9514 1404 393
Answer:
12. x = 5
13. -8, 0
14. 6
Step-by-step explanation:
12. The area of a square with side length s is ...
A = s²
The problem statement tells us the relationship between the areas is ...
(x cm)² = (1/9)(15 cm)²
Taking the square root, we have ...
x cm = (1/3)(15 cm)
x cm = 5 cm . . . . . . . simplify
x = 5
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13. The rule is ...
a[n] = (a[n-1] +8)/2 = (1/2)a[n-1] +4
For a[1] = -24, a[2] = (1/2)(-24) +4 = -8
For a[2] = -8, a[3] = (1/2)(-8) +4 = 0
The next two terms are -8 and 0.
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14. The rule is ...
a[n] = (a[n-1] -1)×5
Solving for the previous term, we find ...
a[n] = 5·a[n-1] -5 . . . . . eliminate parentheses
a[n] +5 = 5·a[n -1] . . . . add 5
a[n-1] = (a[n] +5)/5 . . . . divide by 5
For a[3] = 120, a[2] = (120 +5)/5 = 25
For a[2] = 25, a[1] = (25 +5)/5 = 6
The first term of the sequence is 6.
