Find three consecutive even integers such that the sum of the smallest and the largest is 36.

To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.

The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.  

The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.

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Therefore , the solution of the given problem of complementary angles comes out to be 29° and 61° QED.

Two angles are considered complementary when their sum equals 90 degrees. Two angles are considered submissive when their sum equals 180 degrees. For example, the angles of 40 - 60 degrees complement one another. The difference between a supplementary angle and a supplementing angle is that a Triangle angle has two angles joined to produce a 90 degree angle. When two angles add up to 90 degrees, they are said to be complementary. Alternatively, the complementary angles result in a right angle (90 degrees).

Here,

Given :

Allow x to equal the complementary angle.

Given: x plus 32° the opposite angle

Recognized: Complementary angles sum to 90°

=>x + x + 32° = 90° (Adding the two angles) (Adding the two angles)

2x + 32° = 90° (adding the unknown factors) (adding the unknown variables)

=>2x = 90° - 32° (subtract 32 from both sides) (subtract 32 from both sides)

=> 2x = 58° (assess the right side) (evaluate the right side)

=>x = 29° (split both sides by 2) (divide both sides by 2) (One reply)

=> x + 32° = 61° (Add 32 to x) (Add 32 to x) (The other response)

There are two angles: 29° and 61° QED.

Therefore , the solution of the given problem of complementary angles comes out to be 29° and 61° QED.

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The complete question is "The measure of one angle is 32° greater than the measure of its complement. What are the measures of the angles?"

Answer:

42 inches squared

Step-by-step explanation:

6*7=42

Answer:

42

Step-by-step explanation:

Happy to help plz give brainlest!

Answer:

b=-27/2

Step-by-step explanation:

Answer:

27/2 or 13.5

Step-by-step explanation:

Yes, the sequence is geometric as it follows a pattern where each term is multiplied by a common ratio to get the next term. In this case, we can find the common ratio by dividing any term by its preceding term.

Let's choose the second and first terms:Common ratio = (second term) / (first term)= (-4) / (-2)= 2Now that we know the common ratio is 2, we can use it to find any term in the sequence. For example, to find the fourth term, we can multiply the third term (-16) by the common ratio:Fourth term = (third term) × (common ratio)= (-16) × (2)= -32Therefore, the fourth term of the sequence is -32. We can continue this pattern to find any other term in the sequence.

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Answer:

okkkkk

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Given that sec(t) = -2.475 and angle t is in Quadrant III, the other five trigonometric ratios are as follows: cos(t) ≈ 0.404, sin(t) ≈ -0.916, tan(t) ≈ 2.268, csc(t) ≈ -1.092, and cot(t) ≈ 0.441.

We are given that sec(t) = -2.475, which represents the reciprocal of the cosine of angle t. Since sec(t) is negative and angle t is in Quadrant III, we can deduce that the cosine of t is negative. To find cos(t), we can use the identity sec(t) = 1/cos(t) and solve for cos(t), resulting in cos(t) ≈ 0.404.

Using the Pythagorean identity \(sin^2(t) + cos^2(t)\) = 1, we can find sin(t) as sin(t) = ±\(\sqrt(1 - cos^2(t))\). Since angle t is in Quadrant III, where sine is negative, we take the negative value. Thus, sin(t) ≈ -0.916.

By dividing sin(t) by cos(t), we obtain the tangent of t. Hence, tan(t) ≈ sin(t)/cos(t) ≈ -0.916/0.404 ≈ 2.268.

Cosecant (csc) is the reciprocal of sine, so csc(t) ≈ 1/sin(t) ≈ -1.092.

Similarly, cotangent (cot) is the reciprocal of tangent, so cot(t) ≈ 1/tan(t) ≈ 1/2.268 ≈ 0.441.

In conclusion, when sec(t) = -2.475 and angle t is in Quadrant III, the other five trigonometric ratios are approximately: cos(t) ≈ 0.404, sin(t) ≈ -0.916, tan(t) ≈ 2.268, csc(t) ≈ -1.092, and cot(t) ≈ 0.441.

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Answer:

x = 11.14717238

Step-by-step explanation:

With the help of Commutative Property, the required equivalent expression is 29 + y + z.

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations.

This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.

So, according to what we know, Nigel is organizing his marathon training over a four-day period.

Similar to our given expression, we can write the following as an equivalent expression:

12 + 7 + y + z

Our phrase might be stated more simply as:

29 + y + z

Therefore, with the help of Commutative Property, the required equivalent expression is 29 + y + z.

