What is the meaning of "finite sequences"?

the product of (x + 3/x)² is x² + 6 + 9/x².

Why it is and what is Algebra?

To find the product of (x + 3/x)², we can use the formula for squaring a binomial:

(a + b)² = a² + 2ab + b²

In this case, we have a = x and b = 3/x, so we can substitute these values into the formula and simplify:

(x + 3/x)² = x² + 2(x)(3/x) + (3/x)²

= x² + 6 + 9/x²

Therefore, the product of (x + 3/x)² is x² + 6 + 9/x².

Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols. It involves the use of letters and symbols to represent numbers and quantities in equations and expressions. The primary goal of algebra is to solve mathematical problems and equations using various operations such as addition, subtraction, multiplication, and division.

Algebraic concepts can be applied to a wide range of mathematical and real-world problems, including geometry, physics, engineering, economics, and statistics.

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Complete question:

Find the product of (x + 3/x)²2.

Answer:

A fraction tells you how many parts of a whole there are. When we find a fraction of an amount, we are working out how much that 'part' is worth within the whole. You can see fractions of amounts all around us

Step-by-step explanation:

i may be wrong but I tried

The mode for the region A is 2.6.

What exactly is mode?

In statistics, the mode is the value that has highest frequency in a data set. It is one of the three measures of central tendency, along with the mean and median.

To find the mode of a data set, you simply identify the value that appears most often. If no value is repeated, the data set has no mode.

The mode is particularly useful when dealing with categorical data or data that can be easily grouped into categories, such as colors, types of fruit, or letter grades. In such cases, the mode can provide insight into which category is most common or prevalent.

Now,

As given Values for Region A are

2.3  2.5  2.6  2.6  2.6  2.7  2.7  2.8

Here 2.6 comes most times or frequency of 2.6 is highest of all.

Hence,

           The mode for the region A is 2.6.

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A total possible number of bonuses awarded is given as follows:

6 bonuses.

The total number of bonuses awarded is obtained applying the proportions in the context of the problem.

The total amount of bonuses is of $5,000, and at least one $500 bonus and at least one $1000 bonus were awarded, hence the remaining amount to be awarded is of:

5000 - (500 + 1000) = $3,500.

For an amount of $3,500, a possible division of the bonuses is given as follows:

Hence a possible number of bonuses is given as follows:

2 + 1 + 3 = 6 bonuses.

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Answer:

Dragonflies

Step-by-step explanation:

They can fly on top of the water, but also, they have the fastest turns per second for their wings.

The point on the graph that tells you the amount of sugar you'll use if you don't make any pies is (0, 0).

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order to have a proportional relationship, the variables representing the amount of sugar and time must have the same constant of proportionality:

Constant of proportionality, k = y/x

Constant of proportionality, k = 4/3

Constant of proportionality, k = 12.

Therefore, the required equation is given by:

y = kx

y = 4x/3

When x = 0, the value of y is given by:

y = 4(0)/3

y = 0 pies.

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Therefore , the solution of the given problem of equation comes out to be  f(x) = sin(/2 x) (when x = 1 or 2).

Variable words are commonly used in complex algorithms to show consistency between two statements that are not compatible. Academic expressions called equations are used to show the equality of various academic numbers. In this case, normalization yields b + 7 as opposed to a single formula the fact that split 12 into two parts, which can be used with data collected from y + 7.

Here,

The goal is to construct a trigonometric equation with only answers at

x = 1 and x = 2.

f(x) = A sin(Bx+C+D)

=> B + C + D + A = 0 (equation 1)

=> Equation 2: A sin(2B + C + D) = 0

=> B + C sin A = 0 (equation 3)

=> Sin(2B+C) = A = 0 (equation 4)

Since sin(x) = 0 when x is a multiple of, formulae 3 and 4 can be rewritten as follows:

=> B + C = nπ (equation 5)

=> 2B + C = mπ (equation 6)

with numbers n and m. When we simultaneously solve equations 5 and 6 for B and C, we obtain:

=> B = (m - n)π/2 (equation 7)

=> C = nπ - B (equation 8)

=> When x = 1, C = /2 - /2 = 0.

