![\: \: \: \: \: \:](https://tex.z-dn.net/?f=%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20)
![1 + w](https://tex.z-dn.net/?f=1%20%20%2B%20w)
Step-by-step explanation:
![1 - w + w2](https://tex.z-dn.net/?f=1%20-%20w%20%2B%20w2)
- <u>us</u><u>e</u><u> </u><u>the </u><u>commutative</u><u> </u><u>property</u><u> </u><u>to </u><u>reorder</u><u> </u><u>the </u><u>terms </u>
<u>
</u>
- <u>collect</u><u> </u><u>like </u><u>terms</u>
<u>
</u>
<h2>
<u>hope</u><u> it</u><u> helps</u></h2>
35 T Shirts is correct.
35 shirts times $15 is $525.
220 total shirts minus 35 shirts is 185.
185 times $10 a youth shirt is $1850.
$1850+$525=$2375 :)
Find the radius of each equation:
1.
![x^2 + y^2-2x+2y-1 = 0, \\ x^2-2x+1-1 + y^2+2y+1-1-1 = 0, \\ (x-1)^2+(y+1)^2=3](https://tex.z-dn.net/?f=x%5E2%20%2B%20y%5E2-2x%2B2y-1%20%3D%200%2C%20%5C%5C%20x%5E2-2x%2B1-1%20%2B%20y%5E2%2B2y%2B1-1-1%20%3D%200%2C%20%5C%5C%20%28x-1%29%5E2%2B%28y%2B1%29%5E2%3D3)
, then
![r_1= \sqrt{3}](https://tex.z-dn.net/?f=r_1%3D%20%5Csqrt%7B3%7D%20)
.
2.
![x^2 + y^2-4x + 4y- 10 = 0, \\ x^2 -4x+4-4+ y^2 + 4y+4-4- 10 = 0, \\ (x-2)^2+(y+2)^2=18](https://tex.z-dn.net/?f=x%5E2%20%2B%20y%5E2-4x%20%2B%204y-%2010%20%3D%200%2C%20%5C%5C%20x%5E2%20-4x%2B4-4%2B%20y%5E2%20%2B%204y%2B4-4-%2010%20%3D%200%2C%20%5C%5C%20%28x-2%29%5E2%2B%28y%2B2%29%5E2%3D18)
, then
![r_2= \sqrt{18}=3 \sqrt{2}](https://tex.z-dn.net/?f=r_2%3D%20%5Csqrt%7B18%7D%3D3%20%5Csqrt%7B2%7D%20%20)
.
3.
![x^2 + y^2-8x- 6y- 20 = 0, \\ x^2-8x+16-16+ y^2- 6y+9-9- 20 = 0, \\ (x-4)^2+(y-3)^2=45](https://tex.z-dn.net/?f=x%5E2%20%2B%20y%5E2-8x-%206y-%2020%20%3D%200%2C%20%5C%5C%20x%5E2-8x%2B16-16%2B%20y%5E2-%206y%2B9-9-%2020%20%3D%200%2C%20%5C%5C%20%28x-4%29%5E2%2B%28y-3%29%5E2%3D45)
, then
![r_3= \sqrt{45} =3 \sqrt{5}](https://tex.z-dn.net/?f=r_3%3D%20%5Csqrt%7B45%7D%20%3D3%20%5Csqrt%7B5%7D%20)
.
4.
![4x^2 + 4y^2+16x+24y- 40 = 0, \\ 4x^2+16x+16-16+ 4y^2+24y+36-36- 40 = 0, \\ 4(x+2)^2+4(y+3)^2=92,\\ (x+2)^2+(y+3)^2=23](https://tex.z-dn.net/?f=4x%5E2%20%2B%204y%5E2%2B16x%2B24y-%2040%20%3D%200%2C%20%5C%5C%204x%5E2%2B16x%2B16-16%2B%204y%5E2%2B24y%2B36-36-%2040%20%3D%200%2C%20%5C%5C%20%0A4%28x%2B2%29%5E2%2B4%28y%2B3%29%5E2%3D92%2C%5C%5C%20%28x%2B2%29%5E2%2B%28y%2B3%29%5E2%3D23)
, then
![r_4= \sqrt{23}](https://tex.z-dn.net/?f=r_4%3D%20%5Csqrt%7B23%7D%20)
.
5.
![5x^2 + 5y^2-20x+30y+ 40 = 0, \\ 5x^2-20x+20-20+ 5y^2+30y+45-45- 40 = 0, \\ 5(x-2)^2+5(y+3)^2=105,\\ (x-2)^2+(y+3)^2=21](https://tex.z-dn.net/?f=5x%5E2%20%2B%205y%5E2-20x%2B30y%2B%2040%20%3D%200%2C%20%5C%5C%205x%5E2-20x%2B20-20%2B%205y%5E2%2B30y%2B45-45-%2040%20%3D%200%2C%20%5C%5C%205%28x-2%29%5E2%2B5%28y%2B3%29%5E2%3D105%2C%5C%5C%20%28x-2%29%5E2%2B%28y%2B3%29%5E2%3D21)
, then
![r_5= \sqrt{21}](https://tex.z-dn.net/?f=r_5%3D%20%5Csqrt%7B21%7D%20)
.
6.
