Answer:
A 7.81
Step-by-step explanation:
Use the distance formula to find the distance between coordinates.
![d = \sqrt{(2--4)^2 + (5-0)^2} \\d = \sqrt{(2+4)^2 + (5)^2} \\d = \sqrt{(6)^2 + (5)^2} \\d = \sqrt{36 + 25} \\d = \sqrt{61} \\d=7.81](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%282--4%29%5E2%20%2B%20%285-0%29%5E2%7D%20%5C%5Cd%20%3D%20%5Csqrt%7B%282%2B4%29%5E2%20%2B%20%285%29%5E2%7D%20%5C%5Cd%20%3D%20%5Csqrt%7B%286%29%5E2%20%2B%20%285%29%5E2%7D%20%5C%5Cd%20%3D%20%5Csqrt%7B36%20%2B%2025%7D%20%5C%5Cd%20%3D%20%5Csqrt%7B61%7D%20%5C%5Cd%3D7.81)
Answer:
C: 0.000568 miles
Step-by-step explanation:
Essentially, the exponent on the 10 is how many places to move the decimal point, and negative versus positive dictates whether to move it right or left respectively.
![Let \: Lindsey's \: father's \: age \: be \: = \: x](https://tex.z-dn.net/?f=Let%20%5C%3A%20%20Lindsey%27s%20%20%5C%3A%20father%27s%20%20%5C%3A%20age%20%20%5C%3A%20be%20%5C%3A%20%20%3D%20%5C%3A%20%20x%20)
![Then \: Lindsey's \: age = \frac{1}{2} x - 5](https://tex.z-dn.net/?f=Then%20%5C%3A%20%20Lindsey%27s%20%5C%3A%20%20age%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20x%20-%205)
![Sum \: of \: their \: age = 79](https://tex.z-dn.net/?f=Sum%20%5C%3A%20%20of%20%5C%3A%20%20their%20%5C%3A%20%20age%20%3D%2079%20)
<h3>This can be written in an equation as :-</h3>
![x + \frac{1}{2} x - 5 = 79](https://tex.z-dn.net/?f=x%20%2B%20%20%5Cfrac%7B1%7D%7B2%7D%20x%20-%205%20%3D%2079)
![To \: find \: out \: Lindsey's \: age \: , let \: us \: first \: find \: out \: the \: value \: of \: x .](https://tex.z-dn.net/?f=To%20%5C%3A%20%20find%20%5C%3A%20%20out%20%5C%3A%20%20Lindsey%27s%20%20%5C%3A%20age%20%20%5C%3A%20%2C%20let%20%20%5C%3A%20us%20%20%5C%3A%20first%20%20%5C%3A%20find%20%5C%3A%20%20out%20%20%5C%3A%20the%20%20%5C%3A%20value%20%20%5C%3A%20of%20%5C%3A%20%20x%20.%3C%2Fp%3E%3Cp%3E)
![1 \frac{1}{2} x - 5 = 79](https://tex.z-dn.net/?f=1%20%5Cfrac%7B1%7D%7B2%7D%20x%20-%205%20%3D%2079)
![\frac{3}{2} x - 5 = 79](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B2%7D%20x%20-%205%20%3D%2079)
![\frac{3}{2} x = 79 + 5](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B2%7D%20x%20%3D%2079%20%2B%205)
![\frac{3}{2} x = 84](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B2%7D%20x%20%3D%2084)
![x = 84 \div \frac{3}{2}](https://tex.z-dn.net/?f=x%20%3D%2084%20%5Cdiv%20%20%5Cfrac%7B3%7D%7B2%7D%20)
![x = 84 \times \frac{2}{3}](https://tex.z-dn.net/?f=x%20%3D%2084%20%5Ctimes%20%20%5Cfrac%7B2%7D%7B3%7D%20)
![x = \frac{168}{3}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B168%7D%7B3%7D%20)
![x = 56](https://tex.z-dn.net/?f=x%20%3D%2056)
![Lindsey's \: father's \: age = 56](https://tex.z-dn.net/?f=Lindsey%27s%20%5C%3A%20%20father%27s%20%5C%3A%20%20age%20%3D%2056)
![Lindsey's \: age = 28 - 5](https://tex.z-dn.net/?f=Lindsey%27s%20%5C%3A%20%20age%20%20%3D%2028%20-%205)
![Lindsey's \: age = 23](https://tex.z-dn.net/?f=Lindsey%27s%20%5C%3A%20%20age%20%20%3D%2023)
∴Lindsey's age is 23 .
Sin(theta) = O/H = 5/16 (this us the ratio)
If we go further for the problem:
sin(theta) = 5/16 becomes sin-1 (5/16) = 18.2°
Good luck!