Well a right triangle is made up of a 180 degree angle and take away 90 degrees because the right angle is already there so the answer is that PQR is a right triangle since the other two angles = 90 when added hope this helps i did alot of research:)
Answer:
#4
Step-by-step explanation:
Answer: 9.9
Step-by-step explanation:
SINE RULE:
7/sin(31) = q / sin(47)
Therefore q = 7 / sin(31) * sin(47)
which equals: 9.9 to the nearest tenth.
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)
To answer this, we will look at simple definitions of each term. From the definitions, it will be clear which one is correct.
<u>What is mode?</u>
It is the most occurring number.
<u>What is interquartile range?</u>
It is the difference between third quartile and first quartile.
<u>What is range?</u>
It is largest number minus the smallest number.
<u>What is mean absolute deviation (MAD)?</u>
It is the average distance of each data point from the mean.
<u>What is a quartile?</u>
It is one of the four groups in which a dataset is divided.
From the simple definitions of each term, we can clearly see that Mean Absolute Deviation (MAD), answer choice D, is the correct answer.
Answer: Mean Absolute Deviation