its 54 your welcome because i did this from khan and i got it 54 right so its 54

Answer: 3/72 is your answer.

The equation of the locus of the point P so that the area of triangle PAB is 8.5 square units will be 5 k + h = 34.

Let coordinate of P be (h, t)

We are given the coordinates of A and B as:

A = (2,3) and B = (−3,4)

Now, we also know that Area of triangle PAB is:

A = 1 / 2 (h ( 3 − 4 ) + 2 ( 4 − k ) − 3 ( k − 3 ) )

± 8.5 = 1 / 2 ( h ( - 1 ) + 2 ( 4 - k ) - 3 ( k - 3 ) )

± 17 = ( - h + 8 - 2 k - 3 k + 9 )

± 17 = ( 17 - 5 k - h )

When + 17 is there:

5 k + h = 0

When - 17 is there:

5 k + h = 34

So, locus of the point P will be 5 k + h = 34.

Therefore, the equation of the locus of the point P so that the area of triangle PAB is 8.5 square units will be 5 k + h = 34.

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Your question was incomplete. Please refer the content below:

A(2,3) and B(−3,4) be two given points. Find the equation of the locus of P so that the area of triangle PAB is 8.5 square units.

Answer:

AC = 16.6

Step-by-step explanation:

Use sine rule

9.2 / sin(180-90-61) = AC/ sin(61)

Answer: See explanation

Step-by-step explanation:

g(x)=2x-2

g(x+9)=2(x+9)-2 ==> x+9

(1,2), (4,5)

x=1, x=4: ==> pick the x-coordinates for domain

[1, 4] ==> segment is from 1 to 4 and includes x=1 and x=4

Step-by-step explanation:

2 3 4 6...................

The kinetic energy is 1000J.

Kinetic energy is the energy of motion, observable as the movement of an object, particle, or set of particles. It is the measure of the work that an object does by virtue of its motion.

Kinetic energy is the product of half the product of mass and the square of the speed.

K.I = 1/2 m v²

Here m = 20kg, v = 10m/s

K.I = 1/2 × 20 × 10²

    = 10 ×10²

    = 1000

Therefore the kinetic energy is 1000J.

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Answer:

10 is the answerplease i

The difference of 30000 and 6985 using compensation is 23015

The method of compensation refers to calculating mentally without any paper work.

Here, we are asked to find the difference of 30000 and 6985 which are comparatively large numbers. Everyone would prefer using pen and paper to calculate this. But we can do this by compensation within a few steps.

So the final answer is 23015.

i.e., 30000-6985 = 23015

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Answer:

4,545.45 crates

Step-by-step explanation:

.11x = 500

Divide both sides by .11

x = 4,545.45

The number of crates she picked algebraically is 4545.

Let us consider the variable "c" to represent the number of crates Brianna picked.

We know that she receives 11 cents per crate.

1 crate = $0.11 (11 cents)

Her total earnings from picking "c" crates can be expressed as:

Earnings = 0.11c

Now, we know her total piecework earnings for last week were $500. So, we can set up an equation:

Total Earnings = $500

0.11c = $500

To find the number of crates Brianna picked, we need to solve for "c":

c = $500 / 0.11

c = 4545.45...

c = 4545 crates

So, algebraically, Brianna picked approximately 4545 crates last week.

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Construct potential hypotheses or research questions to relate the variables in each of the following examples -

Political party and support of the affordable care act -

and their ability to express what they think about the Act's purpose.

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Answer:

52x + 29.

Step-by-step explanation:

d = 7x + 11 - (2x + 9)

= 5x + 2.

11th term

= 2x + 9 + (11-1)(5x + 2)

= 2x + 9 + 50x + 20

= 52x + 29.

Answer:−4x+60X,1,2,3y−14

Step-by-step explanation:
1. simplify 3x x 20 to 60x
−4x+60X,1,2,3y−5−9
2. Simplify 3y- 5-9 to 3y - 14
−4x+60X,1,2,3y−14

In the given situation n gives us the number of weeks. after 3 weeks, Jonie and Marco each owed their fathers the same amount.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

We have been given that Marco owed his father in dollars at the end of n weeks can be represented by f(n) = 210 − 20n. and Joni owed her father in dollars at the end of n weeks can be represented by g(n) = 180 − 10n.

Also we get f(n) = g(n)

210 − 20n = 180 − 10n

Now n gives us the number of weeks thus solve for n

210 − 20n = 180 − 10n

210 - 180 = -10n + 20n

30 = 10n

n = 3

Now check your solution;

f(n) = 210 − 20n = 210 - 60 = 250

g(n) = 180 − 10n = 180 - 30 = 150

So our answer checks out after 3 weeks, Jonie and Marco each owed their fathers the same amount.

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The point slope of the the line using the point (3,2) and slope 5 is (y-2)=5(x-3).

Given that A line intersects the points (3, 2) and (5, 12)  and asked to write an equation of line passing through (3,2) and having slope as 5.

