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Answer:
3 3/4 tablespoons of coffee to make 10 cups of coffee
3 3/4 =15/4
10 cups require 15/4 tablespoon of coffee
1 cup require how much
15/4 divide by 10
15/4 ÷ 10
=15/4 * 1/10
=15/40
=3/8 tablespoon of coffee for 1 cup of coffee
The easiest way to prove equivalence is to draw out a truth table and then compare the values. I'm going to show a truth table using proposition logic, it's the same result as using predicate logic.
P(x) v Q(x)
P |Q || PvQ || ~Q->P <----Notice how this column matches the PvQ but if you were to
---|---||--------||---------- <----continue the truth table with ~P->Q it would not be equivalent
T T T T
T F T T
F T T T
F F F F
Let me know if you would like an example, if the truth table doesn't help.
Answer:
y= -x+7, b= sqrt(2P/a), c=3P^2-b
Step-by-step explanation:
First, make a table regarding both of the equations. You will eventually find out that both lines intersect at the point (2, 5) after you find the points on the table. From there, subtract x from both sides in the equation x + y = 2. You will get y = -x + 2. Since they said the line was parallel, find a line that has the slope of negative one. Since we know that this line intersects the point in which the first two lines intersect, we know that the y-intercept will be 7. The equation of the line would be y=-x+7.
Multiply both sides by 2. Then, divide both sides by a to get b^2=(2P/a). Take the square root to get the value of b, which is sqrt(2P/a).
Square both sides of the equation to get P^2=(b+c)/3. Cross multiply to get 3P^2=b+c. Subtract b from both sides to get c=3P^2-b.
