2(x - 2) = -2

solve for x.

Answer:

68 degrees

Step-by-step explanation:

We are given measurements of JFG and GFL already! Because of this, angle JFL will just be the sum of those two

36 + 32 =

68 degrees

So, JFL has a measure of 68 degrees

Answer: 68degrees

Step-by-step explanation:

Add both of the other angle measures to get angle JFL

The linear system of equation y = x+2 and 6x = 4y+10 has only one solution.

The linear equation is y = x+2 and 6x = 4y+10

Now we solve the equations by substitution:

Using the value of y from the first equation and substituting in the second equation we get:

6x = 4y + 10

6x = 4(x+2)+10

or, 6x-4x = 8 + 10

or, 2x = 18

or, x = 9

at x=9 , y =11

Hence solution is (9,11) which represents the point of intersection of the two lines.

The phrase "solution of a linear equation" refers to the set of variable values in a linear equation that results in all possible solutions. Linear equations use unknown quantities as one or more variables to simulate real-world problems.

The intersection or meeting points of the lines or planes used to represent the linear equations are referred to as the solutions. The solution set is the collection of values for each variable in a system of linear equations.

Disclaimer: the complete question is :

How many solutions does this linear system have y = x+2 and 6x = 4y+10 have?

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To simplify the process of expanding a binomial of the type (a+b) n (a + b) n, use Pascal's triangle. The same numbered row in Pascal's triangle will match the power of n that the binomial is being raised to.

A triangular array of binomial coefficients known as Pascal's triangle can be found in algebra, combinatorics, and probability theory. Even though other mathematicians studied it centuries before him in India, Persia, China, Germany, and Italy, it is called after the French mathematician Blaise Pascal in a large portion of the Western world. Traditionally, the rows of Pascal's triangle are listed from row =0 at the top (the 0th row). Each row's entries are numbered starting at k=0 on the left and are often staggered in relation to the numbers in the next rows. The triangle could be created in the manner shown below: The top row of the table, row 0, contains one unique nonzero entry.

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Total investment in the sinking fund compounded monthly will be $277.97

What is sinking fund?

A sinking fund may be a fund that an organization could place the money into from currently on to form their debt repayments easier. the foremost common example may be a bond fund employed by corporations to manage their debt.

Main body:

total money to accumulate = $46000

time = 9 years

rate = 9%

formula for sinking fund:

Contribution = Money to accumulate * (interest / ((interest + 1)compound frequency * period - 1))

investment = 46000((9/10) ^(12*8) - )

investment to be made = $277.97

Hence contribution every month is $277.97

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Answer: x=1

Step-by-step explanation:

A 25-meter-long towing vessel is pulling barges forward. The ship is required to display a minimum of two white masthead lights at night.

A commercial vessel that is pulling, pushing, hauling aboard, or any mixture of pulling, pressing, or hauling alongside, is referred to as a towing vessel.

Thus, a 25-meter-long towing vessel is pulling barges forward. The ship is required to display a minimum of two white masthead lights at night.

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The answer of the equation 8(x-3) +7=2x(4-17) is x=1/2.

An equation is a statement that says that the value of two mathematical expressions is equal i.e., it is a mathematical sentence that has two equal sides separated by an equal sign.

We have the equation : 8(x-3) +7=2x(4-17)

Here we are not given Lin's solution so we can not find the error in her solution but we will solve this equation and find the value of x.

            8(x-3) +7= 2x (4-17)    

      ⇒  8x - 24 +7 = 2x(-13)

      ⇒  8x -17= -26x

      ⇒  34x = 17

      ⇒  x= 17/34

      ⇒ x =1/2.

The solution of the above equation is x= 1/2.

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The  inequality is Amount A= 15.5 x where x>6.

What is inequality?

An inequality compares two values ​​and indicates whether one is less than, greater than, or simply not equal to the other. In mathematics, the relationship between two expressions or values ​​that are not equal  is called an inequality.

Here ,Given , Cost of 1 gift basket = $15.50

Let the no. of gift basket be 'x'

=>  x > 6

Therefore, Amount of money She will spend

=> $15.50x where x > 6

=>A = 15.5x : x > 6

Therefore the inequality is Amount A= 15.5x where x>6.

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The greatest common divisor(GCD) of 15 and 45 is 15.

The greatest common divisor (GCD) of two or more integers, where at least one of them is not zero, is the largest positive integer that is a divisor of both numbers. For example, the GCD of 8 and 12 equals 4.

