Answer:
5a + 9 + 2b
Step-by-step explanation:
(3a + 2a) + (4 + 5) + (b + b)
5a + 9 + 2b
If
is true, then
is false, which in turn means
is true.
If
is false, then
is true, and so
is false.
So, because
in both cases, the statement is a tautology (always true).
If you were to put this in a table, you would have one column each for
. In the first column (
) you can think of
as an independent variable that can only take two values, true and false. In the next column (
), you would negate the value in the previous column. And so on.
It should roughly look like this:
p ... ~p ... ~(~p)
T ... F ... T
F ... T ... F
You can divide the figure as follows:
- A vertical rectangle, 5 meters tall and 2 meters wide, on the top right.
- A horizontal rectangle, 2 meters tall and 5 meters wide, on the bottom left
- A 2x2 meters square on the bottom right, where the two rectangles meet.
The area of the rectangles is 5x2=10 meters squared, while the area of the square is 2x2=4 meters squared.
So, the total area is 10+4=14 meters squared.
Answer:
C
Step-by-step explanation:
In general for arithmetic sequences, recursive formulas are of the form
aₙ = aₙ₋₁ + d,
and the explicit formula (like tₙ in your problem), are of the form
aₙ = a₁ + (n - 1)d,
where d is the common difference. So converting between the two of these isn't so bad. In this case, your problem wants you to have an idea of what t₁ is (well, every answer says it's -5, so there you are) and what tₙ₊₁ is. Using the formulas above and your given tₙ = -5 + (n - 1)78, we can see that the common difference is 78, so no matter what we get ourselves into, the constant being added on at the end should be 78. That automatically throws out answer choice D.
But to narrow it down between the rest of them, you want to use the general form for the recursive formula and substitute (n + 1) for every instance of n. This will let you find tₙ₊₁ to match the requirements of your answer choices. So
tₙ₊₁ = t₍ₙ₊₁₎₋₁ + d ... Simplify the subscript
tₙ₊₁ = tₙ + d
Therefore, your formula for tₙ₊₁ = tₙ + 78, which is answer choice C.
