ABCD is an isosceles trapezoid with legs LINE AB and LINE CD and base LINE BC. If the length of LINE AB is 7y - 4, the length of LINE BC is 4y - 6 and the length of LINE CD is 8y - 18, find the value of y.thank you ! :)

The simplified equation is (π2 / 2) * ∫[0, ∞] (x(2x-1) * e(-x) / (Γ(x) * Γ(1 - x)) DX

a. To prove B(x+1, y) = x * B(x, y), proceed as follows.

Start with B(x+1, y) = [(x+1)! * y!] / ((x+y+2)!) (using the definition of B(x, y)).

Rewrite 1 / (x+1) to (x+y+2 - (y+1)) / (x+y+2) .

Using the formula above, express B(x+1, y) as (x+y+2) / (x+y+2) * [(x+1)! to rewrite. * y!] / ((x+y+2)!) - (y+1) / (x+y+2) * [(x+1)! * y!] / ((x+y+2) !).

Simplify the formula to (x+y+2) / (x+y+2) * B(x, y) - (y+1) / (x+y+2) * B(x, y) increase.

Simplify further to B(x, y) - (y+1) / (x+y+2) * B(x, y).

Note that B(x, y) can be expressed as (x / (x+y+1)) * B(x, y) .

Substitute this formula in the previous step to get,

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y).

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y)

= x * B(x, y)

You have now proved B(x+1, y) = x * B(x, y).

b. We wish to prove the identity Γ(2x) = ((2sin(πx))) * Γ(x) * Γ(x + 1/2).

Integrate ∫[0, ∞] (x(2x-1) * Start with dx.

Evaluating this integral using the permutation u = du is obtained.

Simplify the integral to (1/2) * Γ(x + 1/2).

Express sin(πx) as π / (Γ(x) * Γ(1 - x)).

Let the original integral be π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) * e(-x) * (1/sin( πx) Rewrite.)) DX.

Substituting the equations,

The integral, π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) *

We get * (π / (Γ(x) * Γ(1 - x)))) dx.

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The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

From the question, we have the following parameters that can be used in our computation:

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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The domain is the values of the x coordinate the graph takes, then in this case we have:

The range is the values of the y coordinate the graph takes, then in this case we have:

Therefore the answer is the third option.

Answer:

9,420 colors making exactly 1 car of each color exist

Step-by-step explanation:

Since there is no additional information, such as the number of colors we have to assume the maximum. Since there are over 10 million colors that exist and there is at least one car of each color, then there would be a maximum of 9,420 colors making exactly 1 car of each color exist. On the other end of the spectrum would be 2 colors making 4,710 cars of each color.

The number of different possible colors of vehicle can be found using the relation

\( \frac{9240}{c} \)

The number of different colors possible :

The number of different possible colors can be obtained using the expression :

\( \frac{9240}{c} \)

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The table that includes that information correctly when the problem says an object's displacement is 88.8 m is table B.

It should be noted that a displacement simply means the vector quantity that illustrates how far a particular place is.

In this case, the table that includes that information correctly when the problem says an object's displacement is 88.8 m is table B.

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Answer:A  dude if you already know it say it to make it easier for people don't be lazy

Step-by-step explanation:

Step-by-step explanation:

here's your solution

=> time for Bettinia = 3.8 hrs

=> speed of her = 56 mph

=> distance covered by her = 3.8*56 = 212.8m

=> time for wills = 4.1 hrs

=> speed of wills = 52 mph

=> distance = 4.1 * 52 = 213.2m

=> wills covered more distance = 0.4 m

hope it helps

Answer:

25π

Step-by-step explanation:

The formula for the area of a circle is \(\pi r^{2}\). In this case, \(r\) is 5, to the area will we \(25\pi\).

