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40 x .01 x 1/2          +1          =   1.2     (just as gs85 found!)

Let the distance between the walls be  l

One rope goes from   y = 9 to 0   in length  l       now   let's also make l = 1 for convenience

  equation    y = -9/2x  +9  

other rope goes from 0 to 3   in lenght l (which is 1)

  equation   y = 3/2 x   

set them equal to find 'x'        3x = -9x+9         

                                               12x = 9

                                                 x = 3/4

now find the height by puttin 'x' into one of the equations      y = 3x = 3 * 3/4 = 9/4 meters high at cross

How about:

 2   3    7  11   13  17     

We have 1/2 x 1/100 x 40.

1/2 x 1/100 x 40

= 1/200 x 40

= 40/200

= 1/5

1/5 is less than a number which is 1/5+1=6/5=1.2.

It appears to me that several values for x would work in number 1.  I don't know how to solve it.  Sorry. 

2.   Factor fully by grouping:   5x² + 15x +4x + 12  

I'm not sure what "by grouping" means, but I can factor the quadratic for you.  

First add 15x and 4x                5x² + 19x + 12  

This will factor to                      (5x + 4)(x + 3) 

_.    

Let x be Paulo's current age and x+18 Sandra's. We form an equation of their ages in 13 years.

(x+18)+13=2(x+13)

x+31=2x+26

x=5

Sandra is x+18 so her age is 23 years old.

First, we should assign variables.

Sandra’s Age = X + 18

Paolo’s Age = X

In 13 years, they will be:

(X + 18) + 13 = 2(x + 13)

X + 18 + 13 = 2x + 26

X + 31 = 2x + 26

X – 2x = 26 - 31

-x/-1 = -5/-1

X = 5

Therefore, Sandra is now:

Sandra’s Age = 5 + 18 = 23

Sandra is now 23 years old.

Checking their age:

23 (Sandra) – 5 (Paolo) = 18

If z>=0,
2+z > 1 -- z > -1
2-z <= -1 -- z >= 3

If z<0,
2-z > 1 -- z < 1
2+z <= -1 -- z <= -3

If you graph on a number line, you will find your answer. Check a few values to make sure they work, especially at the boundaries.

Multiply first equatin by   -3      then add to second equation to solve for z     as a start......

then   multiply first equation by -5      and add to third equation  to solve for   y

then use the values of   z   and  y   that you have found in any of the equations to solve for  x

From each of the non-colinear points to each poin on the line  would be   4 x 3 = 12 lines

from each of the 4 to the other three would   (4 x 3)/2 = 6 lines 

PLUS the colinear line

19 lines      (I believe)

14 is the answer because if Hannah is 7 yrs older than Tim was 2 yrs ago then she obviously still is now. If they are apart by 7 then Tim must be 7 and Hannah would be \(2\times7\) or 14. So the answer is \(\boxed{14}\)

Pulling the trigger 6 times in succession will certainly fire the bullet

spinning each time means you may get lucky and never find the bullet chambered.

1/6    chance of getting the bullet

5/6 chance you will NOT get the bullet

 (5/6)^6 =     . 335    you will NOT get the bullet at 6 tries

k +1  = 2(y-1)

k-1   = y+1                          k = kensi   y = k y le

from second equation:

k = y+2         sub into first eqaution   

y+2   +1  = 2y- 2

y = 5                                     (then k=7)                          

If you take out four socks, at least two must match.

The first three can be of different colors but you can't have four socks that are different from one another.

The number of socks of each color does not affect the answer.

Write in vertex form.

\(y=-x^2-4\)

Hello guest!

\(\\ y=-1x^2-4\)

\(f (x) = a(x - h)2 + k\)

(h, k) is the vertex of the parabola.

\(a=-1\)

\(y=-x^2-4\\ \frac{dy}{dx}=-2x=0\\ x_{max}=0\)

\(h=0\)

\(y_{max}=k=-x_{max}^2-4\\ y_{max}=k=0-4\)

\(k=-4 \)

\(f (x) = a(x - h)^2 + k\\ f (x) = -1(x - 0)^2 -4\)

The equation of the parabola in vertex fotm is \(f (x) = -1(x - 0)^2 -4.\)

You can solve the other tasks yourself based on the model.

  !

Perhaps our linguistically challenged 'Guest' can explain their answer?

WolframAlpha finds   x = 1/ 2    or  0          Can Guest provide the solution......or just the answer (which really helps no one) ????

1 - [10 nCr 6] / 2^10 =20.5078125% probability of 6 heads in 10 flips

2 - [100 nCr 60] / 2^100=1.084386671% -probability of 60 heads in 100 flips. 

3 - You  are 20 times more likely to get 6 heads than 60 heads.

answer the question idiot

Hint:   Look at the vertex   2, 0

    when x = 2    the equation for y  = 0         do any of these equations work?

What the heck is wrong with you? Why must you use such explicit words instead of saying something normally?! So what if I got it wrong?

You could try writing out the polynomial.

You could try writing out the polynomial.

Okay let me rephrase that- don't use those non-appropriate words here. And no need to take out so much anger here.