Answer:
10% of 45 is 4.5
30% of 45 is 13.5
Step-by-step explanation:
10% of 45 is 4.5 because you can multiply 4.5 10 times to get 45. Because 30% is 3 times the amount as 10%, you can multiply 4.5 x 3 to get 13.5
Answer:
x = 30°
y = 115°
Step-by-step explanation:
Given = AB ║ DC
∠A = 2x + 10
∠B = 65
∠C = y
∠D = 3x + 20
( AD is the transversal on the parallel lines AB and DC)
∴ ∠A + ∠D = 180 and ∠B + ∠C = 180
(1) ∠A + ∠D = 180
2x + 10 + 3x + 20 = 180
5x + 30 = 180
5x = 180 - 30 = 150
x = 150÷5
x = 30°
(2) ∠B + ∠C = 180
65 + y = 180
y = 180 - 65 = 115
y = 115°
Answer:
Step-by-step explanation:
2. 2c(7c + 1)
3. stays as is
4. 2x^3y^4(4 - 11x^2y^2)
5. ab(10ab + 9b - a)
6. 3m^2(7m^4n^2+2m^2n+5)
7. (a - 8)(a + 8)
8. (y - 17)(y + 17)
9. stays as is
10. (1 - 5n)(1 + 5n)
11. (4x - 7y)(4x + 7y)
12. (w^2 - 10)(w^2 + 10)
13. (c - 9d)(c + 9d)
14. (14a - b)(14a + b)
if the amount of money is say $1, for that to double it'll become $2, so let's use those values.
![\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill&\$2\\ P=\textit{original amount deposited}\dotfill &\$1\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~%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%26%5C%242%5C%5C%20P%3D%5Ctextit%7Boriginal%20amount%20deposited%7D%5Cdotfill%20%26%5C%241%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%7Bannually%2C%20thus%20once%7D%20%5Cend%7Barray%7D%5Cdotfill%20%261%5C%5C%20t%3Dyears%5Cdotfill%20%265%20%5Cend%7Bcases%7D)
![\bf 2=1\left(1+\frac{r}{1}\right)^{1\cdot 5}\implies 2=(1+r)^5\implies \sqrt[5]{2}=1+r \\\\\\ \sqrt[5]{2}-1=r\implies 0.148698\approx r\implies \stackrel{\textit{converting to \%}}{0.148698\cdot 100\approx r\%}\implies 14.8698\approx r \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{rounded up}}{14.87=r}~\hfill](https://tex.z-dn.net/?f=%5Cbf%202%3D1%5Cleft%281%2B%5Cfrac%7Br%7D%7B1%7D%5Cright%29%5E%7B1%5Ccdot%205%7D%5Cimplies%202%3D%281%2Br%29%5E5%5Cimplies%20%5Csqrt%5B5%5D%7B2%7D%3D1%2Br%20%5C%5C%5C%5C%5C%5C%20%5Csqrt%5B5%5D%7B2%7D-1%3Dr%5Cimplies%200.148698%5Capprox%20r%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bconverting%20to%20%5C%25%7D%7D%7B0.148698%5Ccdot%20100%5Capprox%20r%5C%25%7D%5Cimplies%2014.8698%5Capprox%20r%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20%5Cstackrel%7B%5Ctextit%7Brounded%20up%7D%7D%7B14.87%3Dr%7D~%5Chfill)