The distance between the points is 5
Answer:
a) The length of segment AC is approximately 5.83 centimeters.
b) The angle ACD is approximately 34.5º.
Step-by-step explanation:
a) Since
, the length of segment
is determined by Pythagorean Theorem, that is:


The length of segment AC is approximately 5.831 centimeters.
b) Since
, the length of segment
is determined by this Pythagorean identity:


The angle ACD is determined by the following trigonometric expression:





The angle ACD is approximately 34.448º.
1 lb = 16 oz
Translating the unit into oz gives us
166oz - 123oz = 43oz or 2lb 11oz
Total cards = 52
Total red cards = 26
Total black cards = 26
P(one red and one black) = P(red and then black)+ P(black and then red)
P(one red and one black) =(26/52)(26/51) + (26/52)(26/51)
P(one red and one black) = 26/51 (Answer A)
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Answer: 26/51 (Answer A)
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Check the picture below.
now, we have a triangle with all three sides, thus we can use Heron's Area Formula on the triangle.
![\bf \qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=10\\ b=26.695\\ c=22\\ s=29.3475 \end{cases} \\\\\\ A=\sqrt{29.3475(29.3475-10)(29.3475-26.695)(29.3475-22)} \\\\\\ A=\sqrt{29.3475(19.3475)(2.6525)(7.3475)}\implies A\approx \sqrt{11066.007} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A\approx 105.195~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Ctextit%7BHeron%27s%20area%20formula%7D%20%5C%5C%5C%5C%20A%3D%5Csqrt%7Bs%28s-a%29%28s-b%29%28s-c%29%7D%5Cqquad%20%5Cbegin%7Bcases%7D%20s%3D%5Cfrac%7Ba%2Bb%2Bc%7D%7B2%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20a%3D10%5C%5C%20b%3D26.695%5C%5C%20c%3D22%5C%5C%20s%3D29.3475%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20A%3D%5Csqrt%7B29.3475%2829.3475-10%29%2829.3475-26.695%29%2829.3475-22%29%7D%20%5C%5C%5C%5C%5C%5C%20A%3D%5Csqrt%7B29.3475%2819.3475%29%282.6525%29%287.3475%29%7D%5Cimplies%20A%5Capprox%20%5Csqrt%7B11066.007%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20A%5Capprox%20105.195~%5Chfill)