Answer:
a₁₃ = - 27x - 41
Step-by-step explanation:
The nth term of an arithmetic sequence is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 3x + 7
d = a₂ - a₁ = - 5x + 3 - (- 3x + 7)
= - 5x + 3 + 3x - 7
= - 2x - 4
Then
a₁₃ = - 3x + 7 + 12(- 2x - 4)
= - 3x + 7 - 24x - 48
= - 27x - 41
Answer:
m = 
Step-by-step explanation:
Given
y = mx + b ( subtract b from both sides )
y - b = mx ( divide both sides by x )
= m
Has to be greater than 90 degrees.
Answer:
Any one of these three works:
plane MOU
plane MNU
plane NOU
Step-by-step explanation:
A plane can be named by a single letter, such as L in this problem, or by any three non-collinear points that lie on the plane. Non-collinear points are points that do not all lie in a single line.
Points M, N, O, and U lie on plane L, so you can choose any 3 of the 4 points to name the plane with, but make sure all 3 points are non-collinear.
To name plane L with points, you cannot use points MNO together since they are collinear, but you can name it using point U plus any two of the points M, N, and O.
plane L can be named
plane MOU
plane MNU
plane NOU
Do not name it plane MNO
Angle 1 is congruent to angles 3, 5, and/or 7
Angle 2 is congruent to angles 4, 6, and/or 8
Angle 5 is congruent to angles 7, 3 and/or 1
Angle 6 is congruent to angles 8, 4, and/or 2
Any of these answers could work for the blanks.
Angles 1 and 3, 2 and 4, 5 and 7, and angles 6 and 8 are congruent because they are vertical angles. They have the same vertex. Not all of these are congruent to each other if this doesn’t make sense. It’s only 1 is congruent to 3, 2 congruent to 4, etc.
Then you have your corresponding angles. These are ones like angles 2 and 6, then 1 and 5. You can also have 8 and 4, or 7 and 3 as corresponding angles
Transversal angles are different. This would be like angles 3 and 4, or 1 and 2. They are not always congruent. The only time they will be congruent is if they are both 90°. Transversal angles are essentially supplementary angles on the transversal line (the line that intersects through the set of parallel lines)