=> When x = 2, C =  − /2 = 3/2.

Thus, the result is as follows:

when f(x) = sin(/2 x) (when x = 1 or 2)

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The answer to the puzzle is (3)O (7)N which makes word ON, (4)T (10)H (1)E which makes word THE, (6)B (8)E (2)A (9)C (5)H which makes the word BEACH

What is a quadrilateral?

A quadrilateral is a 4 sided polygon. On the basis of its properties quadrilaterals are classified as Trapezium,Kite, Parallelogram, Rectangle, Rhombus and square.

Complete the sentence:

1.Parallelogram-(E)

2.Quadrilateral-(A)

3.Supplementary-(O)

4.Bisect-(T)

5.Congruent-(H)

Using the diagram:

6.Given that KG=17 units, KJ=14 units.

As we know from the figure, GH is congruent to KJ and HJ is congruent to side KG.

Therefore, GH=KJ=14units- (B)

7.∠GKJ=86° and ∠GHJ=(x+6)°

We know that ∠GKJ is congruent to ∠GHJ

Therefore, x+6 = 86

                      x=86-6

                      x=80-(N)

8.Given KH=20 & KF= KH÷2  {diagonal pf parallelogram bisect}

                                  =20 ÷ 2

                                  =10 units-(E)

9.Given ∠HJK=82° & We know ∠HJK+∠GKJ=180°  {consecutive angles}

                                                               ∠GKJ=180-∠HJK

                                                                         =180-82

                                                                         =98°-(C)

10.Give that, ∠HJK=82° & we know  ∠HGK=∠HJK {opposite angles of parallelogram}

                                                            ∠HGK=82°-(H)

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The quadratic equation on the graph can be written as:

y = x² + 6x + 8

Remember that a quadratic equation whose vertex is (h,k) and the leading coefficient is a, can be written as:

y = a*(x - h)² + k

Here we can see that the vertex is at (-3, -1), replacing that we will get:

y = a*(x + 3)² - 1

Now we can also see that it passes through the point (-2, 0), replacing these values we will get:

0 = a*(-2 + 3)² - 1

0 = a - 1

1 = a

Then the quadratic is:

y  = (x + 3)² - 1

Expanding that we get:

y = x² + 6x + 9 - 1

y = x² + 6x + 8

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Answer:

volume = 290m

Step-by-step explanation:

box 1

[tex]vol= lwh\\=3*5*6\\=90m[/tex]

box 2

[tex]vol=lwh\\=8*5*5\\=200m[/tex]

total volume = 90+200 =290m

Answer: 6

Step-by-step explanation:

21 - 1 = 20

20 - 2 = 18

18 - 3 = 15

15 - 4 = 11

11 - 5 = 6

Around [tex]312.57[/tex] yards are required to complete a full lap of the circuit.

The entire movement of an item, independent of direction, is called distance. Regardless of an object's beginning or finishing position, distance may be defined as the amount of ground it has travelled.

As a result, distance is indeed a scalar quantity. The whole path an item has taken can be used to define the distance from it. Think about it this way. If a car drives 5 km east, then turns to head north for 8 km, the final distance driven by the automobile must be 13 km.

The circumference of a semicircle with diameter d is [tex](pi/2)d[/tex]. Therefore, the length of each semicircular section is [tex](pi/2) * 36 = 18pi[/tex].

The total distance around the track is the sum of the lengths of the two straight sections and the two semicircular sections.

Distance around track [tex]= 2(100 yards) + 2(18pi yards)[/tex]

[tex]= 200 yards + 36pi yards[/tex]

[tex]= 312.57 yards[/tex] (rounded to two decimal places)

Therefore, the distance around the entire track is approximately [tex]312.57[/tex]yards.

