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3 years ago

Which number line shows the solution to −3 − (−1)?

Mathematics

1 answer:

Irina18 [472]3 years ago

6 0

Answer:

The 3rd number line (c)

Step-by-step explanation:

The solution is -2

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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

Find the difference between (2x-4) and (6-8x)

antiseptic1488 [7]

Answer:

(2x-4)-(6-8x)

2x-4-6+8x

2x-10+8x

10x-10

Step-by-step explanation:

The question's asking the difference between 2 binomial polynomials.

1. To subtract them, you must use the distributive property to distribute the minus sign on the terms in the second polynomial.

2. Combine like terms. -4-6=-10, 2x+8x=10

Answer is 10x-10

4 0

4 years ago

If I equals √-1 what is the value of I³

ziro4ka [17]

Answer:

-I

Step-by-step explanation:

Given :

I= $\sqrt{-1}$

Now

$I^{2} =-1$

And $I^{3} =-i$

Answer will be -I

8 0

3 years ago

When do you say that a given quadrilateral is a parallelogram?

MrRissso [65]

Answer:

Theorem : If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. Given : ABCD is a quadrilateral in which ∠A = ∠C and ∠B = ∠D. We know that the sum of the angles of a quadrilateral is 360o.

Step-by-step explanation:

hope that helps

3 0

2 years ago

Find the greatest common factor of the following monomials : 10b^5 , 26b^6

charle [14.2K]

Answer:

2b^5.

Step-by-step explanation:

The Greatest Common Factor of 10 and 26 is 2.

The GCF of b^5 and b^6 is 5^5.

Answer is 2b^5.

4 0

3 years ago