In the divisibility preorder relation, the GCD of a and b is their greatest positive common divisor. This signifies that a and b's common divisors are the same as their GCD divisors. The Euclidean algorithm or Euclid's lemma are widely used to establish this. This is the definition of "greatest" in the context of GCD generalizations.

Foe calculating the GCD of 15 and 45, we have to find the factors of 15 and 45.

Factors of 15:

1, 3, 5, 15

Factors of 45:

1, 3, 5, 9, 15, 45

From all these factors we have to choose the greatest factor that is exactly divisible by both 15 and 45,

So, the greatest factor is 15

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Answer:

Dolly Parton

Step-by-step explanation:

hopes this helps please mark brainliest

100% humidity is very common in many coastal zones, near rivers or   lakes or in your bathroom when you take a shower, and possibly in  Alaska as well as UAE.

Relative humidity:

                             Relative humidity is the ratio of the current absolute humidity to the highest possible absolute humidity (which depends on the current air temperature). A reading of 100 % relative humidity means that the air is totally saturated with water vapor and cannot hold any more, creating the possibility of rain. This doesn't mean that the relative humidity must be 100 percent in order for it to rain — it must be 100 percent where the clouds are forming, but the relative humidity near the ground could be much less.

0% humidity means there is an absence of water vapor in the air.

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The point is [-13,-7] when the actual numbers are all at least two units away from 4.

Given that,

To specify the interval (or pair of intervals) on the real number line, use absolute value notation. (Utilize the x variable.) actual numbers are all at least two units away from 4.

We know that,

We get,

|-4-x| = 3

-3 = -4-x = 3

7 = -x = 13

-13 = x = -7

Therefore, The point is [-13,-7] when the actual numbers are all at least two units away from 4.

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By solving the given word problem, the number of multiple-choice questions is 29 and short answers is 7.

In mathematics, word problem refers to a question including mathematical information written in ordinary language and requires students to apply their math knowledge to a real-life scenario. For the given case,

Let M be the number of multiple choice questions and N be the number of short answers.

As multiple-choice questions are worth 2 points each and the short answers are worth 6 points each and there is a total of 100 points:

2M + 6N = 100

The total number of questions on the test are 36:

M + N = 36

M = 36 – N

Substituting this into the first equation:

2(36 – N) + 6N = 100

72 – 2N + 6N = 100

4N = 100 – 72

4N = 28

N = 7

Substituting N in M = 36 – N

M = 36 – 7 = 29

Note: The question is incomplete. The complete question probably is: has a math test tomorrow with both multiple choice and short answer questions the multiple choice questions are worth 2 points apiece and the short answers are worth 6 points apiece. There is a total of 100 points in a test and 36 questions. How many questions of each type are on the test?

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The correct answer will be c. computing the average distance between every pair of observations between two clusters

What is Cluster Analysis?

Grouping "things" into "similar" groups is one of the most fundamental, straightforward, and frequently overlooked techniques (or processes) of comprehending and learning, on which cluster analysis is based. To create clusters of a particular type, this process uses a variety of different algorithms and techniques. It is also a component of data management in statistical analysis.

A multivariate data mining technique called cluster analysis aims to group things (such goods, responders, or other entities) based on a set of user-selected features or characteristics. Data compression, machine learning, pattern recognition, information retrieval, and other areas all use this essential and crucial phase of data mining, which is also a widely used method for statistical data analysis.

Here as per the given question, there are two clusters given.

Hence, computing the average distance between every pair of observations between two clusters.

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The parametric representation for torus is x = bcos ∅ + a cos acos ∅

y = b sin ∅ + a cos a sin ∅

z = a sin a where , 0 ≤ a ≤ 2π , 0 ≤ ∅ ≤ 2π

Parametric equation are the set of equations that express a set of quantities as explicit function of the numbers of independent variables known as parameter

Parametric representation are generally non unique so that the quantities may be expressed by the number of different parameterizations

According to the question,

The torus obtained by rotating about the z-axis the circle in the xz-plane with center (b, 0, 0) and radius a < b.

z = a sin a

y = |PQ| and x = |OP|

but , |OQ| = |OR| + |RQ| = b + a cos a

sin ∅ = |PQ| / |OQ|

So that , y = |OQ| sin ∅ = (b + a cos a ) sin ∅

Similarly ,

cos ∅ = |OP| / |OQ|

so that x =  (b + a cos a ) cos ∅

Hence , a parametric representation for a torus is

x = bcos ∅ + a cos acos ∅

y = b sin ∅ + a cos a sin ∅

z = a sin a

where , 0 ≤ a ≤ 2π , 0 ≤ ∅ ≤ 2π

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The answer is outlier. a value in a set of data that "lies outside" (is much smaller or greater than) the majority of the other values.