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Answer:

a/c = t/v

b/d = u/w

Step-by-step explanation:

Use corresponding sides to complete the fractions.

a/c = t/v

b/d = u/w

The experimental probability that the next train to arrive at Danville Station will be on time is 3/4 or 0.75.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The experimental probability of the next train to arrive at Danville Station being on time is given by the number of on-time trains divided by the total number of trains that arrived -

experimental probability = number of on-time trains / total number of trains

From the information given, we know that out of the last 20 trains to arrive, 15 were on time. Therefore -

number of on-time trains = 15

total number of trains = 20

Substituting these values into the equation, we get -

experimental probability = 15 / 20

Simplifying the fraction, we get -

experimental probability = 3/4

Therefore, the experimental probability value is obtained to be 3/4 or 0.75.

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Answer:assuming its a rectangle its 13.5

Step-by-step explanation: L x H = Area

Area of the rectangle is 72 square inches and the perimeter of the same rectangle is 36 inches by using this parameters Marisol can draw a rectangle.

A quadrilateral or four-sided polygon with four right angles (90° angles) and opposite sides that are parallel and the same length is referred to as a rectangle. It is a two-dimensional shape with four vertices and two pairs of parallel sides.

Given that,

the length is 12 inches and width is 6 inches,

So, The Area of rectangle = (Length × Width)

= 12 inches × 6 inches

= 72 square inches

So the area of the rectangle is 72 square inches.

The perimeter of a rectangle is given by adding up the lengths of all four sides.

The Perimeter of rectangle = (2 × length) + (2 × width)

= 2 × 12 inches + 2 × 6 inches

= 24 inches + 12 inches

= 36 inches

So the perimeter of the rectangle is 36 inches.

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In summary, Marisol's rectangle has a length of 12 inches, a width of 6 inches, an area of 72 square inches, and a perimeter of 36 inches.

Sure, I'd be happy to help you with your question! Marisol has drawn a rectangle that has a length of 12 inches and a width of 6 inches. The rectangle is a two-dimensional shape that has four straight sides and four right angles. To calculate the area of the rectangle, we can use the formula:Area = Length x Width.

In this case, the area of the rectangle is 12 inches x 6 inches = 72 square inches. The perimeter of the rectangle is the distance around the outside of the shape, which is calculated by adding the lengths of all four sides. In this case, the perimeter of the rectangle is 2 x (length + width) = 2 x (12 inches + 6 inches) = 2 x 18 inches = 36 inches.

It's important to note that the length and width of the rectangle can be interchanged and the area and perimeter will remain the same.In conclusion, Marisol's rectangle measures 12 inches long, 6 inches wide, 72 square inches in size, and has a circumference of 36 inches.

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Answer: b

Step-by-step explanation:

We may conclude after answering the presented question that As a equation result, we have demonstrated that mt = mu when t | u.

Make a note of the definition of t | u. It denotes the existence of an integer k such that u = tk.

To get mt = m, substitute u = tk into mt = mu (tk).

Rewrite m(tk) as (mt)k using the associative property of multiplication.

To get mt = (mt)k, substitute (mt)k for m(tk) in the equation mt = mu.

Multiply both sides by mt. If mt is greater than zero, we obtain 1 = k. If mt is zero, we must also have mu = 0, hence the equation holds.

Since 1 Equals k, we get u = tk = t(1) = t.

We get mt = mt by substituting u = t into the original equation mt = mu.

As a result, we have demonstrated that mt = mu when t | u.

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Answer:

Step-by-step explanation:

Ranking:

Compound the interest every month instead of every two months.

Increase the interest rate by 1%.

Let the account increase for one more year.

Increase the starting amount by $100.

Calculations:

If the interest is compounded monthly instead of every two months, the final value would be $1,357.36, which is an increase of $9.18 compared to the original value.

If the interest rate is increased to 6%, the final value would be $1,411.58, which is an increase of $63.40 compared to the original value.

If the account increases for one more year at the same interest rate, the final value would be $1,435.09, which is an increase of $86.91 compared to the original value.

If the starting amount is increased by $100, the final value would be $1,421.61, which is an increase of $73.43 compared to the original value.

The Converse of the Pythagorean Theorem is proved below.

What is Pythagoras Theorem ?

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The converse of the Pythagorean theorem states that if a triangle has sides of length a, b, and c, where c is the longest side, and a² + b² = c², then the triangle is a right triangle.

