Answer:
The solution of |3x-9|≤15 is [-2;8] and the solution |2x-3|≥5 of is (-∞,2] ∪ [8,∞)
Step-by-step explanation:
When solving absolute value inequalities, there are two cases to consider.
Case 1: The expression within the absolute value symbols is positive.
Case 2: The expression within the absolute value symbols is negative.
The solution is the intersection of the solutions of these two cases.
In other words, for any real numbers a and b,
- if |a|> b then a>b or a<-b
- if |a|< b then a<b or a>-b
So, being |3x-9|≤15
Solving: 3x-9 ≤ 15
3x ≤15 + 9
3x ≤24
x ≤24÷3
x≤8
or 3x-9 ≥ -15
3x ≥-15 +9
3x ≥-6
x ≥ (-6)÷3
x ≥ -2
The solution is made up of all the intervals that make the inequality true. Expressing the solution as an interval: [-2;8]
So, being |2x-3|≥5
Solving: 2x-3 ≥ 5
2x ≥ 5 + 3
2x ≥8
x ≥8÷2
x≥8
or 2x-3 ≤ -5
2x ≤-5 +3
2x ≤-2
x ≤ (-2)÷2
x ≤ -2
Expressing the solution as an interval: (-∞,2] ∪ [8,∞)
SAS only. The 3rd side cannot be proven.
Answer:
y = 9.54
and, x = 0.08
Step-by-step explanation:
Given that
x - 2y = -19 .......................(1)
3x + 5y = 48 ...............(2)
Based on the above information
Multiply by 3 in equation 1
So,
3x - 6y = -57
3x + 5y = 48
- - -
-11y = -105
y = 9.54
So, the x would be
x - 2(9.54) = -19
x - 19.08 = -19
x = -19 + 19.08
x = 0.08
Answer:
C) supplementary angles
Step-by-step explanation:
C) supplementary angles
They add up to 180.