Any figure derived from your sample data is referred to as a sample statistic (or simply a statistic). The sample mean, median, sample SD, and percentiles are a few examples. A statistic is a random variable since it is based on information gained by random sampling, which is a random experiment.

A sample is a statistical term for a population that has been analytically subset. As a result of the usage of samples, investigations may be completed faster and with more manageable data.

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The amount of pages the Jorge's printer can in 3/4 hours print is 72 pages.

A printer is a device that accepts text and graphic output from a computer and transfers the information to paper.

Note:

Therefore,

Make P₂ the subject of the equation

Where:

From the question,

Given:

Substitute these values into equation 2

Hence, the amount of pages it can print is 72 pages.

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Answer: ?

Step-by-step explanation: Is that the whole question? I don't really understand the question.

The meaning to translate a triangle type of transformation that takes each point in a figure and slides it the same distance in the same direction.

Lets take an example:

ΔXYZ with coordinates,

X(-9,6) , Y(2,3) AND Z(-2,-8).

Translation:

X - 3 units in x direction

Y - 3 units in x direction

Z - 3 units in x direction

After translation:

New coordinates are represented in yellow dots in the figure uploaded.

X(-9,6)→X(-9+3,6)→X(-6,6)

Y(2,3)→Y(2+3,3)→Y(5,3)

Z(-2,-8)→Z(-2+3,-8)→Z(1,-8)

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The hourly pay before the increase for marta and khalid is 21 and 17.5.

Given:

the ratio of martas hourly pay to khalids hourly pay is 6:5 both marta and Khalid get an increase of 1.50 in their hourly pay The ratio of Martas hourly pay to Khalid hourly pay after this increase is 13:11

Let x and y be the hourly pay before increase

x/y = 6/5

x = 6/5*y

x + 1.50 / y + 1.50 = 13/11

11(x+1.50) = 13(y+1.50)

11x + 16.5 = 13y + 19.5

11(6/5*y) = 13y + 19.5 - 16.5

66y/5 = 13y + 3.5

66y - 13*5y / 5 = 3.5

66y - 65y = 17.5

y = 17.5

x = 6/5*17.5

= 105/5

x = 21

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The angle of elevation from the boat to the cliff top is approximately 31 degrees.

The  boat is 150 meters from the base of a cliff that is 90 meters high. The angle of elevation from the boat to the cliff top can be calculated as follows:

The situation form a right angle triangle. The angle of elevation can be found using trigonometric ratios.

tan ∅ = opposite / adjacent

where

∅ = angle of elevation

Hence,

tan ∅ = 90 / 150

∅ = tan ⁻¹ 0.6

∅ = 30.9637565321

∅ ≈ 31 degrees

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The average book owned by other people is 112 which is greater than Michael's.

What is average?

In standard language, a mean could be a single range taken as representative of a listing of numbers, typically the total of the numbers divided by what numbers are within the list.

Main Body:

Books owned by Michael = 97

Average book owned by people = sum of all books / total people

avg. book owned = (225+142+29+103+61)/5

avg book owned by people = 560/5

                                               = 112

Hence books owned by avg people is 112.

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The next number in sequence is 185.

What is arithmetic progression?

A sequence within which each term is made by adding or subtracting an explicit variety to the preceding variety is an arithmetic sequence.

Main body:

Step 1:

Find the pattern and write the recursive formula: [tex]\left \{ {{a_{n+1} =a_{n} +12} \atop {a_{n+1} =a_{n} +13}} \right.[/tex]

as the sequence is 123,135,148,160,173..

so 1st term 12 is added in 2nd term 13 is added

so after 173 , 12 will be added ,

173+12 = 185

hence, the next number in sequence is 185.

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The Mizzi Corporation ha created a demand function for one of it wrench et. The expense function a a function in term of p is E=−2,254p+81,294.

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Each base angle 72 degrees  is the measure of the vertex angle of an isosceles triangle if the measure of the base angle is 36

For any triangle, the three angles always add to 180 degrees.

In an isosceles triangle, the base angles are the same measure. For now we don't know what they are, so let's call them x. The vertex angle is 36.

