How do you find the verticle asymtote of y = x-4/x-2

Number of students that selected the elective subject of religion in 2014 is 1344

The problem tells us that in 2013, there were 1400 students who selected the elective subject of religion.

Then, in 2014, this figure decreased by 4%. This means that the new figure in 2014 will be 4 percentage less than the figure in 2013.

To calculate what 4% of 1400 is, we need to multiply 1400 by 4/100, which gives us 56. So, 56 students did not select the elective subject of religion in 2014 compared to 2013.

So, the number of students who selected the elective subject of religion in 2014 is

= 1400 - 56

= 1344

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Given:-

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Solution:-

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hope it helps!:)

Bonjour !

Il faut isoler x.

3x + 4 = 2x + 9

3x - 2x = 9 - 4

x = 5

The statement  ((1)/(x))^(n)>(1)/(x)  is FALSE as (1)/(x^n) will always be smaller than (1)/(x).

To evaluate this expression, let's look at the properties of exponents. When we have a fraction raised to a power, it is equivalent to raising both the numerator and denominator to that power.

So, ((1)/(x))^(n) is equivalent to (1^n)/(x^n), which simplifies to (1)/(x^n).

Now, let's compare (1)/(x^n) to (1)/(x). Since x is positive and n is a natural number excluding zero, x^n will always be greater than x.

For example, if x=2 and n=3, then x^n=8 and (1)/(x^n)=(1)/(8) while (1)/(x)=(1)/(2).

So, (1)/(x^n) will always be smaller than (1)/(x).

Therefore, the statement ((1)/(x))^(n)>(1)/(x) is FALSE.

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The given function 3(t^4)-19 is thus written using the function rule in notations as: f(t) = 3(t^4)-19 for the input-output machine.

Although equations are frequently used to represent functions, a sequence of equations all beginning with y = may make it difficult to distinguish between different functions.

A function called f is defined by the notation f(x).

The given function 3(t^4)-19 is thus written using the function rule in notations as:

f(t) = 3(t^4)-19.

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hi

im pretty sure that this is the answer

hope this helps

good luck;)

Consequently, IS has a 24 length as its length. SR is 44, QS is 55, and SU is 6 shorter than IS.

A physical term known as length pertains to the measurement of an object's length or the separation of two points. Ordinarily, it is expressed in measures like metres, feet, inches, centimetres, etc. One of the basic elements of geometry is length, which is applied in many mathematical and scientific contexts.

given

TU and QR are parallel in the illustration below. Find the length of IS if SU is 6 shorter than IS, QS is 55, and SR is 44.

Since TU and QR are parallel, we have:

angle Angle = ISU QSR (matching angles) (corresponding angles)

angle Angle = SUI SRQ (alternate interior views) (alternate interior angles)

Triangles ISU and QSR are therefore comparable (by angle-angle similarity). So, here we are:

SU/QS Equals IS/SR

Inputting the numbers provided yields:

IS/44 = (IS - 6)/55

The result of multiplying both parts by 44*55 is:

55IS = 44(IS - 6) (IS - 6)

If we simplify, we get:

11IS = 264

IS = 24

Consequently, IS has a 24 length as its length. SR is 44, QS is 55, and SU is 6 shorter than IS.

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Answer:

here is your answer

Step-by-step explanation:

13x^2y^2 (3x-4)

Answer:

Step-by-step explanation:

So all that you have to do is just multiply 15 by 110kg and you'll get a answer of 1500kg total.

1. Parallelogram: Opposite sides are congruent, Opposite angles are congruent, Consecutive angles are supplementary, Diagonals bisect each other, Diagonals are congruent, Diagonals are perpendicular.

Congruence is a term used in mathematics to describe the relationship between two geometric figures or objects. When two geometric figures are said to be congruent, it means that the two figures have the same size and shape.

2. Rectangle: Two pairs of consecutive congruent sides, but opposite sides are not congruent, Diagonals are perpendicular, Exactly one pair of congruent angles, Diagonals bisect one pair of angles.

3. Rhombus: Opposite sides are congruent, Opposite angles are congruent, Consecutive angles are supplementary, Diagonals bisect each other, Diagonals are congruent, Diagonals are perpendicular.

4. Kite: Opposite sides are congruent, Opposite angles are congruent, Consecutive angles are supplementary, Diagonals bisect each other, Diagonals are perpendicular, Diagonals bisect angles.

5. Square: Opposite sides of a are congruent, Opposite angles of are congruent, Consecutive angles are supplementary, The diagonals of bisect each other, All four sides are congruent.

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They are relatively prime.

Proof: Let fn and fn-1 be any two consecutive terms in the Fibonacci sequence. By definition, fn = fn-2 + fn-1. Since both fn and fn-1 are integers,

they must have no common factors other than 1,

so they are relatively prime.

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Using prοperties οf quadrilaterals, The line segment in the image that cοrrespοnds tο BC¯¯¯¯¯ in the pre-image is the line segment FG¯¯¯¯¯.

A pοlygοn with fοur sides and fοur vertices is called a quadrilateral (cοrners). It is a twο-dimensiοnal οbject that is flat and can take οn a number οf fοrms.

We knοw that matching sides οf the pre-image and image are identical in length since a reflectiοn maintains the size and shape οf the figure.

Since a reflectiοn preserves the shape and size οf the figure, we knοw that cοrrespοnding sides οf the pre-image and image are equal in length.

Therefοre, the line segment in the image that cοrrespοnds tο BC¯¯¯¯¯ in the pre-image is the line segment FG¯¯¯¯¯.

Tο see why, imagine fοlding the figure alοng the line οf reflectiοn sο that the pre-image and image cοincide. In this fοlded pοsitiοn, the cοrrespοnding sides οf the twο quadrilaterals will be οn tοp οf each οther. In particular, side BC¯¯¯¯¯ οf the pre-image will be οn tοp οf side FG¯¯¯¯¯ οf the image, cοnfirming that FG¯¯¯¯¯ cοrrespοnds tο BC¯¯¯¯¯ in the pre-image.

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Using the formula of the cylinder we know that the height of the given cylinder is 6.36 inches.

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid.

It is regarded as a prism with a circle as its base in basic geometry.

In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.

So, the cylinder formula for the volume is:

V = πr²h

Now, substitute the values as follows:

V = πr²h

180 = 3.14*3²h

180 =  28.26h

180/28.26 = h

6.36 = h

Therefore, using the formula of the cylinder we know that the height of the given cylinder is 6.36 inches.

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The solution is, the value of x is, x = 12.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

from the given figure, we get,

the triangles are similar,

so, we know that, the sides are proportional to each other.

i.e. 8:4 = x: 6

or, x = 8 * 6 / 4

or, x  = 2 * 6

or, x = 12

Hence, The solution is, the value of x is, x = 12.

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The correct answer is d)C(x)=4x+60. This is because an equation should have an equal sign to show that both sides of the equation are equal.

Additionally, the variable "x" should be on one side of the equation and the constants should be on the other side. In this case, the variable "x" is multiplied by 4 and the constant is 60, making the equation C(x)=4x+60. This equation shows the relationship between the variable "x" and the function "C(x)".

It is important to note that the other options are not correct because they do not have an equal sign or the variable and constants are not on the correct sides of the equation. Option a)C(x)−60x+4 does not have an equal sign, option b)C(x)=−60x+4 has the variable and constants on the wrong sides of the equation, option c)C(x)−−4x+60 does not have an equal sign, and option e)C(x)−4x+4 does not have an equal sign.

Therefore, the correct answer is d)C(x)=4x+60.

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The scale factor of dilation is 3.

What is Dilation of a circle?

Dilation is the process of altering an object's or shape's size by reducing or enlarging its dimensions by a certain amount of scale. A circle with a radius of 10 units, for instance, is reduced to a circle with a radius of 5 units. This technique is applied in art and craft, photography, and logo design, among other fields.

Given : Radius of original circle A = 3

            Radius of Dilation circle B = 9

We know that, Scale factor of dilation =

Dimension of Dilation shape / Dimension of original shape

So, Scale factor of given dilation = Radius of Circle B / Radius of Circle A

                                                      = 9/3

                                                      = 3.

Hence, Scale factor of dilation of circle B on Circle A is 3.

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They are not the best factors to use because 12 cannot be simplified further into a perfect square. It is better to factor 48 into perfect squares and simplify each square root separately.

Factors can be classified as prime or composite. A prime factor is a factor that is a prime number, meaning it is only divisible by 1 and itself. For example, the prime factors of 12 are 2 and 3. A composite factor is a factor that is not a prime number, meaning it has more than two factors. For example, 4, 6, and 12 are composite factors of 12.

Let's examine the factors 4 and 12 to see if they can be used to simplify the square root of 48:

4 is a perfect square, and its square root is 2. However, 12 is not a perfect square, and its square root cannot be simplified further.

We can write 48 as 4 x 12, so the square root of 48 can be simplified as the product of the square root of 4 and the square root of 12, or 2√12.

However, this is not the simplest form of the square root of 48. We can further simplify √12 by factoring it into perfect squares: √12 = √(4 x 3) = √4 x √3 = 2√3.

Therefore, the simplest form of the square root of 48 is 2√3, not 2√12.

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An estimate for the mean age of the 50 people on the bus is 34 years.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Let us calculate the sum of the products of the midpoints and their respective frequencies, and divide by the total frequency to obtain the estimated mean age.

The midpoint and frequency data for each age group can be represented as follows:

Age group      Midpoint        Frequency

0 < h ≤ 20           10                    20

20 < h ≤ 40         30                    10

40 < h ≤ 60         50                     10

60 < h ≤ 80         70                     10

To calculate the estimated mean age, we can use the formula:

Estimated mean age = (Σ(midpoint × frequency)) / total frequency

Estimated mean age = ((10 × 20) + (30 × 10) + (50 × 10) + (70 × 10)) / (20 + 10 + 10 + 10)

Estimated mean age = (200 + 300 + 500 + 700) / 50

= 1700 / 50

= 34

Therefore, an estimate for the mean age of the 50 people on the bus is 34 years.

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Answer:

a) When we say "like terms", we mean terms that have the same variables and/or exponents.

b) When we say "combining like terms", we mean adding or subtracting terms with the same variables, so that the two terms become one term.

c) An example of combining like terms is: 6x + 3x = 9x.

(1) The percentage of males that drive sports cars is 46.43 %.

(2) The percentage of all drivers that are male is 25 %.

(3) The percentage of sports car drivers that are male is 46.43 %.

(4) Yes, question 1 and question 3 are the same.

The percentage of males that drive sports cars is calculated as follows;

= 39 / 84  x 100%

= 46.43 %

The percentage of all drivers that are male is calculated as follows;

= 60 / 240  x 100%

= 25%

The percentage of sports car drivers that are male is calculated as;

= 39 / 84  x  100%

= 46.43 %

Thus, question 1 and question 3 are the same.

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This hypothesis test indicates that the team efficiency when working through distance working (e.g. with online meetings) is not generally more efficient than when working with physical presence.

The research question being examined is whether teams that work through distance working (e.g. with online meetings) are generally more efficient than those that work with physical presence. To answer this question, a hypothesis test can be used with a 1% level of significance.

The null hypothesis (H0) is that there is no difference in team efficiency between those teams that work through distance working (e.g. with online meetings) and those that work with physical presence. The alternative hypothesis (H1) is that there is a difference in team efficiency between those teams that work through distance working (e.g. with online meetings) and those that work with physical presence.

To test this hypothesis, a two-tailed independent t-test was used. The mean score for the team that had used online meetings was 2.63 with a standard deviation of 0.92 and for the team that had worked with physical presence the mean was 2.35 with a standard deviation of 0.81. The t-statistic obtained was 1.71 and the corresponding p-value was 0.093.

Since the p-value (0.093) is not less than the level of significance (0.01), the null hypothesis cannot be rejected. Therefore, the data suggests that there is not a significant difference in team efficiency between those teams that work through distance working (e.g. with online meetings) and those that work with physical presence.

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The inequality for the statement "5 is greater than or equal to a" is 5 ≥ a.

To write an inequality for the statement "5 is greater than or equal to a," we can use the greater than or equal to symbol (≥) to represent the relationship between 5 and a. The inequality would be written as:
5 ≥ a
This inequality can also be written as a ≤ 5, which means that a is less than or equal to 5. Both of these inequalities represent the same relationship between 5 and a, and either one can be used to represent the statement "5 is greater than or equal to a."

In Mathematics, the relationship between two values that are not equal is defined by inequalities.

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The required value of x for the triangle is 9 units.

The theorem you are referring to is known as the "Parallel Line Theorem" or "Thales' Theorem".

If a line is drawn parallel to one side of a triangle, then the other two sides of the triangle are divided proportionally.

Consider a triangle ABC with a line parallel to one of its sides, say side AB. Let the parallel line intersect sides AC and BC at points D and E, respectively.

