Answer:
D
Step-by-step explanation:
For some side lengths to create a triangle, any two of the side lengths must have an added length together of less than the third leg. Otherwise, the vertices would simply not be able to be connected by the lines. In a), 3+5=8, but since it is not more, the triangle will not be able to be formed (it would basically just be a line.) In B, 7+8< 16. In C, there is the same situation as with the first example (4+15=19). Finally, in the last one, 5+7>12, and all of the side lengths work out. Therefore, the correct answer is D. Hope this helps!
<span>16 years ago = - 16
Present population -16 = </span><span>15,000 (population)
</span>
11% increase = every year =0.11
present year = <span>15,000 x 0.11^16
= 15,000 x 4.594
approx = 68,925</span>
From the graph, it is obvious that the trend is decreasing from 100 on day 2, to 1 on day 10. So, the answer could either be A or C. The question would be how fast is it decreasing? To illustrate this, let's find the difference of consecutive data:
100 - 26 = 74
26 - 6 = 20
6 - 2=4
2-1=1
It must not be an additive rate because there is no common difference. Let's illustrate if the trend is in multiplicative rate:
100/26 = 3.85
26/6 = 4.33
6/2 = 3
2/1 = 2
More or less, they have a common divider. Hence, the decreasing rate is in multiplicative rate. The answer is A.
Answer: ![\bold{\sqrt[4]{2} }](https://tex.z-dn.net/?f=%5Cbold%7B%5Csqrt%5B4%5D%7B2%7D%20%7D)
<u>Step-by-step explanation:</u>
![\dfrac{1}{2}\sqrt[4]{32} =\dfrac{1}{2}\sqrt[4]{2\cdot 2\cdot 2\cdot 2\cdot 2}=\dfrac{1}{2}\cdot 2\sqrt[4]{2}=\boxed{\sqrt[4]{2} }](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%5Csqrt%5B4%5D%7B32%7D%20%3D%5Cdfrac%7B1%7D%7B2%7D%5Csqrt%5B4%5D%7B2%5Ccdot%202%5Ccdot%202%5Ccdot%202%5Ccdot%202%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%202%5Csqrt%5B4%5D%7B2%7D%3D%5Cboxed%7B%5Csqrt%5B4%5D%7B2%7D%20%7D)
