What is the nature of roots of 2x² 4x 3 0?

The expression  aₙ > 0 and lim n → [∞] aₙ + 1 is true.

The term expression in math is defined as a sentence with a minimum of two numbers or variables and at least one math operation.

Here we have given that if an > 0 and lim n→[infinity] an + 1 an < 1, then lim n→[infinity] an = 0.

And we need to check whether the given statement is true or not.

While we looking into the given question, we have identified the following expression,

=> lim n → [∞] aₙ + 1

Here we have also know that the value of aₙ > 0.

When we equate the given expression with zero, we have get the following expression,

=> lim n → [∞] aₙ + 1 = 0

=>  lim n → [∞] aₙ = -1

Here we have given the condition that,  aₙ >0, so

=> lim n → [∞] aₙ = 0

Therefore, the expression is zero.

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Answer:

y=90 degrees

Step-by-step explanation:

x+y+70=180 degrees  ==> these three angles make up a triangle, and the

                                         the total sum of angles in a triangle is 180 degrees

Notice that y is on a straight line?

Straight lines are 180-degree angles called straight angles.

Hence:

(180-y)+x+70=180  ==>  these three angles also make up a triangle, and the

                                        the total sum of angles in a triangle is 180 degrees

180-y+x+70=x+y+70  ==> since both expressions equal 180, they both are

                                         equal to each other

180-y+x+70 + y = x+y+70 + y ==> add y on both sides to isolate y to one side

180 - y + y + x + 70 = x + y + y + 70  ==> simplify

180 + x + 70 = x + 2y + 70

180+x+70 - x = x+2y+70 - x  ==> subtract x on both sides to eliminate x

180 + x - x + 70 = x - x + 2y + 70  ==> simplify

180 + 70 = 2y + 70

180 + 70 - 70 = 2y + 70 - 70 ==> subtract both sides by 70 to simplify the equation

180 = 2y

y = 180/2

y = 90 degrees

Step-by-step explanation:

always remember Pythagoras for right-angled triangles :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

this principle must be always fulfilled, otherwise it is not a right-angled triangle.

when your have a triangle problem (particularly for a right-angled triangle) with only side information, there is a high chance that you need to use Pythagoras.

in our case

(2×sqrt(3))² = x² + (sqrt(3))²

4×3 = x² + 3

12 = x² + 3

x² = 9

x = 3

that's all.

FYI : sqrt(x²) has actually 2 solutions : -x and +x, as both are squared equal to x².

but a negative number does not make any sense for general side lengths and similar things. so, the positive solution here is the only valid one.

No, 4 is not a linear expression.

A linear expression is an algebraic expression involving two or more variables, where the highest power of each variable is one. Linear expressions can be written in the form of an equation, such as y = 2x + 5. In this equation, y and x are variables, and 2 and 5 are constants. The highest power of each variable is one, so this is a linear expression. In contrast, 4 is a constant and does not involve any variables, so it is not a linear expression.

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Answer:

To find a, you'll put the value 8.3 as x in the equation to get the value of y which is equal to a. For the second point you'll put -10.2 as the value of y in the equation to get x which is equivalent to b.

Step-by-step explanation:

every point represents an ordered pair of (x, y) values.

if the point is on the given line (or any other form of curve/ function), then these x and y values make the functional equation true. if the equation turns out to be false with these values, then the point is not on that functional curve.

so, we need to find a and b to make the equations true.

(8.3, a)

3×8.3 - 4a + 24 = 0

24.9 + 24 = 4a

48.9 = 4a

a = 48.9/4 = 12.225

(b, -10.2)

3b - 4×-10.2 + 24 = 0

3b + 40.8 + 24 = 0

3b + 64.8 = 0

3b = -64.8

b = -64.8/3 = -21.6

This is a geometric sequence since common difference is same between previous and next term.

The sum of arithmetic sequence is know as arithmetic series.

The general formula to find arithmetic series is:

[tex]S_{n} =\frac{n}{2} [2a_{1} +(n-1)d][/tex]

Since 8 17 26 and 35 have a common difference that is d=9 always between previous and next term so given sequence is arithmetic sequence.

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Answer:

140 gallons of water would it use for 10 loads of laundry.

Step-by-step explanation:

w ∝ l

w = kl

k = proportionality constant.

For, w =  28 gallons

l = 2 loads of laundry

Put in the equation;

28 = 2 k

k = 14

Now, when l = 10 loads of laundry, w = ?

w = 14 × 10

w = 140

There are only two factors of the number 31 which are 1 and 31. Then the integer number 31 will be a prime number.

A prime number is a positive integer having exactly two factors which are 1 and the number itself. Any number that does not follow this is termed a composite number.

The prime numbers from 1 to 100 are given below.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

The factor of the 31 will be given as,

31 = 1 x 31

There are only two factors of the number 31 which are 1 and 31.

Thus, the integer number 31 will be a prime number.

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The race result will not be disqualified due to an illegal wind.

In order to determine whether the wind velocity during the race was legal, we need to compare the wind velocity w to the legal wind speed limit of 5 km/hr. In this case, the wind velocity is given as 5ij km/h, which is purely vertical wind. The direction of the wind is not relevant in this case, since the race is run in the direction of the vector v, which is a purely horizontal direction. Since the wind velocity w is purely vertical and the race is run in a purely horizontal direction, the wind velocity w has no effect on the race result. Therefore, the race result will not be disqualified due to an illegal wind.

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We calculated the standard deviation for the given data set is 2.

In the statistics, standard deviation is an estimation that implies how far each available data apart from the mean value.

we have data, 5 5 9 9. Let, X is the list of data and X² is the square of data set.

                       X     X²

                       5      25

                        5      25

                        9      81

                        9      81    

sum of X= ∑X = 28

sum of X² = ∑X² =212

Standard deviation = √[∑X²/N - (∑X/N)²]

where N is the number of data and N= 4

Now standard deviation = √[212/4 - (28/4)²]

                                     = 2

hence, standard deviation is 2

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The term (7 + 3x) is a factor of the quadratic equation 3x² + 7x  .

A number is called a factor of the quadratic equation if that number satisfies the equation .

the term is given as : 7 + 3x ,

solving it we get ; 3x = - 7

So , x = -7/3 .

to check whether it is a factor , we substitute the value of x in the equation ,

we get , 3x² + 7x

= 3(-7/3)² + 7(-7/3)

= 49/3 - 49/3

= 0

Therefore , Yes , (7 + 3x) is the factor of 3x² + 7x  .

The given question is incomplete , the complete question is

Is (7 + 3x) is a factor of the quadratic equation 3x² + 7x  ?

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The value of the discriminant of the given expression x² + 4x +40 = 0  is equal to -144.

As given in the question,

Given expression is equal to :

x² + 4x +40 = 0

Standard formula of the discriminant for the general quadratic equation

ax² + bx + c = 0 is given by :

Discriminant is represented by  'D'

D = b² - 4ac

Here b = 4 , a = 1 and c = 40

Substitute the value in the formula we get,

D = 4² - 4(1)(40)

⇒D = 16 - 160

⇒ D = -144

Therefore , the value of the discriminant of the given expression x² + 4x +40 = 0 is equal to -144.

The above question is incomplete ,the complete question is :

What is the value of discriminant x² + 4x +40 = 0?

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Answer:

Cos A = adjacent/hypotenuse

Cos A = 15/17

Cos A = 2.143

tan A = opposite/adjacent

tan A = 8/15

tan A = 0.533

sin A = opposite/hypotenuse

sin A = 8/17

sin A = 0.471

Step-by-step explanation:

Answer:

7/ 180 degree

8/ 90 degree

9/ 270 degree

10/ 180 degree

Step-by-step explanation:

7/ Each square box is 90 degrees, and we see that the square rotated over 2 boxes, so it is 180 degrees clockwise.

8/ We see that the triangle rotated 90 degrees clockwise.

9/ We see that the triangles rotate over three boxes, which is 270 degrees clockwise.

10/ We see that the triangles rotate over 2 boxes, which is 180 degrees clockwise.

Answer:

7) 180°

8) 90°

9) 270°

10) 180°

Step-by-step explanation:

7)

The notation for rotating 180 degrees clockwise about the origin is (the degrees symbol was omitted): [tex]R_{-180, O} (x,y) - > (-x,-y)[/tex]

This means that when you rotate 180 degrees clockwise about the origin, the coordinates of the figure become their opposite.