Then,

AB/BD = CB/BE

In triangle;

[tex]$\frac{4x}{x-1} =\frac{27}{6}[/tex]

24x = 27x - 27

= 3x = 27

= x = 9

Thus, required value of x is 9.

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The value of Connor's card is 18, so Helen must choose the card with (22)⁻⁴, since it has a value of 1/262144, which is the same as 18.

Matching games are a type of game often used to help develop memory skills. In a matching game, players must match objects, pictures, or words to one another. This can involve matching a picture to a word, or a word to a definition. Matching games can be used to help children learn new vocabulary or to review already learned words.

The card with 2⁻³ has a base of 2 and an exponent of -3. This means that the value of the card is 1/8, which is the same as 2⁻³.

The card with (12)⁻² has a base of 12 and an exponent of -2. This means that the value of the card is 1/144, which is the same as 12⁻².

The card with (22)⁻⁴ has a base of 22 and an exponent of -4. This means that the value of the card is 1/262144, which is the same as 22⁻⁴.

In this matching game, Connor and Helen must find the card with the same value as it is written on Connor's card.

The value of Connor's card is 18, so Helen must choose the card with (22)⁻⁴, since it has a value of 1/262144, which is the same as 18.

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Answer:

48 cups

Step-by-step explanation:

‐-------------------

Answer:

2.90

Step-by-step explanation:

One hundredth is 0.01. 2.89+0.01= 2.90.

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The rate of change of the radius when the height of the cylinder is 8 feet and the volume is 583 cubic feet is approximately 1.854 feet per second.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as;

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

We are given that;

dh/dt = -4 ft/s and dV/dt = 476 ft^3/s. We need to find dr/dt when h = 8 ft and V = 583 ft^3.

Now,

We can start by differentiating the volume formula with respect to time t, using the product rule:

dV/dt = d/dt (πr^2h)

= πh d/dt (r^2) + πr^2 d/dt (h)

= 2πrh (dr/dt) + πr^2 (dh/dt)

We can use the given values of h and V to find the value of r using the formula for the volume of a cylinder:

V = πr^2h

583 = πr^2(8)

r^2 = 583/(8π)

r ≈ 3.031

Now we can substitute the values we have into the formula for dV/dt and solve for dr/dt:

476 = 2π(8)(3.031)(dr/dt) + π(3.031)^2(-4)

dr/dt = (476 + 36π(3.031)^2) / (16π(3.031))

dr/dt ≈ 1.854

Therefore, by the given volume the answer will be 1.854 feet per second.

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Answer:

Answer:

Most poison dart frogs are brightly colored, displaying aposematic patterns to warn potential predators. Their bright coloration is associated with their toxicity and levels of alkaloids. ... Poison dart frogs are an example of an aposematic organism.

Hostas for Full Sun

In general, yellow or gold hostas tolerate partially sunny location without losing their vibrant yellow color. About two hours of daily sun exposure will keep these yellow or golden beauties looking their best. Aim for morning sun to avoid burned leaves.

hope this helps

Step-by-step explanation:

Hope this is the right answer Have a good day!

have a good day

Recall definitions:

Use the triangle to define each ratio.

Use Pythagorean theorem:

Proved

Proved

1. The values of x, y, and z are x = 15.5, y = 9.54, and z = 0. 2. The values of x and y are x = 1.4375 and y = 8. 3. The values of x and y are x = 6 and y = 52.5. 4. X can have any value and the triangles will still be similar

1. We are given that ΔPRS is congruent to ΔCFH.

From ΔPRS, we know that:

∠P = 180 - 28 - ∠R

∠P = 152 - 13y

From ΔCFH, we know that CH is the hypotenuse and CF is one of the legs. So, using the Pythagorean Theorem, we have:

CH^2 = CF^2 + FH^2

39^2 = 24^2 + FH^2

FH^2 = 39^2 - 24^2

FH = sqrt(39^2 - 24^2) = 30

Since ΔPRS is congruent to ΔCFH, their corresponding sides are equal. Therefore:

PS = CH = 39

2x - 7 = CF = 24

Solving for x and y:

2x - 7 = 24

2x = 31

x = 15.5

39 = 2x - 7

46 = 2x

x = 23

∠P = 152 - 13y

28 = 152 - 13y

124 = 13y

y = 9.54

Solving for z:

PS = 2x - 7

39 = 2(15.5) - 7

39 = 31

z = 0

Therefore, the values of x, y, and z are x = 15.5, y = 9.54, and z = 0.

2. We are given that ΔABC is similar to ΔDEF. Therefore, the corresponding sides are proportional:

AB/DE = BC/EF = AC/DF

Substituting the given values:

8/(y-6) = 19/(4x-1) = 14/DF

We can solve for x and y using any two of the three ratios.

Let's first solve for x and y using the first two ratios:

8/(y-6) = 19/(4x-1)

Cross-multiplying, we get:

8(4x-1) = 19(y-6)

Expanding the brackets, we get:

32x - 8 = 19y - 114

32x - 19y = -106

Now let's use the third ratio:

14/DF = 8/(y-6)

Cross-multiplying, we get:

14(y-6) = 8DF

Simplifying, we get:

y = (4/7)DF + 6

Substituting this into the equation we got earlier:

32x - 19y = -106

32x - 19[(4/7)DF + 6] = -106

32x - (76/7)DF - 114 = -106

32x - (76/7)DF = 8

Multiplying both sides by 7, we get:

224x - 76DF = 56

Using the equation we got from the third ratio:

14(y-6) = 8DF

14y - 84 = 8DF

14y = 8DF + 84

y = (4/7)DF + 6

Substituting this into the equation we just got:

14[(4/7)DF + 6] = 8DF + 84

8DF + 84 = (56/7)DF + 84

8DF = (56/7)DF

DF = 7

Substituting DF = 7 into the third ratio:

14/DF = 8/(y-6)

14/7 = 8/(y-6)

2 = y-6

y = 8

Now we can substitute y = 8 into the equation we got earlier:

32x - 19y = -106

32x - 19(8) = -106

32x - 152 = -106

32x = 46

x = 1.4375

Therefore, the values of x and y are x = 1.4375 and y = 8.

3. Since ΔZMK ≈ ΔAPY, we know that the corresponding angles are congruent:

m∠M = m∠A

m∠K = m∠Y

Therefore, we can write two equations:

m∠M = 2y + 7

m∠K = 41°

Also, we know that:

m∠M + m∠K + (13x - 37)° = 180°

Substituting the values we have:

112° + 41° + (13x - 37)° = 180°

13x + 116 = 180

13x = 64

x = 4.9231

Substituting x into the third equation:

112° + 41° + (13x - 37)° = 180°

13x + 116 = 180

13(4.9231) + 116 + m∠K = 180

m∠K = 41°

Substituting m∠K = 41° into the second equation:

m∠K = m∠Y

13x - 37 = 41

13x = 78

x = 6

Substituting x into the first equation:

m∠M = 2y + 7

112 = 2y + 7

105 = 2y

y = 52.5

Therefore, the values of x and y are x = 6 and y = 52.5.

4. Since ΔBTS ≈ ΔGHD, we know that the corresponding angles are congruent:

m∠S = m∠H

m∠B = m∠G

Therefore, we can write two equations:

m∠S = 7y + 5

m∠B = m∠G = 21°

Also, we know that:

m∠B + m∠T + m∠S = 180°

Substituting the values we have:

21° + m∠T + 56° = 180°

m∠T = 103°

Now we can use the fact that the sum of the angles in a triangle is 180° to find m∠G:

m∠B + m∠T + m∠G = 180°

21° + 103° + m∠G = 180°

m∠G = 56°

Since we have a pair of similar triangles, we can use their side lengths to set up a proportion:

BS/BT = GD/GH

Substituting the given values:

25/31 = (4x-11)/GH

Solving for GH:

GH = (31/25)(4x-11)

Now we can use the fact that the sum of the angles in a triangle is 180° to find m∠H:

m∠G + m∠H + m∠D = 180°

56° + m∠H + 90° = 180°

m∠H = 34°

Substituting the values we have:

m∠S = 7y + 5

56 = 7y + 5

51 = 7y

y = 7.2857

Substituting y into the first equation:

m∠S = 7y + 5

m∠S = 7(7.2857) + 5

m∠S = 59

Now we can use the fact that the sum of the angles in a triangle is 180° to find m∠T:

m∠B + m∠T + m∠S = 180°

21° + m∠T + 59° = 180°

m∠T = 100°

Now we can use the fact that we have a pair of similar triangles to find x:

BS/BT = GD/GH

25/31 = (4x-11)/GH

25/31 = (4x-11)/((31/25)(4x-11))

Simplifying:

25/31 = 25/31

Therefore, x can have any value and the triangles will still be similar.

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