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Hey and yes your right it homecoming for you

are you graphing functions?

Call the distance he bikes the first day  =  D

The distance he bikes the  ffth day  =  D + 4(10)  = D + 40

So

Sum  =   [ Distance on first day + Distance on fifth day] * (number of days / 2)

500  =  [ D  + D + 40 ] *  (5/2)     

500 = [ 2D + 40 ]  * (5/2)     multiply both sides by 2/5

200  =   2D + 40     subtract 40 from each side

160  =  2D    divide both sides by 2

80 = D

So....on the fifth day he bikes  80 + 40  =  120 miles     

See the following image :

Since DE is parallel to AB, the triangle DEC is similar to triangle BAC

And BC = 12  and DC  = 6

So the base of triangle DEC  is 1/2 that of triangle BAC

So....the scale factor of triangle DEC to triangle BAC  = 1/2

So....the area of triangle DEC  =   (scale factor)^2 * (area of triangle BAC)  =

(1/2)^2 * (180)   =   (1/4) (180)   =  45

So...the area of ABDE  =   area of triagle BAC - area of triangle DEC  =  180 - 45  =  135 

i do not understand how you got this though

\(miles_1 = M\\ miles_k = miles_1 + 10(k-1),~k=1,2,\dots 5\\ \sum \limits_{k=1}^5 miles_k = \sum \limits_{k=1}^5 M+10(k-1) = 500\\ 5M + 10\sum \limits_{k=0}^4 k = 500\\ 5M + 10\dfrac{(4)(4+1)}{2} = 500\\ 5M + 100 = 500\\ M=80\\ miles_5 = 80 + 10(4) = 120~miles \)

You the best! Thank you. 

\(\dfrac{du}{dt} = \begin{pmatrix}\dfrac{dx}{dt}\\\dfrac{dy}{dt}\end{pmatrix} = \begin{pmatrix}1&-2\\1&4\end{pmatrix}\begin{pmatrix}x\\y\end{pmatrix} = A u\)

thanks i didn't know about the sum of the consecutive odd numbers were squared. 

a hiker climbed down a 90 foot hill in five minutes what is his average change in elevation per minute

Here's a tip:  The word "per" can always be replaced with "divided by"

Change in elevation  =      90 feet

Time to go the distance  =  5 minutes

feet per minute  =  90/5 ft/min  =  18 ft/min

.

thanks guest

Both angles are equal.

Both angles are 45^o.

Both angels are acute.

can you just help me to rewrite it as you mentioned in the first step please?

Where is here?

What are u trying to say? lmao :D

3x + 4

___________         we can solve this with partial fractions

x^2 -6x + 5

3x + 4                                 A              B

___________   =            _____  +    ____           multiply through by  (x -5) ( x - 1)

(x - 5) ( x - 1)                    x - 1          x - 5

3x + 4   = A(x - 5)  + B ( x - 1)

3x + 4  =  Ax - 5A  + Bx - B        

3x + 4  =  (A + B) x  -  (5A + 5B)        equate coefficients

A + B  =  3

-5A - B = 4        add these equations

-4A  = 7     

A =  -7/4

And   

 (-7/4) + B  =  3

-7/4 + B = 12/4

B  = 19/4

So   the solution  is

3x+4                           - 7                      19

__________     =    _________  +  ________

x^2 - 6x + 5               4 ( x - 1)          4 (x - 5)

very much appreciared thank you so much!

5 - x

______  ≥  3         subtract 3  from both sides   

4x + 1

5 - x

_____  -  3   ≥   0        get a common denominator

4x + 1

5 - x  -  3 ( 4x + 1)

_______________    ≥   0

   4x + 1 

5 - x  -  12x  - 3

____________   ≥  0

     4x  + 1 

-13x  + 2

_______      ≥   0

  4x  +  1 

We need to  solve these two  equations

-13x + 2  =  0                 4x  + 1  = 0

2  = 13x                         4x  = - 1

2/13   = x                        x  = -1/4

We have three possible itervals that will solve the original equation

(-inf, -1/4 )    or  ( -1/4, 2/13]   or   [ 2/13, inf)

If  we pick an x value in  (-1/4, 2/13]   , say x =0,    we find that

5 - 0                  5

_______  =      __    =     5      which makes the original inequality true

4(0) + 1             1

So....the solution is  (-1/4, 2/13 ] 

your mighty close to her

I'll  see if I can arrange that..I could then pass Melody..LOL!!!!

x  +  y  = 7       rearrange as   y  = 7 - x   (1)

And using

Rate * Time  = Distance    we have  that

5 * (x)  + 20 (y)   =   110     (2)

Sub  (1)  into (2)  for   y  and we have that

5 * (x)   + 20  ( 7 - x)  =  110       simplify

5x + 140  - 20x   =  110

-15x  + 140  = 110      subtract 140 from both sides

-15x  =  - 30      divide both sides by - 15

x  = 2  hours running

And   7 - x  = 7 - 2   =    5 hours biking

Thanks cphill if i could i would give you a million thumbs up

          A

B        C            D

If   AC bisects BAD,  then BAC =  CAD....so....

2x -5  = 145        add 5 to both sides

2x  = 150          divide both sides by  2

x  = 75