V+F-E=2
F-E=2-V
-E=2-V-F
E=-2+V+F
Answer:
26:39
Step-by-step explanation:
65=2x+3x
65=5x
x=13
26:39
check:
26+39=65
The simplest way of writing this:
<span><span><span><span>7p</span>−1</span>−<span>9p</span></span>+5</span><span>=<span><span><span><span><span><span>7p</span>+</span>−1</span>+</span>−<span>9p</span></span>+5</span></span>Combine Like Terms:<span>=<span><span><span><span>7p</span>+<span>−1</span></span>+<span>−<span>9p</span></span></span>+5</span></span><span>=<span><span>(<span><span>7p</span>+<span>−<span>9p</span></span></span>)</span>+<span>(<span><span>−1</span>+5</span>)</span></span></span><span>=<span><span>−<span>2p</span></span>+4</span></span>Answer:<span>=<span><span>−<span>2p</span></span>+<span>4</span></span></span>
For (2), start with the base case. When n = 2, we have
(n + 1)! = (2 + 1)! = 3! = 6
2ⁿ = 2² = 4
6 > 4, so the case of n = 2 is true.
Now assume the inequality holds for n = k, so that
(k + 1)! > 2ᵏ
Under this hypothesis, we want to show the inequality holds for n = k + 1. By definition of factorial, we have
((k + 1) + 1)! = (k + 2)! = (k + 2) (k + 1)!
Then by our hypothesis,
(k + 2) (k + 1)! > (k + 2) 2ᵏ = k•2ᵏ + 2ᵏ⁺¹
and k•2ᵏ ≥ 2•2² = 8, so
k•2ᵏ + 2ᵏ⁺¹ ≥ 8 + 2ᵏ⁺¹ > 2ᵏ⁺¹
which proves the claim.
Unfortunately, I can't help you with (3). Sorry!
The answer is H1 and H2 on top then T1 and T2 on the bottom.
