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3 years ago

2/16 2 + x = 12 what is the answer to this equation?

Mathematics

1 answer:

Troyanec [42]3 years ago

6 0

Answer:

nomelase pero será chida la imagen que tienes

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Find the equation of ellipse passing throgh (1,4) and (-3,2)

irinina [24]

Answer:

$\displaystyle \frac{ {3x}^{2} }{ 35 } + \frac{{2y}^{2} }{ 35 } = 1$

Step-by-step explanation:

we want to figure out the ellipse equation which passes through (1,4) and (-3,2)

the standard form of ellipse equation is given by:

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

where:

(h,k) is the centre
a is the horizontal redius
b is the vertical radius

since the centre of the equation is not mentioned, we'd assume it (0,0) therefore our equation will be:

$\displaystyle \frac{ {x}^{2} }{ {a}^{2} } + \frac{{y}^{2} }{ {b}^{2} } = 1$

substituting the value of x and y from the point (1,4),we'd acquire:

$\displaystyle \frac{ 1}{ {a}^{2} } + \frac{16}{ {b}^{2} } = 1$

similarly using the point (-3,2), we'd obtain:

$\displaystyle \frac{ 9}{ {a}^{2} } + \frac{4 }{ {b}^{2} } = 1$

let 1/a² and 1/b² be q and p respectively and transform the equation:

$\displaystyle \begin{cases} q + 16p = 1 \\ 9q + 4p = 1 \end{cases}$

solving the system of linear equation will yield:

$\displaystyle \begin{cases} q = \dfrac{3}{35} \\ \\ p = \dfrac{2}{35} \end{cases}$

substitute back:

$\displaystyle \begin{cases} \dfrac{1}{ {a}^{2} } = \dfrac{3}{35} \\ \\ \dfrac{1}{ {b}^{2} } = \dfrac{2}{35} \end{cases}$

divide both equation by 1 which yields:

$\displaystyle \begin{cases} {a}^{2} = \dfrac{35}{ 3} \\ \\ {b}^{2} = \dfrac{35}{2} \end{cases}$

substitute the value of a² and b² in the ellipse equation , thus:

$\displaystyle \frac{ {x}^{2} }{ \dfrac{35}{3} } + \frac{{y}^{2} }{ \dfrac{35}{2} } = 1$

simplify complex fraction:

$\displaystyle \frac{ {3x}^{2} }{ 35 } + \frac{{2y}^{2} }{ 35 } = 1$

and we're done!

(refer the attachment as well)

8 0

3 years ago

What is the graph for y=2x-4

Yuliya22 [10]

This is the graph for the equation y=2x-4.

5 0

3 years ago

The perimeter of a rectangle is 84. If the length is 2 more than three times the width, what are the dimensions of the rectangle

Marina86 [1]

The perimeter solved shows that the dimensions of the rectangle are 32 and 10.

<h3>How to calculate the perimeter</h3>

Let the width be w

Length = 3w + 2

Perimeter = 2(length + width)

Perimeter = 2(3w + 2) + 2w

6w + 4 + 2w = 84

8w + 4 = 84

8w = 84 - 4

w = 80/8

w = 10

Length = 3w + 2

Length = 3(10) + 2

Length = 32

The dimensions of the rectangle are 32 and 10.

Learn more about perimeter on:

brainly.com/question/19819849

5 0

2 years ago

Ben rolls two number cubes. What is the probability that the sum of the numbers he rolls is less than six?

BartSMP [9]

5/12 is the correct answer

4 0

4 years ago

Give the function y=5+2x, what is the output (y) when the input, x=4?

3241004551 [841]

Answer:

Step-by-step explanation:

y=5+2(4)

7 0

3 years ago

Read 2 more answers