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3 years ago

(X+2y)(x-2y) how do I solve this

Mathematics

1 answer:

Fudgin [204]3 years ago

5 0

Step-by-step explanation:

(x+2y)(x-2y)

x^2-2xy+2xy-(2y)^2
x^2-4y^2

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Determine the horizontal vertical and slant asymptote y=x^2+2x-3/x-7

lilavasa [31]

Answer:

<h2>A.Vertical:x=7</h2><h2>Slant:y=x+9</h2>

Step-by-step explanation:

$f(x)=\dfrac{x^2+2x-3}{x-7}\\\\vertical\ asymptote:\\\\x-7=0\qquad\text{add 7 to both sides}\\\\\boxed{x=7}\\\\horizontal\ asymptote:\\\\\lim\limits_{x\to\pm\infty}\dfrac{x^2+2x-3}{x-7}=\lim\limits_{x\to\pm\infty}\dfrac{x^2\left(1+\frac{2}{x}-\frac{3}{x^2}\right)}{x\left(1-\frac{7}{x}\right)}=\lim\limits_{x\to\pm\infty}\dfrac{x\left(1+\frac{2}{x}-\frac{3}{x^2}\right)}{1-\frac{7}{x}}=\pm\infty\\\\\boxed{not\ exist}$

$slant\ asymptote:\\\\y=ax+b\\\\a=\lim\limits_{x\to\pm\infty}\dfrac{f(x)}{x}\\\\b=\lim\limits_{x\to\pm\infty}(f(x)-ax)\\\\a=\lim\limits_{x\to\pm\infty}\dfrac{\frac{x^2+2x-3}{x-7}}{x}=\lim\limits_{x\to\pm\infty}\dfrac{x^2+2x-3}{x(x-7)}=\lim\limits_{x\to\pm\infty}\dfrac{x^2+2x-3}{x^2-7x}\\\\=\lim\limits_{x\to\pm\infty}\dfrac{x^2\left(1+\frac{2}{x}-\frac{3}{x^2}\right)}{x^2\left(1-\frac{7}{x}\right)}=\lim\limits_{x\to\pm\infty}\dfrac{1+\frac{2}{x}-\frac{3}{x^2}}{1-\frac{7}{x}}=\dfrac{1}{1}=1$

$b=\lim\limits_{x\to\pm\infty}\left(\dfrac{x^2+2x-3}{x-7}-1x\right)=\lim\limits_{x\to\pm\infty}\left(\dfrac{x^2+2x-3}{x-7}-\dfrac{x(x-7)}{x-7}\right)\\\\=\lim\limits_{x\to\pm\infty}\left(\dfrac{x^2+2x-3}{x-7}-\dfrac{x^2-7x}{x-7}\right)=\lim\limits_{x\to\pm\infty}\dfrac{x^2+2x-3-(x^2-7x)}{x-7}\\\\=\lim\limits_{x\to\pm\infty}\dfrac{x^2+2x-3-x^2+7x}{x-7}=\lim\limits_{x\to\pm\infty}\dfrac{9x-3}{x-7}=\lim\limits_{x\to\pm\infty}\dfrac{x\left(9-\frac{3}{x}\right)}{x\left(1-\frac{7}{x}\right)}$

$=\lim\limits_{x\to\pm\infty}\dfrac{9-\frac{3}{x}}{1-\frac{7}{x}}=\dfrac{9}{1}=9\\\\\boxed{y=1x+9}$

8 0

3 years ago

Can someone help me w questions 1 and 2 i’ll give u brainliest

Leni [432]

Answer:

1. x^2+5

2.x^2-6x+9

Step-by-step explanation:

these are just translations up and to the right.

since the f(x)=x^2

the transformations would be

1. g(x)=x^2+5

2.g(x)=(x-3)^2 = x^2-6x+9

4 0

2 years ago

Please help me it's due tomorrow

vitfil [10]

The graph represents p(x) = |x|

To graph r(x) and q(x), pick any values of x to graph (I'd pick the numbers on the x- scales, -6, -4, -2, 0, 2, 4, and 6)

As for explaining them, I'm sure something like "multiply the absolute value of x by -1/2" for describing q(x) is an acceptable answer.

6 0

3 years ago

The credit department of Lion's Department Store in Anaheim, California, reported that 30% of their sales are cash, 30% are paid

Oliga [24]

Answer:

Hence the probability that she paid cash is 0.105

Step-by-step explanation:

P(cash) = 0.3

P(credit card ) = 0.3

P(debit card ) = 0.4

P ( more than $50 | cash ) = 0.2

P (more than $50 | credit card ) =0.9

P (more than $ 50 |debit card ) = 0.6

P ( more than $50) = P ( more than $50 | cash )* P (cash) + P (more than $50 credit card ) * P(credit card ) + P (more than $ 50 |debit card )* P(debit card )

= 0.2 * 0.3 + 0.9 * 0.3 + 0.6* 0.4

= 0.57

P ( more than $50) = P ( more than $50 | cash )* P (cash) / P ( more than $50)

= 0.2* 0.3 / 0.57

= 0.105

6 0

3 years ago

I need the answer to this

Arisa [49]

Answer:

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