Answer:
7/2
Step-by-step explanation:
(X+2)(y-5)=0
X+2=0
X=-2
Y-5=0
Y=5
X is horizontal
Y is vertical
the yearly increase of x% assumes is compounding yearly, so let's use that.
![~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\£95000\\ P=\textit{original amount deposited}\dotfill &\£80000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases}](https://tex.z-dn.net/?f=~~~~~~%20%5Ctextit%7BCompound%20Interest%20Earned%20Amount%7D%20%5C%5C%5C%5C%20A%3DP%5Cleft%281%2B%5Cfrac%7Br%7D%7Bn%7D%5Cright%29%5E%7Bnt%7D%20%5Cquad%20%5Cbegin%7Bcases%7D%20A%3D%5Ctextit%7Baccumulated%20amount%7D%5Cdotfill%20%26%5C%C2%A395000%5C%5C%20P%3D%5Ctextit%7Boriginal%20amount%20deposited%7D%5Cdotfill%20%26%5C%C2%A380000%5C%5C%20r%3Drate%5Cto%20r%5C%25%5Cto%20%5Cfrac%7Br%7D%7B100%7D%5C%5C%20n%3D%20%5Cbegin%7Barray%7D%7Bllll%7D%20%5Ctextit%7Btimes%20it%20compounds%20per%20year%7D%5C%5C%20%5Ctextit%7Byearly%2C%20thus%20once%7D%20%5Cend%7Barray%7D%5Cdotfill%20%261%5C%5C%20t%3Dyears%5Cdotfill%20%265%20%5Cend%7Bcases%7D)
![95000=80000\left(1+\frac{~~ \frac{r}{100}~~}{1}\right)^{1\cdot 5}\implies \cfrac{95000}{80000}=\left( 1+\cfrac{r}{100} \right)^5 \\\\\\ \cfrac{19}{16}=\left( 1+\cfrac{r}{100} \right)^5\implies \sqrt[5]{\cfrac{19}{16}}=1+\cfrac{r}{100}\implies \sqrt[5]{\cfrac{19}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[5]{\cfrac{19}{16}}=100+r\implies 100\sqrt[5]{\cfrac{19}{16}}-100=r\implies 3.5\approx r](https://tex.z-dn.net/?f=95000%3D80000%5Cleft%281%2B%5Cfrac%7B~~%20%5Cfrac%7Br%7D%7B100%7D~~%7D%7B1%7D%5Cright%29%5E%7B1%5Ccdot%205%7D%5Cimplies%20%5Ccfrac%7B95000%7D%7B80000%7D%3D%5Cleft%28%201%2B%5Ccfrac%7Br%7D%7B100%7D%20%5Cright%29%5E5%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B19%7D%7B16%7D%3D%5Cleft%28%201%2B%5Ccfrac%7Br%7D%7B100%7D%20%5Cright%29%5E5%5Cimplies%20%5Csqrt%5B5%5D%7B%5Ccfrac%7B19%7D%7B16%7D%7D%3D1%2B%5Ccfrac%7Br%7D%7B100%7D%5Cimplies%20%5Csqrt%5B5%5D%7B%5Ccfrac%7B19%7D%7B16%7D%7D%3D%5Ccfrac%7B100%2Br%7D%7B100%7D%20%5C%5C%5C%5C%5C%5C%20100%5Csqrt%5B5%5D%7B%5Ccfrac%7B19%7D%7B16%7D%7D%3D100%2Br%5Cimplies%20100%5Csqrt%5B5%5D%7B%5Ccfrac%7B19%7D%7B16%7D%7D-100%3Dr%5Cimplies%203.5%5Capprox%20r)
Answer:
d = ![\sqrt{(6 - 9)^{2}+ (3 - (-2))^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%286%20-%209%29%5E%7B2%7D%2B%20%283%20-%20%28-2%29%29%5E%7B2%7D%20%7D)
Step-by-step explanation:
The distance formula is d=
.
6 is
, 9 is
, 3 is y
, and -2 is y
.
When you plug these into the formula, you get d = ![\sqrt{(6 - 9)^{2}+ (3 - (-2))^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%286%20-%209%29%5E%7B2%7D%2B%20%283%20-%20%28-2%29%29%5E%7B2%7D%20%7D)
Answer:
Exact form:
![\sqrt{53}](https://tex.z-dn.net/?f=%5Csqrt%7B53%7D)
Decimal Form:
7.280109889280518
Step-by-step explanation:
Use the distance formula to determine the distance between 2 points.
Distance = ![\sqrt{(x_{2} -x_{1}) ^2+(y_{2} -y_{1}) ^2](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B2%7D%20-x_%7B1%7D%29%20%5E2%2B%28y_%7B2%7D%20-y_%7B1%7D%29%20%5E2)
![\sqrt{6-4^2+(-5-2)^2](https://tex.z-dn.net/?f=%5Csqrt%7B6-4%5E2%2B%28-5-2%29%5E2)
![\sqrt{(2)^2+(-7)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%282%29%5E2%2B%28-7%29%5E2%7D)
![\sqrt{4+49}](https://tex.z-dn.net/?f=%5Csqrt%7B4%2B49%7D)
≈ 7.280109889280518