<h3>
Answer: 14s^4 - 7s^2 + 15</h3>
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Work Shown:
(12s^4-6s^2+4s)+(6s^4-4s+27)-(4s^4+s^2+12)
12s^4-6s^2+4s+6s^4-4s+27-4s^4-s^2-12
(12s^4+6s^4-4s^4)+(-6s^2-s^2)+(4s-4s)+(27-12)
14s^4-7s^2+0s+15
14s^4-7s^2+15
Note: don't forget to distribute the negative to every term in the last parenthesis
<h3>Answer:</h3>
C. The playable area has a width of 9 inches and a height of 6 inches.
<h3>Explanation:</h3>
There are a number of ways you can get there.
1. Check the answers to see which have the right area and aspect ratio.
- A: area = 24 in² — does not match 54 in²
- B: area = 54 in², aspect ratio 6:9 = 2:3 — does not match 3:2 aspect ratio
- C: area = 54 in², aspect ratio 9:6 = 3:2 — <em>matches problem statement</em>
- D: area = 121.5 in² — does not match 54 in²
2. If the screen were 3:2 (inches), its area would be 6 in². The area of 54 in² is 9 times that value, so the actual screen dimensions are √9 = 3 times 3:2. That is, they are width:height = 9:6 inches — matches selection C.
3. You can write equations for width and height and solve.
Substituting w=3/2·h into the second equation gives
... (3/2)h·h = 54
... h² = 36 . . . . . multiply by 2/3
... h = √36 = 6 . . . . square root, result in inches . . . . matches selection C