C(2,-1) -> C'(-2,1)

N(4,-2) -> N'(-4,2)

W(3,-4) -> W'(-3,4)

Y(1,-3) -> (-1,3)

..............fun fact: rotating 180 degrees clockwise is the same as rotating 180 degrees counterclockwise

8)

The notation for rotating 90 degrees clockwise about the origin is (the degrees symbol was omitted): [tex]R_{-90, O} (x,y) - > (y,-x)[/tex]

This means that when you rotate 90 degrees clockwise about the origin, the x and y coordinates flip, and the x coordinate becomes its opposite.

B(-4,-2) -> B'(-2,4)

E(-1,-5) -> E'(-5,1)

I(0,-1) -> I'(-1,0)

..............fun fact: rotating 90 degrees clockwise is the same as rotating 270 degrees counterclockwise

9) The notation for rotating 270 degrees clockwise about the origin is (the degrees symbol was omitted): [tex]R_{-270, O} (x,y) - > (-y,x)[/tex]

This means that when you rotate 270 degrees clockwise about the origin, the x and y coordinates flip, and the y coordinate becomes its opposite.

G(-4,2) -> G'(-2,-4)

Z(-1,5) -> Z'(-5,-1)

T(0,2) -> T'(-2,0)

..............fun fact: rotating 270 degrees clockwise is the same as rotating 90 degrees counterclockwise

10) The notation for rotating 180 degrees clockwise about the origin is (the degrees symbol was omitted): [tex]R_{180,O} (x,y) - > (-x,-y)[/tex]

This means that when you rotation 180 degrees clockwise about the origin, the coordinates of the figure become their opposite.

B(-3,-5) -> B'(3,5)

G(-4,0) -> G'(4,0)

C(-5,-4) -> C'(5,4)

..............fun fact: rotation 180 degrees clockwise is the same as rotation 180 degrees counterclockwise

Answer:

$58.50

Step-by-step explanation:

1.2 kg = 1200g

To get from 200 to 1200, we time 6, so we take $9.75 times 6 to get the price.

$9.75 times 6 = $58.50

So, the cost of 1.2kg cheese is $58.50

The answer is $58.50

I have attached the explanation! :)

What is Clustering method in unsupervised learning?

An method known as unsupervised learning discovers patterns in untagged data. The idea is to compel the computer to create a clear representation of its surroundings and then produce innovative material from it through imitation, which is a crucial learning method for people.

There are several ways to evaluate the performance of a clustering method in unsupervised learning. Some common evaluation metrics include:

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Answer:

85

Step-by-step explanation:

Think of mean as the average of a set of values. In this case, we have to find the average of Danielle's scores. To do this, add all of the values together and divide it by the number of values we have:

We have 11 scores so we will divide all of them by 11:

[tex]\frac{84+85+83+86+80+85+86+88+89+86+83}{11} = \frac{935}{11} = 85[/tex]

Standard Deviation of 7 is  2.983.

How to interpret  standard deviation?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.

                    Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

Describe standard deviation using an example.

Think about the following data: 2, 1, 3, 2, 4. The average and the sum of squares representing the observations' variances from the mean will be 2.4 and 5.2, respectively. This means that (5.2/5) = 1.01 will be the standard deviation.

       Mean = 7,

Standard Deviation of 7 =   2.983.

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Yes, the area and the volume are inversely proportional to each other.

Here we have to verify that the area and volume inversely proportional.

As we all know that in math, the term area is used for the 2 dimensional shapes where as the volume refers the 3 dimensional shapes.

Let us consider the example of square.

We all know that the area of square is a x a whereas the volume of square is a x a x a.

Here we have identified that the volume is one step ahead of the area and each of them are inversely proportional to each other.

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Answer:

81b^2 + 54b + 9

Step-by-step explanation:

(9b+3)^2=

(9b+3)(9b+3)=

9b(9b+3) + 3(9b+3) =

(9b*9b + 3*9b) + (3*9b + 3*3)=

9*9*b*b + 27b + 27b + 9 = 81b^2 + 54b + 9

In class 11 we learn more than the basics of solving quadratic equations.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

A quadratic equation is of the form ax² + bx + c = 0.

Quadratic equations can be solved using one of three main strategies, factoring, the quadratic formula, or completing the square.

