How would you construct a timeline of significant events that led up to the formation of the Roman Empire, listing the events in chronological order?(1 point)

Answer 1

1. 753 BC: Legendary founding of Rome by Romulus and Remus.
2. 509 BC: The Roman Republic is established, marking the end of monarchy in Rome.
3. 264-241 BC: The First Punic War between Rome and Carthage begins after conflicts over control of Sicily.
4. 218-201 BC: The Second Punic War takes place, with Carthaginian general Hannibal invading Italy.
5. 149-146 BC: The Third Punic War concludes with the complete destruction of Carthage, establishing Rome as the dominant power in the Mediterranean.
6. 44 BC: Assassination of Julius Caesar, leading to a power struggle between his supporters (led by Mark Antony) and the senatorial faction (led by Octavian, later known as Augustus).
7. 31 BC: Battle of Actium, where Octavian's forces defeat Antony and Cleopatra, establishing Octavian as the sole ruler.
8. 27 BC: Octavian is granted the title "Augustus" by the Senate, marking the beginning of the Roman Empire.
9. 14 AD: Death of Augustus, succeeded by Tiberius as the second emperor of Rome.
10. 69 AD: Year of the Four Emperors, a period of civil war and power struggles following the death of Nero.
11. 117 AD: Rome reaches its largest territorial extent under emperor Trajan, spanning from Spain to the Persian Gulf.
12. 284 AD: Diocletian becomes emperor and introduces significant administrative and economic reforms, dividing the empire into East and West.
13. 330 AD: Emperor Constantine establishes the new capital of the Roman Empire in Constantinople (modern-day Istanbul) and promotes Christianity.
14. 476 AD: Western Roman Empire comes to an end as the last emperor, Romulus Augustus, is deposed by the Germanic chieftain Odoacer.

Answer 2

x^2-8x=10

Answer 3

To solve the equation x^2 - 8x = 10, we can rearrange it to the form x^2 - 8x - 10 = 0. This is a quadratic equation that can be solved using various methods such as factoring, completing the square, or using the quadratic formula.

Using the quadratic formula:

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.

In this case, a = 1, b = -8, and c = -10.

Plugging these values into the quadratic formula, we have:

x = (-(-8) ± √((-8)^2 - 4(1)(-10))) / (2(1))

Simplifying further:

x = (8 ± √(64 + 40)) / 2

x = (8 ± √(104)) / 2

x = (8 ± 2√26) / 2

Simplifying the expression:

x = 4 ± √26

Thus, the solutions to the equation x^2 - 8x = 10 are x = 4 + √26 and x = 4 - √26.

Answer 4

Which equation is equivalent to 2x^2 -16x−43=−3

Answer 5

To find an equivalent equation to 2x^2 - 16x - 43 = -3, we need to isolate the variable on one side of the equation.

First, let's move the constant terms to the right side:

2x^2 - 16x - 43 + 3 = 0

Simplifying:

2x^2 - 16x - 40 = 0

Next, let's divide the entire equation by 2 to simplify further:

(x^2 - 8x - 20) = 0

Therefore, the equation equivalent to 2x^2 - 16x - 43 = -3 is x^2 - 8x - 20 = 0.