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
Answer:
a) 9r=63
b) 14 mi/h
Step-by-step explanation:
Let say r the speed of the slower cyclist,
2*r the speed of the faster cyclist,
they meet 3 hours later:
a)
<u> (r+2*r)*3=63 </u>
3r*3=63
9r=63
r= 63/9
r=7 (mi/h)
b)
<u>2r=14 (mi/h)</u>
Answer:
A’(-1,1), B’(-1,-2), C’(3,-2), D’(3,2)
Step-by-step explanation:
The problem is just (x+5,y-4)
A. It is a right triangle.
A^2 + B^2 = C^2
3^2 + 4^2 = C^2
9 + 16 = C^2
25 = C^2
Square Root
5 = C
Confirmed Right Triangle.