Now, let's say there are "b" boys and "g" gals... ok... well, we know there are 116 more boys than gals..... so, if there are "g" gals then there must be "g + 116" boys.
what's the total class? well is g + b or g + ( g + 116).
Answer:
no solutions
Step-by-step explanation:
there are no solutions
Answer:
x=90
Step-by-step explanation:
I think you mean "if the points <span>(2,5), (3,2) and (4,5) satisfy an unknown 3rd degree polynomial, what is the polynomial?"
Since 3 roots {2, 3, 4} are known, we might begin by assuming that this poly would have the form y = ax^3 + bx^2 + cx + d (which has three factors). Unfortunately, three roots are not enough to determine all four constants {a, b, c, d}.
So, let's assume, instead, that the poly would have the form y = ax^2 + bx + c. Three given points should make it possible to determine {a, b, c}.
(2,5): 5 = a(2)^2 + b(2) + c => 5 = 4a + 2b + c
(3,2): 2 = a(3)^2 + b(3) + c => 2 = 9a + 3b + 5 - 4a - 2b
(4,5): 5 = a(4)^2 + b(4) + c => 5 = 16a + 4b + 5 - 4a - 2b
Now we have two equations in a and b alone, which enables us to solve for a and b:
</span>2 = 9a + 3b + 5 - 4a - 2b becomes -3 = 5a + b
<span>and
</span>5 = 16a + 4b + 5 - 4a - 2b becomes 0 = 12a + 2b, or 0 = 6a + b, or 0=-6a-b
<span>
Adding this result to -3 = 5a + b, we get -3 = -a, so a =3.
Thus, since -3 = 5a + b, -3 = 5(3) + b, so b = -18
All we have to do now is to find c. Let's do this using </span>5 = 4a + 2b + c.
We know that a = 3 and b = -18, so this becomes 5 = 4(3) + 2(-18) + c.
Thus, 5 = 12 - 36 + c, or c = 29.
With a, b and c now known, we can write the poly as y = 3x^2 - 18x + 29.
Now the only thing to do remaining is to verify that each of the three given points satsifies y = 3x^2 - 18x + 29. Try this, please.
<u>Understanding:</u>
This can be easily solved by using the distance formula which is
distance
coordinates of the first point, in our case it is 
coordinates of the second point, 
<u>Solution:</u>
<u></u>![d=\sqrt{[(4)-(1)]^{2}+[(-1)-(-5)]^2}\\=\sqrt{(3)^2+(4)^2}\\= \sqrt{9+16} \\=\sqrt{25}\\= 5](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%5B%284%29-%281%29%5D%5E%7B2%7D%2B%5B%28-1%29-%28-5%29%5D%5E2%7D%5C%5C%3D%5Csqrt%7B%283%29%5E2%2B%284%29%5E2%7D%5C%5C%3D%20%20%5Csqrt%7B9%2B16%7D%20%5C%5C%3D%5Csqrt%7B25%7D%5C%5C%3D%205)
<u></u>
The distance between the two points is 5.