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Correct question:
Nigel is planning his training schedule for a marathon over a 4-day period. He is uncertain how many miles he will run in two days. One expression for the total miles he will run is 12+y+17+z. Use the Commutative Property to write an equivalent expression.

The conditions for a sampling distribution of a sample mean, when you know the true involve random sampling, independence, and a large enough sample size.

The conditions for a sampling distribution of a sample mean, when you know the true mean, are as follows:

1. Random Sampling:

The samples should be selected randomly from the population to ensure that they are representative of the entire population.

2. Independence:

Each sample should be independent of the others.

This means that the outcome of one sample should not influence the outcome of another sample.

3. Sample Size:

The sample size should be large enough to ensure that the sampling distribution approximates a normal distribution.

In general, a sample size greater than 30 is considered sufficient.

Random sampling is important because it helps to minimize bias and ensure that the sample is representative of the population.

Independence is necessary to avoid any potential confounding factors that may influence the results.

Lastly, a sufficiently large sample size is needed to satisfy the central limit theorem, which states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution.

These conditions are important to ensure the validity and reliability of the statistical analysis.

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Answer:

B:intercepted arc

Step-by-step explanation:

Recall from the knowledge of geometry:

That arc (s) = θ * r(1)

Here;

θ is known as the central angle which is measured in radians

r is the radius of the dimensionless

Hence, suppose the unit circle have a radius of 1 m length. Then, it is pertinent to understand that the arc will also varies directly proportional to the central angle.

Answer:p=-6

Step-by-step explanation:

Answer:

It would be 8p+4

Step-by-step explanation:

dividing (48p + 24) by 6 involves factoring and simplifying the expression to obtain the result of 8p + 4

To divide (48p + 24) by 6, you first factor out the common factor of 6 from the expression, which yields

(48p + 24) = 6(8p + 4).

Then, you can further simplify by dividing each term by 6.

The result is 8p + 4.

This process of division distributes the division operation across all terms in the expression, and as a result, each term's coefficient is divided by 6.

In this case, it simplifies the original expression to 8p + 4.

In summary, dividing (48p + 24) by 6 involves factoring and simplifying the expression to obtain the result of 8p + 4

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Answer:

The length of the actual building is 112 meters long.

Step-by-step explanation:

The key words we need to know are these : scale is 1 millimeter = 7 meters, and 16 millimeters long.

The question is asking for the building's actual height.

To solve this, we need to set up a ratio, have the scale being one ratio and the other 16 millimeters over blank. It's going to look like this :

\(\frac{1 mm}{7 m}\)= \(\frac{16 mm}{x}\)

We need to make sure all the units are lined up - the mm parts of the ratio are next to each other.

Now that we have our ratio set up we can cross product to solve for x.

1(x) = 16(7)

x = 112

So x is 112, or the length of the actual building is 112 meters long.

Hope this helps, please mark brainliest if possible. Have a nice day. :)

Answer:

333+555=888

Step-by-step explanation:

Answer:

5y-3b=0

Step-by-step explanation:

khan

The value of HF is= 76.5

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

The diagonals of a parallelogram bisect each other (divide into two equal parts).  Therefore, point D is the midpoint of diagonal HF, and so HD = DF.

Find the value of x by equating the expressions for HD and DF and solving for x:

HD = HF

x^2 - 34 = x^2 - 4x

x = 8.5

To find the length of HF, substitute the found value of x into the sum of the expressions of HD and DF:

HF = HD + DF

HF = x^2 - 34 + x^2 - 4x

HF = 76.5

Therefore, the length of HF is 76.5 units.

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The area of a square can be found by using the following expression:

where "A" is the area and "l" is the length of each side of the square. The square on this problem has an area of 9 cm², so we can find the sides by replacing A for 9 on the expression above.

To solve it we need to take the square root on both sides of the equation.

Each side of the square has a length of 3 cm, so the sides are 3 cm x 3 cm.

Answer:

300+0.75x=y

Step-by-step explanation:

x(the number of large coffes ordered)

y(the total donation)

Answer:

y=0.75x+300

Step-by-step explanation:

So for this problem, I'm going to put it in slope-intercept form (only because it makes the most sense to me, plus if you need to graph it, this will be helpful)

So Jan is donating $300 first. So whatever you need to do, you need to add 300 afterwards to account for that donation. But then, Jan is going to donate $0.75 for every large coffee ordered. This is means it is a dependent variable. The amount is dependent on how many large coffees ordered.

