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( 1/a + 1/b)             1

_________  =       ___

      a+b                  9

        [a+b]

      ______

        [ab]                      1

___________     =    ____    

                                     9

         a+b

           1                      1

   _________    =  ______

            ab                   9

            ab=9

Two distinct numbers

9 and 1

9+1 or 1+9

Both are equal to 10

sorry if I was unclear. I'm not good at latex

x^2 + 30x + 240= -36 

x^2 + 30x+276=0     Quadratic Formula shows x = -15 +- sqrt (51) i       Take it from here.....

See detailed solution for # 2 here:  https://web2.0calc.com/questions/please-help-question-not-answered#r2

Sorry, I didn't see the "digits", but it depends on how many letters and digits you want in each password. So, if you wanted a password of 4 letters and 2 digits, then it is the same as explained above: 26 x 26 x 26 x 26 x 10 x 10 =26^4 x 10^2 . If you wanted 4 digits and 2 letters, then you would have: 10^4  x  26^2....and so on.

Pam and Jake drive trucks for a produce company. One day, Pam drove 102 miles in 1 1/2 hours. Jake drove 54 miles in 3/4 hours. Who drove at a faster rate? Explain and show all your work!  
 

Arc Length =75 x pi/180 x r (radius)
15pi =75 * pi/180 * r

Solve for r:
15 π = (5 π r)/12

15 π = (5 π r)/12 is equivalent to (5 π r)/12 = 15 π:
(5 π r)/12 = 15 π

Divide both sides by (5 π)/12:
 
r = 36 - the radius of the circle

(2Pi - x) + (Pi + x) = 3Pi  

What is the sum of all positive integers v for which lcm(v,20)=80.

v = 16,  80

Sum = 16 + 80 = 96

a, b, c, d, e, f

How many choices do you have for "a"? 26

How many choices do you have for "b" ? Also 26 [Because repeats are allowed]....and so on for all 5-letter codes.

So, the total for 5-letter codes, or passwords, =26 x 26 x 26 x 26 x 26 =26^5.

Exact same reasoning applies to 6-letter codes or passwords..............= 26^6.

Sorry, I'm afraid that's not correct.

The smallest solution is x = 5*pi/12.

The sum of all values of θ is 3*pi/2.

It would be 3!

Part (b) works out to (a + (2n + 1)d)^2 - (a + (2n)d)^2 + ... + (a + d)^2 - a^2 = (a + (2n + 1) d + (a + 2nd + ... + a + d) + a = n(3a + (n + 2)d).

The largest possible value of b is 3*1 = 3.

14 + 6h

If n represents the cost of each notepad:

6n+52

Is the total amount of money she spent.

If this is a 27% discount from the original price, then it is pretty simple to get the original price. 

27% off is also equal to 73% OF.

That means that if the original price was x, the new price is (73/100)x.

To get back to x, all you need to do is multiply by the reciprocal, which is 100/73. 

So (100/73)*584, which is 800.

The original price is $800.