Select the correct answer.
Which table shows a proportional relationship between x and y?

The coordinate of point P is (7/2, -13)

The formula for calculating the midpoint of coordinates is expressed as shown below:

M(x, y) = {(mx₁+nx₂)/2, (my₁+ny₂)/2}

Given the coordinate points A(-4, 2) and B(3, -6) divided in the ratio 2:5, then;

M(x, y) = {(2(-4)+5(3))/2, (2(2)+5(-6))/2}

M(x, y) = {-8+15)/2, (4-30)/2}

M(x, y) = {7/2, (-26)/2}

M(x, y) = (7/2, -13)

Hence the coordinate of point P is (7/2, -13)

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Recall the beta function definition and gamma identity,

[tex]\displaystyle \mathrm{B}(x,y) = \int_0^1 t^{x-1} (1-t)^{y-1} \, dt = \frac{\Gamma(x) \Gamma(y)}{\Gamma(x+y)}[/tex]

Consider the sum

[tex]\displaystyle S(x) = \sum_{m=1}^\infty \frac{\Gamma(m) \Gamma(x)}{\Gamma(m+x)}[/tex]

Compute it by converting the gammas to the beta integral, interchanging summation with integration, and using the sum of a geometric series.

[tex]\displaystyle S(x) = \sum_{m=1}^\infty \mathrm{B}(m,x) \\\\ ~~~~ = \sum_{m=1}^\infty \int_0^1 t^{m-1} (1-t)^{x-1} \, dt \\\\ \int_0^1 (1-t)^{x-1} \sum_{m=1}^\infty t^{m-1} \, dt \\\\ ~~~~ = \int_0^1 (1-t)^{x-2} \, dt \\\\ ~~~~ = \int_0^1 t^{x-2} \, dt \\\\ ~~~~ = \frac1{x-1} = \frac{(x-2)!}{(x-1)!} = \frac{\Gamma(x-1)}{\Gamma(x)}[/tex]

It follows that

[tex]\displaystyle S(n+x) = \sum_{m=1}^\infty \frac{\Gamma(m) \Gamma(n+x)}{\Gamma(m+n+x)} = \frac{\Gamma(n+x-1)}{\Gamma(n+x)}[/tex]

Now we compute the sum of interest. It's just a matter of introducing appropriate gamma factors to condense the double series into a single hypergeometric one.

Recall the definition of the generalized hypergeometric function,

[tex]\displaystyle {}_pF_q \left(\left.\begin{array}{c} a_1,a_2,\ldots,a_p\\b_1,b_2,\ldots,b_q\end{array}\right\vert z\right) = \sum_{n=0}^\infty \frac{(a_1)_n (a_2)_n \cdots (a_p)_n}{(b_1)_n (b_2)_2 \cdots (b_q)_n} \frac{z^n}{n!}[/tex]

where [tex](a)_n[/tex] denotes the Pochhammer symbol, defined by

[tex]\begin{cases}(0)_n = 1 \\ (a)_n = a(a+1)(a+2)\cdots(a+n-1) = \frac{\Gamma(a+n)}{\Gamma(a)}\end{cases}[/tex]

We'll be needing the following identities later.

[tex](1)_n = n! = \dfrac{\Gamma(n+1)}{\Gamma(1)}[/tex]

[tex](x)_n = \dfrac{\Gamma(n+x)}{\Gamma(x)}[/tex]

[tex](x+1)_n = \dfrac{\Gamma(n+x+1)}{\Gamma(x+1)}[/tex]

The [tex]m[/tex]-sum is

[tex]\displaystyle \sum_{m=1}^\infty \frac{\Gamma(m)}{\Gamma(n+m+x)} = \frac1{\Gamma(n+x)} \sum_{m=1}^\infty \frac{\Gamma(m)\Gamma(n+x)}{\Gamma(n+m+x)} \\\\ ~~~~~~~~ = \frac{S(n+x)}{\Gamma(n+x)} \\\\ ~~~~~~~~ = \frac{\Gamma(n+x-1)}{\Gamma(n+x)^2}[/tex]

Then the double sum reduces to

[tex]\displaystyle \sum_{n=1}^\infty \sum_{m=1}^\infty \frac{\Gamma(n)\Gamma(m)\Gamma(x)}{\Gamma(n+m+x)} = \sum_{n=1}^\infty \frac{\Gamma(n)\Gamma(x)\Gamma(n+x-1)}{\Gamma(n+x)^2}[/tex]

Rewrite the summand. We use the property [tex]\Gamma(x+1)=x\Gamma(x)[/tex] to convert to Pochhammer symbols.

[tex]\displaystyle \frac{\Gamma(n)\Gamma(x)\Gamma(n+x-1)}{\Gamma(n+x)^2} = \frac{\Gamma(n)\Gamma(x)^2\Gamma(n+x-1)}{\Gamma(n+x)^2 \Gamma(x)}[/tex]

[tex]\displaystyle . ~~~~~~~~ = \frac1{x^2} \frac{\Gamma(n)\Gamma(x+1)^2\Gamma(n+x-1)}{\Gamma(n+x)^2\Gamma(x)}[/tex]

[tex]\displaystyle . ~~~~~~~~ = \frac1{x^2} \frac{\Gamma(n) \frac{\Gamma(n+x)}{\Gamma(x)}}{\frac{\Gamma(n+x-1)^2}{\Gamma(x+1)^2}}[/tex]

[tex]\displaystyle . ~~~~~~~~ = \frac1{x^2} \frac{(n-1)! (x)_{n-1}}{\left[(1+x)_{n-1}\right]^2}[/tex]

Now in the sum, shift the index to start at 0, and introduce an additional factor of [tex]n![/tex] to get the hypergeometric form.

[tex]\displaystyle \sum_{n=1}^\infty \frac1{x^2} \frac{(n-1)! (x)_{n-1}}{\left[(1+x)_{n-1}\right]^2} = \frac1{x^2} \sum_{n=0}^\infty \frac{(n!)^2 (x)_n}{\left[(1+x)_n\right]^2} \frac1{n!} \\\\ ~~~~~~~~ = \frac1{x^2} \sum_{n=0}^\infty \frac{[(1)_n]^2 (x)_n}{\left[(1+x)_n\right]^2} \frac1{n!} \\\\ ~~~~~~~~ = \boxed{\frac1{x^2} \, {}_3F_2\left(\left.\begin{array}{c}1,1,x\\1+x,1+x\end{array}\right\vert1\right)}[/tex]

Based on the bisection of line BC by point A, the value of x is 10/3

The given parameters are:

Because the point A bisects BC, then

BA = AC

Substitute the known values in the above equation

So, we have

6x - 3 = 3x + 7

Collect the like terms

6x - 3x = 3 + 7

Evaluate the like terms

3x = 10

Divide both sides of the equation by 3

x = 10/3

Hence, based on the bisection of line BC by point A, the value of x is 10/3

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Answer:

1. their motor neurons are damaged,so their muscles don't react/move causing the person to hit the tree

Answer:

33.4 is x.

Step-by-step explanation:

Hope this helps!

The capacity utilisation of the team is 57.14%

The efficiency is 76.22%

Design capacity= ((number of workers* total hours per day)/time per customer call out)* number of working days in a week

Design capacity = (50*7)/2)*5

Design capacity= 875 jobs per week

The effective capacity = ((number of workers* actual hours per day)/time per customer call out)* number of working days in a week

Effective capacity=(50*5.25)/2)*5

Effective capacity=656 jobs per week

Efficiency rate= Actual capacity/ effective capacity

Efficiency rate=500/656

Efficiency rate=0.7622 or 76.22%

Utilization rate=Actual capacity/Design capacity

Utilization rate = 500/875

Utilization rate = 0.5714 or 57.14%

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The hours did it take to drive to Louisville-3.25 hours

The long is the scenic route from Louisville. 237miles

Jenny traveled to Louisville at 68 miles per hour

Let d is the distance travelled to Louisville and t is the time taken.

68= d/t

On the way back she took the scenic route and drove 56 miles per hour.

distance of way back= d+ 17

time taken=t+1

56=(d+17)/(t+1)

on solving both the equations

t=3.25 hours

d=221miles

scenic route from Louisville is at d+17= 237miles

In everyday use and in kinematics, the velocity (generally called v) of an object is the significance of the trade of its role through the years or the significance of the alternate of its position in step with unit of time; it's miles as a result a scalar quantity.

[1] The average velocity of an item in an interval of time is the gap travelled by using the object divided by using the duration of the interval

[2] the on the spot pace is the restrict of the average velocity as the period of the time c programming language procedures zero. speed isn't similar to pace.

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Answer:

4.49% (rounded to 2 decimal places)

Step-by-step explanation:

Let the tax rate be r%

The tax paid on car = (Final Sale Price) - (Before Tax Price)

= 8652.60 - 8280 =  $372

Tax rate as a decimal = Tax/(Before Tax Price)

= 372/8652.60 ≈ 0.0449275  (rounded to 7 decimal places)

To find tax rate as percentage multiply the above by 100 to get tax rate as
0.0449 x 100 ≈ 4.49275% ≈ 4.49% (rounded to 2 decimal places)

The coordinates of point P on the number line are 16 or 21.

In this question we find a line segment set on a number line and whose endpoints and segment ratio are known. Then, we can determine the location of the point P by using the line segment formula:

P(x) = A(x) + k · [B(x) - A(x)]

Where k is the partition ratio.

