For 3, I would talk to your teacher there’s no way of knowing the total amount they spent since there is no way of knowing the total number of friends there were.
For 4 Dot traveled 18 miles an expression for that would be
2(2)+3+10=m
Then just
18=m
1.vertex form is ![y=a(x-h)^2+k](https://tex.z-dn.net/?f=y%3Da%28x-h%29%5E2%2Bk)
to get into vertex form, complete the square
![y=-x^2+12x-4](https://tex.z-dn.net/?f=y%3D-x%5E2%2B12x-4)
step 1: group x terms
![y=(-x^2+12x)-4](https://tex.z-dn.net/?f=y%3D%28-x%5E2%2B12x%29-4)
step 2: factor coefient in front of x^2 term
![y=-1(x^2-12x)-4](https://tex.z-dn.net/?f=y%3D-1%28x%5E2-12x%29-4)
prep for next step: take 1/2 of linear (1st dgree term) and square it
, ![(-6)^2=36](https://tex.z-dn.net/?f=%28-6%29%5E2%3D36)
step 3: add positive and negative of that previous number inside the parenthasees
![y=-1(x^2-12x+36-36)-4](https://tex.z-dn.net/?f=y%3D-1%28x%5E2-12x%2B36-36%29-4)
factor perfect squaer trionmial
![y=-1((x-6)^2-36)-4](https://tex.z-dn.net/?f=y%3D-1%28%28x-6%29%5E2-36%29-4)
take out that -36 by expansion
![y=-1(x-6)^2+36-4](https://tex.z-dn.net/?f=y%3D-1%28x-6%29%5E2%2B36-4)
![y=-1(x-6)^2+32](https://tex.z-dn.net/?f=y%3D-1%28x-6%29%5E2%2B32)
2. factor out the 2
![2(x^2+8x+12)](https://tex.z-dn.net/?f=2%28x%5E2%2B8x%2B12%29)
what 2 numbers multiply to get 12 and add to get 8?
2 and 6
![2(x+2)(x+6)](https://tex.z-dn.net/?f=2%28x%2B2%29%28x%2B6%29)
3.
for ![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
![x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
in our case
![x^2-7x-6=0](https://tex.z-dn.net/?f=x%5E2-7x-6%3D0)
a=1, b=-7, c=-6
![x=\frac{-(-7) \pm \sqrt{(-7)^2-4(1)(-6)}}{2(1)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-%28-7%29%20%5Cpm%20%5Csqrt%7B%28-7%29%5E2-4%281%29%28-6%29%7D%7D%7B2%281%29%7D)
![x=\frac{7 \pm \sqrt{73}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B7%20%5Cpm%20%5Csqrt%7B73%7D%7D%7B2%7D)
so
and ![x=\frac{7-\sqrt{73}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B7-%5Csqrt%7B73%7D%7D%7B2%7D)
4. remember that
so ![i^2=-1](https://tex.z-dn.net/?f=i%5E2%3D-1)
treat
as a variable
![(-2i)(8i)=](https://tex.z-dn.net/?f=%28-2i%29%288i%29%3D)
![(-2)(i)(8)(i)=](https://tex.z-dn.net/?f=%28-2%29%28i%29%288%29%28i%29%3D)
![(-2)(8)(i)(i)=](https://tex.z-dn.net/?f=%28-2%29%288%29%28i%29%28i%29%3D)
![(-16)(i^2)=](https://tex.z-dn.net/?f=%28-16%29%28i%5E2%29%3D)
![(-16)(-1)=](https://tex.z-dn.net/?f=%28-16%29%28-1%29%3D)
[tex}16[/tex]
Simplifying in the bracket first then following the rules of operations-4+8-[16x1+4]
-4+8-[20]
-16
Positive 37,000 feet.
Step-by-step explanation:
Answer:
four hundred thousand sixtey thousand five thousand ten thousand
Step-by-step explanation:
all you do is put it in word from like i did