Show that 1/x is an integrating factor of the equation dy/dx-y/x = 3x​​

The y-intercept of the equation 5x-4y = -12 is 3.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

We have the equation:

5x-4y = -12

To find the y-intercept:

First, we have to simplify the equation as subject to y.

5x-4y = -12

4y = 5x+ 12

y = (5/4)x+12/4

y =  (5/4)x + 3

Now, we know the slope-intercept form:

y = mx+b,

where m is the slope and b is the y-intercept.

Comparing, both the equation,

b = 3

3 is the y-intercept.

Therefore, y-intercept is 3.

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Answer:

15 people attended the party

An example of value of expression is 5 × 2a.

In the field of mathematics, a value of an expression can be described as such an expression that includes two or more two mathematical numbers. Apart from the numbers, one or more than one mathematical operation is also a part of the value of the expression.

In the example, 5×2a, 5 and 2 are the two mathematical numbers and multiplication (×) is the mathematical operation. Hence, the expression 5×2a serves as an appropriate example of the value of expression in the field of mathematics.

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Answer:

the answer is 20

Step-by-step explanation:

20+0=20

The standard form of the polynomial function with zeroes 1, 2, -2, and -3 is

[tex]x^4[/tex] + 2x³ - 7x² - 8x + 12 = 0.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

The zeroes of a polynomial:

x = 1, 2, -2, and -3.

This can be written as,

(x - 1)(x - 2)(x + 2)(x + 3) = 0

Simplify to get the equation.

(x² - 2x - x + 2)(x² + 3x + 2x + 6) = 0

(x² - 3x + 2)(x² + 5x + 6) = 0

[tex]x^4[/tex] + 5x³ + 6x² - 3x³ - 15x² - 18x + 2x² + 10x + 12 = 0

[tex]x^4[/tex] + 2x³ - 7x² - 8x + 12 = 0

Thus,

The equation of the polynomial is [tex]x^4[/tex] + 2x³ - 7x² - 8x + 12 = 0.

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The common region for all the inequalities y ≥ 2, y ≤ 2x + 2and x + y ≤ 4 is represented by ΔABC (the last graph).

What is an inequality?

"It is a statement which consists of an order relationship (greater than, greater than or equal to, less than, or less than or equal to) between two mathematical expressions."

For given question,

We have been given three inequalities

y ≥ 2 ,

x + y ≤ 4 ,

y ≤ 2x + 2

If we draw the graph of these three inequalities then the common region represents the all the points that fulfill all three inequalities.

An inequality y ≥ 2 represents all the points on and above the line y = 2

An inequality x + y ≤ 4 represents all the points on and below the line       x + y = 4

An inequality y ≤ 2x + 2 represents all the points on and below the line    y = 2x + 2

Consider the following graphs.

The first graph represents the points which fulfill the inequality y ≥ 2

The graph for an inequality x + y ≤ 4 is represented by the shaded blue region.

The graph for an inequality y ≤ 2x + 2 is represented by the shaded green region.

The common region for all the inequalities is represented by ΔABC

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There are two zeros of the polynomial 2x²-3x+4.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial is 2x²-3x+4.

Two times of x square minus three times of x plus four.

2x²-3x+4=0

We find the roots by using quadratic equation formula.

x=-b±√b²-4ac/2a

a=2, b=-3, c=4

x=3±√9-4(8)/4

x=3±i√23/4

So the roots are x=3+i√23/4 and x=3-i√23/4.

A polynomial of degree 2 can have 2 real zeros, 1 real zero, or no real zeros

Hence, there are two zeros of the polynomial 2x²-3x+4.

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Mean and Median are not the same.

Mean is the average value of a given dataset. Mean is calculated by adding all the values in the dataset and divided by the number of values.

Median is defined as the number in the middle of the dataset. Median is calculated by arranging the values in ascending order and finding out the middle most term. If there are two middle terms, then we calculate the average of both.

Mean is the arithmetic average, while median is the positional average. There may be various external factors that contribute in defining the mean. So for uneven data, median is the more robust value. Mean defines the central value of data, but median defines the midpoint of data and classify the data points to two sets, higher value or lower value.

So mean is the average of the given dataset and Median is the mid value of the dataset when arranged in ascending order.

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To see the steps of copy and paste a formula.

Now, According to the question:

Here's how you copy and paste a formula:

1. Select the cell with the formula you want to copy.

2. Press. + C.

3. Click the cell where you want to paste the formula.

4. To quickly paste the formula with its formatting, press + V.

5. Clicking the arrow gives you a list of options.

Let's know to more:

How do I apply the same formula to multiple cells in Excel?

Fill formulas into adjacent cells

1. Select the cell with the formula and the adjacent cells you want to fill.

2. Click Home > Fill, and choose either Down, Right, Up, or Left. Keyboard shortcut: You can also press Ctrl+D to fill the formula down in a column, or Ctrl+R to fill the formula to the right in a row.

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As the standard deviation 35 is high so the values are far from the mean.

In the statistics, standard deviation is an estimation that implies how far each available data apart from mean value. In a word, it is a measure of variances of data in relation to the mean. A low standard deviation indicates that values are closer to mean value and high standard deviation indicates the values are distributed widely.

Standard deviation of a given data set 35 means that all data set are 35 unit far from the mean value. As the value is high so all the values are dispersed widely relative to the mean value.

In the other hand, this high standard deviation implies there are enough variances in the given data in relation to the mean.

Standard deviation is one of the measures of risk assessment. Imagine an organization published a number of statistical observation data. If we find a high standard deviation, then it will be high risk of collapse of the business.

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Answer:

The solution to the system of equations is x = 9/12 and y = 27/60.

Step-by-step explanation:

To solve a system of equations, we can use elimination or substitution. In this case, we can use elimination by adding the equations together. When we add the two equations, the y-terms will cancel out, leaving us with an equation in terms of x only.

First, let's add the equations:

-5y + 3x = 3

-8y + 9x = -12

-----------

-13y + 12x = -9

Then, we can divide both sides of the equation by -13 to get the value of x:

(-13y + 12x) / -13 = (-9) / -13

12x = 9

x = 9/12

Since we know the value of x, we can substitute it back into either of the original equations to find the value of y:

-5y + 3(9/12) = 3

-5y + 27/12 = 3

-5y = -27/12

y = 27/60

Therefore, the solution to the system of equations is x = 9/12 and y = 27/60.

Answer:

i believe it is G

[tex] \frac{7}{3} [/tex]

Conscientiously cleaning your devices is crucial, as any residue that remains on your device may impact the accuracy of your measurements. The material your device is made of plays a significant role in the cleaning method you should use.

A tool used to measure a physical amount is called a measuring instrument. Measurement is the process of gathering and comparing physical quantities of actual things and events in the physical sciences, quality control, and engineering.

The process of measuring yields a number associating the subject under study and the referenced unit of measurement, and established standard objects and occurrences are employed as units. These numerical relations are acquired using measuring devices and rigorous test procedures that specify the instrument's use.

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According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)

Quadrilateral

Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.

Given,

If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.

Here we need to find the coordinate of D'.

In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.

While we looking into the graph, we have identify the point of

A (0,0), B(-4, 3), C(1,5) and D(2,3)

Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).

According to this rule, the new coordinates are written as,

A(0,0) = A'(0,0)

B'(-4,3) = B'(-3,-4)

C(1,5) = C'(5, -1)

D(2,3) = D' (3, -2)

Therefore, the new coordinate of D' is (3, -2).

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According to the SSS disbursement account, it takes 2 business days for approval.

The term disbursement refers to the payment of federal student aid funds to the student by the school.

Here we have to find the number of days taken for SSS disbursement account approval.

In order to find the solution, we must know the process of SSS disbursement policy, that takes the payment data and transforms it into a disbursement instrument.

Here we have given that, as per the SSS disbursement policy, it takes member-borrower shall receive the full short-term loan proceeds in their account within two banking days from the loan date provided the payment instruction of SSS was sent before the cut-off time.

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The probability of an individual scoring above 500 on the GMAT is 0.5984.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the centre of the range.

Given:

[tex]\mu[/tex] = 527

[tex]\sigma[/tex] = 112

Now, z= (500-527)/112

z= -27/112

z= -0.2410

and, P( X>500)= P(z> -0.2401)

                        = 1- 0.4052

                        = 0.5984

Hence, the probability of an individual scoring above 500 on the GMAT is 0.5984.

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Answer:

h = 9

k = -8

Step-by-step explanation:

⭐ [tex]g(x) = (x-h)^2 + k[/tex] is already written in vertex form.

⭐ Vertex form: [tex]f(x) = a(x-h)^2 +k[/tex], where the vertex is (-(-h), k)

We are already given the vertex (9,-8), so we have to substitute these numbers into g(x).

[tex]g(x) = (x-9)^2 -8[/tex]

The equation of parabola is solved and the values of h and k are 9 and -8 respectively

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

y = a ( x - h )² + k

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

The vertex form of a parabola function is given by:

g(x) = a(x - h)² + k

where (h, k) is the vertex.

In this case, we are given that:

g(x) = (x - h)² + k

And the vertex is located at (9, -8)

So we have:

h = 9

k = -8

Therefore, the function g(x) can be written as:

g ( x ) = ( x - 9 )² - 8

Hence , the equation of parabola is g ( x ) = ( x - 9 )² - 8

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Answer:

13

Step-by-step explanation:

39/3

Answer:

a. 1350

b. 6500

Step-by-step explanation:

1.5%×4500=5850

1350+4500=5850

Step-by-step explanation:

The union of two sets is to avoid counting the same elements twice.

The mathematical logic subfield of set theory investigates sets, which can be loosely defined as collections of objects. Although any object can be combined into a set, set theory, as a mathematical discipline, focuses primarily on those that are relevant to mathematics as a whole.

Given union of set

(A ∪ B),

The set of all objects that are members of either A or B, or both, is the union of the sets A ∪ B.

let us take example,

A = { 1, 2, 3, 4}

B = {3, 4, 5, 6, 7}

(A ∪ B) = { 1, 2, 3, 4} ∪  {3, 4, 5, 6, 7}

we can simply write all of A and B's elements in a single set to avoid duplicates to find A U B.

(A ∪ B) = {1, 2, 3, 4, 5, 6, 7}

Hence the  union of two sets is a set that contains all the elements of both set and avoid duplicates.

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Answer:

Solution:

Given,

Ratio of photo to to the photo frame=2:3

Length of photo frame=36cm

= 36÷3

=13

then,

Length of photo = 13 ×2

= 26cm

Step-by-step explanation:

Therefore,the length of the photo is 26cm

Answer:

No

Step-by-step explanation:

9/16 and 5/9 have a common factor is 144

So, we have

81/144  and 80/144

So, 9/16 > 5/9

Answer:

Step-by-step explanation:

no they are not equal, NO

Answer:

l = 2w   (length is twice the width)

P = 2l + 2w

54 = 2l + 2w  (but we know l equals 2w so we can replace l with 2w)

54 =2(2w) + 2w

54 = 6w

w = 9

l =2(9)   (l = 2w

l=18

A = lw

Therefore , the solution to the given problem of the equation whose factors are (x+2)(x+1)(x+3).

Describe equation.

Two expressions joined by an equal sign form a mathematical statement known as an equation.

An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

According to the Given question:

x³ + 6x² + 11x +6

This pattern of coefficients 1, 6, 11, 6 is actually one that you are likely to encounter frequently.

For demonstration reasons, let's see what occurs if we begin by using the typical technique for resolving a general cubic:

We can use a linear substitution, t = x + b/3a, to simplify any cubic of the form ax3 + bx2 + cx + d, resulting in a cubic in the form a + b + et + f without a quadratic term.

This is the most straightforward type of Tschirnhaus transformation.

In our example, a = 1 and b = 6, so we want t = x + 2.

Note that:

=  + 6+ 12x +8

So we find:

+ 6+ 11x +6 =   − (x + 2)

=  - t

= t ( - 1)

= t(t − 1)(t + 1)

= (x+2)(x+1)(x+3)

Therefore , the solution to the given problem of the equation whose factors are (x+2)(x+1)(x+3).

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Answer:

[tex]a_n = \frac{1}{6}(6)^{n-1}[/tex]

Step-by-step explanation:

⭐What is the formula of a geometric sequence/progression?

We are given the geometric sequence.

Thus, we need to find the first term and the common ratio, and substitute those values into the geometric sequence formula.

The first term is [tex]\frac{1}{6}[/tex]

⭐How do we find the common ratio?

I am choosing term 1 and term 2, but you can choose any other 2 terms that are consecutive.

term 1 = [tex]\frac{1}{6}[/tex]

term 2 = [tex]1[/tex]

[tex]\frac{term2}{term1} = \frac{1}{\frac{1}{6}}[/tex]

[tex]\frac{term2}{term1} = 6[/tex]

∴ The common ratio of this sequence is 6.

Now, substitute these values (common ratio & first term) into the geometric sequence equation.

[tex]a_n = \frac{1}{6}(6)^{n-1}[/tex]

So, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.

An exponential function of the form y = a * b^x has a growth factor of b. Therefore, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.

For example, if a = 2, then the function y = 2 * 5^x has a growth factor of 5.

Here is a table showing the values of y for some values of x:

x       y

0        2

1        10

2        50

3        250

4        1250

As x increases, the values of y increase exponentially at a rate determined by the growth factor of 5.

Therefore, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.

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For example, if a = 2, then the function y = 2 * 5^x has a growth factor of 5.

Here is a table showing the values of y for some values of x:

x       y

0        2

1        10

2        50

3        250

4        1250

As x increases, the values of y increase exponentially at a rate determined by the growth factor of 5.

Therefore, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.

The given data (2, 2, 3, 3, 4, 4, 5, 5, 6, 6) has no mode.

A mode is defined as the value that has the highest frequency in a given set of values. It is the value that appears the most number of times.

In statistics, the value that consistently appears in a particular collection is referred to as the mode. The mode or modal value in a data collection is sometimes referred to as the value or number that occurs most frequently in the data set. In addition, to mean and median, it is one of the three measures of central tendency.

The mode is the value that occurs the most often in a given set of data.

Given data:  2, 2, 3, 3, 4, 4, 5, 5, 6, 6.

In the given observations, data is repeated an equal number of times.  

So, the given data has no mode.

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The ratio that describes the number of baskets the player made to the number of baskets the player attempted is 9:15. This can be simplified to 3:5.

The ratio of the number of baskets made by the player to the number of baskets attempted is 9/15. This ratio can be simplified to 3/5, which means that for every 5 baskets attempted, the player made 3 baskets. This ratio can also be expressed as a percentage by dividing the number of baskets made by the number of baskets attempted and multiplying the result by 100%. In this case, the percentage of baskets made by the player is 60% (9 baskets made / 15 baskets attempted * 100% = 60%). This means that out of every 100 baskets attempted by the player, he made 60 baskets.

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