help asappp will give brainliest !!!!!!!!!!!!

A variant expression is a mathematical expression used to analyze the progress of a recursive function and ensure its termination. To guarantee that a recursive function terminates, a variant expression must have two essential properties which are Boundedness and monotonicity.

1. Boundedness: A variant expression must be bounded, which means that it has an upper or lower limit. This limit is often a non-negative integer value, such as 0. The boundedness property ensures that the variant expression cannot grow indefinitely, which would lead to non-termination of the recursive function.

2. Monotonicity: A variant expression must be monotonically decreasing, meaning that its value strictly decreases with each recursive call. Monotonicity ensures that the variant expression is always moving closer to the bound, eventually reaching the limit and causing the function to terminate.

To guarantee the termination of a recursive function, follow these steps:

Step 1: Identify a suitable variant expression for the function. The expression should be related to the problem size or input parameters of the function and should reflect the progress towards the function's termination.

Step 2: Verify the boundedness property of the variant expression. Ensure that the expression has an upper or lower limit, typically a non-negative integer, which it cannot exceed.

Step 3: Verify the monotonicity property of the variant expression. Check that the expression's value strictly decreases with each recursive call, moving closer to the bound.

Step 4: Ensure that the recursive function terminates when the variant expression reaches the bound. This condition is usually implemented as the base case of the function, which prevents further recursive calls and initiates the return process.

In summary, a variant expression must have boundedness and monotonicity properties to guarantee that a recursive function terminates. By verifying these properties and incorporating them into the recursive function, you can ensure that the function will reach its termination condition and not result in infinite recursion.

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Step-by-step explanation:

For denominator:

x²-5x -24 = x² -(8-3)x -24

= x² -8x+3x-24 = x(x-8) +3(x-8)

Taking common (x-8): = (x-8)(x+3)

So option d is accurate.

And for numerator, 7x+56 =7(x+8)

So, option a is accurate.

Because there are no outliers in the data set, the mean is the best indicator of the centre in this particular situation.

An outlier in statistics is an incident that deviates greatly from the predicted range of values for a given dataset. There are several different reasons why outliers can happen, including measurement errors, data entry issues, or genuinely odd numbers in the population getting measured. If they are not handled properly, outliers can significantly affect statistical analysis and skew results. For instance, outliers have a big impact on measurements of variability like the standard deviation as well as central tendency indicators like the mean. Consequently, before conducting statistical analysis on a dataset, it is crucial to find and assess any outliers.

given

There are no extreme outlier numbers in this instance, and the data seems to be rather symmetrical around the core value. As a result, the mean would be a suitable gauge of the centre.

The mean would be impacted by any values that were significantly out of the ordinary, such as a book that cost $100, and might not accurately reflect the data's mean if there were one or more of these values.

Since it is unaffected by extreme values, the median would be a better indicator of the centre in these situations.

Because there are no outliers in the data set, the mean is the best indicator of the centre in this particular situation.

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The number of intervals that feel that America is doing about the right amount to protect the environment is 0.487, and 0.551 intervals

To find the number of adults who feel that America is doing about the right amount to protect the environment, we need to use the confidence interval proportion formula

CI = p ± Zα/2 * √(p * (1-p)/n

where:

p = sample proportion = 519/1000 = 0.519

n = sample size = 1000

Zα/2 = the critical value for the desired confidence level = 1.96

By substuting the values, we get:

CI = 0.519 ± 1.96 * √(0.519 * (1-0.519) / 1000)

= 0.519 ± 0.032

= (0.487, 0.551)

Therefore,  (0.487, 0.551) interval feel that America is doing about the right amount to protect the environment.

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Answer:

area is 2072 [tex]yd^{2}[/tex]  perimeter is 204 yd

Step-by-step explanation:

to find the area use the formula A=L*W (the units is then multiplied together as well which gives you square yards

to find perimeter you just add up all the sides. So you have 2 sides of 74 yd and 2 sides of 28 yd so you have (74+74+28+28)= 204

After 3 hours, approximately 318.5 mg of the painkiller remains in the body.

