Answer:
n = 59
Step-by-step explanation:
There's definitely a better way, i just did math randomly but here goes:
First i squared both sides. which gets you:
![(\sqrt{n+5}-\sqrt{n-10} )(\sqrt{n+5}-\sqrt{n-10} )=1^2\\\\n+5 -2\sqrt{(n+5)(n-10)} +n-10=1](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%2B5%7D-%5Csqrt%7Bn-10%7D%20%29%28%5Csqrt%7Bn%2B5%7D-%5Csqrt%7Bn-10%7D%20%29%3D1%5E2%5C%5C%5C%5Cn%2B5%20-2%5Csqrt%7B%28n%2B5%29%28n-10%29%7D%20%2Bn-10%3D1)
Cleaning this up gives you:
![2n-5 -2\sqrt{(n+5)(n-10)}=1](https://tex.z-dn.net/?f=2n-5%20-2%5Csqrt%7B%28n%2B5%29%28n-10%29%7D%3D1)
Now move everything to the other side so we can square this equation again
![-2\sqrt{(n+5)(n-10)}=-2n+6](https://tex.z-dn.net/?f=-2%5Csqrt%7B%28n%2B5%29%28n-10%29%7D%3D-2n%2B6)
Divide both sides by -2
![\sqrt{(n+5)(n-10)}=n-3](https://tex.z-dn.net/?f=%5Csqrt%7B%28n%2B5%29%28n-10%29%7D%3Dn-3)
square again
![(n+5)(n-10)=(n-3)^2\\n^2-5n-50=n^2-6n+9](https://tex.z-dn.net/?f=%28n%2B5%29%28n-10%29%3D%28n-3%29%5E2%5C%5Cn%5E2-5n-50%3Dn%5E2-6n%2B9)
subtract n^2 from both sides, add 6n, and add 50
![-5n-50=-6n+9\\n-50 = 9\\n=59](https://tex.z-dn.net/?f=-5n-50%3D-6n%2B9%5C%5Cn-50%20%3D%209%5C%5Cn%3D59)
Put this back into the equation and you get a correct answer!
sqrt(59 + 5) = sqrt(64) = 8
sqrt(59-10) = sqrt(49) = 7
8 - 7 = 1
192/4=48
There are 48 students on each bus.
Answer:
36.4776119403
Step-by-step explanation:
The equation of a circle is (x-h)^2 + (y-k)^2 = r^2. Where "x" and "y" are variables, "h" and "k" are the coordinates of the center of the circle, and "r" is the length of the radius. It is given that the center of the circle is (-27, 120). So, h= -27 and k= 120. If the circle passes through the origin, we can assume that the origin is on the circle. Since a circle's radius is constant no matter where it is drawn/is, we can find the radius of the circle by finding the distance between the circle's center (-27, 120) and the origin, (0, 0). The distance formula is: d= √((x[2]-x[1])^2-(y[2]-y[1])^2). If the coordinates of the center of the circle are (x[2}, y[2]), then x[2]= -27 and y[2]= 120. Then, the origin is the (x[1], y[1]). So, x[1] = 0 and y[1] = 0. Plugging the numbers in we get: √((-27-0)^2-(120-0)^2). This gives us √(729+14400) = 123. So since the distance between the center of the circle and a point on the circle is 123 (units), then the radius has a value of 123.
Plugging all the numbers into the equation of a circle, we get: (x-(-27))^2+(y-120)^2=123^2.
Answer:
B) f(x) ≥ 3x + 4
g of x is less than or equal to negative one half times x minus 5
Step-by-step explanation:
From the above graph,
If point B is the solution of the system of inequalities, then point B must satisfies both inequalities
We can see from the graph that
Point B is located above (≥) the boundary line for f(x) and is also below (≤) the boundary line for g(x).
So we can say,
Point b satisfies the inequalities
Therefore,
The system is
f(x) ≥ (3x+4)
g(x) ≤ (-1/2x -5)
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