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2 years ago

Solve each system by elimination. -9x + 4y = 7 -2x-4y=-18

Mathematics

2 answers:

goldenfox [79]2 years ago

7 0

Answer:

X=1

Step-by-step explanation:

-9x + 4y = 7

-2x-4y=-18

Since the variables are opposites add -9x+-2x

and you get -11x 4y + -4y = 0 and -18 +7=11

-11x=-11 divide that by 11 and get 1

IrinaK [193]2 years ago

4 0

Answer:

(1, 4 )

Step-by-step explanation:

- 9x + 4y = 7 → (1)

- 2x - 4y = - 18 → 2)

add (1) and (2) term by term to eliminate y

- 11x + 0 = - 11

- 11x = - 11 ( divide both sides by - 11 )

x = 1

substitute x = 1 into either of the 2 equations and solve for y

substituting into (1)

- 9(1) + 4y = 7

- 9 + 4y = 7 ( add 9 to both sides )

4y = 16 ( divide both sides by 4 )

y = 4

solution is (1, 4 )

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Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (4, 0), (4, 14); endpoints of th

saul85 [17]

Answer:

The standard form of the ellipse is $\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1$ .

Step-by-step explanation:

The major axis of the ellipse is located in the y axis, whereas the minor axis is in the x axis. The center of the ellipse is the midpoint of the line segment between vertices, this is:

$(h, k) =\frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2} (x,y)$ (1)

If we know that $V_{1} (x,y) = (4,0)$ and $V_{2}(x,y) = (4, 14)$ , then the coordinates of the center are, respectively:

$(h,k) = \frac{1}{2}\cdot (4, 0) + \frac{1}{2}\cdot (4,14)$

$(h,k) = (2,0) + (2, 7)$

$(h, k) = (4, 7)$

The length of each semiaxis is, respectively:

$a = \sqrt{(1 - 4)^{2}+(7-7)^{2}}$

$a = 3$

$b = \sqrt{(4-4)^{2}+(0-7)^{2}}$

$b = 7$

The standard equation of the ellipse is described by the following formula:

$\frac{(x-h)^{2}}{a^{2}}+ \frac{(y-k)^{2}}{b^{2}} = 1$

Where:

$h$ , $k$ - Coordinates of the center of the ellipse.

$a$ , $b$ - Length of the orthogonal semiaxes.

If we know that $h = 4$ , $k = 7$ , $a = 3$ and $b = 7$ , then the standard form of the ellipse is:

$\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1$

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3 years ago

I need help ASAP will give brainliest

Tems11 [23]

Answer:

658 + 342 = 1000.

Step-by-step explanation:

Let x be the multiple of 47 and y be the multiple of 19 which gives 1000 while adding.Hence 47x + 19y = 1000On multiplying, find x and yX=14 and y=18So, 47*14= 658 and 19*18= 342 On adding, 658+342=1000Therefore, 658 and 342 are the two parts of 1000.

in simple way

47a + 19b = 1000

a = 14, b = 18

check: 14 x 47 = 658, 18 x 19 = 342, 658 + 342 = 1000.

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