Alan

If 3a + 7b + c = 315 and 4a + 10b + c = 420, what is a + b + c?

If 3x + 1/(2x) = 3, find 8x^3 + 1/(27x^3).

Do you mean something like:

12*143+6*214 = 6*2*143 + 6*214   

6*2*143 + 6*214  = 6*(2*143 + 214)

6*(2*143 + 214) = 6*(286 + 214)

6*(286 + 214) = 6* 500  = 3000

|x-5| >=0 for all values of x, so

| |x-5| + 5| >= 5 for all values of x, so

| | |x-5| + 5| - 5| >= 0 for all values of x. so

| | |x-5| + 5| - 5| + 5 >= 5 for all values of x, so minimum value = 5, when x = 5.

As follows:

1 US ton = 2000 lb

1 UK ton = 2240 lb

1 metric ton (tonne) = 2204 lb

Write it as :  \(x = \sqrt{2+x}\)  

Square both sides and solve for x.

See https://web2.0calc.com/questions/slope-intercept-please-help#r1 

1.  Rewrite the equation in the form:  y = x - 4  This has slope m = 1, so any line parallel to it will have the same slope, so it will look like y = x + k where k is a constant.  To find k, use the fact that it goes through point (-6, -1). i.e.  you get k from:  -1 = 1*(-6) + k.

2.   Rewrite the equation in the form:  y = -x/3 - 2.  This has slope m = -1/3.  Any line perpendicular to this has slope equal to -1/m.  Again get the constant by substituting the specified point value to the perpendicular equation  y = (-1/m)*x + k.

Let f(n) be the sum of the positive integer divisors of n. If n is prime and f(f(n)) is also prime, then call n a bouncy prime. What is the smallest bouncy prime?

3 is prime.  It has positive integer divisors 1 and 3, so f(3) = 4.  

4 has divisors 1, 2 and 4, so f(4) = 7 which is prime.

Hence n = 3 is a bouncy prime.

This doesn't hold for n = 2, so n = 3 is the smallest bouncy prime.