Answer:
-5
Step-by-step explanation:
<u>Given that , </u>
- A number is taken away from 40 and the result is 45 .
<u>L</u><u>et </u><u>:</u><u>-</u><u> </u>
- The required number be x .
<u>According</u><u> to</u><u> Question</u><u> </u><u>:</u><u>-</u><u> </u>
40 - x = 45
- x = 45 - 40
- x = 5
x = -5
<h3>
Hence the required answer is -5 .</h3>
1st equation x - 7 < 14:
x < 14 + 7 (add 7 to both sides)
x < 21 (add 14 + 7 so it can equal 21)
2nd equation x + 13 > 21:
x > 21 - 13 (subtract 13 from both sides)
x > 8 (subtract 21 - 13 so it can equal 8)
The reduction was 1/5.
Because you are given the reduced values, multiply the reduced value by the inverrse of the factor:
Inverse of 1/5 = 5
Height = 3 x5 = 15
Base = 5 x 5 = 25
The base is 25
You can try to show this by induction:
• According to the given closed form, we have
, which agrees with the initial value <em>S</em>₁ = 1.
• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. In particular, we assume

and

We want to then use this assumption to show the closed form is correct for <em>n</em> = <em>k</em> + 1, or

From the given recurrence, we know

so that






which is what we needed. QED