To prove the converse of the Pythagorean theorem, we can use the fact that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. That is, if a triangle has sides of length a, b, and c, where c is the longest side and c² = a² + b², then the triangle is a right triangle.

Proof:

Suppose we have a triangle ABC, with sides of length a, b, and c, where c is the longest side. Assume that a² + b² = c². We want to show that triangle ABC is a right triangle.

We will use the Law of Cosines to show that angle C is a right angle. The Law of Cosines states that for any triangle ABC with sides of length a, b, and c opposite angles A, B, and C, respectively:

c² = a² + b² - 2ab cos(C)

Substituting a² + b² = c² into this equation, we get:

c² = c² - 2ab cos(C)

2ab cos(C) = 0

cos(C) = 0

Since 0 is the cosine of 90 degrees, this implies that angle C is a right angle. Therefore, triangle ABC is a right triangle.

Thus, this completes the proof of the converse of the Pythagorean theorem.

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c) Horizon A would be less deep since there would be less topsoil due to erosion.

the soil profile in a mountainous region would typically be different from the one shown in the illustration, because the soil formation process is affected by different factors such as climate, vegetation, topography, and parent material.

In a mountainous region, the soil profile is likely to be thinner and shallower than in flat areas, due to the steep slopes and higher erosion rates. The topsoil horizon (A) may also be thinner or absent in some areas due to erosion or limited plant growth, which can make it difficult for organic matter to accumulate. In addition, the subsoil horizon (B) may be more prominent and closer to the surface due to the leaching of minerals from the upper layers, which can result in a more rocky and mineral-rich soil.

Therefore, the correct answer would be:

c) Horizon A would be less deep since there would be less topsoil due to erosion.

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Given:-

To find:-

Answer:-

Here since the given triangle is a right angled triangle, we may use the trigonometric ratios . We can see that perpendicular and base are involved in this question whose measures are "x" and "√10" respectively with respect to 60° angle. So here we may use the ratio of tangent as , in any right angled triangle,

[tex]\implies\tan\theta =\dfrac{p}{b} \\[/tex]

and here p = x , and b = √10 . So on substituting the respective values, we have;

[tex]\implies \tan\theta = \dfrac{x}{\sqrt{10}} \\[/tex]

Also the angle here is 60° , so that;

[tex]\implies\tan60^o =\dfrac{x}{\sqrt10} \\[/tex]

The value tan60° is √3 , so we have;

[tex]\implies \sqrt3 =\dfrac{x}{\sqrt10}\\[/tex]

[tex]\implies x =\sqrt{10}\cdot \sqrt{3}\\[/tex]

[tex]\implies x =\sqrt{10\cdot 3} \\[/tex]

[tex]\implies x =\sqrt{30} \\[/tex]

The value of √30 is approximately 5.48 , so that;

[tex]\implies \underline{\underline{\red{\quad x = 5.48\quad }}} \\[/tex]

Therefore the value of x is approximately 5.48 .

Answer:

The length of side x in simplest radical form is [tex]\sqrt{30}[/tex].

Step-by-step explanation:

From inspection of the given right triangle, we can see that the interior angles are 30°, 60° and 90°. Therefore, this triangle is a 30-60-90 triangle.

A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio  1 : √3 : 2.  Therefore, the formula for the ratio of the sides is b: b√3 : 2b where:

We have been given the side opposite the 30° angle, so:

[tex]\implies b=\sqrt{10}[/tex]

The side labelled "x" is the side opposite the 60° angle, so:

[tex]\implies x=b\sqrt{3}[/tex]

Substitute the found value of b into the equation for x:

[tex]\implies x=\sqrt{10}\sqrt{3}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}[/tex]

[tex]\implies x=\sqrt{10 \cdot3}[/tex]

[tex]\implies x=\sqrt{30}[/tex]

Therefore, the length of side x in simplest radical form is [tex]\sqrt{30}[/tex].

