Answer:
the sum of an exterior angle is equal to 360
6+5+a= 360
11+a=360
a= 360-11
a= 349
hope it helps
The area of this prism is 21.
Here's how:
Area= lxwxh/2 <---- That's the formula
Answer:
4800 words
Step-by-step explanation:
First calculate the number of words Anna types in 1 minute:
160 / 2
= 80 words
In 1 hour, there is 60 minutes. So just multiply the number of words Anna types in 1 minute with 60 to get the answer.
80 x 60
=4800 words
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ N(\stackrel{x_1}{-3}~,~\stackrel{y_1}{10})\qquad A(\stackrel{x_2}{6}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ NA=\sqrt{(6+3)^2+(3-10)^2}\implies NA=\sqrt{130} \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_2}{6}~,~\stackrel{y_2}{3})\qquad D(\stackrel{x_1}{6}~,~\stackrel{y_1}{-1}) \\\\\\ AD=\sqrt{(6-6)^2+(-1-3)^2}\implies AD=4 \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20N%28%5Cstackrel%7Bx_1%7D%7B-3%7D~%2C~%5Cstackrel%7By_1%7D%7B10%7D%29%5Cqquad%20A%28%5Cstackrel%7Bx_2%7D%7B6%7D~%2C~%5Cstackrel%7By_2%7D%7B3%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20NA%3D%5Csqrt%7B%286%2B3%29%5E2%2B%283-10%29%5E2%7D%5Cimplies%20NA%3D%5Csqrt%7B130%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20A%28%5Cstackrel%7Bx_2%7D%7B6%7D~%2C~%5Cstackrel%7By_2%7D%7B3%7D%29%5Cqquad%20D%28%5Cstackrel%7Bx_1%7D%7B6%7D~%2C~%5Cstackrel%7By_1%7D%7B-1%7D%29%20%5C%5C%5C%5C%5C%5C%20AD%3D%5Csqrt%7B%286-6%29%5E2%2B%28-1-3%29%5E2%7D%5Cimplies%20AD%3D4%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
now that we know how long each one is, let's plug those in Heron's Area formula.
![\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=\sqrt{130}\\ b=4\\ c=\sqrt{202}\\[1em] s=\frac{\sqrt{130}+4+\sqrt{202}}{2}\\[1em] s\approx 14.81 \end{cases} \\\\\\ A=\sqrt{14.81(14.81-\sqrt{130})(14.81-4)(14.81-\sqrt{202})} \\\\\\ A=\sqrt{324}\implies A=18](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%3D%5Csqrt%7B130%7D%5C%5C%20b%3D4%5C%5C%20c%3D%5Csqrt%7B202%7D%5C%5C%5B1em%5D%20s%3D%5Cfrac%7B%5Csqrt%7B130%7D%2B4%2B%5Csqrt%7B202%7D%7D%7B2%7D%5C%5C%5B1em%5D%20s%5Capprox%2014.81%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20A%3D%5Csqrt%7B14.81%2814.81-%5Csqrt%7B130%7D%29%2814.81-4%29%2814.81-%5Csqrt%7B202%7D%29%7D%20%5C%5C%5C%5C%5C%5C%20A%3D%5Csqrt%7B324%7D%5Cimplies%20A%3D18)
22000
The number that's being added in the sequence increases by 2x.
250 * 2 = 500, which is added to 18500 to equal 19000.
500 * 2 = 1000, which is added to 19000 to equal 20000.
1000 * 2 = 2000, which added to 20000 equals 22000.
