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Let h be the third altitude.  Then by the triangle inequality, h + 12 > 14, h + 14 > 12, and 12 + 14 > h.  The largest integer h that satisfies these inequalities is h = 25.

Your question is super vague, but if we start from 100% on year 0, and eliminate half of our resources every year on, we will be at 0.0762939453% by the 17th year. The answer is 17, no nearest year rounding is needed.

Yellow area is 3/4 of the rectangle.

It was only 198! Thanks for helping!

Think of 705,600's factors.

\(h_e = T(3)C_e(2)\)

_{Singular hen:}

\(h= {E_1\over 1.5(12H)}\)

_{Total between 4 hens:}

\(Total_i = {24\over C_h(4)} \)

_{Individual threshold:}

\(6\)

_{Time for individual completion:}

\(6=3_d({I_t\over C_e[2]})\)

_Answer:

\(9\space days\)

thank you so much!!

If  (a - b) / a  =  b / (a - b)  then what are the values of a/b?

(a - b) / a  =  b / (a - b)

cross-multiply:        (a - b)²  =  a·b

                      a² - 2ab + b²  =  ab

                       a² - 3ab + b²  =  0

Using the quadratic formula (solving for a, using b as a constant):

                 a  =  [ - -3b  +/-  sqrt( (-3b)² - 4·1·b² ) ] / ( 2·1 )

                 a  =  [ 3b +/- sqrt( 9b² - 4b² ) / 2

                 a  =  [ 3b +/- sqrt( 5b² ) / / 2

                 a  =  [ 3b +/- sqrt(5)·b ] / 2

                 a  =  [3 + sqrt(5)] / 2 · b     --->     a/b  =  [3 + sqrt(5)] / 2

                 a  =  [3 - sqrt(5)] / 2 · b      --->     a/b  =  [3 - sqrt(5)] / 2

I had the computer search all the way up 10,000,000 numbers and it couldn't find any such numbers except the example you gave, i.e. 198. That seems to be the only number up to 10,000,000! Unless your Math Teacher wants you to go up the numberline to maybe a googol, or 10^100 !!?? But that would take forever, almost!.

_{12√2 (cos (7pi/6) + i sin (7pi/6)} 

3√3 (cos (pi/4) + i sin (pi/4)                      ⁼

_12√2     

 3√3     ^{[ cos ((7pi/6) - (pi/4)) + i sin ((7pi/6) - (pi/4)) ]              =}

_4√6

3                ^{[ cos (11pi/12) + i sin (11pi/12) ]           =}

   _4√6

    3          cis     (11pi/12)

Let  x  =  number of times he missed the shot. (costing him 25 cents per shot missed)

Then  100 - x  =  number of times that he made a basket.  (gaining him 10 cents per shot made)

0.10(100 - x) - 0.25(x)  =  5.10

  10.00 - 0.10x - 0.25x  =  5.10

              10.00 - 0.35x  =  5.10

                         -0.35x  =  -.90

                                  x  =  14     <---   number of shots missed.

One leg of a right triangle is increased by 10% and the other leg is decreased by 10%.  By what percent does the area of the triangle change?

The legs are 5 and 8

5 * 8 / 2 = 20 u²                  100%

5.5 * 7.2 / 2 = 19.8 u ²         99%

4.5 * 8.8 / 2 = 19.8 u²           99%

The area of the triangle decreased by 1%  

You over counted the answer is 10

The answer is 10

fix your latex please! :) its a bit hard to read

thank you so much again!!!! you're a life saver! :)

Wait I found 2 more.

1. (6, 0)

2. (6, 2)

3. (6, 3)

4. (6, 4)

5. (5, 3)

6. (5, 5)

7. (4, 6)

8. (3, 5)

9. (3, 6)

10. (2, 6)

11. (0, 6)

@melody it's more difficult then you stated in problem 2. I'm not sure about this either, but here's nine possible (x,y)'s:

1. (0, 6)

2. (2, 6)

3. (4, 6)

4. (3, 5)

5. (5, 5)

6. (6, 4)

7. (5, 3)

8. (6, 2)

9. (6, 0)

NOTE: 1 is not a possible value of x or y

I need help here to

For #3, write out the equation C = m / V, where m is the moles of NaCl and V is the total volume of the solution.
 

To find the number of moles, we'd need to refer back to question 2, which states that 1 gram of H2O is equal to 0.055508435061792 mole.

Because the question states there is 2 grams of sodium chloride, we'd multipy 2 and 0.055508435061792 to get the number of moles used.

2 x 0.055508435061792 = 0.11101687012

To get the volume of the water, you would divide the 500 mL by 1,000, to convert it to liters.

500 / 1,000 = 0.5

Your liters is 0.5.

Now, you can use c = 0.1 / 0.5 

Plug in the values you found, and divide them to find the concentration of your solution.

0.1 / 0.5 = 0.25

Your concentration can either be written as 0.25 M OR 0.25 mol/L.

This helped so much! Thank you!!

Oh! That's a really cool. So does that mean if you rotate a matrix, its determinant stays the same?

I tried explaining a bit more so you can understand! Hopefully that helps:) You're very welcome!

oh wow thank you so much!!!!! :)