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:
89
Step-by-step explanation:
Given that,
During a promotional weekend, a state fair gives a free admission to every 179th person that enters the fair.
No of people attending the fair on Saturday is 8,633 amd No of people attending the fair on Sunday is 7,400.
We need to find the no of people that received a free admission over the two days.
Dividing 8,633 by 179 gives 48 as quotient and 41 as remainder. It means on Saturday 48 people entered for free.
Dividing 7,400 by 179 gives 41 as quotient and 61 as remainder. It means on Sunday 41 people entered for free.
Total no of people,
T = 48 + 41
T = 89
Hence, there are 89 people for free entries.
Answer:
Standard form of 
Step-by-step explanation:
Here, the given expression is
Now, simplifying the above expression in parts, we get
hence, combining both parts:
= 
The above expression is of the STANDARD FORM: 
Hence, the standard form of
Answer: 1/20
Step-by-step explanation:
Decimal Fraction Percentage
0.05 1/20 5%
