Which equation describes the graph?
a: y=-|x+2|
b: y=-|x|+2
c: y=-|x-2|
d: y=-|x|-2

OPTION C: y = - |x - 2|

Step-by-step explanation:

To solve problems of this type take any two points on the graph. We take two points:

 This means that when x = 2, y = 0.

And

These two points are on the given line.

So, these two points are substituted to check if they satisfy the given equation.

OPTION A: y = - |x + 2|

Substituting (2, 0):

LHS = y = 0

RHS = - |2 + 2| = - 4 ≠ 0

So, this option is eliminated.

OPTION B: y = - |x| + 2

Substitute (x, y) = (2, 0)

LHS = 0

RHS = - |2| + 2 = - 2 + 2 = 0

LHS = RHS

Now, check for (0, -2)

LHS = -2

RHS = - |0| + 2|

= - |0| + 2 = 2 ≠ -2

So, this option is eliminated as well.

OPTION C: y = - |x - 2|

Substitute (2, 0)

LHS = 0

RHS = - |2 - 2| = 0

LHS = RHS

Now, substitute (0, -2)

LHS = -2

RHS = - |0 - 2|

       = - |- 2|

       = - 2

∴ LHS = RHS for both the points.  

OPTION D: y = - |x| - 2

Substitute (2, 0)

LHS = 0

RHS = - |2| - 2

       = - 2 - 2

       = - 4

This option is eliminated as well.

So, OPTION C is our answer since it satisfies the points.

NOTE: Points satisfying the equation of the graph is only a necessary condition not a sufficient one.

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing im pretty sure that is the right answer

step-by-step explanation:

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step-by-step explanation:

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