Say, for example, there were 15 large coffees ordered. You should multiply 0.75*15, which will give you a product of 11.25. So for all the coffees ordered, Jan will donate a total of $11.25 (which isn't a lot, but that's okay). But that isn't ALL the money that Jan donated because, as stated before, Jan is going to donate $300 regardless of how many coffees ordered. So the total amount of money donated is $311.25

Hope this helps!

To find the equation of an ellipse with vertices at (-7, 4) and (1, 4) and a focus at (-5, 4), we can start by determining the center of the ellipse. The equation of the ellipse is: [(x + 3)^2 / 16] + [(y - 4)^2 / 48] = 1.

Since the center lies midway between the vertices, it is given by the point (-3, 4). Next, we need to find the length of the major axis, which is the distance between the two vertices. In this case, the length of the major axis is 1 - (-7) = 8. Finally, we can use the standard form equation of an ellipse to write the equation, substituting the values for the center, the major axis length, and the focus.

The center of the ellipse is given by the midpoint of the two vertices, which is (-3, 4).

The length of the major axis is the distance between the two vertices. In this case, the two vertices are (-7, 4) and (1, 4). Therefore, the length of the major axis is 1 - (-7) = 8.

The distance between the center and one of the foci is called the distance c. In this case, the focus is (-5, 4). Since the focus lies on the major axis, the value of c is half the length of the major axis, which is 8/2 = 4.

The standard form equation of an ellipse with a center at (h, k), a major axis length of 2a, and a distance c from the center to the focus is given by:[(x - h)^2 / a^2] + [(y - k)^2 / b^2] = 1,

where a is the length of the major axis and b is the length of the minor axis.

Substituting the values for the center (-3, 4), the major axis length 2a = 8, and the focus (-5, 4), we have:

[(x + 3)^2 / 16] + [(y - 4)^2 / b^2] = 1.

The length of the minor axis, 2b, can be determined using the relationship a^2 = b^2 + c^2. Since c = 4, we have:

a^2 = b^2 + 4^2,

64 = b^2 + 16,

b^2 = 48.

Therefore, the equation of the ellipse is:

[(x + 3)^2 / 16] + [(y - 4)^2 / 48] = 1.

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|-80|=80

|x| -≥ this symbol is named as mod

we use this to find the absolute value...

it can be explained easily as meaning like rounding off

I'm that even the number given inside in negative we should write the answer only in positive

negative number can never be the answer of absolute value

hope helpful

mark brainliest

Answer:

7

Step-by-step explanation:

the range is the difference between the highest and lowest value in a data set.

13 is the highest in the distribution

6 is the lowest in the distribution

13-6=7

Give brainliest, please!

Hope this helps :)

Answer:

\(5n^2\)

Step-by-step explanation:

This is a quadratic sequence.

The nth term must have \(n^2\).

The sequence has a factor of \(5\).

\(5n^2\)

\(5(1)^2=5\\5(2)^2=20\\5(3)^2=45\\5(4)^2=80\\5(5)^2=125\)

Few terms to this sequence are:

5, 20, 45, 80, 125, 180, 245, 320, 405, 500, 605, 720, 845, 980, 1125, 1280, 1445, 1620, 1805, 2000, 2205, 2420, 2645, 2880, 3125, 3380, 3645, 3920, 4205, 4500, 4805, 5120, 5445, 5780, ...

Answer:

The equation is unsolvable when the 'a' variable is in it, so if we take it out, then all of them would make the equation open up.

Sorry for not giving a definite answer, but that is what I got.

Hope that this helps!

Answer:

pura na hune kaam hunxa vanera jabarjasti garnu. maybe

Answer: 3x=13

Step-by-step explanation:

The person is blind. They did what they were supposed to except the fact that they didn't multiply the 8 by the -1.

Answer: The error is in step 3

Explanation:

In step 2, they multiplied both sides by 8 to clear out the fractions. In step 3, they forgot to distribute the 8 to each term inside the parenthesis.

This is what the steps should look like

\(\frac{3\text{x}}{8}-1=\frac{5}{8}\\\\\\8\left(\frac{3\text{x}}{8}-1\right)=8\left(\frac{5}{8}\right)\\\\\\3\text{x}-8 = 5\\\\\\3\text{x} = 13\\\\\\\text{x} = \frac{13}{3}\\\\\\\)

In step 4, we added 8 to both sides. Afterward, divide both sides by 3 to fully isolate x.

The improper fraction 13/3 is the same as the mixed number 4 & 1/3.

The answer to the equation is \(x=2.2\)

First, you must subtract 0.33 on both sides.

\(-0.45x=-0.99\)

Then, you must divide -0.45 on both sides.

\(x=2.2\)

Your answer is \(x=2.2\)