Answer:
P(3) is true since 2(3) - 1 = 5 < 3! = 6.
Step-by-step explanation:
Let P(n) be the proposition that 2n-1 ≤ n!. for n ≥ 3
Basis: P(3) is true since 2(3) - 1 = 5 < 3! = 6.
Inductive Step: Assume P(k) holds, i.e., 2k - 1 ≤ k! for an arbitrary integer k ≥ 3. To show that P(k + 1) holds:
2(k+1) - 1 = 2k + 2 - 1
≤ 2 + k! (by the inductive hypothesis)
= (k + 1)! Therefore,2n-1 ≤ n! holds, for every integer n ≥ 3.
Answer:
32/20
Step-by-step explanation:
32 and 20 are both divisible by 4. 4*8=32 and 4*5=20. So this one works. Another way to think about it is if you put them as fractions and reduced them down to their simplest form, they would form the fraction 8/5.Oct 17, 2019
T(14 - 5) = 14t - 5t or t(14) - t(5)
Slope of (6, 9) & (7, 1)
To find the slope, we use the equation : m = y₂-y₁ / x₂-x₁
**Remember : m = slope**
Let's say that (6, 9) is our first set of points, and (7, 1) is our second.
If those are our first and second points, then we now know this :
x₁ = 6, x₂ = 7, y₁ = 9, y₂ = 1
Now that we know that, we can simply plug those points into our slope equation.
m = y₂ - y₁ / x₂ - x₁
m = (1 - 9) / (7 - 6 )
Simplify.
m = -8 / 1
Simplify.
m = -8
So, our slope is -8.
~Hope I helped!~
Should look something like that