The function for the amount of painkiller remaining in the body after h hours can be described :

A(h) = A0 * [tex]e^{-kt}[/tex]

Where:

A(h) is the amount of painkiller remaining in the body after h hours

A0 is the initial amount of painkiller (in this case, 450 mg)

k is the decay constant, which can be determined from the half-life of the painkiller using the formula

k = ln(2)/t1/2, where t1/2 is the half-life

t is the time elapsed in hours

Using the given half-life of 8 hours, we can calculate the decay constant:

k = ln(2)/8 = 0.0866

So the function for the amount of painkiller remaining after h hours is:

A(h) = 450 * [tex]e^{-0.0866h}[/tex]

To find out how much remains after 3 hours, we simply plug in h=3:

A(3) = 450 * )[tex]e^{-0.0866*3}[/tex] = 318.5 mg (rounded to one decimal place)

Therefore, after 3 hours, approximately 318.5 mg of the painkiller remains in the body.

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Answer:

the answer is B) 1/2, 3.

Step-by-step explanation:

To solve the system of linear equations by graphing, we need to graph both lines and find the point where they intersect. This point will be the solution to the system.

The equation y = -1/2x+2 has a y-intercept of 2 and a slope of -1/2. We can plot this on a graph by starting at the y-intercept (0, 2) and then going down 1 unit and to the right 2 units to get another point on the line. We can then draw a straight line through these two points.

The equation y=1/2x-1 has a y-intercept of -1 and a slope of 1/2. We can plot this on the same graph by starting at the y-intercept (0, -1) and then going up 1 unit and to the right 2 units to get another point on the line. We can then draw a straight line through these two points.

The point where these two lines intersect is the solution to the system of equations. From the graph, we can see that this point is approximately (1/2, 3).

the answer is B) 1/2, 3.

To solve the system of linear equations by graphing, we need to plot the lines represented by the equations on the same coordinate plane and find the point of intersection.

|

3 | .

| \

2 | \

| \

1 | . \

| \

0 |_____________

0 1 2 3 4

The probability that there are 3 people between x and y is 1/659470.

The total number of ways in which x and y can stand in a line with 10 other people is (12C2) = 66.

To find the number of ways in which there are exactly 3 people between x and y, we can treat x and y as a single entity and arrange them along with the 10 other people in 8 available spots in the line. This can be done in (8C1) = 8 ways.

Within this arrangement, there are 3 spots where x and y can be placed with 3 people between them,

Once x and y have been placed in one of these 3 spots, the remaining people can be arranged in the remaining spots in

10!/(10-8)! = 1814400 ways.

So the number of ways in which there are exactly 3 people between x and y is,

8 * 3 * 1814400 = 43545600.

Therefore, the probability that there are 3 people between x and y is,

43545600/66 = 659469.69 (rounded to 2 decimal places)

So, the probability is approximately 1 in 659470 or 1/659470.

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The total energy value from these stated amounts is 214 calories.

To calculate the total energy value (in calories) from the stated amounts of protein, carbohydrates, fat, and alcohol, we can follow these steps:
1. Protein: Multiply the amount of protein (8 grams) by the energy value of protein (4 calories/gram).
2. Carbohydrates: Multiply the amount of carbohydrates (25 grams) by the energy value of carbohydrates (4 calories/gram).
3. Fat: Multiply the amount of fat (6 grams) by the energy value of fat (9 calories/gram).
4. Alcohol: Multiply the amount of alcohol (4 grams) by the energy value of alcohol (7 calories/gram).
5. Add the resulting values from steps 1-4 to find the total energy value (in calories).
Applying these steps:
1. Protein: 8 grams * 4 calories/gram = 32 calories
2. Carbohydrates: 25 grams * 4 calories/gram = 100 calories
3. Fat: 6 grams * 9 calories/gram = 54 calories
4. Alcohol: 4 grams * 7 calories/gram = 28 calories
5. Total energy value: 32 + 100 + 54 + 28 = 214 calories.

