Answer: The given logical equivalence is proved below.
Step-by-step explanation: We are given to use truth tables to show the following logical equivalence :
P ⇔ Q ≡ (∼P ∨ Q)∧(∼Q ∨ P)
We know that
two compound propositions are said to be logically equivalent if they have same corresponding truth values in the truth table.
The truth table is as follows :
P Q ∼P ∼Q P⇔ Q ∼P ∨ Q ∼Q ∨ P (∼P ∨ Q)∧(∼Q ∨ P)
T T F F T T T T
T F F T F F T F
F T T F F T F F
F F T T T T T T
Since the corresponding truth vales for P ⇔ Q and (∼P ∨ Q)∧(∼Q ∨ P) are same, so the given propositions are logically equivalent.
Thus, P ⇔ Q ≡ (∼P ∨ Q)∧(∼Q ∨ P).
A because u can clearly see how the line is connected and if u count to where the line is u will see that it is A
ANSWER
The solution is
(x,y)=(1,-5)
EXPLANATION
The equations are:
1st equation: 6x +5y=-19
2nd equation: 12x-8y=52
Multiply the first equation by 2:
3rd equation: 12x +10y=-38
Subtracy the 2nd equation from the 3rd equations.
12x-12x+10y--8y=-38-52
18y=-90
Divide both sides by 18.
y=-5
Put y=-5 into any of the equations and solve for x.
Preferably, the first equation will do.
6x +5(-5)=-19
6x -25=-19
6x=25-19
6x=6
x=1
The solution is
(x,y)=(1,-5)
Answer:
5.5
Step-by-step explanation:
Pemdas
A)
Increase %= (new # - old #)/old * 100
new= 8
old= 5
Increase %= (8-5)/5 * 100
=3/5 * 100
=0.60 * 100
=60% increase
B)
Decrease %= (old # - new #)/old * 100
new= 5
old= 8
Decrease %= (8-5)/8 * 100
= 3/8 * 100
= 0.375 * 100
= 37.5% decrease
ANSWER: a) 60% increase; b) 37.5% decrease
Hope this helps! :) Good luck on your test!!
