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Answer:
D. 2
Step-by-step explanation:
M(0,2b)
N(2a,0)
Then the midpoint P coordinates are
P\left(\dfrac{2a+0}{2},\dfrac{0+2b}{2}\right)\Rightarrow P(a,b)
Use distance formula to find OP and MN:
OP=\sqrt{(a-0)^2+(b-0)^2}=\sqrt{a^2+b^2}\\ \\MN=\sqrt{(2a-0)^2+(2b-0)^2}=\sqrt{4a^2+4b^2}=2\sqrt{a^2+b^2}
So,
MN=2OP
or
OP=1/2 MN
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Answer: It has two distinct real zeros.
Step-by-step explanation:
The formula that is used to calculate the discriminant of a Quadratic function is the one shown below:
![D=b^2-4ac](https://tex.z-dn.net/?f=D%3Db%5E2-4ac)
In this case you have the following Quadractic function provided in the exercise:
![f(x)=6x^2 +10x-1](https://tex.z-dn.net/?f=f%28x%29%3D6x%5E2%20%2B10x-1)
Let's make it equal to 0:
![0=6x^2 +10x-1](https://tex.z-dn.net/?f=0%3D6x%5E2%20%2B10x-1)
You can identify that:
![a=6\\\\b=10](https://tex.z-dn.net/?f=a%3D6%5C%5C%5C%5Cb%3D10)
Knowing these values, you can substitute them into the formula and then evaluate:
![D=10^2-4(6)(-1)\\\\D=124](https://tex.z-dn.net/?f=D%3D10%5E2-4%286%29%28-1%29%5C%5C%5C%5CD%3D124)
Therefore, since:
![D>0](https://tex.z-dn.net/?f=D%3E0)
You can determine that the it has two distinct real roots.
Answer:
8.75×10^3
Step-by-step explanation:
here is the answer