What is length of segment QR? (Show all work)

Mathematics

1 answer:

matrenka [14]4 years ago

5 0

Answer:

$x=15\ units$

Step-by-step explanation:

we know that

The Midpoint Theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the third side

In this problem

Applying the Midpoint theorem we have that

$x=\frac{30}{2}=15\ units$

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If you were asked to convert 75 m/s to km/hr, which conversation factors would you need to use. Select all that apply.

Vilka [71]

Answer:

You need to use A, B, and C.

Step-by-step explanation:

Let's treat the units as variables. I'll illustrate why in a moment.

$75 m/s =\frac{75m}{1s} \\\\\frac{75m}{1s}*\frac{1km}{1000m}=\frac{75m*km}{1000m*s}\\\\\frac{75m*km}{1000m*s}*\frac{60s}{1min}=\frac{(75*60)m*km*s}{1000m*s*min}\\\\\frac{4500m*km*s}{1000m*s*min}*\frac{60min}{1h}=\frac{4500m*km*s*min}{1000m*s*min*h}$

Now, as you can see, we have a giant mess of units to deal with. This is where we can treat the units like separate variables and use a bit of algebra to make our lives easier:

$\frac{4500m*km*s*min}{1000m*s*min*h}=\frac{4500}{1000}*\frac{m*km*s*min}{m*s*min*h}\\\\\frac{4500}{1000}*\frac{m*km*s*min}{m*s*min*h}=\frac{4500}{1000}*\frac{m}{m}*\frac{km}{1}*\frac{s}{s}*\frac{min}{min}*\frac{1}{h}\\\\\frac{4500}{1000}*\frac{m}{m}*\frac{km}{1}*\frac{s}{s}*\frac{min}{min}*\frac{1}{h}=\frac{4500}{1000}*\frac{m*km*s*min}{m*s*min*h}=\frac{4500}{1000}*1*\frac{km}{1}*1*1*\frac{1}{h}\\\\\frac{4500}{1000}*1*\frac{km}{1}*1*1*\frac{1}{h}=\frac{4500}{1000}*\frac{km}{h}\\$