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jarptica [38.1K]
3 years ago
11

A coin is tossed, and a die is rolled. Find the probability of getting heads and then rolling a 6.

Mathematics
1 answer:
Colt1911 [192]3 years ago
8 0

Answer:

1/2 and 1/6

Step-by-step explanation:

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Write x^2 − 2x − 3 = 0 in the form (x − a)^2 = b, where a and b are integers.
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X²-2x-3 = 0     let's start by grouping the "x"s

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so, we have a missing fellow there, in order to make the group, a perfect square trinomial, namely to "complete the square", hmmm so the tell-tale fellow is the middle term.

from a perfect square trinomial we know that the middle term is a product of 2 and the "term on the left" and the "term on the right", like 

\bf \begin{array}{cccccllllll}
 a^2& + &2 a b&+& b^2\\
\downarrow && &&\downarrow \\
 a&& && b\\
&\to &( a +  b)^2&\leftarrow 
\end{array}\qquad \qquad \quad 
\begin{array}{cccccllllll}
 a^2& - &2 a b&+& b^2\\
\downarrow && &&\downarrow \\
 a&& && b\\
&\to &( a -  b)^2&\leftarrow 
\end{array}

\bf \textit{therefore}\qquad 2(x)(\boxed{?})=\stackrel{middle~term}{2x}\implies \boxed{?}=\cfrac{2x}{2x}\implies \boxed{?}=1

aha!!  so our missing fellow is 1.

now, let's keep in mind that all we're doing is borrowing from our very good friend Mr Zero, 0.  So if we add 1², we also have to subtract 1².

(x² - 2x + 1² - 1²) - 3 = 0

(x² - 2x + 1) -1 -3 =0

(x - 1)² - 4 = 0

(x - 1)² = 4
5 0
3 years ago
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