Answer:
- axis of symmetry: x = -3
- root: x = -3
Step-by-step explanation:
As indicated in the example shown, the axis of symmetry is the vertical line through the vertex. That is, its equation is ...
x = <x-coordinate of vertex>
Here, the x-coordinate of the vertex is -3, so the axis of symmetry is ...
x = -3
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The roots are the x-intercepts, the x-values where the graph touches or crosses the x-axis. When the graph only touches the x-axis, there is only one root. Here, the x-value of the point where the graph touches the x-axis is x = -3.
The root is x = -3.
Answer:
x=50
Step-by-step explanation:
-0.2(x-20)=44-x
Distribute
-0.2x+4=44-x
Add x to each side
-.2x +4+x = 44-x+x
.8x+4 = 44
Subtract 4 from each side
.8x+4-4 = 44-4
.8x = 40
Divide each side by .8
.8x/.8 = 40/.8
x=50
The problem statement gives a relation between the amount removed from one bag and the amount removed from the other. It asks for the amount remaining in each bag. Thus, there are several choices for variables in this problem, some choices resulting in more complicated equations than others.
Let's do it this way: let x represent the amount remaining in bag 1. Then the amount removed from bag 1 is (100-x). The amount remaining in bag 2 is 2x, so the amount removed from that bag is (100-2x). The problem statement tells us the relationship between amounts removed:
... (100 -x) = 3(100 -2x)
... 100 -x -3(100 -2x) = 0 . . . . . . subtract the right side
... 5x -200 = 0 . . . . . . . . . . . . . . eliminate parentheses and collect terms
... x -40 = 0 . . . . . . . . . . . . . . . . .divide by 5
... x = 40 . . . . . . . . . . . . . . . . . . . add 40
- 40 kg is left in the first bag
- 80 kg is left in the second bag
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<u>Check</u>
The amount removed from the first bag is 60 kg. The amount removed from the second is 20 kg. The amount removed from the first bag is 3 times the amount removed from the second bag, as described.
The answer that you should get is 5(5x^2- 24x +30)
Answer:
2x+30=x+80 (corresponding angles)
2x-x=80-30
x=50
