Find the perimeter of the shaded region
1 answer:
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Answer:
The value of a = - 1 , And b =
Step-by-step explanation:
Given as :
Function f(x) =
And f(f(1)) = 0 And f(2) = - 3
Now For , x = 2 , y = - 3
I.e f(2) =
or, - 3 =
I.e 2 + a = - 6 - 3b
Or, a + 3b = - 8 ....... 1
Again f(f(1)) = 0
So, = 0
Or, 1 + a = 0
∴ a = - 1
So , put htis value of a i n eq 1 , we get value of b
So , - 1 + 3b = - 8
Or, 3b = - 7
∴ b =
Hence The value of a = - 1 , And b = Answer
To make that graph you follow these steps.
1) Set the cartesian coordinate system:
- vertical axis: y
- horizontal axis: x
- positive x-semi axis: to the right
- negative x-semi axis: to the left
- positive y-semi axis: upward
- negative y semi axis: dwonward
2) solve the inequality for y:
given: -2x + 5y > 15
transpose-2x: 5y > 15 + 2x
divide by 5: y > 3 + (2/5)x
3) Graph
- draw the line y = 3 + (2/5)x, using a dotted line (i.e. - - - - - -)
- remember that 3 is the y intercept, and 2/5 is the slope
- the line is dotted because the solution does not include the points in the line.
- the solution is the region above and to the left of the dotted line.
4) See the figure attached for better visualization: the pink region is the solution of the inequality.
1) Set the cartesian coordinate system:
- vertical axis: y
- horizontal axis: x
- positive x-semi axis: to the right
- negative x-semi axis: to the left
- positive y-semi axis: upward
- negative y semi axis: dwonward
2) solve the inequality for y:
given: -2x + 5y > 15
transpose-2x: 5y > 15 + 2x
divide by 5: y > 3 + (2/5)x
3) Graph
- draw the line y = 3 + (2/5)x, using a dotted line (i.e. - - - - - -)
- remember that 3 is the y intercept, and 2/5 is the slope
- the line is dotted because the solution does not include the points in the line.
- the solution is the region above and to the left of the dotted line.
4) See the figure attached for better visualization: the pink region is the solution of the inequality.