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you are solving by additon 

Yeah.. He's telling the truth..

We are using this property     a^m * a^n  = a^(m + n)

So

4^3 * 4^(-5)   =   4^(3 +  -5)   =  4^(3 - 5)  = 4^(-2)  =   1 / 4^2  =  1/16

5+5=5+5=20

Slope  =       [  subtract the y coordinates in some order ]

                   _____________________________________

                    [ subtract the x coordinates in the same order ]

So.....    (2,12)  (6,11)

 [   12 - 11 ]                     1                       1

_________     =             ___    =         -  ___      

  [2  - 6 ]                         -4                       4

See if you can do the second one, NSS   ........

-1/4

0

Good Job CP (Your new nickname lmao) You have done it once more again ^^... You are very nice to help people out with their math problems ^^ Good Job CP

2x^2 + xy - 13x + 6=y^2 + 13y..........(1)

2 x^2 + xy - 6 x =y^2 + 6y + 8..........(2)

Subtract (2) from (1) and we get:

x = 2 - y  and subbing this in (1) above we get:

y = -2      and subbing this in (2) above we get:

x = 4

 6x+4y=34        multiply through by  -1   →    -6x  - 4y  - 34       (1)

 6x+15y=78          (2)

Add (1)  and (2)   and we get

11y  = 44    divide both sides by 11

y  = 4

Put this into any equation to solve for x

6x + 4(4)   = 34

6x + 16  = 34   subtract 16 from both sides

6x  = 18     divide both sides by 6

x  = 3

Yay a new nickname ^^ lmao

Thanks.....KHM......!!!!!

Thanks CPhill, You have done it once again ... You are a very helpful person, I am glad to have someone like you on this site ... Thanks for the help CPhill, If I ever have a problem, I will always come and ask for some help from this site, because this site has so many helpers, Mainly you.

1. <1 and <2 are supplementary angles. m<1 is 4y+7, and m<2 is 9y + 4. Find m<2.

Supplemental angles sum to 180°....so we have that

[4y + 7 ] + [ 9y + 4] = 180    simplify

13y + 11  = 180       subtract 11 from both sides

13y  = 169         divide both sides by 13

y  = 13

So    m < 2   =  9(13)  + 4  =  117 + 4   = 121°   

2. GI bisects

3. The midpoint of UV is (5, 11). The coordinates of one endpoint are U(3, 5). Find the coordinates of endpoint V.

We can solve this  using the midpoint formula

[ 3 + x ]  / 2  = 5       multiply both sides by 2                    [5 + y ] / 2   = 11    multiply both sides by 2

3 + x  =  10                subtract 3 from both sides               5 + y    = 22        subtract 5 from both sides

x  = 7                                                                                    y  = 17

So.... V  = ( 7, 17)

4. Find the distance between points M(6, 16) and Z(-1, 14) to the nearest tenth. 

Distance   =sqrt  [  ( -1 - 6)^2  + ( 16 - 14)^2 ]    =  sqrt [ (-7)^2 + 2^2 ]  = sqrt [ 49 + 4]  = sqrt [ 53] ≈  7.3 units

Let N be the smaller number....and we have that

N  + 4N = 70

5N  = 70       divide both sides by 5

N  = 14

And 4N  = 4(14)  = 56

5 bags

Option 1....she gets  5 * 2  = $10

Option 2....she gets  .02 +.04 +.08 + .16 + .32  = 62 cents

10 bags

Option 1  .....she gets  10 * 2   = $20

Option 2.... using  the sum of a geometric series....we have that

S  = a₁ [ 1 - r^n] / [ 1 - r]

S  is the sum      a₁  is the first term  = 2 (cents)    

r is the common ratio between terms = 2     and n is the number of bags

So ......she gets   2 [ 1 - 2^10]  / [ 1 - 2 ]  = 2046 cents   =$20.46

So......Option 1 is better for 5 bags, but Option 2 is better for 10 bags

How many bags of leaves would Celia have to fill before method 2 pays more than method 1?

Note that when she fills 9 bags under Option 1  she gets  9 * 2  = $18

And when she fills 9 bags under Option 2 she gets  1022 cents  = $10.22

So...it appears that Option 2 is better than  Option 1 after she fills 10 bags  [or more ]