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I'm sorry, but I don't understand the question.

Really sorry about this. I must be asleep!. This is the correct answer.

Let the first term = F
Common difference=3F
F^2 - F =5/2* [ 2F + 3F*4]
F^2 - F =5F + 30F
F^2 = 6F + 30F
F^2 = 36F
F = 36 -First term

GET  REAL !

thanks

The answer to the question above is 38

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10) r^2 = 35.

11) The length of the chord is sqrt(117).

Sorry!. I missed one F:

Let the first term = F
Common difference=3F
F^2 - F = 2F + 3F*4
F^2 = 3F + 12F
F^2 = 15F, solve for F
F = 15 - First term

Let the first term = F
Common difference=3F
F^2 - F = F + 3F*4
F^2 = 2F + 12F
F^2 = 14F, solve for F
F = 14 - First term

I think there will be 63 points.

The midpoint   =  location of warehouse  =

[ (-2 + 4)/2  ,  (-1 + 7) / 2 ]    =    [ 1, 3]

The distance  that this warehouse from either store is  :

sqrt  [  (1 - 4)^2  + ( 3 - 7)^2 ]   =   sqrt  [ 3^2  + 4^2 ]  =  sqrt (25)   =  5 miles

2x^2 + 4y = 11

x^2 -y^2  =  5/2

Multiply the second equation through by  -  2        and we get that

2x^2  + 4y  =  11

-2x^2 + 2y^2  = - 5        add these

2y^2  + 4y  = 6

2y^2  + 4y - 6  =  0          divide through by 2

y^2  + 2y  - 3   =  0       factor

(y + 3)  ( y - 1)  =  0

Setting each factor to 0   and solving for y   we get that   y   = -3  and  y  =  1

And using 2x^2 + 4y  =  11 we can find the  values for x

2x^2  + 4(-3)  = 11          2x^2  + 4(1) = 11

2x^2  - 12  = 11               2x^2  + 4  = 11

2x^2  =  23                     2x^2  = 7

x^2  =  23/2                     x^2 = 7/2

x = ±√[23/2]                     x = ±√[7/2]

So.....the solutions are

(x, y )   =    (-3, ±√23/2] )   and  ( 1 , ±√[7/2]  )

The two answers you checked are correct......we also have one other answer.....

ln   8

_____

ln  4

We have the  change of base property  that says that

Ln a

____    =     Ln _b a

Ln b

So.....this can be written as

Ln₄ 8

By log properties.....We can write

log x^2   =  log ( 2 * (4x - 6)  )

log x^2 =  log  [ 8x - 12 ]          we can solve this

x^2  =  8x  - 12

x^2  - 8x  + 12  = 0       factor

(x - 6) ( x - 2)  =  0

Set  each factor to 0  and solve for x  and we get that   x  = 6   and  x  = 2

could you check this last one? thank you so much for all your help!

In exponential form we have

10^2  =  x - 8

100  =  x  - 8       add 8 to both sides

108   =   x

Q2

f(x)  =  3^(x -2)        

The inverse is

g(x)  = log ₃ x  + 2

to the right

up

Q1

order of ordered pairs

(2,-1)  ( 6, 0) and (-4, 3)

21 - x  =  9       is not an exponential  equation

I think this   might be

2^(1 - x)  = 9         ???

Take the log of both sides

log 2 ^(1 - x) =  log 9      and we can write

(1 - x) log 2  = log 9       divide both sides by log 2

1 - x    =     log 9  / log 2     rearrange as

x =  1 -  log 9 / log 2   

This is the exact answer in log terms

Evaluating with a calculator  we get   ≈  -2.169925

Solve for x:
(2 log(x))/log(10) = log(4 x - 6)/log(10) + log(2)/log(10)

Subtract log(4 x - 6)/log(10) + log(2)/log(10) from both sides:
-log(2)/log(10) + (2 log(x))/log(10) - log(4 x - 6)/log(10) = 0

Bring -log(2)/log(10) + (2 log(x))/log(10) - log(4 x - 6)/log(10) together using the common denominator log(10):
-(log(2) - 2 log(x) + log(4 x - 6))/log(10) = 0

Multiply both sides by -log(10):
log(2) - 2 log(x) + log(4 x - 6) = 0

log(2) - 2 log(x) + log(4 x - 6) = log(2) + log(1/x^2) + log(4 x - 6) = log((2 (4 x - 6))/x^2):
log((2 (4 x - 6))/x^2) = 0

Cancel logarithms by taking exp of both sides:
(2 (4 x - 6))/x^2 = 1

Multiply both sides by x^2:
2 (4 x - 6) = x^2

Expand out terms of the left hand side:
8 x - 12 = x^2

Subtract x^2 from both sides:
-x^2 + 8 x - 12 = 0

The left hand side factors into a product with three terms:
-(x - 6) (x - 2) = 0

Multiply both sides by -1:
(x - 6) (x - 2) = 0

Split into two equations:
x - 6 = 0 or x - 2 = 0

Add 6 to both sides:
x = 6 or x - 2 = 0

Add 2 to both sides:

 x = 6     or     x = 2

Solve for x:
log(x - 8)/log(10) = 2

Multiply both sides by log(10):
log(x - 8) = 2 log(10)

2 log(10) = log(10^2) = log(100):
log(x - 8) = log(100)

Cancel logarithms by taking exp of both sides:
x - 8 = 100

Add 8 to both sides:

x = 108

2.   CORRECT    !!!!

3.  CORRECT   !!!

4 .   We can solve

x / ( 4x - 1)  = 5

x  = 5(4x - 1)

x = 20x  - 5

-19x  = - 5

x   =5/19

CORRECT!!!!

GOOD JOB !!!!!

Awesome!! (: thank you

(5√5)^(-2x + 1) =   (1/5) * 125^(x - 3)

We can write

(5^(3/2)) ^(-2x + 1)  =  (1/5) (5^3)^(x - 3)

5 ^ ( - 3x + 3/2)  =  (5^-1) ( 5)^(3x - 9)

5^( -3x + 3/2)  =  5^( -1 + 3x - 9)        we have the same bases.....solve for the exponents

-3x + 3/2  =  - 1 + 3x  - 9

-3x + 3/2  =  -10 + 3x

6x  =  10 + 3/2

6x  =  11.5

x  =  11.5 / 6    =    23 / 12

So....CORRECT!!!!

thank you.