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defon
3 years ago
13

Solve the following systems of equations. Express your answer as an ordered pair in the format (a,b), with no spaces between the

numbers or symbols. 3x+4y=16 -4x-3y=-19
Mathematics
1 answer:
kodGreya [7K]3 years ago
4 0

Answer:

(4, 1)

Step-by-step explanation:

3x+4y=16 /*4

-4x-3y= - 19 /*3

 12x + 16y = 64

<u>- 12x -   9y = - 57 </u>

            7y = 7

              y = 1

3x+4y=16

3x + 4*1 = 16

3x = 16 - 4

3x = 12

x = 4

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The center of an ellipse is located at (0, 0). One focus is located at (12, 0), and one directrix is at x = 14 1/12.
muminat
The standard equation for an ellipse is
\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} =1
where
(h,k) = coordinates of the center
a, b = semi-major and semi-minor axes

Refer to the figure shown below.
The center of the ellipse is at (0,0). 
Therefore, h=0, k=0.

One focus is at (12, 0)
Therefore
c = 12

One directrix is at  14 1/12 = 169/12.
Because the directrix is located at x = a²/c, therefore
a²/12 = 169/12
a² = 169/144
a = 13

Because c² = a² - b², obtain
b² = a² - c²
     = 169 - 144 = 25
b = 5

Answer:
The equation for the ellipse is
\frac{x^{2}}{169} + \frac{y^{2}}{25} =1

6 0
3 years ago
Read 2 more answers
Help with these questions please!
Alisiya [41]

Answer:

1.  16

2.  -4

Step-by-step explanation:

First factor the expression

lim x→1  (x^3 + 5x^2 + 3x-9)/(x-1)

lim x→1  (x-1) (x+3)^2/(x-1)

Canceling the x-1  in the top and bottom

lim x→1   (x+3)^2

Let x=1

lim x→1   (1+3)^2 = 4^2 = 16


2.  lim x→0 (x^2 -6x+8) /(x-2)          

First factor the expression

    lim x→0 (x-4) (x-2) /(x-2)        

Canceling the x-2  in the top and bottom

lim x→0 (x-4)

Let x=0

lim x→0   (0-4) = -4

Filling in the table

x     -.1      -.01       -.001     .001     .01     .1

f(x) -4.1  -4.01    -4.001   -3.999   -3.99  -3.9

4 0
3 years ago
Read 2 more answers
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I got d ... hope this helps
8 0
3 years ago
The method of completing the square was used to solve the equation 2x^2 – 12x + 6 = 0. Which equation is a correct step when usi
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Answer:

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Step-by-step explanation:

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2 years ago
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Answer:

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