recall that for any root say x - a, namely x - a = 0, thus x = a, for such a root of a polynomial, f(x), based on the remainder theorem f(a) = 0.
to put it in different lingo, since we know that we have two factors (x - 2 ) and (x+1), that simply means we have two roots of x = 2 and x = -1, well, using the remainder theorem that simply means f(2) = 0 and f(-1) = 0.
![\bf x^3+ax^2+2x+b\\\\ -------------------------------\\\\ \stackrel{x=2}{f(2)}=(2)^3+a(2)^2+2(2)+b\implies \stackrel{\stackrel{f(2)}{\downarrow }}{0}=8+4a+4+b \\\\\\ \boxed{0=4a+b+12} \\\\\\ \stackrel{x=-1}{f(-1)}=(-1)^3+a(-1)^2+2(-1)+b\implies \stackrel{\stackrel{f(x)}{\downarrow }}{0}=-1+a-2+b \\\\\\ 0=a+b-3\implies \boxed{3-b=a}\\\\ -------------------------------](https://tex.z-dn.net/?f=%20%5Cbf%20x%5E3%2Bax%5E2%2B2x%2Bb%5C%5C%5C%5C%20-------------------------------%5C%5C%5C%5C%20%5Cstackrel%7Bx%3D2%7D%7Bf%282%29%7D%3D%282%29%5E3%2Ba%282%29%5E2%2B2%282%29%2Bb%5Cimplies%20%5Cstackrel%7B%5Cstackrel%7Bf%282%29%7D%7B%5Cdownarrow%20%7D%7D%7B0%7D%3D8%2B4a%2B4%2Bb%20%5C%5C%5C%5C%5C%5C%20%5Cboxed%7B0%3D4a%2Bb%2B12%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7Bx%3D-1%7D%7Bf%28-1%29%7D%3D%28-1%29%5E3%2Ba%28-1%29%5E2%2B2%28-1%29%2Bb%5Cimplies%20%5Cstackrel%7B%5Cstackrel%7Bf%28x%29%7D%7B%5Cdownarrow%20%7D%7D%7B0%7D%3D-1%2Ba-2%2Bb%20%5C%5C%5C%5C%5C%5C%200%3Da%2Bb-3%5Cimplies%20%5Cboxed%7B3-b%3Da%7D%5C%5C%5C%5C%20-------------------------------%20)
![\bf \stackrel{\textit{\textit{using the a value in the first equation found}}}{0=4(3-b)+b+12}\implies 0=12-4b+b+12 \\\\\\ 0=24-3b\implies 3b=24\implies b=\cfrac{24}{3}\implies b=8\\\\ -------------------------------\\\\ \stackrel{\textit{and since we know that }}{3-b=a}\implies 3-8=a\implies -5=a\\\\ -------------------------------\\\\ x^3-5x^2+2x+8](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cstackrel%7B%5Ctextit%7B%5Ctextit%7Busing%20the%20a%20value%20in%20the%20first%20equation%20found%7D%7D%7D%7B0%3D4%283-b%29%2Bb%2B12%7D%5Cimplies%200%3D12-4b%2Bb%2B12%20%5C%5C%5C%5C%5C%5C%200%3D24-3b%5Cimplies%203b%3D24%5Cimplies%20b%3D%5Ccfrac%7B24%7D%7B3%7D%5Cimplies%20b%3D8%5C%5C%5C%5C%20-------------------------------%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Band%20since%20we%20know%20that%20%7D%7D%7B3-b%3Da%7D%5Cimplies%203-8%3Da%5Cimplies%20-5%3Da%5C%5C%5C%5C%20-------------------------------%5C%5C%5C%5C%20x%5E3-5x%5E2%2B2x%2B8%20)
and you can graph that, you'll see the roots or x-intercepts of -1 and 2 there.
90+30x+30y. This is because the first day, 90 labels were printed, then you will use 30 times x to find how many minutes. This is the same for 30 times y. Youre trying to figure out how many minutes each machine printed for.
Answer:
Angle A would be 10
Step-by-step explanation:
The reason is because 10+20 is 30 so if you got from 30 and skip by 20's you'd get 170
<h3>The distance between two landmarks is 123 meters</h3>
<em><u>Solution:</u></em>
We have to find the distance between two landmarks
<em><u>Use the law of cosines</u></em>
The third side of a triangle can be found when we know two sides and the angle between them
![c^2 = a^2 + b^2 - 2ab\ cos c](https://tex.z-dn.net/?f=c%5E2%20%3D%20a%5E2%20%2B%20b%5E2%20-%202ab%5C%20cos%20c)
Here, angle between 90 meters and 130 meters is 65 degrees
From figure,
a = 90
b = 130
c = d
Therefore,
![d^2 = 90^2 + 130^2 - 2(90)(130)\ cos 65\\\\d^2 = 8100 + 16900 - 23400\ cos\ 65\\\\d^2 = 25000 - 23400 \times 0.4226\\\\d^2 = 25000 - 9889.267\\\\d^2 = 15110.73\\\\d = 122.92\\\\d \approx 123](https://tex.z-dn.net/?f=d%5E2%20%3D%2090%5E2%20%2B%20130%5E2%20-%202%2890%29%28130%29%5C%20cos%2065%5C%5C%5C%5Cd%5E2%20%3D%208100%20%2B%2016900%20-%2023400%5C%20cos%5C%2065%5C%5C%5C%5Cd%5E2%20%3D%2025000%20-%2023400%20%5Ctimes%200.4226%5C%5C%5C%5Cd%5E2%20%3D%2025000%20-%209889.267%5C%5C%5C%5Cd%5E2%20%3D%2015110.73%5C%5C%5C%5Cd%20%3D%20122.92%5C%5C%5C%5Cd%20%5Capprox%20123)
Thus, the distance between two landmarks is 123 meters
Answer:
poop
Step-by-step explanation: