if x=-2, y=-6 and z=4, Find the value of 4xy 3marks

(x+1) & (x-5) are the factors of given equation.

The given Equation is,

x3- \(3x^{3}\) - 9

Here, If we substitute x =5, in the given equation, then we find

     (5)3 - 3(5)3 - 9*5 -5 = 0

x-5 is factor of given equation to find another factor dividing given equation by x-5

    we will get =(x2+2x+1) after dividing the equation by x - 5

Hence x3- \(3x^{3}\) - 9 =(x2+2x+1) (x-5)

                            =(x+2)2 (x-5)

To learn more about Equation click the link

brainly.com/question/29657983

#SPJ4

The horizontal and vertical translations applied to ΔABC:

A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.

It is possible to represent linear transformations and solve systems of linear equations using matrices, which are collections of numbers arranged into a predetermined number of rows and columns. A matrix is a rectangular array of letters, numbers, or expressions in mathematics that are arranged in rows and columns. As well as in the sciences like physics, engineering, and economics, matrices are frequently used in computer graphics, image processing, and data analysis. Data manipulation and analysis can be done using well-defined matrix operations like addition, subtraction, multiplication, and inversion.

Given that,

\(\left[\begin{array}{ccc}1&1&4\\4&1&1\\\end{array}\right] + \left[\begin{array}{ccc}-7\\4\end{array}\right] * \left[\begin{array}{ccc}1&1&1\\\\\end{array}\right]\)   = ?

After using matrix operation it can be further solved as,

\(\left[\begin{array}{ccc}5&5&8\\-3&-6&-6\\\end{array}\right]\)

Hence, A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.

To know more about matrix check:

https://brainly.com/question/29132693

#SPJ1

Answer:

13 weeks

Step-by-step explanation:

1. $400-$75= 325

2. 25w=325 (because you save $25 a week)

3. w=325/25

4. w= 13 (325 divided by 25 is 13)

The division expression 5/9 divided by 1/2, when rewritten as an improper fraction, is 10/9.

Given that the expression 5/9 divided by 1/2.

To rewrite the division expression 5/9 divided by 1/2 as an improper fraction, and perform the division operation and express the result in the form of a single fraction.

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. In this case, multiply 5/9 by the reciprocal of 1/2.

Reciprocal of 1/2 = 2/1

So, the division expression can be rewritten as:

5/9 ÷ 1/2 = 5/9 x 2/1

Multiplying the fractions:

(5 x 2) / (9 x 1) = 10/9

An improper fraction is one where the numerator is equal to or greater than the denominator. In this case, 10/9 is an improper fraction because the numerator (10) is greater than the denominator (9).

Therefore, the division expression 5/9 divided by 1/2, when rewritten as an improper fraction, is 10/9.

Learn more about fractions and division click here:

https://brainly.com/question/17205173

#SPJ6

Let p = 0.2 be the probability of a ticket holder failing to show up. Then, the probability of a ticket holder showing up is q = 1 - 0.2 = 0.8. Given that the airline wants to be 99% confident that all ticket holders who do show up will be able to board the plane, we want to find the maximum number of tickets that the airline can sell, such that the probability of more than 400 passengers showing up is no more than 1%.

Solution:

n = the maximum number of tickets that the airline can sell on a flight with 400 seats.

First, we need to check whether the conditions for applying the Central Limit Theorem are satisfied or not. Here, we are dealing with a binomial distribution, which satisfies the following conditions for applying the Central Limit Theorem:

np = 400(0.8)

= 320 ≥ 10nq

= 400(0.2)

= 80 ≥ 10

Since both of the above conditions are satisfied, we can approximate the binomial distribution with a normal distribution with mean

μ = np = 320 and variance σ2 = npq = 64.

The probability of more than 400 passengers showing up is P(X > 400), where X is the number of passengers showing up, which can be approximated by a normal distribution with the same mean and variance. Hence, we need to find the value of n, such that

P(X > 400) = P(Z > (400 - 320 + 0.5)/√64)

= P(Z > 2.37) ≤ 0.01

where Z is the standard normal variable with mean 0 and variance

1. Using the standard normal distribution table, we find that

P(Z > 2.37) = 0.009 is the closest value to 0.01. Therefore, we can set

P(Z > 2.37) = 0.009

in the above equation and solve for n as follows:

2.37 = (n - 320 + 0.5)/8n - 320 + 0.5

= 2.37 × 8n - 319.5 = 18.96n

n ≈ 338.55

≈ 339 (rounded up to the nearest integer)