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Option D. between 6 and 9 is correct.

Since we don't have the specific function, we cannot definitively determine which interval shows the function is increasing.

However, based on the information given, we can say that the function increases within one of these intervals.

It is important to know the specific function to identify the correct interval.

To determine the correct answer, we first need to understand the terms "domain," "function," and "increasing."
- Domain: The set of all possible input values (x-values) for a given function.
- Function: A mathematical relationship between input (x) and output (y) values, often represented as y = f(x).
- Increasing: A function is increasing when the output (y-value) increases as the input (x-value) increases.
Now, let's analyze the given options:
A. between 0 and 6
B. between 3 and 9
C. between 3 and 6
D. between 6 and 9

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Question:

Step-by-step explanation:

Area of each of the ends    pi r^2   there are TWO

  TWO x  pi ( 7^2)   = 98 pi     in^2

SIDE area is   circumference ( pi * d )   *   height ( 2)

        Side =  pi ( 7x2) * 2   = 28 pi   in^2

Total  =  98 pi  +  28 pi  =  126 pi     in^2      <=====exact answer

                                       = 395.84    in^2      <===== approx answer

If average size of bass caught in strawberry lake is normally distributed, then the probability that the size of fish we caught is more than 15 inches is 0.3085.

The mean-size of the bass caught is (μ) = 13 inches,

The standard-deviation of the bass caught is (σ) = 4 inches,

we have to find probability that size of fish we caught is more than 15 inches.

We will use the z-score formula:

⇒ z = (x - μ)/σ,

So,

⇒ z = (15 - 13)/4 = 0.5,

Now, we need to find the probability of getting a z-score of 0.5 or higher. We use a standard normal distribution table to find this probability.

⇒ P(Z > 0.5) = 0.3085

Therefore, the required probability is 0.3085 or 30.85%.

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a. The null hypothesis 2 is correct.

b. 0.1346 is the -value for your hypothesis test in part (a).

c. We lack sufficient data to draw the conclusion that Tulsa's average household water rate differs considerably from the average residential water rate paid by U.S. public utilities.

d.  The critical value is  -1.5277.

a. The hypotheses can be formulated as follows:

Null Hypothesis: The population mean rate per ccf of residential water charged by U.S. public utilities is equal to the rate charged by Tulsa (μ = [tex]\mu_0[/tex]).

Alternative Hypothesis: The population mean rate per ccf of residential water charged by U.S. public utilities differs from the rate charged by Tulsa (μ ≠ [tex]\mu_0[/tex]).

The correct null hypothesis is 2.

b. To test the hypotheses, we can use a two-sided t-test with a significance level of α = 0.05.

Using the data in the "residential water" file, we can calculate the test statistic and p-value as follows:

Sample mean = 2.358

Sample standard deviation = 1.011

Sample size = 50

Hypothesized population mean = 2.44 (the rate charged by Tulsa)

t = (2.358 - 2.44) / (1.011 / [tex]\sqrt{(50)}[/tex]) = -1.5277

Degrees of freedom = 50 - 1 = 49

Using a t-distribution table or calculator, the p-value for a two-sided test with 49 degrees of freedom and a t-statistic of -1.5277 is approximately 0.1346.

The p-value for the hypothesis test is 0.1346.

c. At α = 0.05, the critical value for a two-sided t-test with 49 degrees of freedom is ± 2.0096.

Since the calculated t-statistic (-1.5277) falls within the range of the critical values, we cannot reject the null hypothesis.

Therefore, we do not have enough evidence to conclude that the mean rate per ccf of residential water charged by U.S. public utilities differs significantly from the rate charged by Tulsa.

d. Using the critical value approach, we would compare the calculated t-statistic (-1.5277) with the critical values from the t-distribution table.

At α = 0.05 and 49 degrees of freedom, the critical values are ±2.0096.

Since the calculated t-statistic (-1.5277) falls within the range of the critical values, we cannot reject the null hypothesis.

