CPhill

y -  1 = 7x - 2     add 1 to both sides

y  = 7x  -  1

The y intercept is at   (0, -1)

Let x  = 1  and  y = 7(1)  - 1    =  6

So....the points  (0, -1)   and  (1, 6 )  are on the graph

Plot these points and connect them with a line.....that will be your graph

Since   x  = -3 is the only value that makes the quadratic  = 0.....then this has a "double" root

So...the sum  of the roots  =  -3 + -3  =  -6

And the sum of the roots  in the form ax^2 + bx + c  =  -b/a 

So...in our case, the sum of the roots are  =  - m / 1  =   -m

So

-m   = -6

m  = 6

Nice answer, Melody.....

I believe I answered the last two, here :

https://web2.0calc.com/questions/more-questions

HAHAHA, EP!!!!!......hectictar gave me that tip...!!!

Second one

Because DC is parallel o AB, then triangle BAF  is similar to triangle EDF

And   since   the side of the square =  sqrt (36)  = 6

Then DE  + EC  = 6

DE + 2DE  = 6

3DE = 6

DE  = 2

So 

[AB ] / [AD + DF ]  =  DE / DF

6 / [ 6 + DF ]  =  2 / [  DF ]     cross-multiply

6 [  DF ] = 2 [ 6 + DF ]

 6DF  =  12 + 2DF    subtract 2DF from  both sides

4DF  = 12    divide both sides by 4

DF  = 3  =  height of triangle    DEF

So  area of DEF  = (1/2)DE * DF  =  (1/2) * 2 * 3   =  3 units^2

Note, Knockout....if you right click on the pic  and select  "Copy Image Address"....you can paste this address in a new browser window  and view the image

First one

Triangle AEB  is similar to  triangle DEC

Note that   EC /EB  =    4/5   so...this is the scale factor of triangle DEC to triangle AEB

So......the area  of triangle DEC  =

[ scale factor  of  triangle DEC to triangle AEB ]^ 2 *  area of triangle AEB  =

[ 4/5] ^2  *  50  =

[ 16 / 25 ] * 50  =

16 *  2  =

32

-3^x   +  4

"Range" refers to the y values covered by the function

Note that when x is a large negative, the function reaches its highest point  ≈  4

As  x appoaches 0, the function approaches  3

As x gets more and more positive, the finction gets more and more negative

So..... "B"  is correct

Look at the graph  here to confirm  this for yourself  :   https://www.desmos.com/calculator/pw6f0aztxl

Triangles  ADE  and DCE  are under the same height....so....their areas are to each other as their bases.....so  AD /DC  =  9 / 6  =  3 / 2

So...AD   /  AC  =   3 / 5

And triangles ADE  and ABC are similar

So......the scale factor of  AC / AD  =  5/3

And the area of triangle ABC  =  [scale factor AC /AD]^2  *  area of triangle ADE =

(5/3)^2  *  9  =

 ( 25 / 9 )  *  9  =

25  =  [ ABC ]