Mathematics, 26.10.2020 16:10 huwoman

Segment CD is formed by C(-5, 9) and D(7, 5). If line t is the perpendicular bisector of segment CD , write a linear equation for t in slope-intercept form.

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Answer from: Ayalij

Given:

Segment CD is formed by C(-5, 9) and D(7, 5).

Line t is the perpendicular bisector of segment CD.

To find:

The linear equation for t in slope-intercept form.

Solution:

Line t is the perpendicular bisector of segment CD. It means line t passes through the midpoint of CD.

$Midpoin=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$Midpoin=\left(\dfrac{-5+7}{2},\dfrac{9+5}{2}\right)$

$Midpoin=\left(\dfrac{2}{2},\dfrac{14}{2}\right)$

$Midpoin=\left(1,7\right)$

Slope of CD is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m_{1}=\dfrac{5-9}{7-(-5)}$

$m_{1}=\dfrac{-4}{12}$

$m_{1}=\dfrac{-1}{3}$

Product of slopes of two perpendicular lines is -1.

Let slope of line t be m_2 .

$m_1\times m_2=-1$

$\dfrac{-1}{3}\times m_2=-1$

m_2=3

Point slope form of a line is

y-y_1=m(x-x_1)

where, m is slope.

The slope of line t is 3 and it passes through (1,7). So, point slope form of line t is

y-7=3(x-1)

Therefore, the point slope form of line t is y-7=3(x-1) .

Answer from: Quest

the clues that signal the reader should change tone are the punctuation marks, the grammatical signs. for example, the quotation marks at the beginning of something someone else said literally or the exclamation marks.

the tone of the first line of dialogue until "gettysburg" is a kind tone, a tone of advise. the narrator is trying to the other person in doing something he or she obviously is finding hard to do by giving a piece of advise and bringing up a memory of a successful similar case.

the clue that the reader understand how to read the word "bang" is the exclamation mark. it gives the word a surprise tone, a strong accent.

the best tone for reading the word "bang" is an exciting tone, a surprise one, even a loud one.

the words that should be read with a formal tone are the ones that give factual information. the sentence: mister lincoln couldn't think of anything to say at the gettysburg" gives information about an event and it needs to be read formally, also, when the narrator wants to transmit calmness, a formal and slow tone is needed, because people also transmit messages with the vibrations of our voices and tones.

Answer from: Quest

$2^{2x+11}=3^{x-31}$

take the logarithm of both sides (the base of the log doesn't matter):

$\ln2^{2x+11}=\ln3^{x-31}$

apply the exponent property - this says that $\ln a^b=b\ln a$ :

$(2x+11)\ln2=(x-31)\ln3$

distribute the log terms on both sides:

$(2\ln2)x+11\ln2=(\ln3)x-31\ln3$

group like terms together:

$(2\ln2-\ln3)x=-11\ln2-31\ln3$

divide through both sides by the coefficient on $x$ :

$x=-\dfrac{11\ln2+31\ln3}{2\ln2-\ln3}$

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

$x=-\dfrac{\ln2^{11}+\ln3^{31}}{\ln2^2-\ln3}$

$x=-\dfrac{\ln2^{11}3^{31}}{\ln\frac43}$

$x=-\log_{4/3}2^{11}3^{31}$

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Segment CD is formed by C(-5, 9) and D(7, 5). If line t is the perpendicular bisector of segment CD...

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