Mario is writing a coordinate proof to show that the perpendicular bisector of an isosceles triangle's base divides it into two triangles of equal area.

a triangle is graphed on a coordinate plane. the vertices of triangle are labeled as a, b and c. the vertex labeled as a lies on begin ordered pair 0 comma 0 end ordered pair. the vertex labeled as b lies on begin ordered pair x comma y end ordered pair. the vertex labeled as c lies on begin ordered pair 2 x comma 0 end ordered pair. point d lies on side a c. an altitude is drawn from point b to point d.

enter your answers in the boxes to complete mario's proof.

since a perpendicular bisector bisects a segment, the coordinates of d are (
,
).

in △bcd, the length of the base is
and the height is y. so an expression for the area of △bcd is 12xy .

in △abd, the length of the base is
and the height is
. so an expression for the area of △abd is 12xy .

comparing the two areas shows that the perpendicular bisector of an isosceles triangle divides the triangle into two triangles of equal area.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

i dont know the answer but here's a picture of a dog

they aren't great and cause destruction, idk man

answer:

at time x=0 we have 1000, at time x=1 we have 2000, at time x=2 we have 4000.  

so that's an initial value of 1000 and a ratio of 2,

y = 1000 (2^x)

hope this !