Therefore, the maximum number of tickets that the airline can sell on a flight with 400 seats is n = 339,

such that it can be approximately 99% confident that all ticket holders who do show up will be able to board the plane. Given that an airline wants to sell as many tickets as possible for a flight, there is always a risk that some ticket holders might not show up on the day of the flight. The airline usually overbooks the flight to compensate for this risk. However, overbooking can lead to inconvenience for passengers, as there might be more passengers than the available seats on the flight. In order to avoid such inconvenience, it is necessary to determine the maximum number of tickets that the airline can sell, such that the probability of more than 400 passengers showing up is no more than 1%.To solve this problem, we used the Central Limit Theorem to approximate the binomial distribution with a normal distribution, since np and nq are both greater than or equal to 10. Using the de Moivre-Laplace 1/2-correction, we found that n = 339 is the maximum number of tickets that the airline can sell on a flight with 400 seats, such that it can be approximately 99% confident that all ticket holders who do show up will be able to board the plane.

Thus the airline can sell a maximum of 339 tickets on a flight with 400 seats, such that it can be approximately 99% confident that all ticket holders who do show up will be able to board the plane.

To know more de Moivre-Laplace 1/2-correction,  visit:

brainly.com/question/29750103

#SPJ11

Answer:

17.37 (Ignore this it asked for 20 characters)

Answer:

-0.4 or 2.3

Step-by-step explanation:

simple

each box is 0.1 unit

Answer:

Step-by-step explanation:

The answer is where the graph cuts the x-axis.

I can't see it very well but it looks like x = -0.4 and 2.3.

Answer:

Inverse Function = 4x -8

Step-by-step explanation:

replace x with y and replace x with y

solve for y (meaning isolate y)

y=(1/4x) +2

x= (1/4y) +2

x-2 = 1/4y

multiply by 4 on each side to remove 1/4 from the right side

4(x-2) = y

y= 4(x-2)

y= 4x -8

Inverse Function = 4x -8

The relation between a function and it's inverse function is given as follows:

Reflected through y = x.

Suppose we have a function with definition given as follows:

y = f(x).

To obtain the inverse function, we must exchange the variables x and y, and then isolate the variable y.

This entire procedure is equivalent to a reflection over the line y = x, hence the third option is the correct option for this problem.

More can be learned about inverse functions at brainly.com/question/3831584

#SPJ1

Answer:

8

Step-by-step explanation:

Add the top numbers together and get 64

add the bottom numbers together and get 8

8 divided by 64 equals 8.

Brainliest?

Answer:

Step-by-step explanation:

\(\sf n^{th}\) roots of a complex number is given by DeMoivre's formula.

   \(\sf \boxed{\bf r^{\frac{1}{n}}\left[Cos \dfrac{\theta + 2\pi k}{n}+i \ Sin \ \dfrac{\theta+2\pi k}{n}\right]}\)

Here, k lies between 0 and (n -1) ; n is the exponent.

\(\sf -1 + i\sqrt{3}\)

a = -1 and b = √3

\(\sf \boxed{r=\sqrt{a^2+b^2}} \ and \ \boxed{\theta = Tan^{-1} \ \dfrac{b}{a}}\)

\(\sf r = \sqrt{(-1)^2 + 3^2}\\\\ = \sqrt{1+9}\\\\=\sqrt{10}\)

                   \(\sf \theta = tan^{-1} \ \dfrac{\sqrt{3}}{-1}\\\\ = tan^{-1} \ (-\sqrt{3})\)

                   \(\sf = \dfrac{-\pi }{3}\)

n = 4

For k = 0,

          \(\sf z = \sqrt[4]{10}\left[Cos \ \dfrac{\dfrac{-\pi}{3} +0}{4}+iSin \ \dfrac{\dfrac{-\pi}{3}+0}{4}\right] \\\\\\z= \sqrt[4]{10} \left[Cos \ \dfrac{ -\pi }{12}+iSin \ \dfrac{-\pi}{12}\right]\\\\\\z = \sqrt[4]{10}\left[-Cos \ \dfrac{\pi}{12}-i \ Sin \ \dfrac{\pi}{12}\right]\)

For k =1,

         \(\sf z = \sqrt[4]{10}\left[Cos \ \dfrac{5\pi}{12}+i \ Sin \ \dfrac{5\pi}{12}\right]\)

For k =2,

       \(z = \sqrt[4]{10}\left[Cos \ \dfrac{11\pi}{12}+i \ Sin \ \dfrac{11\pi}{12}\right]\)

For k = 3,

      \(\sf z = \sqrt[4]{10}\left[Cos \ \dfrac{17\pi}{12}+i \ Sin \ \dfrac{17\pi}{12}\right]\)

For k = 4,

      \(\sf z =\sqrt[4]{10}\left[Cos \ \dfrac{23\pi}{12}+i \ Sin \ \dfrac{23\pi}{12}\right]\)

