identify the vertex, the axis of symmetry, the maximum or minimum value, and the range of the parabola of y=x^2+8x+13

Step-by-step explanation:

y=x²+8x+13=x²+8x+(8/2)²-(8/2)²+13=x²+8x+16-16+13=(x+4)²-3

vertex (-4,-3)

minimum value=-3

maximum value=∞

range:[-3,∞)

axis of symmetry:x+4=0 or x=-4

answer: 1722

step-by-step explanation:

given: the mass of saturn=

the mass of mercury=

the number of times the mass of saturn is greater than the mass of mercury

hence, the mass of saturn is 1722 times greater than the mass of mercury.

geometry: triangles

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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+

25.45584