Adding the three angles (x, x, and 36) and setting that equal to 180 will help us find the value of x.

x+x+36 = 180

2x+36 = 180

2x+36-36 = 180-36 .... subtract 36 from both sides

2x = 144

2x/2 = 144/2 .... divide both sides by 2

x = 72

This triangle has two base angles of 72 each and the vertex angle of 36. As a check, the three angles should add up to 180

72+72+36 = 144+36 = 180

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Using Taxable income formula,

a) $22,200

b) Non- business loss = $12,200 ; business loss

= $10,000

c) $10,000

We have given that

Julie's taxpayer data as following

Net loss = $40,000

Income wage = $30,000

standard deduction = $12,200

a)Computation of taxable income of Julie for 2020

total taxable income is sum of wager , net loss and standard deduction

= - $40,000 + $30,000 - $12,200

= - $22,200

negative sign indicates loss

b) business wages = $30,000

net loss = $40,000

business loss = $30,000- $40,000

= -$10,000

Non- business loss = $12,200 = standard deduction.

c) Julie's 2019 NOL ( net operating loss) is just equal to business net loss

= $30,000- $40,000 = - $10,000

Hence, we get all required answers about Julie's loss.

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The length of the RS is 25 units, using SAS Congruence.

What is SAS Congruence?

Congruent refers to figures that are equal in all respects, particularly in terms of size and shape. Congruence is a mathematical concept that describes the relationship between two congruent figures. The relationship between two congruent figures is referred to as congruence. Let's now talk about the triangle SAS congruence. The phrase SAS congruence often referred to as Side Angle Side congruence, is used to define the relationship between two congruent figures. To fully grasp the significance of SAS, let's talk in-depth about the triangle SAS congruence.

We have specified that TQ is 18 units in length.

TQ = RT as a result,

and 2x + 10 = 18

2x = 18 - 10

2x = 8x2 = 4 units.

Now that both triangles satisfy the Right Angled Hypotenuse Side criteria or SAS concurrency criteria,

RS = QS.

= 9x - 11

= 9(4) - 11

= 25 units.

Hence, the length of the RS is 25 units, using SAS Congruence.

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The probability we use is empirical probability.

The given statement,

The relative frequency of an event is used to calculate what type of probability,

Here, we use empirical probability.

The relative frequency of an event is closely related to an empirical probability, also known as an experimental probability. Empirical probability bases its estimation of the likelihood that a specific result will recur on the number of instances of that outcome within a sample set. The chance of "event X" occurring will be determined by how many times it occurs out of 100 trials.

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The sequence is convergent and the sum of the geometric series is 3/2=1.5.

The geometric series was significant in the early development of calculus, is utilized throughout mathematics, and can serve as an introduction to commonly used mathematical tools such as the Taylor series, complex Fourier series, and matrix exponential.

The name geometric series implies that each phrase is the geometric mean of its two nearby terms, in the same way that the word arithmetic series implies that each term.

Given the geometric series 1+1/3+1/9+1/27+...we must verify the value of its common ratio to determine whether the geometric series is convergent or divergent. The value of a geometric series common ratio is used to determine whether it is convergent or divergent.

If |r| <1, the series is convergent.

If |r| >1, the series is divergent.

The common ratio is r.

The common ratio r = (1/3)/1 = (1/9)/(1/3) = (1/27)/(1/9)=1/3 is derived from the given series.

Because r = 1/3, which is smaller than one, the series is convergent.

Because the geometric series tends to infinity, we will apply the formula for calculating a geometric series sum to infinity to get its sum.

The first term = 1

S = a/1-r

a is the first term = 1

r is the common ratio = 1/3

S = 1/1-(1/3)

S= 1/(2/3)

S= 3/2

S=1.5

The sum of the geometric series is 3/2=1.5

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If it takes 6 minutes to set up an experiment using barium-122, then  12.5g of  barium-122 will be left when the experiment begins

Half life of barium-122 = 2 min

Mass of sample = 100 g

Mass of barium remain after 6 min = ?

Number of half lives = Time elapsed / half life

Number of half lives = 6 min/ 2 min

Number of half lives = 3

At time zero = 100 g

At 1st half life = 100 g/2 = 50 g

At 2nd half life = 50 g/2 = 25 g

At 3rd half life = 25 g/2 = 12.5 g

Therefore, If it takes 6 minutes to set up an experiment using barium-122, then  12.5g of  barium-122 will be left when the experiment begins.

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