Answer:
are corresponding angles and are congruent to each other.
are alternate exterior angles and thus congruent to each other.
are interior angles on the same side, and they are supplementary(sum=180°).
Step-by-step explanation:
Given:
Line 
Line 
is traversal.
By angle properties we can name the angle relationship of given angle pairs.
are corresponding angles and are congruent to each other.
are alternate exterior angles and thus congruent to each other.
are interior angles on the same side, and thus they are supplementary.
Answer: Answer is D, if I'm not mistaking
Step-by-step explanation:
sorry if im wrong.
For this case we have the following system of equations:
We solve by the substitution method:
We substitute the first equation in the second equation:
We apply distributive property considering that 
We subtract 69 from both sides of the equation:
We divide by 8 on both sides of the equation:
We look for the value of the variable y:
Thus, the solution of the system is 
Answer:
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.
Answer:
- 5, 2, 9, 16 and d = + 7
Step-by-step explanation:
to obtain the first four terms substitute n = 2, 3, 4 into the recursive formula
f(1) = - 5 ← given
f(2) = f(1) + 7 = - 5 + 7 = 2
f(3) = f(2) + 7 = 2 + 7 = 9
f(4) = f(3) + 7 = 9 + 7 = 16
common difference d = 16 - 9 = 9 - 2 = 2 - (- 5) = 7
