For this case we must add the terms of the following expression:
It is noted that the terms are similar, so we can add:
We take common factor 
We add the terms within the parenthesis:
finally we have:
Answer:
Answer:
Consider the proposition C=(p∧q∧¬r)∨(p∧¬q∧r)∨(¬p∧q∧r)
Step-by-step explanation:
This compound proposition C uses the outer disjunction (∨) then the proposition is true if and only if one of the three propositions (p∧q∧¬r),(p∧¬q∧r),(¬p∧q∧r) is true.
First, it is impossible that two or three of these propositions are simultaneously true. For example, if (p∧q∧¬r) and (p∧¬q∧r) are both true, then ¬r is true (from the first conjuntion) and r is true (from the second one), a contradiction. All the other possibilities can be discarded reasoning in the same way.
Since these propositions are mutually excluyent, C is true if and only if exactly one of the three propositions is true (and false otherwise). This can only happen if exactly two of p,q, and r are true and the other one is false. For example, (p∧q∧¬r) is true when p and q are true, and r is false.
Answer:
3) x = 15; 95 and 85 4) x = 12; 98 for both angles
Step-by-step explanation:
2x + 65 + 3x + 40 = 180 Set the equations equal to 180
5x + 105 = 180 Combine like terms
- 105 - 105 Subtract 105 from both sides
5x = 75 Divide both sides by 5
x = 15
Plug 15 into both equations
2(15) + 65 = 95
3(15) + 40 = 85
4) 5x + 38 = 9x - 10 Set the equations equal to each other
- 5x - 5x Subtract 5x from both sides
38 = 4x - 10
+ 10 + 10 Add 10 to both sides
48 = 4x Divide both sides by 4
12 = x
Plug 12 into both equations
5(12) + 38 = 98
9(12) - 10 = 98
Answer: OPTION C.
Step-by-step explanation:
Direct variation, by definition, has the form shown below:
y=kx
Where k is the constant of proportionality.
Then if you solve fo y from the given equation, you obtain the following form:
Therefore y varies directly with x².
