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,∞)
LM is 6.9 to 1dm and LM is 8
Vinegar is the x or horizontal oil is the y or vertical
the point represent the amount of vinegar and oil so for 1 tbsp vinegar you need 1.5tbsp oil
First find the rate of growth
45000=18000(1+r)^(2010-2005)
Solve for r
r=((45,000÷18,000)^(1÷5)−1)×100
R=20%
Use it to find the population in 2015
P=45000(1+0.20)^(2015-2010)
P==111,974.4
Answer:
21.9
Step-by-step explanation:
circumference = pi x diameter
3.14 x 7 = 21.9
