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,∞)
Answer:
z = 113
y = 31
Step-by-step explanation:
j || n and line a is their transversal. (given)
Therefore,
z° = 180° - 67° (exterior angles on the same side of transversal)
z°= 113°
z = 113
(5y - 88)° = 67° (exterior alternate angles)
5y - 88 = 67
5y = 67 + 88
5y = 155
y = 155/5
y = 31
I believe the answer is 0
Answer:
9π or 28.27 cm
Step-by-step explanation:
The circumference formula is 2πr or dπ. The diameter is 9 cm so we multiply 9 with pi to get the answer.
Answer:
Step-by-step explanation:
294% = 2.94 = 2 and .94 = 2 94/100 = 2 47/50
