt{[(10-8)^2 + (5-10)^2] }\)

Distance Yq = \(\sqrt{8 + 25 }\)

Distance Yq =\(\sqrt{ 33}\)

Distance 5B = \(\sqrt{[(3-2)^2 + (2-3)^2] }\)

Distance 5B = \(\sqrt{2}\)

Since οppοsite sides are cοngruent, √33 = √2x, where x is the length οf the missing side οf the parallelοgram. Sοlving fοr x, we get:

x = (33/2)

Next, we can find the slοpe οf the line passing thrοugh pοints Y and q,

Slοpe Yq = (10-5)/(8-10) = -5/2

Slοpe B-missing vertex = -5/2

write the equatiοn οf the line passing thrοugh B and the missing vertex:

y - 2 = (-5/2)(x - 3)

Simplifying, we get:

y = (-5/2)x + (19/2)

Therefοre, the cοοrdinates οf the missing vertex are (19/2, x), where x = 2 + (33/2) = 19.5.

Sο the cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).

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The equilibrium price is $0 and the equilibrium quantity is 5 units.

To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied and solve for the equilibrium values.

Setting Q_d = Q_s, we can equate the equations for demand and supply:

-2Q - 2Q_d = -5 + 3Q_s

Since we know that Q_d = Q_s, we can substitute Q_s for Q_d:

-2Q - 2Q_s = -5 + 3Q_s

Now, let's solve for Q_s:

-2Q - 2Q_s = -5 + 3Q_s

Combine like terms:

-2Q - 2Q_s = 3Q_s - 5

Add 2Q_s to both sides:

-2Q = 5Q_s - 5

Add 2Q to both sides:

5Q_s - 2Q = 5

Factor out Q_s:

Q_s(5 - 2) = 5

Q_s(3) = 5

Q_s = 5/3

Now that we have the value for Q_s, we can substitute it back into either the demand or supply equation to find the equilibrium price. Let's use the supply equation:

P = -5 + 3Q_s

P = -5 + 3(5/3)

P = -5 + 5

P = 0

Therefore, the equilibrium price is $0 and the equilibrium quantity is 5 units.

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Answer:

c. 1.5 hours

Step-by-step explanation:

12x1.5=18

8x1.5=12

12+18=30

Answer:

1.5

Step-by-step explanation:

i took the test

Answer:

Well, if we consider \(r\) as y and \(q\) as x.

Step-by-step explanation:

So, typically, a linear function is either represented using function notation

\(f(x)=mx+b\)

Or in slope-intercept form

\(y=mx+b\)

This question is oddly using the variables r and q in place of y and x. If we replace them to be y and x, it will be a linear equation (because the slope is constantly changing).

But, if you aren't allowed to replace r and q to be y and x, then it isn't a linear function.

Answer: Yes

Step-by-step explanation: 6x24=144x2=228

As per the given condition, by the end of the second day they shipped 288 orders which implies that the condition has been met.

Given that,
To meet its production orders, the warehouse of Basic Office Supplies has to pack and ship 6 orders every hour. The warehouse run 24 hours per day. If the warehouse reports that they have packed and shipped 288 orders by the end of the second day, are they meeting their goal of 6 orders every hour is to be determined.

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,
Rate of doing work per hour = 6 orders / hours,
in 2 day there are 2(24) = 48 hours,
number of orders that must be shipped in 48 hours = 48 (6) = 288 orders,
As of the statment, the warehouse reports that they have packed and shipped 288 orders by the end of the second day.

Thus, as per the given condition, by the end of the second day, they shipped 288 orders which implies that the condition has been met.

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Answer:

74 degrees

Step-by-step explanation:

180-59-47=74

C. The image shows two right triangles with one pair of congruent leg and congruent hypotenuse. Therefore, the congruence is HL.

D. This shows two right triangles that share one side (a leg) and have the other leg also congruent to each other. Therefore, their congruence is LL and SAS (leg, right angle, leg).

E. This shows two triangles with a pair of congruent sides, a pair of congruent angles, and they have a common side, therefore congruent since they are the same.

So, their congruence is SAS.

F. This shows two right triangles sharing the same hypotenuse, and with a pair of congruent angles. Therefore, their congruence is HA.

G. This shows two right triangles with congruent hypotenuses, one congruent pair of legs, and two congruent pairs of angles (if we include the right angle).

So, their congruence is HA and HL.

H. The two triangles here have a right angle, a pair of congruent sides, and a pair of angles that are opposite by vertex, so they are also congruent angles.

Therefore, their congruence is ASA.

Answer:

Beach and Mountains = 482

Not mountains and Beach = 256

Mountains and Not Beach = 124

Not mountains and Not Beach = 15

Answer:

According to Venn diagram we have:

The table content would be:

                             | Mountains | Not Mountains

Beach                   |       482      |      256            

Not Beach            |       124       |       15              

Step-by-step explanation:

yes, in a similar way as division is a shortcut for repeated subtraction.

you do know, that you normally have to add the points win in a game, right ?

so, your score grows by 200 points each time you score.

that means

200

200

200

...

