PLEASEEE HELPPPPP ILL GIVE BRAINLIEST

The form of the partial fraction decomposition of the given function is:

[tex]\frac{A}{x+5}+\frac{B}{x-4}[/tex]

To find the form of the partial fraction:

The rational expression given is: [tex]\frac{x-20}{x^2+x-20}[/tex]

Factor the provided rational expression's denominator:

[tex]\begin{aligned}\frac{x-20}{x^2+x-20} &=\frac{x-20}{x^2+5 x-4 x-20} \\&=\frac{x-20}{x(x+5)-4(x+5)} \\&=\frac{x-20}{(x+5)(x-4)}\end{aligned}[/tex]

Apply the partial fraction decomposition method now:

[tex]\begin{aligned}\frac{x-20}{x^2+x-20} &=\frac{x-20}{(x+5)(x-4)} \\&=\frac{A}{x+5}+\frac{B}{x-4}\end{aligned}[/tex]

Therefore, the form of the partial fraction decomposition of the given function is:

[tex]\frac{A}{x+5}+\frac{B}{x-4}[/tex]

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The correct question is given below:
Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients.

[tex]\frac{x-20}{x^2+x-20}[/tex]

The weight average of the coordinates is 5

The given parameters are:

The weight average is then calculated as:

Weight average = Sum of (Weight * Coordinate)/Sum of Weights

So, we have:

Weight average = (-1 * 1 + 4 * 2 + 9 * 2)/(1 + 2 + 2)

Evaluate the quotient

Weight average = 5

Hence, the weight average of the coordinates is 5

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Using the distance between two points to find the side lengths, the area of the parallelogram is of 60.3 square units.

The area of a parallelogram of dimensions l and w is given by the multiplication of these dimensions, that is:

A = lw.

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Hence, for this problem, the side lengths are:

Hence:

l = 6, w = 10.05, and:

A = 6 x 10.05 = 60.3.

The area of the parallelogram is of 60.3 square units.

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Answer:

child: 74 adult: 117 student: 37

Step-by-step explanation:

x=2z

x+y+z=191

7.5x+9.75y+8z=1593.5

The number of tickets sold for child is 86.

The number of tickets sold for adults is 62.

The number of tickets sold for child students is 43.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Total tickets sold = $1593.50 _____(1)

Total number of tickets sold = 191 _____(2)

Let the number of tickets sold for child = P _____(3)

Let the number of tickets sold for adults = Q _______(4)

Let the number of tickets sold for students = R ______(5)

Cost of child ticket = $7.50 ______(6)

Cost of adult tickets = $9.75 ______(7)

Cost of student tickets = $8 _______(8)

We can make equations as:

From (2), (3), (4), and (5)

P + Q + R = 191 ____(9)

From (1), (6), (7), and (8)

7.50P + 9.75Q + 8R = 1593.50 _____(10)

We have,

P = 2R putting in (9) and (10)

2R + Q + R = 191

We get,

3R + Q = 191 _____(11)

15R + 9.75Q + 8R = 1593.50

23R + 9.75Q = 1593.50 _____(12)

From (11).

Q = 191 - 3R putting in (12)

23R + 9.75 (191 - 3R) = 1593.50

23R + 1862.25 - 29.25R = 1593.50

-6.25R = -268.75

R = 43 putting in Q = 191 - 3R

We get,

Q = 191 - 3 x 43 = 191 - 129 = 62

Putting R = 43 in P = 2R

We get,

P = 2x43 = 86

We have,

P = 86, Q = 62 and R = 43

Thus,

The number of tickets sold for child is 86.

The number of tickets sold for adults is 62.

The number of tickets sold for child students is 43.

