Alan

Use the approach given here: https://web2.0calc.com/questions/help-asap-also-i-m-very-confused-how-to-even-solve#r1 

I suspect this question should read something like:

If sinθ=3/5, find θ, where 0º < θ < 360º  (or, perhaps, some other upper limit on θ).

We have Ax + By = 3   (1)

If this passes through (7, -2) then  7A - 2B = 3   (2)

We can rearrange equation (1) in the form  y = -(A/B)x + 3/B  The slope of this equation is -A/B

The equation x + 3y = -5 can be rearranged as  y = -(1/3)x -5/3  the slope of which is -1/3

For the two lines to be parallel the slopes must be the same, hence  -A/B = -1/3   (3)

Now you have two equations ((2) and (3)) that can be solved for A and B.

Can you take it from here?

Rearrange the equations to get y = ...

-2x + y = k  becomes  y = k + 2x                 (1)

0.5x + y = 14 becomes  y = 14 - 0.5x          (2)

Now equate (1) and (2)

k + 2x = 14 - 0.5x   or  k = 14 - 2.5x  (3)

Replace x in (3) by -8.4 to find k.

Here's a clue:

See https://web2.0calc.com/questions/probability-question_35#r5

Like so:

1.   Try  \(f(x) = (x-\sqrt2)(x+\sqrt2)(x+\sqrt5)(x-\sqrt5)\)

I'll leave you to expand it.

The area of a triangle can be obtained from Heron's formula:

\(Area = \sqrt{s(s-a)(s-b)(s-c)}\)

where a, b and c are the lengths of the sides and s = (a+b+c)/2

In this case a = b = c = 12/3 = 4 and s = 12/2 = 6 so

\(Area = \sqrt{6\times 2^3}=\sqrt{48}=4\sqrt3\)

I'll leave you to turn this into a decimal to the nearest tenth.

Can be done as follows: