Answer:
![p=117](https://tex.z-dn.net/?f=p%3D117)
Step-by-step explanation:
Given number is
.
Two-third of the number = ![\frac{2}{3}p](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7Dp)
One-third of the number = ![\frac{p}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bp%7D%7B3%7D)
The sum of a certain quantity
together with two-third of that number, and one-third of that number, becomes 234.
![p+\frac{2}{3}p+\frac{p}{3}=234\\\\\frac{3p+2p+p}{3}=234\\\\\frac{6p}{3} =234\\\\2p=234\\p=117](https://tex.z-dn.net/?f=p%2B%5Cfrac%7B2%7D%7B3%7Dp%2B%5Cfrac%7Bp%7D%7B3%7D%3D234%5C%5C%5C%5C%5Cfrac%7B3p%2B2p%2Bp%7D%7B3%7D%3D234%5C%5C%5C%5C%5Cfrac%7B6p%7D%7B3%7D%20%3D234%5C%5C%5C%5C2p%3D234%5C%5Cp%3D117)
Quadratics have 2 solutions
Factor the Quadratic
x^2 +3x -4 = 0
(x-1) (x+4) = 0
set each term = 0
x-1=0 x+4 = 0
solve
x=1 x=-4
The solutions are 1, -4
Answer:
The proof is shown in the explanation below.
Step-by-step explanation:
Analysis:
The proof by induction focuses on n. In this case, let n = 1, and
will be a linear operator since
The exercise will show that
is a linear operator on V and that
is also a linear operator on V. This, follows that:
![L^{n+1} (av) = L(L^{m}(v_{1}+v_{2})\\ = L(L^{m} (v_{1} + L^{m}v_{2})\\ = L(L^{m}v_{1} + L(L^{m}v_{2})\\ = L^{m+1}(v_{1}) + L^{m+1}(v_{2})](https://tex.z-dn.net/?f=L%5E%7Bn%2B1%7D%20%28av%29%20%3D%20L%28L%5E%7Bm%7D%28v_%7B1%7D%2Bv_%7B2%7D%29%5C%5C%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%3D%20L%28L%5E%7Bm%7D%20%28v_%7B1%7D%20%2B%20L%5E%7Bm%7Dv_%7B2%7D%29%5C%5C%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%3D%20L%28L%5E%7Bm%7Dv_%7B1%7D%20%2B%20L%28L%5E%7Bm%7Dv_%7B2%7D%29%5C%5C%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%3D%20L%5E%7Bm%2B1%7D%28v_%7B1%7D%29%20%2B%20L%5E%7Bm%2B1%7D%28v_%7B2%7D%29)
Answer: Do you know the values of u and v?
Step-by-step explanation: