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7^4^32^21^9*6 = ((infinity))^9*6

Very nice, Guest......I know two other ways of solving this [ there may be more].......but......I like the way you did it, maybe best of alll.....!!!!

I'll post my method in a while......it's a little different

Let x = miles on flat land, y = miles on the hill.  He goes out and back, so total miles = 2 (x+y).

The times spent on each segment is the distance travelled divided by the speed:

x/4mph + y/3mph + x/4mph + y/6mph = 5 hours

Multiply both sides by 12 mph to clear the denominator of the fractions; the numbers are now all in miles:

3x + 4y + 3x + 2y = 6x + 6y = 6(x+y) = 12*5 = 60.

So (x+y) = 60/6 = 10 miles ... so the total distance is 20 miles.

What program did you use for that.......????......I like it.....!!!

Hi Chris,

Scaled pic

Drawing these pics to scale is always a time consuming but pleasant challenge :)

I guess you have something like this???

sqrt(-4)  / [ (7 - 3i) + ( 2 + 5i)]       simplify

2i / [ 9 + 2i]        multiply top and bottom  by the conjugte of  9 + 2i  =   9 - 2i

[2i] [ 9 -2i] / [ 81 - 4i^2] =

[-4i^2 + 18i]  / [ 85]  =

[ 4 + 18i] /  [85]

Looks like C is the likely candidate.......

Going throught the problem I was able to make it as easy as possible.

64431.2053588942257963+(8*5^(7/2)*The square root of pi*x

Nice pic, Melody........this one would be difficult to "scale" properly.....

 ABD = 105° and ABD will form a triangle.....then angle ADB will  =   180 - 43  -105 = 32°

And, since AD is parallel to BC,  angle CBD will have the same measure as angle ABD  = 32°    because they are alternating interior angles between  these parallels

Learn to use the calculator here. Use ( ) to make things much easier.

Hi Mellie,

In trapezoid ABCD, BC || AD, angle ABD =105°, angle A=43°, and angle C=141°. Find angle CBD, in degrees.

ok, the first thing I did is tried to work out what the trapezium looked like. 

THEN the answer became obvious.

BUT

it also became ovvious that I did not need to know what the trapezium looked like in ordet to answer this question.

Draw ANY trapezium where BC||AD

Label <ABD as 105 degrees.   (It doesn't need to LOOK anythink like 105 degrees, mine looks like an acute angle)

Label <A as 43 degrees 

Label < C as 141 degrees

Now you can see that <CBD is an alternate angle on parallel lines to <BDA. So they are congruent.

< BDA+105+43=180     Angle sum of triangle ABD

<BDA = 32 degrees

Therefore <CBD = 32 degrees

Here is a diagram most definitely not to scale.   

Rationalize the denominator of square root of negative four over open parentheses 7 minus 3 i close parentheses plus open parentheses 2 plus 5 i.

A. quantity of negative 16 plus 18 i over 7

B. quantity of 16 plus 18 i over 145

C. quantity of 4 plus 18 i over 85

D. quantity of negative 4 plus 18 i over 77

Why don't  you write your expressions in mathematical form? Something like this:-4/[(7-3i)+(2+5i)]=?

Is that what you meant in your first sentence? Write them ALL like that.

No........when I answered this, there was no indication that anyone else was answering at the same time.....   Then.....I saw your answer..........weird......!!!!!!

This is just the graph of the parent function,   f(x)  =  l  x l ,   that is inverted, with its "vertex" shifted to the left 4 units and up 3 units.......the "2" out front means that it is half as wide as the parent function

Here's the graph :   https://www.desmos.com/calculator/uz0x7tn8n1

I am curious Chris, when I started answering this question there was no indication that you were already answering.

I do not know what time that was.

When you started answering, did you see me?  I suppose I had not logged in so it doesn't mean much.  I do not think I have ever seen a note saying that a guest is answering.  Maybe guests cannot see that anyone is already answering either???

I would like to ask you this question again when I am logged in properly. I want to know how it works. :/

If I had known you were already answering I would have moved on to another question...........

I certainly couldn't have done this one........but.....here's your answer....

http://math.stackexchange.com/questions/919956/the-diagonals-of-a-trapezoid-are-perpendicular-and-have-lengths-8-and-10-find-t

The area of trapezoid ABCD is 60. One base is 4 units longer than the other, and the height of the trapezoid is 5. Find the length of the median of the trapezoid.

Let the parallel sides be  x and x+4

The area of a trapezium is  the average or the parallel sides multiplied by the height

\(Area=\frac{(x+x+4)}{2}*h\\~\\ Area=\frac{(2x+4)}{2}*5\\~\\ Area=\frac{2(x+2)}{2}*5\\~\\ Area=5(x+2)\\ 60=5(x+2)\\ 12=x+2\\ x=10 \)

The parallel sides are 10 and 14 units

Now the median length is the average of the paralel side lengths

Length of median = (10+14)/2 = 12 units

We have :

60  = 5/2 * ( x  +   x + 4)     where x is the length of the shorter base

60 (2/5)  = 2x + 4

24  = 2x + 4     subtract 4 from both sides

20  = 2x     divide both sides by 2

x = 10      and the longer base = 14

The  median  is  just  the average of the bases =    [10 +  14 ] / 2   =   24/2    = 12   units

The anser is 2

The sum of the measures of the interior angles of a quadrilateral = 360°........so we have

x +  [5x + 15] + [3x - 25] + [ 4x - 20]   = 360      simplify

13x - 30   = 360     add 30 to both sides

13x  = 390      divide both sides by 13

x = 30

The largest angle  is  5x + 15  =   165°

Look at the graph of cos

it is '1' at 360 degrees (remember 360 degrees = 2pi)    if you go 4pi  you are back at the same point....

if you go 6pi, 8pi.....20pi   you are back at the same point where cos=1

Let's look at the First One

Since Force = Mass x Acceleration   ( F = ma)  you can substitute the values given to get

F = 2.6KG x 1520 m/sec^2 =  3952 N         Now do you see?    You should be able to do the  rest of the problems.

A   kg-m/s^2 is a Newton    Make sure all of your units are in kg and m/s^2 to get the correct number of Newtons !

Go online and use this mixed fractions calculator:

http://www.calculatorsoup.com/calculators/math/mixednumbers.php

I still don't understand, please help.