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1rst lemme ask ya somethin':

Do you consider Venezuelan yourself?

2nd fun fact: " there are 32,641,749 people right now in venezuela"

3rd I'm Venezuelan, but livin' in TX.

I'm confused. How does this relate to my question?

thank you!

(c)  If  1/a^2 and 1/b^2   are roots...we must have that

(x - 1/a^2 ) ( x - 1/b^2)  = 0

x^2   - [ 1/ a^2 + 1/b^2] x  +   1 /(ab)^2   = 0

x^2 - [  1/a^2 +1/ b^2] / (ab^2) + 1/4^2  =  0

x^2 -  [  ( a^2 + b^2) / (ab)^2 ] x  + 1/16  = 0

x^2  - [ (17/4) / 16 ] x  + 1/16 = 0

x^2 - (17/64)x + 1/16 = 0       multiply through by 64

64x^2 - 17x + 4 =  0

So....the quadratic is

64x^2 - 17x + 4

Do the LHS first: (5/8) / -(5/9) =(5/8) x -(9/5) =(5 x -9) / (8 x 5) =-45 / 40.
Now, do the RHS: n / (8 / 15) =n x (15 / 8) = 15n / 8
Now, put the LHS and the RHS together:
-45/40 = 15n/8          Cross multiply
-45 x 8 =15n x 40
-360 = 15n x 40          Divide both sides by 15 x 40 =600
-360/600 = n
n = -0.6

1)  (2x+3)^3 -6

Write

y = (2x+3)^3 - 6     add 6 to both sides

y + 6 =  (2x+ 3)^3      take the cube root of each side

∛ (y + 6)  = 2x + 3      subtract 3 from both sides

∛ ( y + 6) - 3  =  2x      divide both sides by 2

 [  ∛  ( y + 6) - 3 ] / 2   = x     "swap"  x and y

[ ∛ ( x + 6) - 3 ] / 2   = y  = the inverse

Putting this into    (2x+3)^3 -6  we get

( 2  [ ∛ ( x + 6) - 3 ] / 2  + 3)^3 - 6  =

(  ∛ ( x + 6) - 3 + 3 )^3  -  6 =

x + 6  - 6  = x

And    putting the original into the inverse

[ ∛ ( [   (2x+3)^3 -6 ] + 6) - 3 ] / 2  =

[  ∛ { (2x + 3)^3 - 3 ] / 2 =

[2x + 3 - 3 ] / 2  =

2x / 2 =   x

So...they are inverses !!!!

Straight line distance will be

sqrt [   (x1-x2)^2   +   (y1-y2)^2  ]    =   sqrt ( -6-4)^2 + (3-3)^2 )  = sqrt100 = 10 units

Hello! If I'm understanding your question correctly, it would be 10 units. 10 units would be the answer :)

Put in -3 for x     

8/ ( 1 + 3e^-(.7(-3)) = .31374...

No problem!!

Thank you so much! 

Area of a triangle = 1/2 base x height    b = b    h = b-5    area = 42 in^2  (given)

42 = 1/2   b (b-5)

84 = b^2-5b

b^2-5b - 84 = 0    factor    (or use quadratic formula)

(b+7)(b-12)= 0      so b  can =  12 or -7      toss out -7 because you can't have a negative length

so b = 12

h = b-5 = 12-5 = 7   

Check:  Area  = 1/2 b h = 1/2  12  7  = 42    Correct !

Hi!

So what you need to know for this, is the formula for the area of a triangle which is 1/2 x base x height

The area of the triangle is given to you.

So  42 = 1/2 x b x 5-b

Then after that, you can probably use Algebra to find out the answer. This would require the use of quadratic roots and zeroes, like you said. So you would find answers that look like this (x-2)=0- and (x+2)=0. I'm not saying this is exactly what you'll get, but something along the lines of that.

Then you just solve! :) Hope this helps... I tried L:

1)

Circle O is a unit circle. Segment AS has length 12/5 and is tangent to circle O at A. If P is the intersection of OS with circle O, find length PS.

AS  = 12/5      AO  = 1

SO  =  sqrt [ (12/5)^2  + 1 ]  =   sqrt [  144 + 25] / 5  =  13/5

So...PS   =   SO  - PO  =   13/5  -  1  =     8/5

2)

Angle A: Angle P: Angle ASP are in ratio 1: 2: 2. Find the degree measure of angle BSA.

Angle A  =  36°......Angle P, ASP  =  72°

Angle  ASP  =  (1/2)minor arc AS  =  angle BSA  =  72°

what is x value ?

#4       A) (7, 9)   B) (1, 5) 

Midpoint  ( [ 7 + 1] /2 , [ 5 + 9] /2)    =  ( 4, 7)

Slope  =  [9 - 5 ] / [ 7 - 1 ] =  4/6 = 2/3

Neg reciprocal slope = -3/2      (1)

Using  midpoint  and  (1)   we have

y = (-3/2) ( x - 4) + 7

y = (-3/2)x + 6 + 7

y = -(3/2)x + 13

It's calculated exactly like the mod of a positive number. In arithmetic modulo cc, we seek to express any xx as qc+rqc+r, where rr must be a non-negative integer.

Why don't we test it out with an example?

Take −100−100 mod 8=48=4. This is because of 8⋅−13=−1048⋅−13=−104. The remainder is 44.

So now let's take (37−54)(37−54) mod 55. It's equal to −17−17 mod 5=35=3. Substitute in and do the computation: Method 11 gives 33, which is what we want, and method 22 gives −2−2, so the correct approach is method 11  

#3     A) (8, 1)  B) (0, -1) 

1)  Find the midpoint  =  ( [ 8 + 0] / 2, [ -1 + 1] / 2)  =  (4, 0 )

2) Find the slope  =  [ -1 -1 ] / [ 0 - 8 ] =   -2/ -8 =  1/4

3) Take the negative reciprocal o the slope =  -4

Using the midpoint and  (3)   we have

y = -4(x - 4)

y = -4x + 16

THANK YOU SOOO MUCH!