Answer: number 4 the last option
Step-by-step explanation: too lazy to write it out.... 0-0
It will take him 3 hours driving at 65 miles an hour
Answer:
These have no solution:
- 2x < x+1 and x+1 > 3
- 3x -5 > 1 and x < 2
Step-by-step explanation:
1. 2x < x+1
x < 1 . . . . . subtract x
__
x + 1 > 3
x > 2 . . . . subtract x
No solution: x cannot be both > 2 and < 1.
_____
2. 3(x +2) > x
3x + 6 > x . . . . eliminate parentheses
2x + 6 > 0 . . . subtract x
x + 3 > 0 . . . . . divide by 2
x > 0
Solution: 0 < x < 2
_____
3. 5x ≥ 10
x ≥ 2 . . . . . divide by 5
__
2x ≤ 4
x ≤ 2 . . . . . divide by 2
Solution: 2 ≤ x ≤ 2 . . . . x = 2
_____
4. 3x -5 > 1
3x > 6 . . . . . . . add 5
x > 2 . . . . . . . . divide by 3
No solution: x cannot be both < 2 and > 2.
Remember the basic trig identity
<u />
We can move the cosine term to the right side to get
We can then replace
in the original equation and basically factor the resulting equation like a quadratic:
Then, we can see that
either equals
or
. But since the range of cosine is only from
, cosine can't equal
at all! So, you just have to solve for x when
, which is when
(The last part of the solution says that k can be any integer.)
If you only want solutions in the range
, then your answer is just