1)y=2x^2-12x+14 in vertex form with steps asap please

y = 2 ( x + 3 ) 2 − 4

Step-by-step explanation:

Use the form a x 2 + b x + c , to find the values of a , b , and c . a = 2 , b = 12 , c = 14 Consider the vertex form of a parabola. a ( x + d ) 2 + e Substitute the values of a and b into the formula d = b 2 a . d = 12 2 ( 2 ) Simplify the right side. d = 3 Find the value of e using the formula e = c − b 2 4 a . e = − 4 Substitute the values of a , d , and e into the vertex form a ( x + d ) 2 + e . 2 ( x + 3 ) 2 − 4 Set y equal to the new right side. y = 2 ( x + 3 ) 2 − 4

geometry: triangles

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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+

25.45584

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.