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2 years ago

Will give brainliest... Please I need this answer so badly

Mathematics

1 answer:

m_a_m_a [10]2 years ago

8 0

(6 - x) * (6 + x) - ( (2 - x) * (2 + x) ) =

6^2 - x^2 - ( 2^2 - x^2 ) =

36 - x^2 - ( 4 - x^2 ) =

36 - x^2 - 4 + x^2 =

36 - 4 =

32 square feet

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Rove the sum of two rational numbers is rational where a, b, c, and d are integers and b and d cannot be zero.

liubo4ka [24]

Answer:

$\frac{ad+bc}{bd}$

Step-by-step explanation:

$Greetings!$

$I'm~Isabelle~Williams~and~I~will~be~answering~your~question!$

$Let,\frac{a}{b} ~and ~\frac{c}{d}~be~two~rational~numbers, ~where~ b ~and~ d ~are~ not~ zero ~and~ a, ~b, ~c ~and \\~d ~are~ integers.$

$1.~Given:$

$\frac{a}{b} +\frac{c}{d}$

$2.~Now,~we~multiply~to~get~a~common~denominator:$

$\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{cb}{db}$

$3.~Then~simplify:$

$\frac{a}{b}+\frac{c}{d}=\frac{ad}{bd}+\frac{cb}{db}=\frac{ad+bc}{bd}$

$4.~Since,b\neq 0,~d\neq 0,~then,~bd,~ad,~bc~and~ad+bc~are~integers~too.~So~the\\ fraction~will~be:$

$\frac{ad+bc}{bd}$

$Thus,~making~it~a~rational~number!$

$Hope~this~answer~helps!~and~have~an~amazing~day~ahead!$

$-Isabelle~Williams$

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2 years ago

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What is x if n≠m? Please help!

lorasvet [3.4K]

Answer: $x = \frac{mn(q - p)}{n-m}\\\\$

================================================

Work Shown:

Part 1

$\frac{x-m}{m} + p = \frac{x-n}{n} + q\\\\\frac{x-m}{m} - \frac{x-n}{n} = q - p\\\\\frac{n(x-m)}{mn} - \frac{m(x-n)}{mn} = q - p\\\\\frac{xn-mn}{mn} - \frac{xm-mn}{mn} = q - p\\\\\frac{xn-mn-(xm-mn)}{mn} = q - p\\\\$

Part 2

$\frac{xn-mn-xm+mn}{mn} = q - p\\\\\frac{xn-xm}{mn} = q - p\\\\\frac{x(n-m)}{mn} = q - p\\\\x(n-m) = mn(q - p)\\\\x = \frac{mn(q - p)}{n-m} \\\\$

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

Explanations:

There are quite a bit of steps. I decided to break things into two parts.
The goal is to get x all by itself on its own side, which is why I subtracted (x-n)/n from both sides in part 1, step 2. I also subtracted p from both sides.
Afterward, I gave each fraction the LCD mn. I multiplied top and bottom of the first fraction by n/n. I did a similar operation to the second fraction, but with m instead.
From there, we distribute and simplify. The mn terms cancel on the left side numerator (second step of part 2).
The n≠m is there to prevent the denominator (n-m) from being zero. We cannot divide by zero.
If the formulas don't properly display, then you might have to refresh the page.

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2 years ago

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