Answer:
x <7
Step-by-step explanation:
3x – 4 < 17
Add 4 to each side
3x – 4+4 < 17+4
3x < 21
Divide each side by 3
3x/3 < 21/3
x <7
<span>In order to prove this for all integers n ≥ 0, we first prove the basis step P(0) and then prove the
inductive step, that P(k) implies P(k + 1).
1. BASIS STEP: Now in P(0), the left-hand side has just one term, namely 2, and the right-hand side is
1â’(â’7)1
4 =
8
4 = 2. Since 2 = 2, we have verified that P(0) is true.
2. INDUCTIVE STEP: For the inductive step, we assume that P(k) is true and and derive from it the truth of P(k + 1), which is the equation
2 â’ 2 · 7 + 2 · 72 ⒠· · · + 2(â’7)k + 2(â’7)k+1 =1 â’ (â’7)(k+1)+1/4
To prove an equation like this, it is usually best to start with the more complicated side and manipulate
it until we arrive at the other side. In this case we start on the left. Note that all but the last term
constitute precisely the left-hand side of P(k), and therefore by the inductive hypothesis, we can replace
it by the right-hand side of P(k). The rest is algebra:
2 â’ 2 · 7 + 2 · 72 ⒠· · · + 2(â’7)k + 2(â’7)k+1 =1 â’ (â’7)k+1/4+ 2(â’7)k+1
=1 â’(â’7)k+1 + 8(â’7)k+1/4
=1 + 7(â’7)k+1/4
=1 â’ (â’7) · (â’7)k+1/4
=1 â’ (â’7)(k+1)+1/4</span>
Answer:
20%
Step-by-step explanation:
4/5=.80
1-.80=.20
.20=20%
Answer:
x= 1/4, 4
Step-by-step explanation: