Without sketching the graph, find the x-intercepts and y-intercepts of the graph of the equation y=x²-x-6 What is/are the x-inte
1 answer:
Given the equation:
Let's find the x-intercepts and the y-intercepts of the graph.
• x-intercept:
The x-intercept are the points where the parabola crosses the x-axis. At x-intercept the y-value is zero.
To find the x-intercepts, substitute 0 for y and solve for x.
We have:
Rewrite the equation:
Factor the left hand side of the equation:
Equate each factor to zero:
x - 3 = 0
Add 3 to both sides:
x - 3 + 3 = 0 + 3
x = 3
x + 2 = 0
Subtract 2 from both sides:
x + 2 - 2 = 0 - 2
x = -2
Therefore, the x-intercepts are:
3, -2
• y-intercept:
The y-intercept is the point where the parabola crosses the y-axis. The x-value at the y-intercept is zero.
To find the y-intercept, substitute 0 for x and solve:
Therefore, the y-intercept is -6.
In point form:
x-intercept: (3, 0), (-2, 0)
y-intercept: (0, -6)
ANSWER:
A. The x-intercepts are (3, 0), (-2, 0)
A. The y-intercept is (0, -6)
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Answer:
#1: 5
#2:
Step-by-step explanation:
Inverse of Pythagorean Theorem: c²-b²=a²
c² b² a²
13²- 12² = 25
= 5
Pythagorean Theorem: a²+b²=c²
a² b² c²
2² + 6² = 40
c =
Answer:
Step-by-step explanation:
- The Romanov Dynasty (1613 to 1917) was the last imperial dynasty to rule Russia. During the Romanov reign Russia became and remained a major European power.
- The Romanovs share their origins with a handful of other Russian noble families. One of the ancestors of the world-renowned dynasty was Andrey Kobyla – a boyar who lived during the middle of the 14th century. Kobyla was documented in contemporary chronicles only once, in 1347, when he was said to have been sent to Tver with the purpose of meeting the daughter of Alexander I of Tver. Later generations assigned other more illustrious pedigrees to Kobyla, however, they are highly unlikely to be true.
- An 18th century genealogy chart even claimed that Kobyla was the son of the Prussian prince Glanda Kambila, who came to Russia in the second half of the 13th century, fleeing the invading Germans. Indeed, one of the leaders of the Prussian rebellion of 1260-1274 against the Teutonic order was named Glande, but the theory acquired no further proof.
- In another theory, which is more likely to be true even though it is less complementing, Kobyla's origins were not that spectacular – his relatives were nicknamed after horses and other house animals (“kobyla” means “mare” in Russian), thus suggesting his descent from one of the royal equerries.
- One of Kobyla's sons, Feodor, a boyar in the boyar Duma of Dmitry Donskoy, was nicknamed Koshka, or “cat.” His descendants took the surname Koshkin and then changed it to Zakharyin. Later the family split this surname into two branches: Zakharyin-Yakovlev and Zakharyin-Yuriev. During the reign of Ivan the Terrible, the former family became known as Yakovlev, whereas the grandchildren of Roman Zakharyin-Yuriev changed their name to Romanov.
- The Romanov Dynasty began with the election of Mikhail Romanov, a 16-year-old boyar, by the Zemsky Sobor, or Assembly of the Land – the first Russian parliament of the feudal estates type.
- Initially, Mikhail’s mother protested against the election of such a young and inexperienced man, but the boyars assured her that Mikhail would be held responsible to God for the destruction of Russia and other mortal sins if he persisted in his refusal to accept the title.
- When young Mikhail learned he was about to be granted the highest title anyone could dream of in Russia, he burst into tears of fear and despair. He was finally persuaded to accept the throne by his mother who saw no way out, so she blessed the young man who had to obey. Mikhail Romanov was crowned on 22 July 1613.
- The first member of the Romanov Dynasty and founder of the clan dedicated the time of his reign to reforms, thus changing the political situation that had formed by that time in ancient Russia.
- The first task of the new Tsar was to clear the land of the invaders infesting it – thus Sweden and Poland were dealt with respectively.
