Answer:
80° , 100°, 80°
Step-by-step explanation:
∠ 1 and ∠ 2 form a straight line and sum to 180° , then
2x + 40 + 2y + 40 = 180
2x + 2y + 80 = 180 ( subtract 80 from both sides )
2x + 2y = 100 → (1)
∠ 1 and ∠ 3 are vertical angles and are congruent , then
2x + 40 = x + 2y ( subtract x from both sides )
x + 40 = 2y ( subtract 40 from both sides )
x = 2y - 40 → (2)
Substitute x = 2y - 40 into (1)
2(2y - 40) + 2y = 100
4y - 80 + 2y = 100
6y - 80 = 100 ( add 80 to both sides )
6y = 180 ( divide both sides by 6 )
y = 30
Substitute y = 30 into (2)
x = 2(30) - 40 = 60 - 40 = 20
Thus x = 20 and y = 30
Then
∠ 1 = 2x + 40 = 2(20) + 40 = 40 + 40 = 80°
∠ 2 = 2y + 40 = 2(30) + 40 = 60 + 40 = 100°
∠3 = x + 2y = 20 + 2(30) = 20 + 60 = 80°
Answer:
Say your not home!
Step-by-step explanation:
Say your not home,the set a date when yall can meet again!
The least amount an artist could show is 2 (since they have to show more than 1)
30 / 2 = 15
15 artists could be featured
Answer:
5x + 2
Step-by-step explanation:
Since logarithm has the following property:
If
and
,
Then
and 
Therefore,

Answer:
The least possible number of coins the Pirate has = 81
Step-by-step explanation:
Given:
Pirate Jack has equal number of gold and silver coins.
When the pirate splits the coins into 7 equal piles he has 4 coins left.
When the pirate splits the coins into 11 equal piles he has 4 coins left.
Every pile has at least 1 coin.
To find the least possible number of coins Pirate Jack has.
Solution:
In order to find the least possible number of coins pirate Jack has, we must find the least common multiple of the number of piles the coins are split into.
So, the least common multiple of 7 and 11 can be found by listing the multiples.


So, we find the least common multiple of 7 and 11 is 77.
Number of coins left = 4
Total number of coins the pirate must have = 
We can check the answer by dividing 81 by 7 and 11. I both cases we get remainder = 4.
So, the least possible number of coins the pirate has = 81