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:
10000
Step-by-step explanation:
F(x)=-2e^x
x=3
f(3)=-2e^3
pemdas so exponents first
e^3
e=2.718281828454590
cube that
20.0855
now we have
-2 times 20.0855=-40.1711
answer should be -40.1711
(I see what you did wrong, if -6=-2 times e^3, divide -2, 3=e^3, maybe you just put -2 times 3 by mistake)
All of the centra angles in a regular polygon must add up to 360 degrees. Also, because you're told that it is a regular polygon, the "regular" indicates that all of the central angles will be the same. Divide 360 degrees by 18 degrees to get the number of central angles, which is the same as the number of sides. 360/18 = 20. Therefore, the polygon has 20 sides. Hope that helps!
Answer:
The slope of the line must be 3
Step-by-step explanation:
<u><em>The picture of the question in the attached figure</em></u>
step 1
we know that
The volume of a rectangular prism is equal to
----> equation A
where
B is the area of the base of the prism
h is the height of the rectangular prism
step 2
The volume of a square pyramid is equal to
-----> equation B
where
B is the area of the square base of pyramid
h is the height of the pyramid
step 3
substitute equation A in equation B
Find the relationship between the volume of a rectangular prism and the volume of a square pyramid
therefore
The slope of the line must be 3
let's check it
To solve for the slope of the line, you must choose two coordinates first and use the formula
Choosing the points (2,6) and (3,9)
substitute
----> is correct
