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:
Y = -24
Step-by-step explanation:
For this problem, evaluate simply means for each x, replace the value with -2. So, let's do that.
Y = 6*2x
Y = 6*2(-2)
Y = 6*-4
Y= -24
Cheers.
Answer:
Angle 4 and Angle 1 are supplementary to each other.
Step-by-step explanation:
A line is 180°. Because angle 4 and angle 1 and right next to each other and they share a straight line, both of their angles should add up to 180°, making these two angles supplementary.
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A:C
Step-by-step explanation:
Solution
- 89 gallons contains 40 gallons twice such that:
- This means that we can find at least 200% of 40 gallons in 89 gallons. This gives us what to expect.
- To get the percentage we are looking for, we should use the formula:
New, in this case, is 89 gallons, Old is 40 gallons.
- Thus, we can calculate the percentage as follows:
Thus, the answer is 222.5%
