Answer:
59
Step-by-step explanation:
When rounding to the nearest whole number we round the ones digit which is 8. We look at the next digit to determine if we need to round up or not. If it is 5 or above we round up. 6>= 5 so we will round the 8 to a 9
58.6 rounds to 59
Answer:
![BC=4\sqrt{5}\ units](https://tex.z-dn.net/?f=BC%3D4%5Csqrt%7B5%7D%5C%20units)
Step-by-step explanation:
see the attached figure with letters to better understand the problem
step 1
In the right triangle ACD
Find the length side AC
Applying the Pythagorean Theorem
![AC^2=AD^2+DC^2](https://tex.z-dn.net/?f=AC%5E2%3DAD%5E2%2BDC%5E2)
substitute the given values
![AC^2=16^2+8^2](https://tex.z-dn.net/?f=AC%5E2%3D16%5E2%2B8%5E2)
![AC^2=320](https://tex.z-dn.net/?f=AC%5E2%3D320)
![AC=\sqrt{320}\ units](https://tex.z-dn.net/?f=AC%3D%5Csqrt%7B320%7D%5C%20units)
simplify
![AC=8\sqrt{5}\ units](https://tex.z-dn.net/?f=AC%3D8%5Csqrt%7B5%7D%5C%20units)
step 2
In the right triangle ACD
Find the cosine of angle CAD
![cos(\angle CAD)=\frac{AD}{AC}](https://tex.z-dn.net/?f=cos%28%5Cangle%20CAD%29%3D%5Cfrac%7BAD%7D%7BAC%7D)
substitute the given values
![cos(\angle CAD)=\frac{16}{8\sqrt{5}}](https://tex.z-dn.net/?f=cos%28%5Cangle%20CAD%29%3D%5Cfrac%7B16%7D%7B8%5Csqrt%7B5%7D%7D)
----> equation A
step 3
In the right triangle ABC
Find the cosine of angle BAC
![cos(\angle BAC)=\frac{AC}{AB}](https://tex.z-dn.net/?f=cos%28%5Cangle%20BAC%29%3D%5Cfrac%7BAC%7D%7BAB%7D)
substitute the given values
----> equation B
step 4
Find the value of x
In this problem
----> is the same angle
so
equate equation A and equation B
solve for x
Multiply in cross
![(8\sqrt{5})(\sqrt{5})=(16+x)(2)\\\\40=32+2x\\\\2x=40-32\\\\2x=8\\\\x=4\ units](https://tex.z-dn.net/?f=%288%5Csqrt%7B5%7D%29%28%5Csqrt%7B5%7D%29%3D%2816%2Bx%29%282%29%5C%5C%5C%5C40%3D32%2B2x%5C%5C%5C%5C2x%3D40-32%5C%5C%5C%5C2x%3D8%5C%5C%5C%5Cx%3D4%5C%20units)
![DB=4\ units](https://tex.z-dn.net/?f=DB%3D4%5C%20units)
step 5
Find the length of BC
In the right triangle BCD
Applying the Pythagorean Theorem
![BC^2=DC^2+DB^2](https://tex.z-dn.net/?f=BC%5E2%3DDC%5E2%2BDB%5E2)
substitute the given values
![BC^2=8^2+4^2](https://tex.z-dn.net/?f=BC%5E2%3D8%5E2%2B4%5E2)
![BC^2=80](https://tex.z-dn.net/?f=BC%5E2%3D80)
![BC=\sqrt{80}\ units](https://tex.z-dn.net/?f=BC%3D%5Csqrt%7B80%7D%5C%20units)
simplify
![BC=4\sqrt{5}\ units](https://tex.z-dn.net/?f=BC%3D4%5Csqrt%7B5%7D%5C%20units)
You can solve the by dividing the change in y by the change in x. the answer should be D
![\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\\ t=year \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Ctextit%7BCompound%20Interest%20Earned%20Amount%7D%0A%5C%5C%5C%5C%0AA%3DP%5Cleft%281%2B%5Cfrac%7Br%7D%7Bn%7D%5Cright%29%5E%7Bnt%7D%0A%5Cquad%20%0A%5Cbegin%7Bcases%7D%0AA%3D%5Ctextit%7Baccumulated%20amount%7D%5C%5C%0AP%3D%5Ctextit%7Boriginal%20amount%20deposited%7D%5C%5C%0Ar%3Drate%5Cto%20r%5C%25%5Cto%20%5Cfrac%7Br%7D%7B100%7D%5C%5C%0An%3D%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%5Ctextit%7Btimes%20it%20compounds%20per%20year%7D%0A%5Cend%7Barray%7D%5C%5C%0At%3Dyear%0A%5Cend%7Bcases%7D)
![\bf 1.185\implies 1+0.185\qquad\quad and\quad n=1 \\\\\\ A=P\left(1+\frac{r}{n}\right)^{nt}\implies A=P\left(1+0.185\right)^{nt}\implies A=P\left(1+\frac{0.185}{1}\right)^{1\cdot t}](https://tex.z-dn.net/?f=%5Cbf%201.185%5Cimplies%201%2B0.185%5Cqquad%5Cquad%20and%5Cquad%20n%3D1%0A%5C%5C%5C%5C%5C%5C%0AA%3DP%5Cleft%281%2B%5Cfrac%7Br%7D%7Bn%7D%5Cright%29%5E%7Bnt%7D%5Cimplies%20A%3DP%5Cleft%281%2B0.185%5Cright%29%5E%7Bnt%7D%5Cimplies%20A%3DP%5Cleft%281%2B%5Cfrac%7B0.185%7D%7B1%7D%5Cright%29%5E%7B1%5Ccdot%20%20t%7D)
so, the percentage of the rate is 0.185, what's that as a percentage? well, 0.185 * 100, 18.5%.