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Answer: (12a + b)(12a - b)

Step-by-step explanation:

1. Begin by writing the expression in expanded form: 12a - b

2. Rewrite the expression as 12a + (-b)

3. Factor out 12a from the expression: 12a(1 + (-b))

4. Factor out 1 from the expression: (12a)(1 + (-b))

5. Rewrite (1 + (-b)) as (1 - b): (12a)(1 - b)

6. Rewrite (12a)(1 - b) as (12a + b)(12a - b): (12a + b)(12a - b)

The answer is decreases.

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations. For example, 3x² − 2xy + c is an algebraic expression.

The algebraic equation can be written in the many forms. It can be in one variable , two variable or even three or four variable. There are also many ways to put all into the equations.

So, as the question stated As x is increases, the value of the expression decreases.

Therefore, the answer is decreases.

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Answer:

$33.80

Step-by-step explanation:

If Noah gave away 2/7, that means that he still has 5/7

[tex]\frac{5}{7}[/tex] x [tex]\frac{4732}{1}[/tex] = [tex]\frac{23660}{7}[/tex] = 3380

Helping in the name of Jesus.

The amount that is left using a dollar sign and decimal point is $33.80.

Pennies saved by Noah are 4732 pennies.

He gave 2/7 of the pennies in the missionary offering.

The number of pennies he gave in missionary offerings is:

PENNIES = (2/7) × 4732

PENNIES = 1352

Hence, he gave 1352 pennies.

Therefore, he has left with:

LEFTOVER PENNIES = TOTAL PENNIES - PENNIES GIVEN

LEFTOVER PENNIES = 4732 - 1352

LEFTOVER PENNIES = 3380

Therefore, The amount that is left using a dollar sign and the decimal point is $33.80.

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The learner has misunderstood the concept of fractions, the misconception that the learner has is that the model they have provided does not represent a fraction.

Fractions are written using numerator (the number on top) and denominator (the number on bottom).

The model they have provided does not represent a fraction because fractions are used to compare two parts of a whole. In this model, there are only two parts, coloured dots and not coloured dots, and there is no whole to compare them to.

Therefore, the learner has misunderstood the concept of fractions and the model they have provided does not represent a fraction.

To make this model represent a fraction, it would need to represent two parts of a whole.

If the model had 12 dots and 6 were coloured, it could represent a fraction of 6/12 (or 1/2). This is because the 6 coloured dots would be 1 part of the whole which is 12 dots.

Therefore, the misconception that the learner has is that the model they have provided does not represent a fraction. The model only has two parts, coloured dots and not coloured dots.

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The misperception that the student has is that the model they have presented does not reflect a fraction; as a result, the learner has misinterpreted the idea of fractions.

When writing fractions, the denominator (the lower number) and the numerator are used. (the number on bottom).

Given that fractions are meant to compare two parts of a whole, the model they have presented does not reflect a fraction. There are only two components in this model: coloured dots and non-colored dots, and there is no whole to which they can be compared.

As a result, the learner misinterpreted the idea of fractions, and the example they gave does not accurately depict a fraction.

This model would have to depict two pieces of a whole in order to represent a fraction.

The model might represent a fraction of 6/12 (or 1/2) if it had 12 dots, of which 6 were coloured. This is because the six different colours would make up one part of the total of twelve dots.

Because of this, the learner believes that the offered model does not represent a fraction, which is a misunderstanding. The model consists of just two components: coloured dots and blank spaces.

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The area of the square whose diagonal length is 2√2 is 4 square units.

what is area of square?

In mathematics, the area is a measure of the size or extent of a two-dimensional figure or shape, typically measured in square units. It is the amount of space inside the boundary of a flat object, such as a triangle, rectangle, circle

In the given question,

The diagonal of a square divides it into two congruent right triangles, where the hypotenuse of each triangle is the diagonal of the square and the legs are the sides of the square.

Let the side length of the square be "s". Then, by the Pythagorean theorem, we have:

s² + s² = (2√2)²

Simplifying the right-hand side gives:

2s² = 8

Dividing both sides by 2 gives:

s² = 4

Taking the square root of both sides gives:

s = 2

Therefore, the area of the square is:

A = s² = 2² = 4

So the area of the square whose diagonal length is 2√2 is 4 square units.

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Answer:

x = -9

20 degrees

Step-by-step explanation:

The measure of a central angle is equal to the arc that it intercepts. The angle in the diagram is 139 + x while the arc is 130. Therefore, we can set them equal using an equation:

139 + x = 130

Subtracting 9 from both sides yields:

x = -9

For the second question, central angles are always twice inscribed angles. So a central angle of 40 degrees corresponds to a inscribed angle of 20 degrees

In circle geometry, the inscribed angle that intercepts the same arc as a central angle is half the measure of that central angle. Thus, if the central angle is 40 degrees, the inscribed angle will be 20 degrees.

In circle geometry, a central angle is an angle whose vertex is the center of the circle and whose sides are radii of the circle. An inscribed angle, on the other hand, is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the angle.

In this case, you are given a central angle of 40 degrees. According to the inscribed angle theorem, an inscribed angle that intercepts the same arc as a central angle is half the measure of the central angle. Therefore, an inscribed angle that intercepts the same arc as a 40-degree central angle would measure 20 degrees.

To summarize, the theorem states that the measure of the angle inscribed in a circle is half the measure of the central angle that intercepts the same arc. So if the central angle is 40 degrees, then the inscribed angle is 20 degrees.

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The speed of the other train is approximately 37 1/3 miles per hour.

What is the speed?

Speed is defined as the rate at which an object moves. It is a scalar quantity that refers to the distance traveled by an object per unit of time, without regard to the direction of motion.

Let the speed of the other train be x miles per hour.

The two trains are approaching each other, so their combined speed is (25 3/4 + x) miles per hour.

We know that they pass each other 4 1/2 hours after they start traveling, and that they were 252 miles apart when they started.

Using the formula distance = rate × time, we can set up the following equation:

252 = (25 3/4 + x) × 4 1/2

To simplify this equation, we can first convert 4 1/2 to an improper fraction:

4 1/2 = 9/2

Now we can distribute the 9/2 to the expression (25 3/4 + x):

252 = (25 3/4 + x) × 9/2

Expanding the right side of the equation, we get:

252 = (231/4 + 9/2x)

To solve for x, we can first subtract 231/4 from both sides:

252 - 231/4 = 9/2x

Multiplying both sides by 2/9, we get:

(504/9) × (2/9) = x

x = 112/3

Therefore, the speed of the other train is approximately 37 1/3 miles per hour.

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Answer:

Step-by-step explanation:

According to given information, the truck has 4.75 pounds of sand when it arrives at the yard.

What is distance?

Distance is a numerical description of how far apart objects or points are. It is a scalar quantity that is typically measured in units such as meters, kilometers, miles, etc. Distance is a fundamental concept in geometry, physics, and other fields of science and engineering.

The initial amount of sand the truck carried is 9.35 pounds.

The amount of sand the truck loses on the way is 4.6 pounds.

Therefore, the amount of sand the truck has when it arrives at the construction yard is:

9.35 - 4.6 = 4.75 pounds.

So the truck has 4.75 pounds of sand when it arrives at the yard.

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Answer: 3x - 2y - 6 = 0

Step-by-step explanation:

The equation would be on the line, so you would have to work it out through using x and y values.

When the beginning value or ending value is closing the set, a square bracket is used. A parenthesis is used to show that the beginning value or ending value is open. A parenthesis is always used with open intervals.

When we use an interval notation to describe sets of numbers, parentheses, and brackets have different meanings. Parentheses "(" and ")" describes an open interval, which means that the endpoints are not included in the set. For example, the interval (-3,5) includes all real numbers greater than -3 and less than 5, but it does not include -3 or 5 themselves. On the other hand, brackets "[" and "]" denote a closed interval, which means that the endpoints are included in the set. For example, the interval [-3,5] includes all real numbers greater than or equal to -3 and less than or equal to 5. If the endpoint is included in the set, use a bracket; if it is not, use a parenthesis.

