Enter the values for a, b, and c in the factored form.<br> P(x) = (x

The system of equations

cupoosta [38]

Answer:

z = -12

Step-by-step explanation:

The given system of equations is:

xy/(x + y) = 1 ...........................(1)

xz/(x + z) = 2...........................(2)

yz/(y + z) = 3...........................(3)

From (1): x + y = xy

=> y = xy - x

y = x(y - 1)

x = y/(y - 1).......................................(4)

From (2): 2(x + z) = xz

=> 2x + 2z = xz

2x = xz - 2z

2x = z(x - 2)

z = 2x/(x - 2) ....................................(5)

From (3): 3(y + z) = yz

=> 3y + 3z = yz

3y = yz - 3z

3y = z(y - 3)

z = 3y/(y - 3)....................................(6)

Comparing (5) and (6)

2x/(x - 2) = 3y/(y - 3)

2x(y - 3) = 3y(x - 2)

2xy - 6x = 3xy - 6y

6(y - x) = xy .................................(7)

But from (1): xy = x + y

Using this in (7), we have

6(y - x) = x + y

6y - y - 6x - x = 0

5y - 7x = 0

5y = 7x

x = 5y/7................................................(8)

Using this in (4)

5y/7 = y/(y - 1)

1/(y - 1) = 5/7

(y - 1) = 7/5

y = 1 + 7/5

y = 12/5..........................................(9)

Using this in (8)

x = 5(12/5)/7 = 12/7 .......................(10)

Using (10) in (5)

z = 2x/(x - 2)

z = 2(12/7) ÷ (12/7 - 2)

= 24/7 ÷ -2/7

= 24/7 × (-7/2)

= -24/2 = -12

z = -12.

4 0

2 years ago

Find an equation of the line containing the centers of the two circles whose equations are given below.

Anna35 [415]

Answer:

Step-by-step explanation:

The general equation of a circle is expressed as x²+y²+2gx+2fy+c = 0 with centre at C (-g, -f).

Given the equation of the circles x²+y²−2x+4y+1 =0 and x²+y²+4x+2y+4 =0, to get the centre of both circles,<em> we will compare both equations with the general form of the equation above as shown;</em>

For the circle with equation x²+y²−2x+4y+1 =0:

2gx = -2x

2g = -2

Divide both sides by 2:

2g/2 = -2/2

g = -1

Also, 2fy = 4y

2f = 4

f = 2

The centre of the circle is (-(-1), -2) = (1, -2)

For the circle with equation x²+y²+4x+2y+4 =0:

2gx = 4x

2g = 4

Divide both sides by 2:

2g/2 = 4/2

g = 2

Also, 2fy = 2y

2f = 2

f = 1

The centre of the circle is (-2, -1)

Next is to find the equation of a line containing the two centres (1, -2) and (-2.-1).

The standard equation of a line is expressed as y = mx+c where;

m is the slope

c is the intercept

Slope m = Δy/Δx = y₂-y₁/x₂-x₁

from both centres, x₁= 1, y₁= -2, x₂ = -2 and y₂ = -1

m = -1-(-2)/-2-1

m = -1+2/-3

m = -1/3

The slope of the line is -1/3

To get the intercept c, we will substitute any of the points and the slope into the equation of the line above.

Substituting the point (-2, -1) and slope of -1/3 into the equation y = mx+c

-1 = -1/3(-2)+c

-1 = 2/3+c

c = -1-2/3

c = -5/3

Finally, we will substitute m = -1/3 and c = 05/3 into the equation y = mx+c.

y = -1/3 x + (-5/3)

y = -x/3-5/3

Multiply through by 3

3y = -x-5

3y+x = -5

<em>Hence the equation of the line containing the centers of the two circles is 3y+x = -5</em>

5 0

2 years ago

Mr. Malloy wants to make sure Amo and Javier get the best possible grade after five tests and can either give a grade based on t

joja [24]

The data has been properly arranged in tabular form and is shown below in the image.

First we need to find the mean and median of scores of both students.

1) For Amo:
Mean = $\frac{97+92+89+55+90}{5}=84.6$
Median = Middle Value when data is arranged in ascending order = 90

2) For Javier:
Mean = $\frac{68+97+65+92+95}{5}=83.4$
Median = Middle Value when data is arranged in ascending order = 92

For both the students, value of Median is larger then the mean. So in order to give the best possible grade Mr. Malloy should use the median score for both students.

8 0

2 years ago

Read 2 more answers

RESTAURANT MANAGEMENT

yan [13]

Answer:

33%

Step-by-step explanation:

3 0

1 year ago

Which percentage of weight was lost if a patient weighed 102 kg and is currently 96 kg?

galina1969 [7]

Answer:

Step-by-step explanation:

you have to make a box like this:

║ ---------- ║------------ ║ label one side percent and the other amount

║ x% ║ 96 kg ║

║ _ _ _║_____ _║ Now if the patient originally weighed 102 kg which

║100% ║ 120 kg ║ is 100% place the numbers in the bottom box.

║ _ _ _ ║ _ _ _ ║ and if the patient currently weighs 96 kg then let

Percent Amount percentage of the weight lost be x. Now cross multiply. You should get 100*96=120*x. Simplify that to get 9600=120x, now divide by 120 on both sides and you get 80 so x= 80. But the problem isn't done yet. Now you have to subtract 80% from 100% to find the weight lost, because 80% is the percentage of the current weight. after you have subtracted you get 20

20% of the original weight was lost.

4 0

2 years ago

Enter the values for a, b, and c in the factored form. P(x) = (x – 5)(ax2 + bx + c)