Answer: Invasions by Barbarian tribes
The most straightforward theory for Western Rome's collapse pins the fall on a string of military losses sustained against outside forces. Rome had tangled with Germanic tribes for centuries, but by the 300s “barbarian” groups like the Goths had encroached beyond the Empire's borders
Step-by-step explanation:
Answer:look below
Step-by-step explanation:
To graph y= 4x +2 plot the point (0,2) on the graph because the y-intercept is 2 then use the slope: 4 to find another point. Another point would be (1,6).
Answer:
52°
Step-by-step explanation:
The angle 38° and m∠1 equal 90°, so 90-38=52.
Answer:
- a. incorrect
- A. equal to
- 59.20 ÷ 10 = 5.920
Step-by-step explanation:
What Douglas doesn't seem to realize is that it is not the act of removing the trailing zero that gives division by 10. It is the act of moving the decimal point left one place that divides the number by 10.
![\bf \cfrac{(x-2)(x+3)}{2x+2}\implies \cfrac{x^2+x-6}{2x+2}~~ \begin{array}{llll} \leftarrow \textit{2nd degree polynomial}\\ \leftarrow \textit{1st degree polynomial} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{vertical asymptote}}{2x+2=0}\implies 2x=-2\implies x=-\cfrac{2}{2}\implies x=-1](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B%28x-2%29%28x%2B3%29%7D%7B2x%2B2%7D%5Cimplies%20%5Ccfrac%7Bx%5E2%2Bx-6%7D%7B2x%2B2%7D~~%20%5Cbegin%7Barray%7D%7Bllll%7D%20%5Cleftarrow%20%5Ctextit%7B2nd%20degree%20polynomial%7D%5C%5C%20%5Cleftarrow%20%5Ctextit%7B1st%20degree%20polynomial%7D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bvertical%20asymptote%7D%7D%7B2x%2B2%3D0%7D%5Cimplies%202x%3D-2%5Cimplies%20x%3D-%5Ccfrac%7B2%7D%7B2%7D%5Cimplies%20x%3D-1)
when the degree of the numerator is greater than the denominator's, then it has no horizontal asymptotes.
quick note:
when the degree of the numerator is 1 higher than the degree of the denominator, then it has an slant-asymptote, so this one has a slant-asymptote.
