Simplify 3 (x+2y) +5x (-y+7)

Good luck with answering the question. :)

VladimirAG [237]

Answer:

Step-by-step explanation:

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✨✨HOPE IT HELPS✨✨

5 0

3 years ago

Read 2 more answers

at the science school, there is one microscope for every 5 students. The principal figures that in order to have one for every 4

Gennadij [26K]

Answer: 120 students

Explanation:

Let x be the number of scopes
Let a be the number of student at school

1x = 5 students
But 5x = a

1x = 4 students
But the principal needs 6 additional scope so that all the students can use it.

=> (x + 6) = 4 students
=> 4(x + 6) = a

Thus,
5x = 4(x + 6)
5x = 4x + 24
5x - 4x = 24
x = 24

So, there are 24 scopes.

Plug x in both equation and compare:

5x = a
5(24) = a
120 = a

4(x + 6) = a
4(24 + 6) = a
4(30) = a
120 = a

Therefore, the students at the school are 120

6 0

3 years ago

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

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Snowcat [4.5K]

Answer:

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4 0

3 years ago

A 55% decrease followed by a 25% increase

Lina20 [59]

Let's say the item starts off at $100.

A 55% decrease means 100%-55% = 45% of the value is still there. The item is now worth 0.45*100 = 45 dollars.

Now increase this by 25%. The long way to do this is to add 25% of 45 onto 45

(25% of 45) + (45) = 0.25*45+45 = 11.25+45 = 56.25

Or, we can multiply 45 by 1.25 since the multiplier 1.25 represents a 25% increase

1.25*45 = 56.25

-----------------------------------------------------

The item was $100, it drops to $45 after the 55% decrease, then it is $56.25 after the 25% increase.

Let's compute the percent difference

A = 100 = old value

B = 56.25 = new value

C = percent difference

C = 100*(B-A)/A

C = 100*(56.25-100)/100

C = -43.75%

The negative C value indicates a percent decrease.

So combining a 55% decrease and a 25% increase leads to an overall decrease of 43.75%

-----------------------------------------------------

A shortcut is to multiply 0.45 and 1.25 to get 0.5625

Then subtract this from 1 to get 1-0.5625 = 0.4375

This is another way to see we have a 43.75% decrease.

8 0

4 years ago

Simplify 3 (x+2y) +5x (-y+7)​

Simplify 3 (x+2y) +5x (-y+7)