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Helga [31]
3 years ago
12

if a line segment has endpoints A(3x+5, 3y) and B(x-1,-y), what are the coordinates of the midpoint of ab

Mathematics
1 answer:
Galina-37 [17]3 years ago
7 0
Just add the x values and divide by 2, then add the y values and divide by 2

3x+5+x-1 = 4x+4. divide by 2 you get 2x+2
3y+-y=2y, divided by 2 gives y

midpoint is (2x+2, y)
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If 1/a + 1/b =1/c and ab=c,what is the average of a and b?
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If we solve the left side of the given equation,
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4 0
3 years ago
A 95-foot wire attached from the top of a cell phone tower makes a 62 degree angle with the ground. Joey is standing 150 feet be
a_sh-v [17]

Answer:

23.32 degrees

Step-by-step explanation:

We set up a large right triangle that has 2 triangles within it.  The large triangle is a right triangle.  The height of it is the height of the tower, the base angle is 62, the hypotenuse is 95, and the base measure is y.  The other triangle has the same height which is the height of the tower, the angle is what we are looking for, and the base measure is 150 feet beyond y, so its measure is y + 150.  We have enough information to find the height of the tower, so let's do that first.  Going back to the first smaller triangle.  

sin62=\frac{x}{95} so the height of the tower is 83.88 feet.  Now we need to solve for y.  Using that same triangle and the tangent ratio, we find that tan62=\frac{83.88}{y}.  Now let's do the same thing for the other triangle with the unknown angle.

tan\beta =\frac{83.88}{y+150}

Solve both of these for y.  The first one solved for y:

y=\frac{83.88}{tan62}

The second one solved for y will simplify to:

y=\frac{83.88-150tan\beta }{tan\beta }

Now that these are both solved for y, and y = y, we can set them equal to each other by the transitive property of equality:

\frac{83.88-150tan\beta }{tan\beta }=\frac{83.88}{tan62}

Cross multiply to get this big long messy looking thing:

tan62(83.88-150tan\beta )=83.88tan\beta

Distribute through the parenthesis to get

83.88tan62-[(tan62)(150tan\beta)]=83.88tan\beta

Get the unknown angles on the same side so it can be factored out:

83.88tan62=83.88tan\beta +[(tan62)(150tan\beta )]

And then factoring it out gives you:

83.88tan62=tan\beta(83.88+150tan62)

Divide to get

tan\beta =\frac{83.88tan62}{83.88+150tan62}

Do this on your calculator in degree mode to give you an angle measure of 23.32°.  I know this is really hard to follow without being able to draw the pics for you like I do in my classroom, but hopefully you can follow my description and draw your own triangles and follow from that!

4 0
3 years ago
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