Point slope form:

The point-slope form of a stright line is y-y1=m(x-x1)

Here (x1,y1) is the fixed point with which the line passes and m is the slope of the line

Here, (x1,y1)  is given as (3,2) and m(slope)=5

The equation straight line in point-slope form is (y-2)=5(x-3).

Therefore,The point-slope form of the the line using the point (3,2) and slope 5 is (y-2)=5(x-3).

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Answer:

w is -4

Step-by-step explanation:

W is -4 because a positive number times a negative number is always a negative that is why the answer is a negative and 6 times 4 is 24 but for the 24 to be a negative the 4 has to be a negative 4.

1) Sheryl was wrong, the solution of w² = 49 and w² +49 = 0 are not same.

2) The solution of 4x² - 9 = 0 this quadratic equation is 3/2 and -3/2 through using factoring method.

3)

4) The solution of both quadratic equations will give same results.

Explanation:

1) Sheryl says that the solutions of the quadratic equations w² = 49 and

w² +49 = 0 are the same. Do you agree with Sheryl? Justify your answer.

Solution:-

 According to Sheryl says that the solutions w² = 49 and w² +49 = 0 are the same.

Let's find the solution of given quadratic equations

        w = √49      ( ∵√49 = 7 )

         w = ±7

    So the solution of this quadratic equation 7 and -7

        w² = -49

        w  = √(-49)      ( ∵√49 = 7 )

         w = ±7 √-1       ( ∵√-1 = i )

   So the solution of this quadratic equation 7i and -7i

2. Patricia says that it's more appropriate to use the method of factoring

than extracting square roots in solving the quadratic equation

4x² - 9 = 0. Do you agree with Patricia? Explain your answer.

Solution:-

Patricia says that it's more appropriate to use the method of factoring

than extracting square roots in solving the quadratic equation

       4x² - 9 = 0.

Now, let's solve that quadratic equation through factoring method.

      (2x)² - (3)² = 0                {∵ a²-b²= (a-b)(a+b)

   (2x-3)(2x+3) = 0

    If       (2x-3) = 0  

               2x-3 = 0      

                   2x = 3

                      x = 3/2

   And if  (2x+3) = 0

               2x+3 = 0      

                   2x = -3

                      x = -3/2

3. If you are to choose between completing the square and factoring in

finding the solutions of each of the following equations, which would you

choose? Explain and solve the equation using your preferred method.

a. 4x² - 20x = 11

b. x² + 7x + 12 = 0.

Solution:-

a. 4x² - 20x = 11

For solve this quadratic equation, we can use completing the square method, because this equation is very hard to get it's factors.

So,

    4x² - 20x = 11

[tex]x^2-5x+(\frac{5}{2})^2 = \frac{11}{4} +(\frac{5}{2})^2\\x^2-2\times \frac{5}{2} \times x+(\frac{5}{2})^2 = \frac{11}{4} +\frac{25}{4}\\(x-\frac{5}{2})^2 = \frac{11+25}{4}\\(x-\frac{5}{2})^2 = \frac{36}{4}\\(x-\frac{5}{2})^2 = 9\\(x-\frac{5}{2})^2 = (3)^2\\(x-\frac{5}{2}) = \pm (3)\\\\[/tex]

 For taking + sign,

x - [tex]\frac{5}{2}[/tex] = 3

    x = 3 + [tex]\frac{5}{2}[/tex]

    x = [tex]\frac{6+5}{2}[/tex]

     x = [tex]\frac{11}{2}[/tex]

  For taking - sign,

x - [tex]\frac{5}{2}[/tex] = -3

    x =  [tex]\frac{5}{2}[/tex] - 3

    x = [tex]\frac{5-6}{2}[/tex]

     x = [tex]\frac{-1}{2}[/tex]

b. x² + 7x + 12 = 0.

For solve this quadratic equation, we can use factoring method, because that is very easy to get it's factors.

So,

            x² + 7x + 12 = 0

      x² + 4x +3x + 12 = 0

          x(x+4) +3(x+4) = 0

                 (x+4)(x+3) = 0

                If       (x+4) = 0  

                           x+4 = 0      

                               x = -4

             And if  (x+3) = 0

                           x+3 = 0      

                               x = -3

4. The values of a, b, and e of a quadratic equation written in standard form are -2, 8, and 3, respectively. Another quadratic equation has 2, -8, and -3 as the values of a, b, and c, respectively. Do you agree that the two equations have the same solutions? Justify your answer.

Solution:-

We know that the standard form of quadratic equation is

From question we have two values of a,b and c.

For 1st quadratic equation the value of a,b and c is -2, 8, and 3, respectively.

So, the quadratic equation is

For 2nd quadratic equation the value of a,b and c is 2, -8, and -3, respectively.

So, the quadratic equation is

Now, we have to find the solution of both equations are same or not.

So, the solution of 1st quadratic equation

       -2x²+8x+3 = 0

           2x-8x-3 = 0            (multiplying - with both sides)

Now, this equation convert in the form of 2nd quadratic equation. So we can say that the solution of both quadratic equations will give same results.