![2x^2 + 2y^2-28x-32y- 8= 0, \\ 2x^2-28x+98-98+ 2y^2-32y+128-128- 8= 0, \\ 2(x-7)^2+2(y-8)^2=234,\\ (x+2)^2+(y+3)^2=117](https://tex.z-dn.net/?f=2x%5E2%20%2B%202y%5E2-28x-32y-%208%3D%200%2C%20%5C%5C%202x%5E2-28x%2B98-98%2B%202y%5E2-32y%2B128-128-%208%3D%200%2C%20%5C%5C%202%28x-7%29%5E2%2B2%28y-8%29%5E2%3D234%2C%5C%5C%20%28x%2B2%29%5E2%2B%28y%2B3%29%5E2%3D117)
, then
![r_6= \sqrt{117}=3\sqrt{13}](https://tex.z-dn.net/?f=r_6%3D%20%5Csqrt%7B117%7D%3D3%5Csqrt%7B13%7D%20)
.
7.
![x^2 + y^2+12x-2y-9 = 0, \\ x^2+12x+36-36+ y^2-2y+1-1- 9 = 0, \\ (x+6)^2+(y-1)^2=46](https://tex.z-dn.net/?f=x%5E2%20%2B%20y%5E2%2B12x-2y-9%20%3D%200%2C%20%5C%5C%20x%5E2%2B12x%2B36-36%2B%20y%5E2-2y%2B1-1-%209%20%3D%200%2C%20%5C%5C%20%28x%2B6%29%5E2%2B%28y-1%29%5E2%3D46)
, then
![r_7= \sqrt{46}](https://tex.z-dn.net/?f=r_7%3D%20%5Csqrt%7B46%7D%20)
.
Hence
![r_1= \sqrt{3}](https://tex.z-dn.net/?f=r_1%3D%20%5Csqrt%7B3%7D%20)
,
![r_2=3 \sqrt{2}](https://tex.z-dn.net/?f=r_2%3D3%20%5Csqrt%7B2%7D%20%20)
,
![r_3=3 \sqrt{5}](https://tex.z-dn.net/?f=r_3%3D3%20%5Csqrt%7B5%7D%20)
,
![r_4= \sqrt{23}](https://tex.z-dn.net/?f=r_4%3D%20%5Csqrt%7B23%7D%20)
,
![r_5= \sqrt{21}](https://tex.z-dn.net/?f=r_5%3D%20%5Csqrt%7B21%7D%20)
,
![r_6= 3\sqrt{13}](https://tex.z-dn.net/?f=r_6%3D%203%5Csqrt%7B13%7D%20)
,
![r_7= \sqrt{46}](https://tex.z-dn.net/?f=r_7%3D%20%5Csqrt%7B46%7D%20)
and
![r_1\ \textless \ r_2\ \textless \ r_5\ \textless \ r_4\ \textless \ r_3\ \textless \ r_7\ \textless \ r_6](https://tex.z-dn.net/?f=r_1%5C%20%5Ctextless%20%5C%20r_2%5C%20%5Ctextless%20%5C%20r_5%5C%20%5Ctextless%20%5C%20r_4%5C%20%5Ctextless%20%5C%20r_3%5C%20%5Ctextless%20%5C%20r_7%5C%20%5Ctextless%20%5C%20r_6)
.
Sdf sdf sdf sd fsd fs fd sdf sdf sdf sdf sd fsd fsd fsd f sdf sd fsd
so the investigator found the skid marks were 75 feet long hmmm what speed will that be?
![s=\sqrt{30fd}~~ \begin{cases} f=\stackrel{friction}{factor}\\ d=\stackrel{skid}{feet}\\[-0.5em] \hrulefill\\ f=\stackrel{dry~day}{0.7}\\ d=75 \end{cases}\implies s=\sqrt{30(0.7)(75)}\implies s\approx 39.69~\frac{m}{h}](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B30fd%7D~~%20%5Cbegin%7Bcases%7D%20f%3D%5Cstackrel%7Bfriction%7D%7Bfactor%7D%5C%5C%20d%3D%5Cstackrel%7Bskid%7D%7Bfeet%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20f%3D%5Cstackrel%7Bdry~day%7D%7B0.7%7D%5C%5C%20d%3D75%20%5Cend%7Bcases%7D%5Cimplies%20s%3D%5Csqrt%7B30%280.7%29%2875%29%7D%5Cimplies%20s%5Capprox%2039.69~%5Cfrac%7Bm%7D%7Bh%7D)
nope, the analysis shows that Charlie was going faster than 35 m/h.
now, assuming Charlie was indeed going at 35 m/h, then his skid marks would have been
![s=\sqrt{30fd}~~ \begin{cases} f=\stackrel{friction}{factor}\\ d=\stackrel{skid}{feet}\\[-0.5em] \hrulefill\\ f=\stackrel{dry~day}{0.7}\\ s=35 \end{cases}\implies 35=\sqrt{30(0.7)d} \\\\\\ 35^2=30(0.7)d\implies \cfrac{35^2}{30(0.7)}=d\implies 58~ft\approx d](https://tex.z-dn.net/?f=s%3D%5Csqrt%7B30fd%7D~~%20%5Cbegin%7Bcases%7D%20f%3D%5Cstackrel%7Bfriction%7D%7Bfactor%7D%5C%5C%20d%3D%5Cstackrel%7Bskid%7D%7Bfeet%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20f%3D%5Cstackrel%7Bdry~day%7D%7B0.7%7D%5C%5C%20s%3D35%20%5Cend%7Bcases%7D%5Cimplies%2035%3D%5Csqrt%7B30%280.7%29d%7D%20%5C%5C%5C%5C%5C%5C%2035%5E2%3D30%280.7%29d%5Cimplies%20%5Ccfrac%7B35%5E2%7D%7B30%280.7%29%7D%3Dd%5Cimplies%2058~ft%5Capprox%20d)