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Happy V-day.

Thanks, turtleman.

Here's  a rough pic of the situation

                                          D

                           x - 7                    x - 4        

                           H______________G

                    x + 3                                   2x

          E  ______________________________F

A segment parallel to a base of a triangle splits the sides in equal proportions

So

DH / HE  =  DG / GF      so we have

[ x - 7 ] / [ x + 3 ]  = [ x - 4 ] / [ 2x  ]   cross-multiply

2x (x - 7)  =  (x + 3) ( x - 4)   simplify

2x^2  - 14x    =  x^2  - x  - 12       rearrange as

x^2 - 13x  + 12  =  0

Factor   as

(x - 12) ( x - 1)  = 0

Setting to 0  and solving for x produces  x  = 12   or x  = 1

Reject the second soution since it makes (x - 7)  and (x - 4)  negative lengths

So  x  = 12    ⇒   FG  =  2(12)  =  24

Check that this works    5 / 15   =  8 / 24      true  !!!

(ax-7)(bx+5) = 6x^2+cx-35    If ab = 6 and a - b =  -1 what are two possible values of c?

(ab x^2  - 7bx + 5ax  -  35)  =  6x^2 + cx  -35

6x^2  + ( 5a - 7b) x - 35   =   6x^2  +  cx  -  35

5a  - 7b   =  c

If   a  - b  = - 1      then     b  =  a + 1

And

ab  = 6   ⇒   b   =  6/a

So

b   =   b

a  + 1   =  6/a           multiply through by a    and rearrange

a^2  + a  -  6   =  0   factor

(a - 2)  ( a + 3)  =  0      

Set each factor to 0  and solve and we get that   a  = 2  , a  = -3

When a  =  2      b  =  6 / a   =  3

When  a  = - 3     b  =  6/-3  =  -2

So

(a, b )  =   (2, 3)   or  ( -3, -2)

Using   5a  - 7b  = c

5(2)  - 7(3)  =  c  =  - 11

5(-3) - 7(-2)  = c  =  -1

Proof

a = 2  b = 3

( 2x - 7) ( 3x +  5)  =  6x^2  - 21x + 10x - 35   = 6x^2 - 11x - 35   ⇒   c  =  11

a = - 3, b = -2

(-3x - 7) (-2x + 5)  =   6x^2  - 15x + 14x - 25 = 6x^2 - 1x - 35       ⇒  c  = -1

36sqrt3 was right! Thanks you guys!

a=2

b=3

(2x-7)(3x+5) substitute

6x²+10x-21x-35 expand

6x²-11x-35 rearrange

c=-11

or

c=11

choose option b)

Find the area of triangle ABC if AB = BC = 12 and angle ABC = 120 degrees.

                          B          

        12           120         12

A                                                C

Area  =   (1/2) (12) (12)sin (120)  =

72 * sin (120)  =

72  * √3  / 2  =

36 √3   units ^2   ≈   62.35 units^2

Maybe they want the  exact value  [ first answer ]. ACG

in surds form= 36√3cm²

does it say to any particular decimal place or significant figure?

This is the equation of a line....it has infinite "solutions"  -  x , y values  - that  make it true

A savings account, which earns no interest, receives a deposit of $723 per month.

Linear......let  A be the amount accumulated in dollars and M  the number of months the deposit is made

The value of a machine depreciates by 17% per year.

Exponential.....let  V be the value in dollars  after  T  years

A liter of water evaporates from a swimming pool every day.

Linear......let A be the amount of water in liters remaining in the pool after D  days

I think the last is supposed to be  

Every 124 minutes, 1/2 of a drug dosage remains in the body.

Exponential.....this is a decay situation.....let   A_O be the original amount (in cm^3)  and A_T the amount remaining after T minutes  

happy  Valentines day  to you to my friend 

Good job, QS.....!!!

ab=3a+2b+c

ab-3a=2b+c

a(b-3)=2b+c

a=2b+c/b-3

ab   =  3a + 2b + c   subtract  3a from both sides

ab - 3a   =   2b + c       factor the left side

a (b - 3)   =   2b + c        divide both sides by  ( b - 3)

a  =  [ 2b + c  ] / [  [ b - 3  ]

Thanks for helping.

thanks for helping.

sure.

Thanks for helping.

Thanks for helping.

Thanks both of you for helping.

Thanks for your help.

Thanks for your help.

thanks

Thanks, both of you.