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Find the domain of the function $\frac{x^4-4x^3+6x^2-4x+1}{x^2-4}$.

Hello olivia!

\(x^2-4\neq0\\ x\neq\{-\sqrt{2},\sqrt{2}\} \)

\( x\in\mathbb R\ |\ x\notin\{-\sqrt{2},+\sqrt{2}\}\)

  !

An incenter is a point in a triangle where all 3 angle bisectors intersect.

So, the answer is a.

We know that the ratio of midsegment WX to side TV is 1 : 2

So, we have     2 * WX = TV

                         2(23 - 2x) = 64 - 10x

                         x = 9/4

                        TV = 64 - 10(9/4) = 83/2

Is this missing any details? On my screen I can't see the numbers... 

Let s = soft shell tacos, and h = hard shell tacos

6s + 2h = 12

3s + 1h = 6

Im not sure you can even write a system for this since they are proportionate. 

(3s + 1h = 6) * 2 --> 6s + 2h = 12, which is the first sentence. If you wrote a system, it would just be "0 + 0 = 0"; you can't cancel anything out.

However, you could make a good guess to what the answer might be since the numbers aren't big. 

s could equal 1 and h could equal 3. 

Take your first equation:

.13x   +   .05y    +   .29z    =    .1 (x+y+z)       This is for A

There are numerous solutions to x, y, z: 

such as x =70,  y = 80  and  z =10 . Sub these values for x, y, z and you get:

0.13 *70  + 0.05 * 80  + 0.29 * 10 =0.10*(70+80+10)

9.1            +     4             +      2.9      =0.10*(160)

                 16                                        =16

Thank you so much~!!

I plotted this, and got a width of 8.

50.25 * 3 = $150.75 a day

150.75 * 7 = B) $1055.25, which is your answer :)

Sum of angles in a triangle =  180 

    Sooooo     X+14+x+32+90   = 180

                       2x = 180-90-32-14              I think you can take it from here !

A + B + C = 8.

1/a + 1/b = (b + a) / ab

1/b - 1/a = (a - b) / ab

When multiplied, you get: (a + b)(a - b) / a²b²

                                              = (a² - b²) / a²b²

                                      = 1/b² - 1/a²

This means you want b = 3, since you want it to be the smallest it can be. Then you want a = -1, since you want it to be the biggest it can be. 

This gives you:
 

1/3² - 1/(-1)²

= 1/9 - 1

= -8/9, which is your answer :)

I'm a little confused....   are a,b,c  in your solution   corresponding to   Substance 1   2 and 3 ?

3.5 / 3 = 6.5   (3.5 + 3)

32.5 ÷ 6.5 = 5, which means he needs to make 5 batches.

3.5 gallons of fruit punch concentrate per batch, which means he'll need 3.5 * 5 = 17.5 gallons of fruit punch concentrate :)

The ratio of quarters to dimes right now is 3:12

If we look at this like a fraction, it's 3/12, but we want to get it to 1/2. 

1/2 = 6/12, which means there needs to be 3 more quarters in order for the ratio to be 6:12, or 1:2. 

7x²⁰¹⁴ / 4x²⁰¹³ = 7x/4 

2x²⁰¹² / 28x²⁰¹¹ = x/14

9x²⁰⁰⁷ / x²⁰⁰⁸ = 9/x

8x²⁰⁰⁹ / 6x²⁰¹⁰ = 4/3x

= (252x²) / (168x²)

= 252 / 168

= 3/2, which is your answer :)

a=0;p=0; b=0;c=0;n=0.62*a    + 0.77*b    +  0.13*c +0.13*a   +   0.05*b    +   0.29*c+0.25*a   +   0.18*b    + 0.58* c  ;if(n==0.10*(a+b+c) + 0.50*(a+b+c) +0.4*(a+b+c), goto loop, goto next);loop:p=p+1;printp," =",a,b,c,n;next:a++;if(a<150, goto4,0);a=0;b++;if(b<150, goto4, 0);a=0;b=0;c++;if(c<150, goto4,0)

OUTPUT: By adding up the  3 equations, there appear to be many solutions such as:

a = 20,   b=140,   c=40

Sorry, I meant \(3^{-2}\).