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0z = 0

(0 + 2z + 4z + 8z)/4 = 14z/4 = 3.5z

What is the volume of this container?

Sorry, I didn't notice that! Then the "smallest positive integer is k = 1"

Which is a positive integer ?

For n = 4 and p = 0.12, what is P(X = 0)?

I cant edit my prevous comment because of the whole guest thing, but what I ment to say is where are the legs of the triangle.. Is it a right triangle cuz then i can just use the pythagrom therum? (I cant spell well) If so what is the other leg? I understand that one of the legs is 6 but what about the other? would it be 6 as well? Thx so much

Thank you so much! this helps me but I am still confused how to convert that answer to a squre root? If you could help with that I would be super gratfull! Thx I understand how to do it know I just am now confused with the square root :P

I'm assuming that you mean this:  ₄C₀·(0.12)⁰·(0.88)⁴  =  0.600

Number 2)  The circle has radius = 14, so its diameter = 28. The chord = 12

Draw the chord and the diameter of the circle which is perpendicular to the chord.

The chord divides the diameter into two parts, a short part from the chord to the circle (call this "x") 

and a longer part from the chord through the center of the circle to the other end of the circle (this is 28 - x).

The chord is divided into two equal parts, each part = 6.

There is a theorem that says that if you multiply the two parts of one chord you will get the same answer when

you multiply the two parts of the other chord (the diameter).  Thus:  x·(28 - x)  =  6·6

Solving:  28x - x²  =  36

               x² - 28x + 36  =  0

Using the quadratic formula:  x  =  1,351  (approximately)

The distance from the chord to the center of the circle is 14 - 1.351  =  12.649   (approximately)

After doing this, I realize that there is a much easier way --

-- draw the chord and the perpendicular bisector (the same as above)

-- draw the radius from the center of the circle to an end of the chord, creating a right triangle.

-- the hypotenuse of the triangle is the radius of the circle (14)

-- one leg of the right triangle is one-half the chord (6)

-- use the Pythagorean Theorem to find the distance ...

Find an equation of the circle that has center (-2, 4) and passes through (2, -1).

i=0;a=1000000;c=a/2;printc;d=c*5;printd;i=i+1;a=d;i++;if(i < 1000, goto2, 0)

OUTPUT: The last integer in the sequence is: 5^12

thx I understand this question now :D 

Number 1:

Point M divides BC into two equal segments; call each segment "x".

Point N divides AC into two equal segments; call each segment "y".

Triangle(BCN) is a right triangle with BC = 2x, CN = y, and hypotenuse BN = 13.

--->   (2x)² + (y)²  =  (13)²   --->   4x² + y²  =  169          [Pythagorean Theorem]

Triangle(AMC) is a right triangle, with AC = 2y, CM = x, and hypotenuse AM = 19.

--->   (2y)² + (x)²  =  (19)²   --->   4y² + x²  =  361          [Pythagorean Theorem]

Combining these two equations:

     4x² +   y²  =  169   --->   x 4    --->   16x² + 4y²  =   676

       x² + 4y²  =  361   --->   x -1   --->      -x² - 4y²  =  -361

Adding down:                                        15x²           =   315

                                                                          x²   =  21

                                                                           x   =  sqrt(21)

Substituting:   4x² +   y²  =  169   --->   4( sqrt(21) )² + y²  =  169

                                                                           84    + y²  =  169

                                                                                      y²  =  85

                                                                                      y   =  sqrt(85)

This means that one side of triangle(ABC)  =  2·sqrt(21)  while the other side  =  2·sqrt(85).

You can now use the Pythagorean Theorem to find the hypotenuse ...

Hi Geno3141: Here is a solution courtesy of Mathematica 11 Home Edition:

Solve for x:
(x + 57)^(1/3) - (x - 57)^(1/3) = 6^(1/3)

Subtract (x + 57)^(1/3) from both sides:
-(x - 57)^(1/3) = 6^(1/3) - (x + 57)^(1/3)

Raise both sides to the power of three:
57 - x = (6^(1/3) - (x + 57)^(1/3))^3

Subtract (6^(1/3) - (x + 57)^(1/3))^3 from both sides:
57 - x - (6^(1/3) - (x + 57)^(1/3))^3 = 0

57 - x - (6^(1/3) - (x + 57)^(1/3))^3 = 108 + 3 6^(2/3) (x + 57)^(1/3) - 3 6^(1/3) (x + 57)^(2/3):
108 + 3 6^(2/3) (x + 57)^(1/3) - 3 6^(1/3) (x + 57)^(2/3) = 0

Simplify and substitute y = (x + 57)^(1/3).
108 + 3 6^(2/3) (x + 57)^(1/3) - 3 6^(1/3) (x + 57)^(2/3) = 108 + 3×6^(2/3) (x + 57)^(1/3) - 3 6^(1/3) ((x + 57)^(1/3))^2
 = -3 6^(1/3) y^2 + 3 6^(2/3) y + 108:
-3 6^(1/3) y^2 + 3 6^(2/3) y + 108 = 0

