Hey there I need to see the figure to help. no I didn't post to get points I want to help I will no matter what get you the answer but I need the figure
Answer:
The two real solutions are
and ![x=-\frac{12}{18} =-0.6667](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B12%7D%7B18%7D%20%3D-0.6667)
Step-by-step explanation:
The equation
is a quadratic function of the form
that can be solved by using the Quadratic Formula.
![x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%C2%B1%5Csqrt%7Bb%5E%7B2%7D%20-4ac%7D%20%7D%7B2a%7D)
The plus and minus mean that the equation has two solution.
In order to identify is the equation has two real solutions we use the discriminant equation
. Depending of the result we got:
1. If the discriminant is positive, we get two real solutions.
2. if the discriminant is negative, we get complex solutions.
3. If the discriminant is zero, we get just one solution.
Solution:
The equation
has a=9, b=0, and c=-4
Using the discriminant equation to know if the quadratic equation has two real solutions:
![b^{2} -4ac](https://tex.z-dn.net/?f=b%5E%7B2%7D%20-4ac)
The discriminant is positive which mean we get two real solutions.
Using the Quadratic Formula
![x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%C2%B1%5Csqrt%7Bb%5E%7B2%7D%20-4ac%7D%20%7D%7B2a%7D)
![x=\frac{-0±\sqrt{0^{2} -4(9)(-4)} }{2(9)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-0%C2%B1%5Csqrt%7B0%5E%7B2%7D%20-4%289%29%28-4%29%7D%20%7D%7B2%289%29%7D)
![x=\frac{±\sqrt{144} }{18}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%C2%B1%5Csqrt%7B144%7D%20%7D%7B18%7D)
![x=±\frac{12}{18}](https://tex.z-dn.net/?f=x%3D%C2%B1%5Cfrac%7B12%7D%7B18%7D)
then
and ![x=-\frac{12}{18} =-0.6667](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7B12%7D%7B18%7D%20%3D-0.6667)
<h3>
Answer:</h3>
48
<h3>
Step-by-step explanation:</h3>
Let x represent the distance OC. Then CD = x+2, and DP = 16-x. The radius of circle P is ...
... CD +DP = (x+2) +(16-x) = 18
The radius of circle O is ..
... OC + CD = (x) + (x +2) = 2x+2
The length OP is ...
... OC + CP = (x) + (18) = x+18.
Now, the perimeter of ΔAOP is ...
... radius of circle O + radius of circle P + OP = 80
... = (2x+2) + 18 + (x+18) = 3x+38 = 80
Then x is ...
... x = (80 -38)/3 = 14
and the radius of circle O is
... 2x +2 = 2·14 +2 = 30
The desired sum is ...
... OB + BP = (radius of circle O) + (radius of circle P) = 30 + 18
... OB + BP = 48
Answer:
<u>11/12</u><u> </u><u>is</u><u> </u><u>the</u><u> </u><u>fraction</u><u> </u><u>that</u><u> </u><u>is</u><u> </u><u>closer</u><u> </u><u>to</u><u> </u><u>1</u><u>.</u>
At least means that at the lowest or smallest amount, it is that number, which is 4. So, the equation for this would be n≥4