Answer:
![=-3](https://tex.z-dn.net/?f=%3D-3)
Step-by-step explanation:
![\left(-3\right)^3+\left(-4\right)^2-\left(-2\right)^3\\Follow\:the\:PEMDAS\:order\:of\:operations\\\mathrm{Calculate\:exponents}\:\left(-3\right)^3\::\quad -27\\\left(-3\right)^3\\\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=-a^n,\:\mathrm{if\:}n\mathrm{\:is\:odd}\\\left(-3\right)^3=-3^3=-27\\=-27+\left(-4\right)^2-\left(-2\right)^3\\\mathrm{Calculate\:exponents}\:\left(-4\right)^2\::\quad 16\\\left(-4\right)^2](https://tex.z-dn.net/?f=%5Cleft%28-3%5Cright%29%5E3%2B%5Cleft%28-4%5Cright%29%5E2-%5Cleft%28-2%5Cright%29%5E3%5C%5CFollow%5C%3Athe%5C%3APEMDAS%5C%3Aorder%5C%3Aof%5C%3Aoperations%5C%5C%5Cmathrm%7BCalculate%5C%3Aexponents%7D%5C%3A%5Cleft%28-3%5Cright%29%5E3%5C%3A%3A%5Cquad%20-27%5C%5C%5Cleft%28-3%5Cright%29%5E3%5C%5C%5Cmathrm%7BApply%5C%3Aexponent%5C%3Arule%7D%3A%5Cquad%20%5Cleft%28-a%5Cright%29%5En%3D-a%5En%2C%5C%3A%5Cmathrm%7Bif%5C%3A%7Dn%5Cmathrm%7B%5C%3Ais%5C%3Aodd%7D%5C%5C%5Cleft%28-3%5Cright%29%5E3%3D-3%5E3%3D-27%5C%5C%3D-27%2B%5Cleft%28-4%5Cright%29%5E2-%5Cleft%28-2%5Cright%29%5E3%5C%5C%5Cmathrm%7BCalculate%5C%3Aexponents%7D%5C%3A%5Cleft%28-4%5Cright%29%5E2%5C%3A%3A%5Cquad%2016%5C%5C%5Cleft%28-4%5Cright%29%5E2)
![\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=a^n,\:\mathrm{if\:}n\mathrm{\:is\:even}\\\left(-4\right)^2=4^2=16\\=-27+16-\left(-2\right)^3\\\mathrm{Calculate\:exponents}\:\left(-2\right)^3\::\quad -8\\\left(-2\right)^3\\\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=-a^n,\:\mathrm{if\:}n\mathrm{\:is\:odd}\\\left(-2\right)^3=-2^3=-8\\=-27+16-\left(-8\right)\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:-27+16-\left(-8\right)\::\quad -3\\-27+16-\left(-8\right)](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aexponent%5C%3Arule%7D%3A%5Cquad%20%5Cleft%28-a%5Cright%29%5En%3Da%5En%2C%5C%3A%5Cmathrm%7Bif%5C%3A%7Dn%5Cmathrm%7B%5C%3Ais%5C%3Aeven%7D%5C%5C%5Cleft%28-4%5Cright%29%5E2%3D4%5E2%3D16%5C%5C%3D-27%2B16-%5Cleft%28-2%5Cright%29%5E3%5C%5C%5Cmathrm%7BCalculate%5C%3Aexponents%7D%5C%3A%5Cleft%28-2%5Cright%29%5E3%5C%3A%3A%5Cquad%20-8%5C%5C%5Cleft%28-2%5Cright%29%5E3%5C%5C%5Cmathrm%7BApply%5C%3Aexponent%5C%3Arule%7D%3A%5Cquad%20%5Cleft%28-a%5Cright%29%5En%3D-a%5En%2C%5C%3A%5Cmathrm%7Bif%5C%3A%7Dn%5Cmathrm%7B%5C%3Ais%5C%3Aodd%7D%5C%5C%5Cleft%28-2%5Cright%29%5E3%3D-2%5E3%3D-8%5C%5C%3D-27%2B16-%5Cleft%28-8%5Cright%29%5C%5C%5Cmathrm%7BAdd%5C%3Aand%5C%3Asubtract%5C%3A%5Cleft%28left%5C%3Ato%5C%3Aright%5Cright%29%7D%5C%3A-27%2B16-%5Cleft%28-8%5Cright%29%5C%3A%3A%5Cquad%20-3%5C%5C-27%2B16-%5Cleft%28-8%5Cright%29)
![-27+16=-11\\=-11-\left(-8\right)\\\mathrm{Apply\:rule\:}-\left(-a\right)\:=\:+a\\-\left(-8\right)=+8\\=-11+8\\-11+8=-3\\=-3](https://tex.z-dn.net/?f=-27%2B16%3D-11%5C%5C%3D-11-%5Cleft%28-8%5Cright%29%5C%5C%5Cmathrm%7BApply%5C%3Arule%5C%3A%7D-%5Cleft%28-a%5Cright%29%5C%3A%3D%5C%3A%2Ba%5C%5C-%5Cleft%28-8%5Cright%29%3D%2B8%5C%5C%3D-11%2B8%5C%5C-11%2B8%3D-3%5C%5C%3D-3)
Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.
<h3>Inverse of functions</h3>
In order to determine if the function f(x) and g(x) are inverses of each other, the composite function f(g(x)) = g(f(x))
Given the function
f(x)= 5-3x/2 and
g(x)= 5-2x/3
f(g(x)) = f(5-2x/3)
Substitute
f(g(x)) = 5-3(5-2x)/3)/2
f(g(x)) = (5-5+2x)/2
f(g(x)) = 2x/2
f(g(x)) = x
Similarly
g(f(x)) = 5-2(5-3x/2)/3
g(f(x)) = 5-5+3x/3
g(f(x)) = 3x/3
g(f(x)) =x
Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.
Learn more on inverse of a function here: brainly.com/question/19859934
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Answer:
143 square meters
Step-by-step explanation:
The surface has a width of 11 meters and a length of 13 meters.
13 x 11 = 143.
Is this correct?
Answer:
270 students
Step-by-step explanation:
First, you need to do a ratio.
30 x
------- = --------
50 450
In order to solve this, you need to multiply 450 times 30 and that equals 13500. 13500 divided by 50 is 270. That means that about 270 students will vote for Lynn.