Answer:
1. a. Q° = 95°
b. a = 20.3; b = 19.3
2. p = 36; q = 14.4
Step-by-step explanation:
Question 1:
Recall: The Exterior Angle Theorem of a Triangle states that the size of the exterior angle of a triangle equals the sum of the two sizes of the two opposite angles of the triangle.
a. Based on the theorem,
Q° = 41° + 54° = 95°
b.
✔️122° = 4a + 2a (exterior angle theorem)
122 = 6a
Divide both sides by 6
122/6 = a
a = 20.3
✔️122° + 3b = 180° (angles on a straight line)
3b = 180 - 122
3b = 58
b = 58/3
b = 19.3
Question 2:
Recall: Opposite angles of a parallelogram are equal while adjacent/consecutive angles are supplementary.
✔️2p + 3p = 180° (adjacent angles)
5p = 180
p = 180/5
p = 36
✔️2p = 5q (opposite angles)
Plug in the value of p
2(36) = 5q
72 = 5q
72/5 = q
q = 14.4
Answer:
48
Step-by-step explanation:
I know I'm super late, so so sorry but for another in the future, it's 48
The third answer because if you use the FOIL method or the box method to multiply binomials
Answer:
e^4 d^2
-------------------------
b^3
Step-by-step explanation:
b^-3 c^0 d^2
-------------------------
e^-4
Negative exponents flip positions
e^4 c^0 d^2
-------------------------
b^3
c to the zero power is 1
e^4 d^2
-------------------------
b^3
Answer:
362880 ways
Step-by-step explanation:
Given
10 digits
Required
Number of 10 digits that can be formed if no repetition and 2 must always start;
Since digit 2 must always start and no repetition is allowed, then there are 9 digits left
Digit 2 can only take 1 position
9 digits can be arranged without repetition in 9! ways;
Calculating 9!
![9! = 9 * 8 *7 * 6 * 5 * 4 * 3 * 2 * 1](https://tex.z-dn.net/?f=9%21%20%3D%209%20%2A%208%20%2A7%20%2A%206%20%2A%205%20%2A%204%20%2A%203%20%2A%202%20%2A%201)
![9! = 362880](https://tex.z-dn.net/?f=9%21%20%3D%20362880)
Number of arrangement = 1 * 362880
Number of arrangement = 362880 ways