Divide both sides by -3 6^(1/3):
y^2 - 6^(1/3) y - 6 6^(2/3) = 0

The left hand side factors into a product with three terms:
-(3 6^(1/3) - y) (y + 2 6^(1/3)) = 0

Multiply both sides by -1:
(3 6^(1/3) - y) (y + 2 6^(1/3)) = 0

Split into two equations:
3 6^(1/3) - y = 0 or y + 2 6^(1/3) = 0

Subtract 3 6^(1/3) from both sides:
-y = -3 6^(1/3) or y + 2 6^(1/3) = 0

Multiply both sides by -1:
y = 3 6^(1/3) or y + 2 6^(1/3) = 0

Substitute back for y = (x + 57)^(1/3):
(x + 57)^(1/3) = 3 6^(1/3) or y + 2 6^(1/3) = 0

Raise both sides to the power of three:
x + 57 = 162 or y + 2 6^(1/3) = 0

Subtract 57 from both sides:
x = 105 or y + 2 6^(1/3) = 0

Subtract 2 6^(1/3) from both sides:
x = 105 or y = -2 6^(1/3)

Substitute back for y = (x + 57)^(1/3):
x = 105 or (x + 57)^(1/3) = -2 6^(1/3)

Raise both sides to the power of three:
x = 105 or x + 57 = -48

Subtract 57 from both sides:
x = 105 or x = -105

(x + 57)^(1/3) - (x - 57)^(1/3) ⇒ (57 - 105)^(1/3) - (-57 - 105)^(1/3) = -(-6)^(1/3) ≈ -0.90856 - 1.57367 i
6^(1/3) ⇒ 6^(1/3) ≈ 1.81712:
So this solution is incorrect

(x + 57)^(1/3) - (x - 57)^(1/3) ⇒ (57 + 105)^(1/3) - (105 - 57)^(1/3) = 6^(1/3) ≈ 1.81712
6^(1/3) ⇒ 6^(1/3) ≈ 1.81712:
So this solution is correct

The solution is:

x = 105

I graphed it and found that the two answers are  105  and  -105.

I haven't been able to figure out a way to do it algebraicly.

32 people ate chicken and the four symbols for chicken represent the 32 persons, so each symbol

represents  32 / 4  =  8 persons.

There are 10 complete symbols and 2 half-symbols, making a total of 11 symbols.

Since each symbol represents 8 persons, 11 symbols will represent  8 x 11  =  88 persons.

If  f(x)  were a function like:  f(x)  =  (5x² + 2x + 8) / (x - 1)  it would have an oblique asymptote of  y  = 5x + 7.

This would make the final function:  y  =  [ (5x² + 2x + 8) / (x - 1) ] / (x - 2)

and would simplify to:                       y  =  (5x² + 2x + 8) / [ (x - 1)(x - 2) ]

or:                                                     y  =  (5x² + 2x + 8) / (x² - 3x + 2)

which would have an horizontal asymptote of  y  =  5.

Now, this is just an example, but I believe that this would be true for all examples, so the equation of the horizontal

asymptote woulld always be:  y  =  5.

-pd  - pz  = -2z + 59

2z-pz = 59+pd

z(2-p)  = 59 + pd

z =  (59+pd) / (2-p)

90 m/hr   x   1/3 hr = 30 miles    from the airport    in direction 250⁰             (20 minutes is 1/3 hour)

1/7  + 1/5  = 1/x      x is the time together

5/35  + 7/35  = 1/x

12/35   = 1/x

x = 35/12 = 2.92 hours  =   2 hours 55 min

a=1; b=0;c=gcd(6*a+1, 6*a+2, 6*a+3, 6*a+b); if(c==1, goto4, goto5);printc, a, b; a++;if(a<100, goto2, 0);a=1;b++;if(b<100, goto2, discard=0;

OUTPUT: It works for all k from k = 0 to infinity. So, the "smallest k = 0".

I accidentally posted the same question twice because my internet was acting slow.

1. Draw a line down from that top left corner, perpendicular to the bottom line. 

2. That creates a right triangle with hypotenuse = 7 and bottom leg = 3. 

3. Use Pythagoras' Theorem to solve for the third side of the right triangle.  

4. The answer you got in # 3. is the length of the missing side. 

Hint:  It's sqrt(40) but show your work so the teacher will think you did it. 

_.

290 cm of wide and 402 cm long, to reduce it to a piece of paper of Din-A4 29.7cm ? long 21 cm wide, which is scaled to make the room fit perfectly?

290/21 = 13.8095238095238095

402/29.7 = 13.5353535353535354

There is no perfect fit but

1:14

would make it

290/14 = 20.7142857142857143

402/14 = 28.7142857142857143

Scale 1:14

the fit would be  20.71 wide and 28.71 long.

(b) How far did the ball travel horizontally? Use your answer from Part (a) in your calculations. Round your answer to the nearest tenth of a foot. 

(a) No one interferes with the ball. How long does it take the ball to hit the ground? Round your answer to the nearest hundredth of a second. Show all your work.