A -gallon [gal] quantity of molten (liquefied) plastic is going to be used to make a 1-foot [ft] by 8-inch [in] plastic block. If liters [L] of the plastic is lost in the manufacturing process, how thick is the final plastic block, in units of inches [in]?

x  = 1,77 in

Step-by-step explanation:

Total volume of molten plastic to make  a block is

1 [gal] - 1 L (lost in the process)  =  3,7854 - 1  =  2,7854

Now the volume of the block is:

1 foot  * 8 inches * x ( thick of the block )

1 foot is 0,3048 meter  and 1 inch is 0,0254 meter

Then  in m³  the volume of the block is

0,3048 * 8 * 0,0254 * x  =  0,06193536 * x  [ m³ ]

That volume should be equal to  2,7854 / 1000

Therefore

 0,06193536 * x  = 2,7854 / 1000        x in m³

x = 2,7854 /61,93536  m

x  =  0,044972  m      and    1 m  =  39,37 in

x  = 1,77 in

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3