Generally, quadratic equation starts from mid school where we learn all the basics and then we learn to solve word problems using quadratic equations and in high school, we learn quadratic equations of complex numbers.

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The probability that 5 people sit in the correct order in either direction clock or anti-clock is equal to the probability of any one of the orders occurring, which is 1/2, or 50%.

To calculate the probability that they sit in the correct order in both directions, you would multiply the probability of each event occurring. Since the probability of either event occurring is 1/2, the probability of both events occurring is (1/2) * (1/2) = 1/4, or 25%. This means that there is a 25% chance that the 5 people will sit in the correct order in both directions around the table.

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Answer:

  (i) height: 36.6 m

  (ii) BP = 36.6 m

  (iii) AB = 51.8 m

  (iv) AC = 73.2 m

Step-by-step explanation:

Given angles of elevation of 45° and 30° to the same point A from locations 100 m apart, you want to know the height of A, and distances BP, AB, and AC in the diagram.

The figure is divided into two special triangles. The one on the left is an isosceles right triangle with side lengths in the ratio 1:1:√2. The one on the right is a 30°-60°-90° triangle with side lengths in the ratio 1:√3:2. The common side AP corresponds to one ratio unit in each of these ratios.

BP = AP = 1 ratio unit means BP : PC = 1 : √3, and ...

  BP/BC = 1/(1+√3)

  BP = BC/(1+√3) ≈ (100 m)/2.73205

  BP ≈ 33.6 m

  AP = 33.6 m . . . . . . same as BP

AB is √2 times AP, so is ...

  AB = √2 · 36.6 m

  AB ≈ 51.8 m

AC is 2 times AP, so is ...

  AC = 2·(36.6 m)

  AC = 73.2 m

Answer:

[x] is the greatest integer function, which returns the greatest integer less than or equal to x. This can be written as a piecewise linear function as follows:

f(x) =

x-1, if x is not an integer and x>1

x, if x is an integer or x<=1

For example, if x=6, then f(x)=6. If x=6.5, then f(x)=5. If x=0.5, then f(x)=0.

So, the piecewise linear function for f(x)=[x] is:

f(x) =

x-1, if x is not an integer and x>1

x, if x is an integer or x<=1

The value of the given and completed expression in this problem is

-1

Combined operations are defined as a set of operations applied to the same problem, for example addition, subtraction, multiplication, are frequently used in arithmetic polynomials.

In this case we have an arithmetic polynomial.

We complete the expression as follows:

1 + 2 - 3 + 4 - 5

We group the positive terms on one side and negative terms on the other:

The value of the expression (1 + 2 - 3 + 4 - 5) is -1

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83% of pupils passed the test as a group.

An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls)

It is claimed that two ratios are in proportion if they are the same. A/B Equals C/D if the four elements are a, b, c, and d in that order. The terms a and d are referred to as extremes, whereas b and c are referred to as medium terms. The ratio equates the product of extremes to the product of means.

Results in total: 65% of the review was finished.

The desired results were 55% exam pass.

The percentage is as follows:

p = 55/65 x 100%

  = 82.3%.

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Answer:

The percentage of decrease from 63.2 to 35 is 44.5%.

Step-by-step explanation:

To calculate the percent of decrease from 63.2 to 35, we can use the following formula:

percent of decrease = (original value - new value) / original value * 100%

Plugging in the values given in the question, we get:

percent of decrease = (63.2 - 35) / 63.2 * 100%

Solving for the percent of decrease, we get:

percent of decrease = 44.5%

Therefore, the percentage of decrease from 63.2 to 35 is 44.5%.

Answer:

44.6202532 % decrease

Step-by-step explanation:

To find the percent decrease, take the original amount, subtract the new amount and then divide by the original amount

(63.2 - 35) /63.2

28.2/63.2

.446202532

Change to percent form

44.6202532 %

Answer: [tex]p + 254 \leq 471[/tex]

Step-by-step explanation:

The number of people in the theater plus 254 )the number of people already in the theater) must be less than or equal to the maximum amount allowed to be seated, 471.

So, [tex]p + 254[/tex] represents the number of people in the theater.

471 is the maximum amount of people.

So, p + 254 must be less than or equal to [tex]p + 254[/tex].

Therefore, we can say that:

[tex]p + 254 \leq 471[/tex]