Angles 1 and 4 are alternate angles and thus have the same measurement. You will set their equations equal to each other and solve for the variable.
6n + 1 = 4n + 19
Subtract 1 and 4n from both sides to get variables on one side and constants on the other.
6n - 4n = 19 - 1
Combine like terms and solve for n.
2n = 18
n = 18 / 2
n = 9
Angles 1 and 2 are congruent as labeled in the graph.
So angle 2 is also 6n + 1
Plug in for 9 for n
6(9) + 1
54 + 1
55
Option C is your answer.
the point, M, that divides segment AB into a ratio of 3:1
A is at (-4, -2) and B is at (4, -10).
Apply section formula
Here m,n is the ratio
m =3, n= 1
A is (-4,-2) that is (x1,y1)
B is at (4, -10) that is (x2,y2)
plug in all the values in the formula
(2, -8)
Point M is (2,-9)
Answer:
B' = 105°
C = 27°
A = 48°
Step-by-step explanation:
Given
B = 105°
C = (2x - 3)°
C' = (5x - 48)°
Rotation = 90°
Before solving the requirements of this question, it should be noted that rotation do not change the angle of shapes.
i.e. an angle retain its measurements pre and after rotation.
Solving (a): The measurement of B'
Using the analysis above.
B' = B
Recall that
B = 105°
So:
B' = 105°
Solving (b): A and C
First, I'll solve for C.
Using the same analysis above.
C = C'
Substitute values for C and C'
5x - 48 = 2x - 3
Collect like terms
5x - 2x = 48 - 3
3x = 45
Multiply both sides by ⅓
⅓*3x = ⅓*45
x = 15
Substitute 15 for x in
C = (2x - 3)°
C = 2 * 15 - 3
C = 30 - 3
C = 27°
Solving for A
The sum of angles (A, B and C) is represented as:
A + B + C = 180
Substitute values for B and C
A + 105° + 27° = 180°
A + 132° = 180°
Collect like terms
A = 180° - 132°
A = 48°
Take 3 out of both of them
3(5x+2)
The solution to your problem about the probability <span>of getting first a red and then a black marble is as follows:
</span><span>(3 red / 8 total) * (2 black / 7 total) = 3/28
</span>
Therefore, the probability of getting first a red and then a black marble is 3/28.
:)