Will someone please help me with this because I don't understand and I don't want to fail my class.
1 answer:
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You're looking for the volume of the prism. The dead giveaway there is that you're looking for "cubic" measurement. Cubic measures are indicators that the volume is being determined, just like "square feet" or inches, etc indicates area is being determined. The volume for this prism is found by multiplying the length times the width times the height. In decimal form, 45×30×40=54,000. But that is in cubic inches and we want cubic feet. So we will use dimensional analysis to convert that. Setting up the DA looks like this, keeping in mind that there are 12 cubic inches in 1 cubic foot: 
. The label of cubic inches cancels out leaving us with cubic feet, and doing the division there gives us 54,000/(12*12*12) which is 31.25 cubic feet.
Answer:
C
Step-by-step explanation:
Calculate AC using Pythagoras' identity in ΔABC
AC² = 20² - 12² = 400 - 144 = 256, hence
AC = = 16
Now find AD² from ΔACD and ΔABD
ΔACD → AD² = 16² - (20 - x)² = 256 - 400 + 40x - x²
ΔABD → AD² = 12² - x² = 144 - x²
Equate both equations for AD², hence
256 - 400 + 40x - x² = 144 - x²
-144 + 40x - x² = 144 - x² ( add x² to both sides )
- 144 + 40x = 144 ( add 144 to both sides )
40x = 288 ( divide both sides by 40 )
x = 7.2 → C