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The loan is to be repaid in 5 equal payments over the next 5 years. If the lender charges a 9% interest rate, your yearly payment on the car would be 2,320.

To find your yearly payment on the car, follow these steps:

First, identify the loan amount, which is 8,000, and the interest rate, which is 9% or 0.09.

Calculate the yearly interest amount by multiplying the loan amount by the interest rate:

8,000 × 0.09 = 720.

Divide the total interest amount by the number of years to find the total interest over 5 years:

720 × 5 = 3,600.

Add the total interest to the loan amount to find the total amount to be repaid:

8,000 + 3,600 = 11,600.

Divide the total amount to be repaid by the number of years to find the yearly payment:

11,600 / 5 = 2,320.

So, your yearly payment on the car would be 2,320.

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The faster puppy takes 12 seconds to eat the bowl of kibble, and the slower puppy takes 12 + 24 = 36 seconds to eat the same bowl.

To solve the student question about how long it takes for each puppy to

eat the bowl of kibble individually, we can set up a rate equation.

Let x be the time it takes for the faster puppy to eat the bowl of kibble.

Then, the time it takes for the slower puppy is x + 24 seconds.

Since the two puppies can eat the bowl together in 9 seconds, their

combined rate is 1 bowl per 9 seconds.

The rate of each puppy eating individually is 1/x for the faster puppy and

1/(x+24) for the slower puppy.

Now, we can set up the equation for their combined rate:

1/x + 1/(x+24) = 1/9

To solve this equation, we need to find a common denominator, which is

x(x+24). We can then rewrite the equation as:

(x+24) + x = x(x+24)/9

Now, simplify the equation:

[tex]2x + 24 = x^2 + 24x / 9[/tex]

Next, multiply both sides by 9 to get rid of the denominator:

[tex]18x + 216 = x^2 + 24x[/tex]

Move all terms to one side:

[tex]x^2 + 6x - 216 = 0[/tex]

Now, factor the quadratic equation:

(x+18)(x-12) = 0

There are two solutions: x = -18 and x = 12. However, since time cannot

be negative, we only consider x = 12 seconds.

for the faster puppy.

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Answer: 1 4/8 or 1 1/2

Step-by-step explanation:

1 5/8

-1/8

5/8 - 1/8 = 4/8  

add 1.....  1 4/8

Given that Steve handed him a black king, the probability of Scott's second card being a red card is 13/25, or around 0.52.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

A conventional deck of playing cards has 52 cards, including two black kings. When Steve deals a black king to Scott, the deck has 51 cards, 26 of which are red.

We only need to analyse the likelihood of obtaining a red card on the second draw because we know Scott's initial card is a black king. There are 50 cards remaining in the deck, 26 of which are red. As a result, the likelihood that Scott's second card will be a red card is:

P(red card drawn on second draw) = 26/50 = 13/25

Given that Steve handed him a black king, the likelihood of Scott's second card being a red card is 13/25, or around 0.52.

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The similarity between <2 and <B is that both arcs have a 65° measure.

When two angles add up to 180 degrees, they are said to be each other's auxiliary angles.

For instance, since x + y = 180°, x and y are complementary angles to one another.

The triangle's angles are 50° and 65°.

50° and 65° are the angles on the path.

We are aware that a triangle's total number of angles is 180°. Consequently, the B measure is

50° + 65° + ∠B = 180°

∠B = 180° - (50° + 65°)

∠B = 65°

So, 65 degrees is the gauge of the B.

The total number of angles on the specified line will be due to the fact that all angles are extra angles, and will be 180 degrees.

∠2 + 50° + 65° = 180°

∠2 = = 65°

As a result, 65° is the measure of the 2.

As we can see, both arcs have a measure of 65 degrees.

Therefore, the relationship between 2 and B is that both angles have a value of 65°.

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