Answer:
The measure of angle KLM is 62°
Step-by-step explanation:
* Lets revise the properties of the rhombus
- The rhombus has 4 equal sides in length
- Every two opposite angles are equal in measure
- The two diagonals bisect each other
- The two diagonals perpendicular to each other
- The two diagonals bisect the vertices angles
* Lets solve the problem
∵ JKLM is a rhombus
∴ m∠MJK = m∠KLM ⇒ opposite angles in the rhombus
∵ JL and KM are diagonals in the rhombus and intersect each
other at N
∴ JL bisects ∠MJK
∴ m∠KJL = m∠MJN
∵ m∠KJL = (2x + 5)°
∵ m∠MJN = (3x - 8)°
∴ 2x + 5 = 3x - 8 ⇒ subtract 2x from both sides
∴ 5 = x - 8 ⇒ add 8 to both sides
∴ 13 = x
∴ The value of x = 13
∵ m∠KJL = (2x + 5)° ⇒ substitute the value of x
∴ m∠KJL = 2(13) + 5 = 26 + 5 = 31°
∵ m∠KJL = 1/2 m∠MJK
∴ m∠MJK = 2 m∠KJL
∴ m∠ MJK = 2 × 31° = 62°
∵ m∠MJK = m∠KLM ⇒ opposite angles in the rhombus
∴ m∠KLM = 62°
Answer:
4 feet and 2 inches
Step-by-step explanation:
5 feet and 6 inces= 66 inches
66-16=50
50= 4 feet and 2 inches
Answer:
D
Step-by-step explanation:
We need the formula for arc length (in radians) to solve this problem. The formula is:
Where
s is the arc length
r is the radius of the circle
is the intercepted angle
In this diagram, we can see that is beign intercepted by the big arc with measure 20 cm. So arc length, s, is 20
Also, if we look, we see that the radius is 5 cm, so r = 5
Now, we substitute into formula and find :
This is given in radians, so is 4 radians
D is the correct answer choice.
Answer: 34.965%
Step-by-step explanation:
Number of ways of selecting 8 songs from 14 songs = = 14! / [ 8! × (14-8)! ]
= 14! / (8! × 6!)
= 3003
If you listended to exactly four country songs, then you should listen to four pop songs because you listened to 8 songs
Number of ways of selecting 4 country songs from total 8 country songs
= 8! / [ 4! × (8-4)! ]
= 8! / (4! × 4!)
= 70
Number of ways of selecting 4 pop songs from total 6 pop songs
= 6! / [ 4! × (6-4)! ]
= 6! / (4! × 2!)
= 15
Number of ways of playing 4 country songs and 4 pop songs in total 8 songs = 70 × 15
= 1050
So Probability that you listened to exactly four country songs =1050/3003
= 0.34965
= 34.965%
Answer:
Step-by-step explanation:
Thanks