I believe that the correct answer C.
Answer:
(–5, 12) is the correct answer.
Step-by-step explanation:
We are given the following values:
Now, we know the following identities:
Now, the values are:
Sine value is positive and cos, tan values are negative.
It can be clearly observed that 
is in 2nd quadrant.
2nd quadrant means, the value of 
will be negative and 
will be positive.
Let us have a look at the value of 
:
Please refer to the attached image for clear understanding and detailed explanation.
Hence, the correct answer is coordinate (x,y) is (–5, 12)
If you zoomed in i could've helped more. Bummer...
I don't know what the "six-step method" is supposed to be, so I'll just demonstrate the typical method for this problem.
Let <em>x</em> be the amount (in gal) of the 50% antifreeze solution that is required. The new solution will then have a total volume of (<em>x</em> + 60) gal.
Each gal of the 50% solution used contributes 0.5 gal of antifreeze. Similarly, each gal of the 30% solution contributes 0.3 gal of antifreeze. So the new solution will contain (0.5 <em>x</em> + 0.3 * 60) gal = (0.5 <em>x</em> + 18) gal of antifreeze.
We want the concentration of antifreeze to be 40% in the new solution, so we need to have
(0.5 <em>x</em> + 18) / (<em>x</em> + 60) = 0.4
Solve for <em>x</em> :
0.5 <em>x</em> + 18 = 0.4 (<em>x</em> + 60)
0.5 <em>x</em> + 18 = 0.4 <em>x</em> + 24
0.5 <em>x</em> - 0.4 <em>x</em> = 24 - 18
0.1 <em>x</em> = 6
<em>x</em> = 6/0.1 = 60 gal