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Answer:  110 grams of the 99% cocoa, and 90 grams of the 70% cocoa.

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

Work Shown:

x = amount of the 99% cocoa

200-x = amount of the 70% cocoa

0.99x = amount of pure coca from the first batch

0.70(200-x) = amount of pure cocoa from the second batch

0.99x+0.70(200-x) = total amount of pure cocoa

0.99x+0.70(200-x) = 200*0.86

0.99x+0.70*200-0.70x = 200*0.86

0.99x+140-0.70x = 172

0.29x+140 = 172

0.29x = 172-140

0.29x = 32

x = 32/0.29

x = 110.344827586207

x = 110

200-x = 200 - 110 = 90

Lyle needs 110 grams of the 99% cocoa, and 90 grams of the 70% cocoa.

Both of these values are approximate.

The equation formed using the given data is 195 = x + 12 and your final score is 183 points.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say your final score is x

Given that,

Your final score x is 12 points less than your friend's final score.

So,

x = friend final score - 12

Now,

Friend final score = 195

So,

x = 195 - 12

x + 12 = 195

195 = x + 12

Now,

x = 195 - 12 = 183

Hence "The equation formed using the given data is 195 = x + 12 and your final score is 183 points".

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From the given graph, we can conclude that at a time of 15, the position is 8m; At a time of the fourth tic on the x-axis, the position is 20.25 m

From the given distance time graph, we can see that the y-axis is represented by position in meters while x-axis is represented by time taken.

A) Tracing x = 3 tic, we can get see that the time is at x = 3 * 5 = 15 s

B) Tracing the fourth tic mark on the graph, we can see that y = 2.25 = 2.25 * 9 = 20.25 m

C) Now, when t = 15 seconds, we can see that it will be the third tic on the x-axis and as such at the third tic,

(15 * 1.75)/3 = 8 m

Thus, we can conclude that at a time of 15, the position is 8m; At a time of the fourth tic on the x-axis, the position is 20.25 m

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Answer:

4 miles east and 3 miles north (4, 3)

Total 790 number of handshakes occur within the group.

According to the given question.

Total number of people = 50

Number of people who know each other = 30

Number of people who know no one = 20

Since, 20 people doesn't knw each any one, so they will shake hands.

So, the total number of hand shakes by these 20 people

= 20(20 -1)/2

= 10(19)

= 190

Also, we have to consider  that other 30 people will also shake hands with these 20 people.

So, the total number of hanshakes by these 30 and 20 people = 30 × 20 = 600

Therefore, the total number of handshakes occur within the group

= 600 + 190

= 790

Hence, total 790 number of handshakes occur within the group.

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Answer:

1.96 m or 2m when rounded to nearest tenth

Step-by-step explanation:

The question is referring to a square right pyramid. The base is square and the perpendicular axis is vertical to the base.

These are the different parts of a square right pyramid .

See figure for detailed description(taken from Wolfram website)

The ones of interest here are

Answer slant height s = 1.96 = 2 m when rounded to nearest tent

The response to this question is that p has a value of 8, or the cube root of 8. i.e. p=∛8.

An integer y such that y³ = x is known as the cube root of a number x in mathematics. All nonzero complex numbers have three different complex cube roots, while all nonzero real numbers have exactly one real cube root and two complex conjugate cube roots. When we multiply a factor three times to obtain a number, we have obtained the cube root of that factor. Three cube root of, ending cubic root is the sign for the cube root. In contrast to cubing an integer, finding its cube root is a mathematical operation.

According to the equation, p³=8

We can clearly see that the power of p is 3.

Now by taking cube root on both the sides, we can see that the value of p is

∛p³=∛8

⇒p=∛8        

The value of p in the equation cube root of 8.

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Two complex of numbers with a difference of 9 is 19 + i3 and 10 + i3

The term complex numbers is used in mathematics to refer to numbers that are of two parts the real part and the imaginary part. The real part of a complex number appears like a number real number while the imaginary part has the letter i before the number.

This is two numbers that there difference will be 9

so subtracting the two complex numbers we have:

( 19 + i3 ) - ( 10 + i3 )

= ( 19 - 10 ) - ( i3 - i3 )

= 9 - 0

= 9

Hence we can say that two complex of numbers with a difference of 9 is 19 + i3 and 10 + i3.

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Answer:(0,4)

Step-by-step explanation: Graph the line using the slope and y-intercept, or two points.

Slope: -5

y-intercept:

(0,4)

x     y

0    4

1    -1

Greetings from Brasil...

In this type of problem, we will use Set Theory

n(D ∪ S) = n(D) + n(S) - n(D ∩ S)
as n(U) - n(D ∪ S) = 10, then

n(D ∪ S) = 70, so

n(D ∩ S) = 5  (read both)

n(D) - n(D ∩ S) = 40  (read only D)

n(S) - n(D ∩ S) = 25 (read only S)

see attached figure

_________________________________
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Answer:

for part c

JM=36

AD=12

36=3

JKLM is 3x bigger than polygon ABCD