Let s represent the measure of the second angle.
The measure of the first angle is 15° less than the second, so we can represent the first angle by (s-15).
The measure of the third angle is 45° more than half the second, so we can represent the third angle by (45+(s/2)).
The sum of these angles is 180°, so we can represent the sum as
... (s-15) + s + (45+s/2) = 180
Collecting terms, we have
... 2.5s +30 = 180
... 2.5s = 150 . . . . . . subtract 30
... s = 150/2.5 = 60 . . . . divide by the coefficient of s
The first angle is 60-15 = 45.
The second angle is 60.
The third angle is 45+60/2 = 75.
_____
<u>Check</u>
The sum of the three angles is 45 +60 +75 = 180.
Answer:
true
since: a = 1, or >1 and <10
5x/2 = 10/11
55x = 20
x = 4/11
**Not sure if I did this right I think I did
<span>a.{x | x is a real number such that x^2 = 1}
x^2 = 1 => x = +/- 1
=> {-1, 1} <------ answer
b.{x | x is a positive integer less than 12}
1 ≤ x < 12 => {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} <------ answer
c.{x | x is the square of an integer and x < 100}
x = n^2 < 100 => n^2 - 100 < 0
=> (n - 10) (n + 10) < 0
=> a) n - 10 > 0 and n + 10 < 0 => n > 10 and n < - 10 which is not possible
b) n - 10 < 0 and n + 10 > 0 => n < 10 and n > - 10 => - 10 < n < 10
=> n = { - 9, - 8, - 7, - 6, - 5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
=> x = {0, 1, 4, 9, 16, 25, 36, 49, 64, 81} <---- answer
d.{x | x is an integer such that x^2 = 2}
</span>
x = {∅ } because x is √2 which is not an interger but an irrational number
=> Answer: { ∅ }