[tex]\hrulefill[/tex]

We can also calculate the length of side x using the tangent trigonometric ratio:

[tex]\boxed{\tan \theta=\sf \dfrac{O}{A}}[/tex]

where:

From inspection of the given right triangle:

Substitute these values into the formula:

[tex]\implies \tan 30^{\circ}=\dfrac{\sqrt{10}}{x}[/tex]

[tex]\implies \dfrac{\sqrt{3}}{3}=\dfrac{\sqrt{10}}{x}[/tex]

[tex]\implies x\sqrt{3}=3\sqrt{10}[/tex]

[tex]\implies x=\dfrac{3\sqrt{10}}{\sqrt{3}}[/tex]

Rationalise the denominator by multiplying the numerator and denominator by √3:

[tex]\implies x=\dfrac{3\sqrt{10}}{\sqrt{3}}\cdot \dfrac{\sqrt{3}}{\sqrt{3}}[/tex]

[tex]\implies x=\dfrac{3\sqrt{10}\sqrt{3}}{3}[/tex]

[tex]\implies x=\sqrt{10}\sqrt{3}[/tex]

[tex]\implies x=\sqrt{10\cdot3}[/tex]

[tex]\implies x=\sqrt{30}[/tex]

Therefore, the length of side x in simplest radical form is [tex]\sqrt{30}[/tex].

1. {0, 1, 3, 4, 6}; 2. {4, 6}.

Step-by-step explanation:

1. А={0, 1, 2, 3}, B={2, 4, 5, 6}, C={2, 5, 7, 9}; (A∪B)-(B∩C)-?

a) A∪B⇔{0, 1, 2, 3, 4, 5, 6};

b) B∩C⇔{2, 5};

c) (A∪B)-(B∩C)⇒{0, 1, 3, 4, 6}.

2. A={4, 6, 8, 10}, B={4, 6, 8}, C={1, 2, 3, 4, 7}, D={3, 5, 6, 7}; A∩(D∪(B∩C))=?

a) B∩C⇔{4};

b) D∪(B∩C)⇔{3, 4, 5, 6, 7};

c) A∩(D∪(B∩C))⇒{4, 6}.

Answer:

You divide by five because it's the common factor of 5 and 15 in the 4th line of work and the goal is to solve for x. The only way to get x alone in the inequality 5x>15 is to divide each side by 5. This would give you x and 3, hence the answer: x > 3

[tex]\frac{5x}{5} =x\\\\\frac{15}{5} =3[/tex]

Answer:313:)

Step-by-step explanation:

Answer:

[tex]3^2-5[/tex]

Step-by-step explanation:

    Given equation:

 ( 3 - 2^2) + 5

  3 - 4 + 5   (Simplify exponent)

 -1 + 5  (Solve 3 - 4)

  4 (Simplified)

Evaluation

2^2 + 5

4 + 5

9 (not the answer)

3^2 - 5

9-5

4  (answer)

Step-by-step explanation:

the perimeter is the sum of the lengths of all outside sides.

at the top is a triangle.

at the bottom is a rectangle.

the triangle looks like an isoceles triangle (both legs are equal), but the given measurement tells us otherwise.

if it were isoceles, the height would split the baseline into 2 equal halves (20/2 = 10ft).

per Pythagoras the 12 ft Hypotenuse would be

Hypotenuse² = 10² + 10² = 100 + 100 = 200

Hypotenuse = sqrt(200) = 14.14213562... and NOT 12 ft.

so, we need to calculate the actual part of the 20ft baseline (again Pythagoras) :

12² = 10² + part²

144 = 100 + part²

44 = part²

part = sqrt(44) = 6.633249581... ft

that means the 2nd part of the baseline is

20 - 6.633249581... = 13.36675042... ft

and we get the second leg of the large triangle again via Pythagoras :

leg² = 10² + 13.36675042...² = 100 + 178.6700168...

leg² = 278.6700168...

leg = sqrt(278.6700168...) = 16.69341238... ft

we need to sum up both legs of the triangle, 2 widths and one length of the rectangle, as the triangle base line and the second length of the rectangle cover each other up, and are not visible to the outside of the combined object.

P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈

≈ 64.69 ft