The percentage of the red roses did Fancy Flowers Florist use to decorate for the grand opening at the museum is 80%

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Given that, a flower shop received a shipment of 250 red roses, they will use 200 out of this for decorating for the grand opening of the Historical Museum,

We need to find the percentage of the red roses used there,

So, the percentage of the red roses used in decoration =

200 / 250 x 100

= 0.8 x 100

= 80%

Hence. the percentage of the red roses did Fancy Flowers Florist use to decorate for the grand opening at the museum is 80%

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Answer:

8

Step-by-step explanation:

friend formula of Range = Max(Maximum) - Min(Minimum)

Maximum= 9 - Minimum = 1

Range = 8.

if it helps don't forget to like and mark me down

Answer:

The answer is 8

Step-by-step explanation:

The biggest number in the set is 9, and the smallest is 1, so if you subtract you get 8.

  9

-  1

-------

  8

Answer:

C

Step-by-step explanation:

Line A is Parallel to Line B

Line C intersects Line A and B

Answer:

line C

Step-by-step explanation:

The number of years the annuity will last if it pays $300 per year is 18 years.

An annuity is an investment that pays the investor a fixed periodic amount for many years in the future.

The annuity payment may be monthly or yearly, as the case may be.

An online finance calculator can compute the annual payment (annuity).

I/Y (Interest per year) = 7%

PV (Present Value) = $3,000

PMT (Periodic Payment) = $-300

FV (Future Value) = $0

Results:

N = 17.795

Sum of all periodic payments = $-5,338.44

Total Interest $2,338.44

Thus, for an annuity with a present value of $3,000, earning 7% per annum and paying $300 per year will last almost 18 years.

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The present value of an annuity is $3,000 and earns 7% per annum.

Find the number of years the annuity will last if it pays $300 per year.

By Angle-Angle-Side (AAS) triangle congruence theorem we know that two triangles are congruent if they have two sets of congruent angles and a set of non-included congruent sides.

Since no figure is given in the question we employ the reflexive characteristic to demonstrate that the overlapping sections are congruent in order to demonstrate that overlapping triangles are congruent.

If two triangles are precisely the same size and shape—that is, if they have the same side lengths and angle measurements—they are said to be congruent. If we are aware that two triangles have all the same sides and angles, we can conclude that the triangles are congruent.

To demonstrate that two triangles are congruent, however, we don't necessarily need to know that all of their sides and angles are congruent.

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(9) The slope of a line perpendicular to the line, f(x) = 0.75x + 6 is - 4/3.

(10) The slope of a line parallel to this line, y = 10 -8x is -8.

The slope of a line perpendicular to the line is the negative reciprocal of the slope of the line equation.

Question 9.

f(x) = 0.75x + 6

where;

The slope of a line perpendicular to this line = -1/0.75 = -100/75 = -4/3

Question 10.

For the equation of another line, y = 10 - 8x

The slope of a line parallel to this line is equal to the slope of this line and it is calculated as follows;

y = 10 - 8x

where;

slope of a line parallel to the line = -8

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For y to be parallel to x,

Thus, the value of x is 9.6.

Answer:

i dont know what you are asking but 3/10-8/10

Step-by-step explanation:

Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units

Statistical methods are the processes of collecting, presenting, analyzing data, and drawing conclusions.

These methods are divided into two groups: descriptive statistics and inferential statistics.

The scope of descriptive statistics includes distributions of random and random variables, discrete and continuous random variables. For inference statistics, including statistical inference from one or two populations, analysis of variance, regression analysis, and analysis of categorical data from both random and normal populations.

Statistical techniques include many ways to collect, present, analyze, and draw conclusions from data. By considering these methods, you can choose which method to use according to the characteristics of your data.

Choosing the right method leads to drawing the right conclusions.

