Rewrite without absolute value for the given conditions: y=|x-3|+|x+2|-|x-5|, if x>5
2 answers:
Answer:
Step-by-step explanation:
It might interest you to know what this question means without the restriction. See graph 36b. This shows exactly what happens to the absolute value. There are all sorts of turns and twists in it. Notice all the changes in direction and the minimum at -2,-2. The y intercept is at 0,0.
0,0 is also one of the x intercepts as well. The other is -4,0. The whole point of showing you this is to make you aware of what the restriction does.
The graph is reduced to a line starting at (5,9)
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Solution :
From the figure,
The coordinates of --
A = (-5,-3)
B = (-6,-1)
C = (-3,-1)
D = (-2,-3)
When it undergoes reflection about x-axis, we have the coordinates of the quadrilateral as
A' = (-5,+3)
B' = (-6,+1)
C' = (-3,+1)
D' = (-2,+3)
Now A'B'C'D' is translated 3 units to right, so the coordinates will be --
A" = (-2,3)
B" = (-3,1)
C" = (0,1)
D" = (1,3)
When the quadrilateral moves third and two units up, we get
A"' = (3,3)
B"' = (2,1)
C"' = (5,1)
D"' = (6,3)
First of all, you add 1/3 and 4/5, so you get:
To add 2 fractions, they need to have the same denominator. Since 3 and 5 don't have a common factor, so you multiply 1/3 by 5, and 4/5 by 3, so you get:
Now, the two fractions got the same denominator, and you can add them by adding the numerators over the same denominator. (You don't add denominators in addition) so you get:
That's the sum of 1/3 + 4/5.
Now, they want the sum of the 2 fractions 7 times. So you multiply 17/15 by 7. And as you know, 7 = 7/1. So you get:
In multiplication no need to have the same denominator. You multiply nominators by nominators and denominators by denominators. So you get:
Since 119 and 15 don't have a common factor, so they can't be simplified.
So, the answer is 119/15.
Hope this Helps! :D
To add 2 fractions, they need to have the same denominator. Since 3 and 5 don't have a common factor, so you multiply 1/3 by 5, and 4/5 by 3, so you get:
Now, the two fractions got the same denominator, and you can add them by adding the numerators over the same denominator. (You don't add denominators in addition) so you get:
That's the sum of 1/3 + 4/5.
Now, they want the sum of the 2 fractions 7 times. So you multiply 17/15 by 7. And as you know, 7 = 7/1. So you get:
In multiplication no need to have the same denominator. You multiply nominators by nominators and denominators by denominators. So you get:
Since 119 and 15 don't have a common factor, so they can't be simplified.
So, the answer is 119/15.
Hope this Helps! :D