200

what do you think you do to get the total ? you add all the points.

you don't multiply them, because e.h 200×200 would be the shortcut of adding 200 for 200 times.

but you did not have 200 hits, you only got 12 hits.

so, you either do the effort of adding 200 12 times, or you simply multiply 200 by 12 (as this is the mentioned shortcut).

and you don't just add 12 to 200. that would give you only 212. and you did not earn 12 points to add. you earned 12 times 200 points to add.

that is how multiplication works and helps with additions.

Answer:

its yes

bc yeah just......do it

Step-by-step explanation:

here,

1o

so X is equal to 10

Answer:

1 : 4

Step-by-step explanation:

Remember, your units have to match, so

3 in : 1 ft

doesn't look right, change 1 ft to 12 in.

3 in : 12 in

reduce by 3

1 : 4

Answer:

this is a negative association

Step-by-step explanation:

Answer

3.7 or approximately 4 gallons

Step-by-step explanation:

7x2=14 total liters.

3.78 liters=1 gallon

14/3.78= 3.7 gallons

The half of the time that Arnold skied without falling is 712 as 2 x 356=712>223 .

Inequality is a mathematical statement that illustrates the connection between two expressions by using the inequality symbol. The phrases on both sides of an inequality sign are distinct. It indicates that the left expression should be larger or smaller than the right expression, or vice versa. When the link between two algebraic expressions is expressed using inequality symbols, literal inequalities arise.

The discrepancy represents the incident in which Kelvin skied for more than twice as long as anybody else in his family:

2f < 223

Here 223 is the time for Kelvin.

Check for Lori as follows:

2f < 223

2 x 55=110 < 223

Kelvin skied without falling more than twice as long as Lori.

Check for Vanessa as follows:

2f < 223

2 x 265=530>223

Check for Arnold as follows:

2f < 223

2 x 356=712>223

Kelvin skied without falling less than twice as long as Arnold.

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Complete question:

Kelvin wants to know whether he skied without falling more than twice as long as anyone else in his family. His dad tells him that he can check by using the inequality 2f < 223, where f is the time skied in seconds for each person. Plug the values for the time skied by each person into the inequality to find the answer.

Lori 55

Vanessa 265

Devon 172

Celia 112

Arnold 356

The proportional relationship connecting the circumference of the circle and the length of its radius is:

\(C = kr\)

\(y = kx\)

In this problem:

Hence, the formula is:

\(C = kr\)

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To calculate the sample variance for the given data, we need to find the average of the squared differences between each data point and the mean.

The sample standard deviation is the square root of the variance, and the range is the difference between the maximum and minimum values.Step 1: To calculate the sample variance, we start by finding the mean (average) of the data. Adding up all the values and dividing by the number of data points, we get (-11 + 6 + 5 + 10 + 14) / 5 = 2.8. Next, we find the squared differences between each data point and the mean, and then calculate their average. The squared differences are (-11 - 2.8)^2, (6 - 2.8)^2, (5 - 2.8)^2, (10 - 2.8)^2, and (14 - 2.8)^2. The sum of these squared differences is 632.8. Dividing this sum by the number of data points minus one (n - 1) gives us the sample variance. In this case, the variance is 632.8 / 4 = 158.2, rounded to one decimal place.

Step 2: The sample standard deviation is the square root of the variance. Taking the square root of 158.2, we get the standard deviation: √158.2 ≈ 12.6, rounded to one decimal place. This represents the dispersion or spread of the data points around the mean.

Step 3: The range is calculated by finding the difference between the maximum and minimum values in the dataset. In this case, the maximum value is 14, and the minimum value is -11. Therefore, the range is 14 - (-11) = 25. The range provides a measure of the spread of the data from the lowest to the highest value, indicating the total span of the dataset. In summary, the sample variance is approximately 158.2, the sample standard deviation is approximately 12.6, and the range is 25 for the given data.

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Answer:

I don't understand the question what is the quarter????

When multiplying or dividing a number by 1,000, it is the same as moving the decimal point three places to the right or left, respectively.

When multiplying a number by 1,000, it is the same as moving the decimal point three places to the right. This can be represented through the formula x * 1000 = x/1000. For example, if the number is 5, then 5 * 1000 = 5,000. This is the same as moving the decimal point three places to the right of 5, which results in 5.000. The same concept can be applied when dividing a number by 1,000. For example, if the number is 5,000, then 5,000 / 1000 = 5. This is the same as moving the decimal point three places to the left of 5,000, which results in 5.000. Therefore, when multiplying or dividing a number by 1,000, it is the same as moving the decimal point three places to the right or left, respectively.

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