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:
<em>Choice B. 16 feet.</em>
<em>The height of the tree is 16 ft</em>
Step-by-step explanation:
<u>Similar Triangles</u>
Similar triangles have their corresponding side lengths proportional by a fixed scale factor.
We are given the drawings of a tree and a wall and it's assumed both triangles are similar. We need to find the scale factor and find the height of the tree.
Comparing the corresponding distances from the viewer to the base of the tree and the base of the wall, we can calculate the scale factor as 24/6=4.
Applying the same factor to the height of the model, we get the height of the tree is 4*4 = 16 ft.
Choice B. 16 feet
The height of the tree is 16 ft
Answer:
f(x) = x
Step-by-step explanation:
note : slope is positive 1, so the x term must be positive
also note the graph intersects the curve at y = 0, which means that they y-intercept is zero .
if we substitute this into the general equation for a line
y = mx + b, where m = +1 and b = 0,
we get y = x
or f(x) = x (in function form)
Answer:
x = 2
Step-by-step explanation:
Bases are equal. So, compare powers
2x - 1 = 3
Add 1 to both sides,
2x = 3+1
2x = 4
Divide both sides by 2
x = 4/2
x = 2
The Answer Is 60
2.5 x 8 The Number Of Sides On That Shape Was 8
2.5 x 8 = 20
20 times the radius 3
20 x 3 = 60
60cm^2
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