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Schach [20]
1 year ago
11

A line passes through the points (-8, 1) and (-1, 6). A second line passes through the points (-3,0) and (-8,-5). What is the po

int of intersection of the two lines?
Mathematics
1 answer:
finlep [7]1 year ago
6 0
\begin{gathered} y=mx+b \\ m=\frac{6-1}{-1+8}=\frac{5}{7} \\ 6=\frac{5}{7}(-1)+b \\ 6+\frac{5}{7}=b \\ b=\frac{42+5}{7}=\frac{47}{7} \\ y=\frac{5}{7}x+\frac{47}{7} \end{gathered}

For the second line

\begin{gathered} y=mx+b \\ m=\frac{-5-0}{-8+3}=\frac{-5}{-5}=1 \\ 0=1(-3)+b \\ b=3 \\ y=x+3 \end{gathered}

The intersection will be

\begin{gathered} y=\frac{5}{7}x+\frac{47}{7} \\ x+3=\frac{5}{7}x+\frac{47}{7} \\ x-\frac{5}{7}x=\frac{47}{7}-3 \\ \frac{7x-5x}{7}=\frac{47-21}{7} \\ \frac{2x}{7}=\frac{26}{7} \\ 14x=182 \\ x=\frac{182}{14} \\ x=13 \\  \\ y=13+3=16 \end{gathered}

Therefore, the point of intersection is (13, 16)

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Take half of the coefficient of x:  It is 3, and half that is 3/2.


Then   <span>x^2+3x=6  becomes:

</span><span>           x^2+3x + (3/2)^2 =6 + (3/2)^2, and

             (x+3/2)^2 = 6 + 9/4

You were not asked to solve the equation, but why not do it for the practice?

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Probability helps us to know the chances of an event occurring. The probability being a Sophomore given she is a girl is 1/3.

<h3>What is Probability?</h3>

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\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}

The probability of being a girl and Sophomore is 9/37. While the probability of being a girl is 27/37. Therefore, the probability being a Sophomore given she is a girl is,

P(Girl l Sophomores) = P(Girl and Sophomore)/ P(Girl)

                                  = (9/37) / (27/37)

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Hence, the probability being a Sophomore given she is a girl is 1/3.

Learn more about Probability:

brainly.com/question/795909

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Step-by-step explanation:

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