Answer:

Step-by-step explanation:

They have raised $1,750 so far. 70% of $2,500 is $1,750

Answer:

$1750

Step-by-step explanation:

70% of 2500 is 1750

Answer:

1. ひよこ     は     ちいさい     。

2. おおかみ     は     どうくつ     に     すんでいます     。

3. せんせい     は     どうぶつたち     を     みます     。

Answer:

6

Step-by-step explanation:

Step 1:

12 - 4 = x + 2

Step 2:

8 = x + 2

Step 3:

8 - 2 = x

Answer:

x = 6

Hope This Helps :)

The two clowns charge the same amount of money at 16.66 hours.

Payment for work based on hours worked (or sometimes per day or per amount of work done).

Here, let the duration of birthday party be x hours.

For Clown A,

Initial fee = $ 105

Additional charge = $ 9 per hour

Total amount of clown A = $ (9x + 105)   ...........(i)

For Clown B,

Initial fee = $ 155

Additional charge = $ 6 per hour

Total amount of clown B = $ (6x + 155)   ...........(i)

Now, according to question

9x + 105 = 6x + 155

9x - 6x = 155 - 105

3x = 50

x = 50/3

x = 16.66 hours

Thus, the two clowns charge the same amount of money at 16.66 hours.

Learn more about Wages from:

https://brainly.com/question/14718127

#SPJ1

Answer:

A theater group has 7 boys and 19 girls. What is the ratio of girls to the entire group?

Step-by-step explanation:

One ratio problem would be:

A theater group has 7 boys and 19 girls. What is the ratio of girls to the entire group?

In order to solve this problem we would first need to calculate the total number of individuals in the theater group. We do this by adding the number of boys with the number of girls.

7 + 19 = 26

Now since we know there are 19 girls, the ratio would be 19 girls for every 26 individuals, or in ratio format it would be ...  19 : 26

Let x be the number of laps Jada plans to swim.

According to the problem, 4 laps is 2/5 of the number of laps she plans to swim, so we can write:

4 = 2/5 * x

To solve for x, we can first multiply both sides by the reciprocal of 2/5, which is 5/2:

4 * 5/2 = x

Simplifying the left side:

10 = x

Therefore, Jada plans to swim 10 laps.

The possible values of x % 10, where x is an integer, are integers between 0 and 9, inclusive, i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

The modulo operation (represented by the percent symbol %) returns the remainder of the division of one number by another. For example, when x is divided by 10, the result of x % 10 is the remainder of that division.

Since 10 is a positive integer, when x is divided by 10, the result is always a non-negative integer. Furthermore, since the range of x is all integers, the result of x % 10 will always be less than 10.

Therefore, the possible x % 10 are integers in the range of 0 to 9, including 0 and 9. These are the remainders that can result from dividing x by 10. For example:

7 % 10 = 7

17 % 10 = 7

27 % 10 = 7

In all of these cases, the remainder is 7 when the number is divided by 10.

Learn more about modulo operation and remainders in arithmetic at:https://brainly.com/question/30326087

#SPJ4

Answer:\(a^5=\frac{4}{5}\)

Step-by-step explanation:

The 5th term of the arithmetic sequence is 4/5

What is Arithmetic Progression?

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the arithmetic progression be represented as A

Now , the value of A is

A = 1/5 , 7/20 , 1/2 , 13/20 ....

Now , the first term of the arithmetic sequence is a₁ = 1/5

The second term a₂ = 7/20

The common difference d = second term - first term

So , the common difference d = 7/20 - 1/5

The value of d = 3/20

Now , the nth term of the AP is given by

Tn = a + (n - 1) d, where Tₙ = nth term

Substituting the values in the equation , we get

T₅ = ( 1/5 ) + ( 5 - 1 ) ( 3/20 )

On simplifying the equation , we get

T₅ = ( 1/5 ) + ( 4 x 3 ) / 20

T₅ = 1/5 + 12/20

T₅ = 16/20

T₅ = 4/5

Therefore , the value of T₅ is 4/5

Hence , the 5th term of the arithmetic sequence is 4/5

To learn more about arithmetic progression click :

https://brainly.com/question/1522572

#SPJ2

The answers are underneath each problem. The reason this makes sense is  due to the distributive property.

27. GCF of 27 and 12 is 3

3(4+9)

28. GCF of 12 and 36 is 12

12(1+3)

29. GCF of 16 and 20 is 4

4(4+5)

30. GCF of 2x and 8 is 2

2(x+4)

31. GCF of 30 and 12x is 6

6(5+2x)

32. GCF of 42x and 49 is 7

7(6x+7)

To do this, find the GCF and then divide each number by so. Then, add them in parenthisis and multiply it by the GCF

Answer:

a=41

Step-by-step explanation:

Answer:

a = 49

Step-by-step explanation:

41 + a + 90 = 180

solve for a

hope this helped

have a good day ^^

The surface area of the pyramid is given by the equation A = 170.4 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of the pyramid be represented as A

Now , the equation will be

The slant height of the pyramid h = 6 inches

The side of the equilateral triangle = 12 inches

So , the perimeter of the triangle = 3 x side length

Substituting the values in the equation , we get

The perimeter of the triangle = 36 inches

The area of the base = 62.4 inches²

So , Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Substituting the values in the equation , we get

Surface Area of Pyramid = 62.4 + ( 1/2 ) ( 36 x 6 )

On simplifying the equation , we get

Surface Area of Pyramid = 62.4 + ( 108 )

Surface Area of Pyramid = 170.4 inches²

Hence , the surface area of pyramid is 170.4 inches²

To learn more about surface area of pyramid click :

https://brainly.com/question/15050758

#SPJ1

Answer:

4n+40

.................

The vertex, focus, and directrix of the parabola 5x^2 + 16y = 0 are (0, 0), (-4/5, 0), and x = 4/5, respectively.

To find the vertex, focus, and directrix of the parabola with the equation 5x^2 + 16y, we can use the standard form of the equation for a parabola:

y = (1/4p)(x - h)^2 + k

where (h, k) is the vertex and p is the distance between the vertex and the focus or the vertex and the directrix.

Comparing the given equation to the standard form, we have:

5x^2 + 16y = 0
=> 16y = -5x^2
=> y = -(5/16)x^2

From this, we can determine that the vertex is at the origin (0, 0).

To find p, we can use the formula p = 1/(4a), where a is the coefficient of x^2. In this case, a = -5/16, so p = 1/(4*(-5/16)) = -4/5.

Therefore, the vertex is (0, 0), the focus is (-4/5, 0), and the directrix is x = 4/5.

In conclusion, the vertex, focus, and directrix of the parabola 5x^2 + 16y = 0 are (0, 0), (-4/5, 0), and x = 4/5, respectively.

Know more about directrix here,

https://brainly.com/question/29498952

#SPJ11

The distance of the triathlon, given the time Ingrid spent swimming, biking, and running, is  61.5 miles

To find the distance of the triathlon, find the distance of the individual events which are the running, swimming, and biking. Then sum these distances up to find the triathlon distance that Ingrid ran.

The distance for swimming:
= Rate x Number of hours

= 3 x 0.5 hours

= 1.5 miles

The distance for biking:

= 12 x 3

= 36 miles

The distance for running:
= 6 x 4

= 24 miles

The triathlon distance is:

= 1.5 + 36 + 24

= 61.5 miles

Find out more on distance at https://brainly.com/question/2436048

#SPJ1

Step-by-step explanation:

according to the given question

there are 10 bags each have 15kg potatoes so basically, we have 150 kg of poatoes

i want these potatoes to be equally distributed in 50 bags

therefore, mass of potato in 1 bag = total kg's of potatoes÷nuber of bags

mass of potato in 1 bag=150÷50 equals 3 kg

and so, each bag will have mass 3 kg

Answer:

Step-by-step explanation:

You have to count the total weight of potatoes: 10 bags x 15 kg (each bag) = 150 kg. Now, you divide the total weight by the number of bags you want to make: 150 (total weight)/50(# of bags) = 3 kg per bag.  So you have to put 3 kg of potatoes in each bag.

The 95% confidence interval for the proportion of the population who prefer brand named items is:

CI = (0.102, 0.232)

What is confidence interval?

A confidence interval is a statistical tool used to estimate the range of possible values in which a population parameter, such as the mean or proportion, is expected to lie with a certain level of confidence based on the observed sample data.

To find the 95% confidence interval for the population proportion, we use the formula:

CI = p′ ± z*\(\sqrt{(p'q'/n)\)

where:

CI: confidence interval

p′: sample proportion

q′: 1 - p′

z: z-score from the standard normal distribution for the desired confidence level (95% in this case)

n: sample size

Substituting the given values, we get:

CI = 0.167 ± 1.96\(\sqrt{((0.1670.833)/180)\)

Simplifying, we get:

CI = 0.167 ± 0.065

Therefore, the 95% confidence interval for the proportion of the population who prefer brand named items is:

CI = (0.102, 0.232)

This means that we can be 95% confident that the true population proportion of people who prefer brand named items falls within this range.

To learn more about confidence interval visit:

https://brainly.com/question/15712887

#SPJ4

Answer:

Step-by-step explanation: