<span>52.14 dollars per week.
</span>
Answer:
To find the perimeter of this triangle, we add up all the sides together.
(8 · √3) + (8 · √3) + √384
But before we add them, let's simplify them.
(8 · 1.7) + (8 · 1.7) + 19.6
13.6 + 13.6 + 19.6
27.2 + 19.6
= <u>46.8</u>, is the perimeter of this triangle.
Now to find the area, we use the formula:
(formula for area of a triangle)
A = BH · 1/2
Where 'B' represents the base, 'H' stands for the height, and 1/2 means that you divide the product of the base and height by 2.
<u><em>What we know:</em></u>
- Base = 8 · √3 which equals <u>13.6</u>.
- Height = 8 · √3 which equals <u>13.6</u>.
Plug in the values into our formula:-
A = BH · 1/2
A = 13.6(13.6) · 1/2
A = 184.96 · 1/2
A = 184.96/2
A = <u>92.48</u>, is the area for this triangle.
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
Subtract the powers
c. 9-7 so 10^2
d. 8-1 so 5^7
