The answer is B because -3.62 is less than -3.5 and greater than -3.8.
Let l, t, b represent the numbers of lions, tigers, bears, respectively.
2l +3t +3b = 156 . . . . . . . 156 meals per day are supplied
l +t = 3b . . . . . . . . . . . . . . there are 3 times as many great cats as bears
l +t +b = 68 . . . . . . . . . . . there are a total of 68 animals
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The last 2 equations tell you
.. 4b = 68
.. b = 17
Subtracting 3 times the last equation from the first gives
.. -l = -48
There are 48 lions, 3 tigers, and 17 bears.
1)
I:x-y=-7
II:x+y=7
add both equations together to eliminate y:
x-y+(x+y)=-7+7
2x=0
x=0
insert x=0 into II:
0+y=7
y=7
the solution is (0,7)
2)
I: 3x+y=4
II: 2x+y=5
add I+(-1*II) together to eliminate y:
3x+y+(-2x-y)=4+(-5)
x=-1
insert x=-1 into I:
3*-1+y=4
y=7
the solution is (-1,7)
3)
I: 2e-3f=-9
II: e+3f=18
add both equations together to eliminate f:
2e-3f+(e+3f)=-9+18
3e=9
e=3
insert e=3 into I:
2*3-3f=-9
-3f=-9-6
-3f=-15
3f=15
f=5
the solution is (3,5)
4)
I: 3d-e=7
II: d+e=5
add both equations together to eliminate e:
3d-e+(d+e)=7+5
4d=12
d=3
insert d=3 into II:
3+e=5
e=2
the solution is (3,2)
5)
I: 8x+y=14
II: 3x+y=4
add I+(-1*II) together to eliminate y
8x+y+(-3x-y)=14-4
5x=10
x=2
insert x=2 into II:
3*2+y=4
y=4-6
y=-2
the solution is (2,-2)
Check the picture below, so the parabola looks more or less like so, with a vertex at (0 , -7), let's recall the vertex is half-way between the focus point and the directrix.
so this horizontal parabola opens up to the left-hand-side, meaning that the "P" distance is a negative value.
![\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Ctextit%7Bhorizontal%20parabola%20vertex%20form%20with%20focus%20point%20distance%7D%20%5C%5C%5C%5C%204p%28x-%20h%29%3D%28y-%20k%29%5E2%20%5Cqquad%20%5Cbegin%7Bcases%7D%20%5Cstackrel%7Bvertex%7D%7B%28h%2Ck%29%7D%5Cqquad%20%5Cstackrel%7Bfocus~point%7D%7B%28h%2Bp%2Ck%29%7D%5Cqquad%20%5Cstackrel%7Bdirectrix%7D%7Bx%3Dh-p%7D%5C%5C%5C%5C%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%20%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%5C%5C%5C%5C%20%5Cstackrel%7B%22p%22~is~negative%7D%7Bop%20ens~%5Csupset%7D%5Cqquad%20%5Cstackrel%7B%22p%22~is~positive%7D%7Bop%20ens~%5Csubset%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
![\begin{cases} h=0\\ k=-7\\ p=-9 \end{cases}\implies 4(-9)(x-0)~~ = ~~[y-(-7)]^2 \\\\\\ -36x=(y+7)^2\implies x=-\cfrac{1}{36}(y+7)^2](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%20h%3D0%5C%5C%20k%3D-7%5C%5C%20p%3D-9%20%5Cend%7Bcases%7D%5Cimplies%204%28-9%29%28x-0%29~~%20%3D%20~~%5By-%28-7%29%5D%5E2%20%5C%5C%5C%5C%5C%5C%20-36x%3D%28y%2B7%29%5E2%5Cimplies%20x%3D-%5Ccfrac%7B1%7D%7B36%7D%28y%2B7%29%5E2)
