The interval notation is ![(-\sqrt{11}-4, \sqrt{11}-4)](https://tex.z-dn.net/?f=%28-%5Csqrt%7B11%7D-4%2C%20%5Csqrt%7B11%7D-4%29)
Explanation:
The inequality is ![x^{2}+8 x+5](https://tex.z-dn.net/?f=x%5E%7B2%7D%2B8%20x%2B5%3C0)
Let us complete the square, we get,
![x^{2}+8 x+5+4^{2}-4^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%2B8%20x%2B5%2B4%5E%7B2%7D-4%5E%7B2%7D%3C0)
Simplifying, we have,
![(x+4)^{2}+5-4^{2}](https://tex.z-dn.net/?f=%28x%2B4%29%5E%7B2%7D%2B5-4%5E%7B2%7D%3C0)
![(x+4)^{2}-11](https://tex.z-dn.net/?f=%28x%2B4%29%5E%7B2%7D-11%3C0)
Adding both sides of the equation by 11, we get,
![(x+4)^{2}](https://tex.z-dn.net/?f=%28x%2B4%29%5E%7B2%7D%3C11)
Since, we know that for
, if n is even then ![-\sqrt[n]{a}](https://tex.z-dn.net/?f=-%5Csqrt%5Bn%5D%7Ba%7D%3Cu%3C%5Csqrt%5Bn%5D%7Ba%7D)
Thus, writing the above expression in this form, we get,
![-\sqrt{11}](https://tex.z-dn.net/?f=-%5Csqrt%7B11%7D%3Cx%2B4%3C%5Csqrt%7B11%7D)
Also, if
then
and ![u](https://tex.z-dn.net/?f=u%3Cb)
Then ,we have,
and ![x+4](https://tex.z-dn.net/?f=x%2B4%3C%5Csqrt%7B11%7D)
Solving the inequalities, we get,
and ![x+4](https://tex.z-dn.net/?f=x%2B4%3C%5Csqrt%7B11%7D%5C%5Cx%20%5C%20%5C%20%5C%20%5C%20%5C%20%3C%5Csqrt%7B11%7D-4)
Merging the intervals, we have,
![-\sqrt{11}-4](https://tex.z-dn.net/?f=-%5Csqrt%7B11%7D-4%3Cx%3C%5Csqrt%7B11%7D-4)
Hence, writing the solution in interval notation, we have,
![(-\sqrt{11}-4, \sqrt{11}-4)](https://tex.z-dn.net/?f=%28-%5Csqrt%7B11%7D-4%2C%20%5Csqrt%7B11%7D-4%29)
Therefore, the answer is ![(-\sqrt{11}-4, \sqrt{11}-4)](https://tex.z-dn.net/?f=%28-%5Csqrt%7B11%7D-4%2C%20%5Csqrt%7B11%7D-4%29)
Marcia dissolved 1 kg of salt in 3 litres of water.
Bobby dissolves 2 pounds of salt in 7 pints of water
2.11 pints = 1 litre
7 pints = 7/2.11
= 3.32 litre
1 pound =0.45 kg
2 pound = o.45*2 kg
= 0.9 kg
So we find that Bobby is dissolving 0.9kg of salt in 3.32 litre of water
Marcia is dissolving 1 kg of salt in 3 litres of water.
So it can be said that Marcia made a more concentrated salt solution.
Answer:
1.11
2.14
3.7
4.10
Step-by-step explanation:
1. 6÷x +9
6÷3=2
2+9=11
2. 8x-3+y
8×2 -3+1
=16-3+1
= 16-2=14
3. 2xy
=2×5×-3
=10-3 =7
4. 2x^2-y
=2×3^2-8
=2×9-8
=18-8
=10
Answer:
i agree
Step-by-step explanation: