Alan

Lie the two given lengths on top of each other.  If you join them with a third length of 9 units you will have a straight line, but if you increase the length of the third length by 1 unit while keeping the ends joined you will get a triangle.  Hence shortest third length is 10 units.  I'm sure you can add up the lengths to get the perimeter.

Let a = 10n + m  and  b = 10m + n

Then  a - b =  9(n - m)

and    a + b = 11(n + m)

These are perfect squares if n - m = 1 and n + m = 11

i.e. n = 6 and m = 5

This makes a = 65 and b = 56

"For alcohol the formula is 2,4 J/g·°C and for olive oil it is 1,65 J/g·°C. John heats up both substances using a calorimeter, first an unknown amount of alcohol and then, when the calorimeter has cooled completely, the same amount of olive oil. He heats up both liquids from 20 °C to 50 °C. How long does it take to heat up the alcohol when the heating up of the olive oil took 2,5 minutes?"

As follows:

That's right.

"Given is the function f(x) = -3x + 2 

a. The graph of g starts from the graph of f by multiplying the x axis with the factor - 2/3 and shift it up 1/3. What is the function notation of g?

b. The graph of the function h(x) = -12x + 10  starts from the graph of f by multiplying the x axis and then shift it. With which factor do you have to multiply and how does the graph translate. 

c. The graph of h can also start from the graph of f by first translating and then multiplying. Show how. "

Is this what you are looking for:

"Let A be a 2*2 matrix such that det(A) = 7. Find det(3A)"

As follows:

The expression (1/2)*b*h refers to a single triangle. 

The kite can be considered as two large triangles of base 19in and height 9.5in; or four triangles, two of base 12in and height 9.5in, and two of base 7in and height 9.5in.

Hence you should double your result of 90.25 in².

"What is the probability of rolling six standard, six-sided dice and getting six distinct numbers?"

Doesn't matter what the first one is: probability = 1

There are 5 possibilities for the second one:  probability = 5/6

There are 4 possibilities for the third one:  probability = 4/6

There are 3 possibilities for the fourth one:  probability = 3/6

There are 2 possibilities for the fifth one:  probability = 2/6

There is 1 possibility for the sixth one:  probability = 1/6

Overall probability is obtained by multiplying all the above together (then reduce to lowest terms).

Use the sine rule:   sin(P)/34 = sin(78)/46

so P = sin^-1(34*sin(78)/46)