E. 3/12 is equivalent to 1/4, which is the ratio of the cylinders.
rearrange into the form y = mx + b
subtract 6x from both sides of the equation
7y = - 6x + 14
divide all terms by 7
y = - 
x + 2 → in slope- intercept form
Answer:
(a) ¬(p→¬q)
(b) ¬p→q
(c) ¬((p→q)→¬(q→p))
Step-by-step explanation
taking into account the truth table for the conditional connective:
<u>p | q | p→q </u>
T | T | T
T | F | F
F | T | T
F | F | T
(a) and (b) can be seen from truth tables:
for (a) <u>p∧q</u>:
<u>p | q | ¬q | p→¬q | ¬(p→¬q) | p∧q</u>
T | T | F | F | T | T
T | F | T | T | F | F
F | T | F | T | F | F
F | F | T | T | F | F
As they have the same truth table, they are equivalent.
In a similar manner, for (b) p∨q:
<u>p | q | ¬p | ¬p→q | p∨q</u>
T | T | F | T | T
T | F | F | T | T
F | T | T | T | T
F | F | T | F | F
again, the truth tables are the same.
For (c)p↔q, we have to remember that p ↔ q can be written as (p→q)∧(q→p). By replacing p with (p→q) and q with (q→p) in the answer for part (a) we can change the ∧ connector to an equivalent using ¬ and →. Doing this we get ¬((p→q)→¬(q→p))
Answer:
6 pk noisemakers (6 x 5 = 30 noisemakers)
1 pk balloons (1 x 30 = 30 balloons)
Step-by-step explanation:
divide 30 by 5, = 6
buy 6 packs noisemakers and one pack of balloons
Answer:
Standard form: 
Center: 
Radius: 
Step-by-step explanation:
The equation of a circle in the standard form is
Where the point (h, k) is the center of the circle
To transform this equation 
this equation in the standard form we use the method of square.
First, we group similar variables
Divide both sides of equality by 4
Now we complete square for variable x.
Take the coefficient "b" that accompanies the variable x and divide by 2. Then, elevate the result to the square:
Now add 
on both sides of the equality
Factor the expression and simplify the independent terms
Then
and the center is
radius
