Answer:
D. If John owns a dog, then he owns a cat
Step-by-step explanation:
The implication p → q (if p, then q) has the same truth table as the logical expression ~p∨q. You have the expression ...
~(John owns a dog) ∨ (he owns a cat)
Matching parts of this expression to the components of the expression ~p∨q, we see we can choose ...
- p = John owns a dog
- q = he owns a cat
and put those into the structure of the implication: if p, then q.
If John owns a dog, then he owns a cat. . . . . matches choice D
Answer:
y = 0
Step-by-step explanation:
It is always a good idea to look at the question and make some observations about it. Here, you might observe ...
- all of the bases are powers of 3: 243 = 3^5; 9 = 3^2
- y is a factor of every exponent
The latter observation is important, because it means that when y=0, every exponential expression has a value of 1. Hence y = 0 is a solution.
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To solve the equation, you can write it in terms of powers of 3.
(3^5)^(-y) = (3^-5)^(3y)·(3^2)^(-2y)
3^(-5y) = 3^(-15y)·3^(-4y)
3^(-5y) = 3^(-19y)
-5y = -19y . . . . . . . . equating exponents; equivalent to taking log base 3
14y = 0 . . . . . . . . . . add 19y
y = 0 . . . . . . . . . . . one solution
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The rules of exponents we used are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
1/a^b = a^-b
Answer:
C. b²< 40
Step-by-step explanation:
2x²+ bx + 5=0 has no real solutions
=> D< 0
b² < 4ac
b²< 4(2)(5)
b²< 40
19. 5x - 5 = 3x -9
2x = -4
x = -2
19. Answer is A
If you mean proof that the opposite sides of a parallelogram are equal, you draw a diagonal then prove that the 2 triangles formed are congruent.
