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3 years ago

A line segment has endpoints at (8, 3) and (2,5). What would be the equation of this line's perpendicular bisector?

Mathematics

1 answer:

ale4655 [162]3 years ago

7 0

Answer:

y = −1/3x+17/3

Step-by-step explanation:

The line segment has slope -1/3. This means that any line perpendicular to it will have a slope of 3 (negative reciprocal)

Any line that bisects the line segment will pass through its midpoint. The midpoint is (5,4)

Midpoint formula: $( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )$

So perpendicular bisector of this line is simply a line with slope −1/3 that passes through point (5, 4)

y - 4 = -1/3 (x-5)=

y = −1/3x+17/3

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3 years ago

Please help me with this for 20 points

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$\large a)\ f(x)=\dfrac{5}{9}(x-32)\\\\b)\ f^{-1}(x)=\dfrac{9}{5}x+32\\\\9^oC=48.2^oF$

Step-by-step explanation:

$C=\dfrac{5}{9}(F-32)\\\\a)\ f(x)=\dfrac{5}{9}(x-32)\\\\b)\ C=\dfrac{5}{9}(F-32)\\\\\text{solve for F}\\\\\dfrac{5}{9}(F-32)=C\qquad\text{multiply both sides by 9}\\\\5(F-32)=9C\qquad\text{divide both sides by 5}\\\\F-32=\dfrac{9}{5}C\qquad\text{add 32 to both sides}\\\\F=\dfrac{9}{5}C+32\\\\f^{-1}(x)=\dfrac{9}{5}x+32$

$c)\ \text{Put}\ x=9\ \text{to}\ f^{-1}(x):\\\\f^{-1}(9)=\dfrac{9}{5}(9)+32=\dfrac{81}{5}+32=16.2+32=48.2\\\\9^oC=48.2^oF$

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3 years ago

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3 years ago

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if we look on one side, we already have one measurement. 4 cm. ok, that's the measurement on that side. look to the left now. that other side is also the same length, so we take that number and multiply it be 2 to get

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Wait! we're not done yet. look at the top. do you see the 3? well that's the width for the top of the rectangle. the bottom must be the same to right? so we get

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add both equations and you get

$(4 \times 2) + (3 \times 2)$

The answer is 14cm! Don't forget to label. ;)

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3 years ago