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3 years ago

Simplify fully12xy24xy

Mathematics

1 answer:

Darina [25.2K]3 years ago

5 0

Answer:

288xy

Step-by-step explanation:

First, you multiply 12 by 24 and you get 288. Next, you can't forget the variables, so you add those to the end and get, 288xy.

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*Asymptotes* g(x) =2x+1/x-3 Give the domain and x and y intercepts

Nataly [62]

Answer: Assuming the function is $g(x)=\frac{2x+1}{x-3}$ :

The x-intercept is $(\frac{-1}{2},0)$ .

The y-intercept is $(0,\frac{-1}{3})$ .

The horizontal asymptote is $y=2$ .

The vertical asymptote is $x=3$ .

Step-by-step explanation:

I'm going to assume the function is: $g(x)=\frac{2x+1}{x-3}$ and not $g(x)=2x+\frac{1}{x}-3$ .

So we are looking at $g(x)=\frac{2x+1}{x-3}$ .

The x-intercept is when y is 0 (when g(x) is 0).

Replace g(x) with 0.

$0=\frac{2x+1}{x-3}$

A fraction is only 0 when it's numerator is 0. You are really just solving:

$0=2x+1$

Subtract 1 on both sides:

$-1=2x$

Divide both sides by 2:

$\frac{-1}{2}=x$

The x-intercept is $(\frac{-1}{2},0)$ .

The y-intercept is when x is 0.

Replace x with 0.

$g(0)=\frac{2(0)+1}{0-3}$

$y=\frac{2(0)+1}{0-3}$

$y=\frac{0+1}{-3}$

$y=\frac{1}{-3}$

$y=-\frac{1}{3}$ .

The y-intercept is $(0,\frac{-1}{3})$ .

The vertical asymptote is when the denominator is 0 without making the top 0 also.

So the deliminator is 0 when x-3=0.

Solve x-3=0.

Add 3 on both sides:

x=3

Plugging 3 into the top gives 2(3)+1=6+1=7.

So we have a vertical asymptote at x=3.

Now let's look at the horizontal asymptote.

I could tell you if the degrees match that the horizontal asymptote is just the leading coefficient of the top over the leading coefficient of the bottom which means are horizontal asymptote is $y=\frac{2}{1}$ . After simplifying you could just say the horizontal asymptote is $y=2$ .

Or!

I could do some division to make it more clear. The way I'm going to do this certain division is rewriting the top in terms of (x-3).

$y=\frac{2x+1}{x-3}=\frac{2(x-3)+7}{x-3}=\frac{2(x-3)}{x-3}+\frac{7}{x-3}$

$y=2+\frac{7}{x-3}$

So you can think it like this what value will y never be here.

7/(x-3) will never be 0 because 7 will never be 0.

So y will never be 2+0=2.

The horizontal asymptote is y=2.

(Disclaimer: There are some functions that will cross over their horizontal asymptote early on.)

6 0

3 years ago

2 dogs/ 3 cats and 10 dogs/ 15 cats are an example of

Bad White [126]

2 dogs/ 3 cats and 10 dogs/ 15 cats are an example of

b. Equivalent ratios
__________________________

$\frac{10 \: dogs}{15 \: cats} = \frac{5 \times 2 \: dogs}{ 5 \times 3 \: cats} = \frac{2 \: dogs}{3 \: cats} \\$

We can see that they are equivalent ratios.

6 0

3 years ago

On a coordinate plane, point AS

nlexa [21]

Answer:

√1370 or about 37.01

Step-by-step explanation:

use distance formula

√(x2-x1)^2+(y2-y1)^2

sqrt(8-7)^2+(41-4)^2

sqrt(1)^2+(37)^2

sqrt 1+1369

sqrt 1370

= about 37. 01

3 0

2 years ago

1x -1y =100 x. what is the answer

Bad White [126]

Answer:

y=-99x

Step-by-step explanation:

it's imposible to answer y in terms of a number, but it is possible to do it in terms of x.

x-y=100x

x=100x+y

-99x=y

y=-99x

8 0

3 years ago

I'LL GIVE BRAINLIEST IF YOU EXPLAIN THE ANSWER: B or C

IrinaVladis [17]

I think it’s b since it looks like a trapezoid

4 0

3 years ago

Simplify fully12xy24xy​

Simplify fully12xy24xy