What are the solutions of the system? solve by graphing. y = -x^2 - 3x + 2 y = -2x + 2

Solutions are (0,2) and (-1,4).

Step-by-step explanation:

There are two equations given for which graphing is to be done.

Equations are y = -2x+2------(1)

and y = -x²-3x+2---------(2)

Now we will solve the equations to get the values of x and y or the coordinates of intersection of these two graphs.

By substituting y from equation 2 into equation 1.

- x²-3x+2 = -2x+2

-x²-3x+2x = 0

-x²-x = 0

x²+x = 0

x(x+1)=0 ⇒ x = 0 and x = -1

Now we put these values of x in equation 2.

For x = 0 y = -2×0+2 = 2

For x = -1 y = 2+2 = 4

So they intersect each other at (0,2) and (-1,4).

geometry: triangles

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lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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