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The solution to the compound inequality is 1200 < x < 1600 and the meaning is she must keep her calories consumed between 1200 and 1600

The compound inequality is given as

2450 < 2x + 50 and 2x + 50 < 3250

Subtract 50 from both sides of the inequality

So, we have

2400 < 2x and 2x < 3200

Divide through the inequality by 20

So, we have

1200 < x and x < 1600

Combine the inequalities

1200 < x < 1600

Hence, the solution to the compound inequality is 1200 < x < 1600 and the meaning is she must keep her calories consumed between 1200 and 1600

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Answer:

3+3×1/4×3

3+3/12

3×12+3/12

39/12

Answer:

-47^6

Step-by-step explanation:

Answer:

Step-by-step explanation:

4x-6x²-2

Step one use PEMDAS

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

as a guidance

Everything in the parenthesis is simplified, and there isn't any exponent so we onto step 3 which is multiply.

There is a negative infant of the parenthesis -(2x²+8-3x)

that negative sign actually is a -1

therefore multiply -1 to each number inside the parenthesis

Product: -2x²-8+3x

Last step combine like terms

-4x²-2x²=-6x²

x+3x= 4x (remember there is an invisible 1 infront of that x variable)

6-8=-2

Answer:

Step-by-step explanation:

The first one its easy

The statements are:

x . y = m/n

substituting the values.

a/b . y = m/n

multiplication property of equality.

b/a . a.b . y  = m/n . b/a

simplify.

y = mb/na

The product of a rational number with an irrational number is an irrational number. To see this assume that x is a rational number and y an irrational number. Then let us assume that the product xy is rational, which means that there are integers a,b such that xy=a/b. But then we obtain y=(1/x)(a/b) which is also rational since the set of rational numbers is closed under multiplication. But this is a contradiction since y was assumed to be an irrational number.

Hence we made the required conclusion.

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Answer:

Step-by-step explanation:

Answer : Original price 382

55% of 382 = $210

Answer:

-6.1, 6.3, 630%

Step-by-step explanation:

-610%, 630%, 630%

Answer:

20

Step-by-step explanation:

To find this, we need to figure out what 1/5 is as a decimal

5/5 = 1, so 5 groups of 1/5 equals 1

Multiply this by 4, 20 groups of 1/5, or 20/5 = 4

Now we confirm this

1/5=0.2

4/0.2=20

So it is true

Hope this helps!^^

Answer:

1915

Step-by-step explanation:

nth term = 15n + 400

term to term = 15

n = position

eg:

n=1

1x15=15 + 400 = 415

n=2

2x15=30 + 400 = 430

n=101

101x15= 1515 + 400 = 1915

Answer:

1915

Step-by-step explanation:

formula for the nth term is

an = d times n + first term - d

an = n*d + a1 - d

find the difference between the numbers

it's 15 which is d

first term is a1 which is 415

a101 = 15 times 101 + (415 minus 15)

a101 = 1515 + 400

a101 = 1915

(i) Maximum students were watching T.V for 4-5 hours.

(ii) 34 students watched T.V for less than 4 hours.

(iii) 14 students spent more than 5 hours watching TV.

Given from the graph we can say that:

The process of acquiring, storing, and displaying data in a way that makes it easy for others to use (read or fetch data), such as in graphs or charts, is known as data handling. Statistics is another name for it. Additionally, it is employed for data comparison and mean, median, and mode extraction.

(i) maximum number of students watching TV  =32

Almost 32 students watched TV for 4-5 hours.

(ii) For students watching TV for less than 4 hours = ?

= 4 ₊ 8 ₊ 22

= 34

(iii) students who spent more than 5 hours watching  TV = ?

= 8 ₊ 6

= 14

Hence we get the desired answers.

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Answer: 13

Step-by-step explanation:

x = 3, y = 5

xy - 2=

(3)(5)-2=

15-2=13

The point-slope form of the equation for the line with a slope of [tex]\frac{6}{19}[/tex] that passes through the point[tex](-1,\frac{7}{5} )[/tex] is [tex]6x-19y=-\frac{163}{5}[/tex]

As per the question statement, we are supposed to find the point-slope form of the equation for the line with a slope of [tex]\frac{6}{19}[/tex] that passes through the point[tex](-1,\frac{7}{5} )[/tex] .

