Helppppp please!! :/

Solve 7x – 2y = –3 14x + y = 14 a. (4,5/7) b. (4,7/5) c. (5/7,4) d. (7/5,4)

den301095 [7]

7x - 2y = -3 . . . (1)
14x + y = 14 . . . (2)
(1) x 2 => 14x - 4y = -6 . . . (3)
(2) - (3) => 5y = 20
y = 20/5 = 4
From (1); 7x - 2(4) = -3
7x - 8 = -3
7x = -3 + 8 = 5
x = 5/7

Solution = (5/7, 4)

3 0

4 years ago

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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

(4.3×10 2 )×(4.0×10 −3 ) in scientific notation??

DIA [1.3K]

(4.3×10²) × (4.0×10⁻³) in scientific notation?

(4.3 x 4.0) x (10² x 10⁻³) = 17.2 x (10² x 10⁻³) =

= 17.2 x 10²⁻³ = 17.2 x 10⁻¹ = 1.72 x 10¹ x 10⁻¹ = 1.72 x 10¹⁻¹ = 1.72 x 10⁰ = 1.72 x 1

Answer : 1.72 x 10⁰ = 1.72

Hope this helps!

$\textit{\textbf{Spymore}}$

4 0

4 years ago

Help may oplpkpk.........

Diano4ka-milaya [45]

Answer:

A.

Step-by-step explanation:

The answer is A.

Good luck!

5 0

3 years ago

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A student wants to report on the number of meals his friends buy each week. The collected data are below: 4 19 3 3 2 3 2 4 Which

Strike441 [17]

The median or the mode which is three, but not the average because there is an outlier in the set, which is 19 and would skew the data higher than it should be.

3 0

3 years ago

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