If we know that A(x) = 6, B(x) = 31 and k = 3 / 5, then the location of the point P is:

P(x) = 6 + (3 / 5) · (31 - 6)

P(x) = 6 + (3 / 5) · 25

P(x) = 6 + 15

P(x) = 21

P(x) = 6 + (2 / 5) · (31 - 6)

P(x) = 6 + (2 / 5) · 25

P(x) = 6 + 10

P(x) = 16

The coordinates of point P on the number line are 16 or 21.

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Answer:The answer would be a.

Step-by-step explanation:I hope this helps.

Answer:

[tex](g \circ f)(x) = x^2-10x+25[/tex]

Step-by-step explanation:

Given:

[tex]\begin{cases}f(x)=-x+7\\g(x)=x^2-4x+4 \end{cases}[/tex]

Function composition is an operation that takes two functions and produces a third function.

The composite function (g o f)(x) means to substitute the function f(x) in place of the x in function g(x).

[tex]\begin{aligned} \implies (g \circ f)(x) & = g\left[f(x)\right]\\& = g(-x+7)\\& = (-x+7)^2-4(-x+7)+4\\& = (-x+7)(-x+7)+4x-28+4\\& = x^2-14x+49+4x-28+4\\& = x^2-14x+4x+49-28+4\\& = x^2-10x+25\end{aligned}[/tex]

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Answer:

x² - 10x + 25

Step-by-step explanation:

The given information is,

→ f(x) = -x + 7

→ g(x) = x² - 4x + 4

The equation we form is,

→ (gof)(x)

→ g[f(x)]

→ f(x)² - 4f(x) + 4

Let's solve the problem,

→ f(x)² - 4f(x) + 4

→ (-x + 7)² - 4(-x + 7) + 4

→ x² - 14x + 49 + 4x - 28 + 4

→ x² - 10x + 25

Hence, answer is x² - 10x + 25.

No, The sum of the lengths of any two sides of a triangle must be greater than the length of the third side according to Pythagorean theorem.

What is the Pythagorean theorem?

The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.

a right triangle needs to follow the Pythagorean theorem, that is,

a2 + b2 = c2

where c is the length of the hypotenuse and a and b are the lengths of the other sides of the right triangle.  We can check to see if this property holds for the given triangle.  Since

5² + 10² = 15²

25 + 100 = 225

the Pythagorean theorem does not hold for the given triangle, meaning that it can not be a right triangle.

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Answer:

36

Step-by-step explanation:

Each time it goes up it adds the next highest odd number.

1

+3

4

+5

9

+7

16

+9

25

And so we can reasonably assume that the next number in the sequence will be the previous number (25) plus the next highest odd number (11). This means that the next number in the sequence is most likely 36.

Answer:

Ans is 36 ...

Step-by-step explanation:

Well,

lets add these number with odd number

1

3+1=4

5 + 4= 9

7+ 9= 16

9 + 16=25

11 + 25 = 36.........

Hope you will get it.

Answer:

See below

Step-by-step explanation:

When you see PER think fractions. Miles PER hour is

[tex] \frac{miles}{hour} [/tex]

We are given miles and told to solve for time. Use your knowledge of fractions to get what you need

The reciprocal of mi/hr would get what we need

[tex]miles \times \frac{hours}{miles} [/tex]

Miles cancels out here. So that means you can do this

[tex] \frac{1hour}{50miles} \times 999.9 \: miles[/tex]

In your calculator. Same with the other rate.

Answer:

$10.17

Step-by-step explanation:

145.34×7%= $10.17 in tax

Which brings total cost to $155.51

Radius of a quarter circle is 2  then area is the π

Area of quarter circle is [tex]= (A = \pi r^2/4)[/tex]

A circle is a locus (collection) of points that are a defined distance apart from one another. The fixed point and fixed distance are referred to as the "center" and "radius," respectively. A quarter-circle is one-quarter of a circle. As a result, the area of a quarter circle is one-fourth of the size of a full circle.

A quarter circle is the area (or part) created by two perpendicular radii and one-fourth of the circumference of a circle. This is also known as a circular quadrant. For example, if a circle is divided into four equal pieces, each half is a quarter circle (or) a quadrant.

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The product of the given equation for the fourth root is 7.

The 4th root of an amount is the number that, when multiplied four times by itself, yields the original number.

For, the given question;

= ⁴√7 × ⁴√7 × ⁴√7 × ⁴√7

This equation can be written as;

=(⁴√7)⁴

Further writing the fourth root in terms of fraction;

= (7)∧(1/4)×4

Both power will cancel each other.

= 7

Therefore, the product of the fourth root is found as 7.

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The correct question is-

What is the following product?

⁴√7 × ⁴√7 × ⁴√7 × ⁴√7

Answer: x*y/2

Step-by-step explanation:

x*y is the product of x and y.

1/2 * x* y is half the product of x and y.

Answer: x*y/2

Answer:

See below.

Step-by-step explanation:

Part A: The Vertical Angles Theorem states that the opposite (vertical) angles of two intersecting lines are congruent.

Part B: b & 40, a &c

Part C: a=140, b=40, c=140

Hope this helps.

The time Emma should take for the run must be less than 15 minutes to bear her previous record.

Emma's previous record was 1 hour and 10 minutes. This is equivalent to

60+10 minutes equals 70 minutes.

She already has run 55 minutes;

So, let us consider the remaining time, x, added to 55, must be less than 70 to overcome her previous time:

x + 55 < 70

The inequality is obtained.

Subtract 55 from each side:

x + 55-5 < 70-55

x < 15

Therefore, the remaining time of the run by Emma must be less than 15 minutes to beat her previous record.

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Answer:

(-2 , 0)

Step-by-step explanation:

The solution to this system of equations is the x and y values where the two lines cross.  That is where x is -2 and y is 0.  You can check/verify by putting these x and y values into the original equations.

Answer:

40,300,520 is greater because if you line the numbers up you’ll see that the one with more numbers is always greater

Step-by-step explanation:

Answer:

40,300,520 is greater how u can tell is that there is more digits at the end of the numbers

Step-by-step explanation:

The position of the stadium, given the data is 60 Km east and 10 Km south

Speed is the distance travelled per unit. Mathematically, it can be expressed as:

Speed = distance / time

With above formula, we can determine the position of the stadium. Details below

Speed = distance / time

Cross multiply

Distance = speed × time

Distance = 120 × 1/2

Distance = 60 Km east

Speed = distance / time

Cross multiply

Distance = speed × time

Distance = 60 × 1/6

Distance = 10 Km south

Thus, we can conclude that the position of the stadium is 60 Km east and 10 Km south

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Option D) is the correct option. That is the volume of the sphere is

3054 mm³.

The formula for the volume of the sphere is given as :

     V = [tex]\frac{4}{3}\pi r^{3}[/tex]

where, r = radius of the sphere

           V = volume of the sphere

According to the question we have been given that

          radius of the sphere, r = 9mm

Putting the required value in the above formula we get

                   [tex]V = \frac{4}{3} \pi 9^{3} \\ = \frac{4}{3} \ (\frac{22}{7} ) (729) \\[/tex]

                V = 3054.85 mm³ ≈ 3054 mm³

Hence the volume of the sphere is 3054 mm³. That is option D) is correct.

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Answer:

[tex]f(x)=-|x-3|+7[/tex]

Step-by-step explanation:

The parent function of an absolute function is the modulus function:

[tex]f(x)=|x|[/tex]

Graph of Modulus function:

(see 2nd attachment)

[tex]f(x)=|x|=\begin{cases} \textsf{\:\:\:$x$, \quad if $x\geq 0$}\\\textsf{$-x$, \quad if $ x < 0$} \end{cases}[/tex]

Its vertex is at the origin (0, 0).

Its line of symmetry is x = 0.

It opens upwards.

Given information:

The axis of symmetry is the x-value of the vertex of an absolute function. 

The y-value of the range is the y-value of the vertex of an absolute function.  

Therefore, the vertex of the absolute function f(x) is (3, 7).

Graphing

To find the equation of the absolute function, work out the series of transformations that take the parent function to the given function.

As the function f(x) has a range of (-∞, 7), it opens downwards.  Therefore, the parent function has been reflected in the x-axis:

[tex]\implies -f(x)=-|x|[/tex]

As the function f(x) is symmetric about the line x=3, the parent function has been translated 3 units to the right:

[tex]\implies -f(x-3)=-|x-3|[/tex]

Finally, as the highest y-value of the function is y = 7, the y-value of its vertex is y = 7.  Therefore, the parent function has been translated 7 units up:

[tex]\implies -f(x-3)+7=-|x-3|+7[/tex]

Therefore, the equation of the absolute function with the given parameters is:

[tex]f(x)=-|x-3|+7[/tex]

Answer:

I think 12 minutes

Step-by-step explanation:

Part A

x = number of years

275x = number of people that left the city after x years go by

37000 - 275x = number of remaining people after x years

37000 - 275x = 35350  is the final answer to part A

=======================================================

Part B

37000 - 275x = 35350

-275x = 35350 - 37000

-275x = -1650

x = -1650/(-275)

x = 6

It takes exactly 6 years to have the population reach 35350.

Answer:

The 100 emoji is used in digital communication to express or emphasize achievement, support, approval, and motivation. It also generally means “absolutely” or “keep it 100” (keep it real). Related words: keep it 100. keep it hot.