Answer:
0.57, which is a number between 0 and 1
Step-by-step explanation:
The fraction 4/7 is approximately equal to 0.57 as a decimal, so you would plot 4/7 where 0.57 should go
Answer:
48 cubic feet
Step-by-step explanation:
V=lwh
V=6*4*2
V=48
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
Solve the top equation for x and then substitute that into the bottom equation and solve for y:
Top equation: subtract 4 from both sides to get x = y - 4
Substitution and simplify:
y = 4(y - 4) - 10
y = 4y - 16 - 10
y = 4y - 26
-3y = -26
y = 26/3 or 8 1/3 or 8.333 (those are all the same but in different forms)
If you look carefully at the graph, you may see that the slope of the line is
3-4 -1
---------------- = ------ = m
7-4 3
thus, you have the slope of the line and two points on the line. Suppose we
choose the point (4,4) and subst. the known slope and the coordinates of this point into the point-slope formula for the eqn of a str line:
y-y1 = m (x-x1)
y-4 = (-1/3)(x-4)
This is the desired equation. You could, if you wished, change this into slope-intercept form.