Before solving the question, we need to know about the point - slope form of the line i.e., [tex]y-y_{1} =m(x-x_{1} )[/tex]

where m = slope = [tex]\frac{6}{19}[/tex]

[tex]x_{1} =-1[/tex] and [tex]y_{1} = \frac{7}{5}[/tex]

Now substituting values, we get

[tex]y-\frac{7}{5} =\frac{6}{19} (x-[-1])[/tex]

[tex]y-\frac{7}{5} = \frac{6}{19} (x+1)[/tex]

[tex]19y - \frac{133}{5} = 6x+6[/tex]

Rearranging,

[tex]6x-19y+6+\frac{133}{5} =0[/tex]

[tex]6x-19y+\frac{163}{5} =0[/tex]

[tex]6x-19y=-\frac{163}{5}[/tex]

Hence our required equation is [tex]6x-19y=-\frac{163}{5}[/tex]

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The probability is 1/4 that the winners will be wearing numbers 2, 4, and 7.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

We have been given that a group of 12 dance competition contestants is wearing the numbers 1 through 12.

To determine the probability that the winners will be wearing numbers 2, 4 and 7

Here are favorable outcomes that the contestants wearing numbers 2, 4, and 7

So the number of favorable outcomes = 3

And there is a total number of outcomes = 12

Required probability = 3/12

Required probability = 1/4.

Thus, the probability is 1/4 that the winners will be wearing numbers 2, 4, and 7.

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The third term of the arithmetic sequence is 18.

The arithmetic sequence formula can be represented as follows:

nth term = a + (n - 1)d

where

Therefore, 4 numbers are inserted between 4 and 39.

Hence,

a = 4

39 = 4 + 5d

39 - 4 = 5d

35 = 5d

d = 35 / 5

d = 7

Hence, the common difference of the arithmetic sequence is 7.

Therefore, the sequence of the arithmetic sequence is as follows:

4, 11, 18, 25, 32, 39

Therefore, the third term of the arithmetic sequence is  18

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Answer:

assuming you wanted the value of m

[tex]m=\frac{5D}{9}+36[/tex]

__________

         [tex]D=\frac{9}{5}\left(m-36\right)\\=\frac{9}{5}\left(m-36\right)=D\\5\cdot \frac{9}{5}\left(m-36\right)=5D\\=9\left(m-36\right)=5D\\\frac{9\left(m-36\right)}{9}=\frac{5D}{9}\\=m-36=\frac{5D}{9}\\m-36+36=\frac{5D}{9}+36\\m=\frac{5D}{9}+36[/tex]

__________

Hope this helps.

Answer:

Step-by-step explanation:

(25x-5) 12X- Ax15

The perimeter of Stephanie’s triangle is half the perimeter of Juan’s triangle.Numerical expression to describe the perimeter of Stephanie’s triangle is S =(1/2) J;

Let as assume that

Stephanie's triangle has a perimeter (S)

And, Juan's triangle has a perimeter (J);

According to question, it implies:

S =(1/2) J;

The whole length of any closed shape's boundary is known as its perimeter. Let's use an illustration to try to comprehend this. You may have a sizable square-shaped farm, for instance. You now decide to fence your farm in order to protect it from stray animals. Finding the entire length of the farm's boundary is as simple as multiplying the length of one side of the farm by 4. There are a lot of situations like this when we can be applying the perimeter-finding notion without even realizing it.

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Answer:  6  8

Step-by-step explanation:

the dot will be line 6 and 8

if that makes sence

??

Answer:

x=12

Step-by-step explanation:

x÷4=3

x=4x3

x=12

12÷4=3

The average number of viewers over the two weeks written in scientific notation is 3.85 × 10^8. option C

Average number of viewers over the two weeks = (First week + Second week) / 2

= {(3.6 x 10⁴) + (4.1 x 10⁴)} / 2

= {3.6 + 4.1 × 10^(4×4) } / 2

= (7.7 × 10^16) / 2

= 3.85 × 10^8

Therefore, the average number of viewers over the two weeks written in scientific notation is 3.85 × 10^8.

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The probability of getting heads is 31/50.

Number of tosses = 50

Number of heads = 31

The probability of getting heads will be:

= Number of heads / Total number of tosses

= 31/50

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