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Answer:

1584mm^2

Step-by-step explanation:

20 x20 = 400 and there are 3 of them

400+400+400 = 1200

1/2(16x24 ) =192 and there are 2 of them

192+192 = 384

1200+384

Answer:

1408

Step-by-step explanation:

20·16+24·16+20·16+12·﹣204+2·(20·24)2+2·(20·20)2﹣244+2·(24·20)2﹣204=1408

if i did something wrong please let me know

(i might have done it wrong, please use the answer above which would be 1584mm^2)

Answer:

g(1) = 1

Step-by-step explanation:

the absolute value function always gives a positive result, that is

| - a | = | a | = a

to evaluate g(1) substitute x = 1 into g(x)

g(1) = - 3| 1 - 2| + 4

    = - 3| - 1| + 4

   = - 3(1) + 4

  = - 3 + 4

  = 1

n⁴ - 2n³ - 23n² + 24n + 144 is the standard form of given zeroes.

What is a linear equation in mathematics?

A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables.

                              A linear equation is an equation that raises a variable to the first power. ax+b = 0 is an example of a 1 variable. x is a variable and a and b are real numbers.  

Roots : -3(mult . 2), 4(mult.2)

the function is given as

     f(n) = (n + 3)² (n - 4)²

         = (n + 3) (n + 3 ) ( n - 4 ) ( n - 4)

        = (n² + 6n + 9) (n² - 8n + 16 )

        = n⁴ - 8n³ + 16n² + 6n³ - 48n² + 96n + 9n² - 72n + 1

collecting like term,

    f(n) = n⁴ - 2n³ - 23n² + 24n + 144

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The length of the side opposite to the reference angle is 7.77 units.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

If we take the reference angle 45°, The side 'x' is opposite and the side having a length of 11 units is the hypotenuse.

We know, sin = opposite/hypotenuse.

Therefore,

sin45° = x/11.

1/√2 = x/11.

x = 11/√2.

x = 7.77 units.

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Answer:

m=1352

Step-by-step explanation:

(118.64-24)/0.07=m

Log22/Log9 express log_9 22 in terms of common logarithms

Common logarithms, is commonly describd as base-10 logarithms.

It is a type of logarithm that involve taking the logarithm of a number with respect to the base of 10.

This means that common logarithms show how many powers of ten must be increased to get a particular number. The usual logarithm of 100, for example, is 2, because 10 raised to the power of 2 equals 100.

The answer provided is based on the full question below;

-------------express log_9 22 in terms of common logarithms

a. Log 22/9

b. Log 198

c. Log22/Log9

d. Log9/Log22

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When there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents. The number of flags will be 40.

From the information, there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents.

It should be noted that this simply means that we should find the highest multiple for 2, 4, and 5 between 20 and 50. This is 40.

Therefore, the number of flags is 40.

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Answer:

(-2 , 8)

Step-by-step explanation:

\(\begin{cases}y=-4x&\\ y=4x+16&\end{cases}\)

We substitute y by -4x in the second equation of the system:

-4x = 4x + 16

⇔ -8x = 16

⇔ x = 16/(-8)

⇔ x = -2

Now ,we substitute x by -2 in the first equation of the system:

y = -4 × (-2) = 8

then

the solution of the system is {(x = -2 , y = 8)}

The volume of the figure created is 98 cubic units.

Given that:

A triangle with coordinates (0,0), (0, 7), and (6,0) is rotated 360 degrees about the x-axis.

A cone is formed when a triangle rotates. Then the volume created is calculated as,

V = 1/3 x 7² x 6

V = 49 x 2

V = 98 cubic units

The volume is 98 cubic units.

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The smallest number of students who go to one of these clubs is 21.

A stem-and-leaf diagram is a quantitative assessment of a collection of data in which the data values are divided into a "stem" (the first digit of the number) and a "leaf" (the remainder of the number) (the last digit of the number).

Based on the given stem and leaf diagram, the smallest number of students who go to one of these clubs is represented by the leaf value "1" in the stem "2."

Therefore, the smallest number of students who go to one of these clubs is 21.

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Answer:

(a) X = {Bilk, Jas, Piaf, Sydow, Wil}

(b) Y = {Jas, Sydow, Tixo}

Hope that helps.

Answer:

d

Step-by-step explanation:

f(x)-g(x)=2x²+4x-6-[2x²+2x+8]=2x²+4x-6-2x²-2x-8=2x-14