Express x^2-5x+8 in the form (x-a)^2+b

x^2 - 5x + 8 = (x - 5/2)^2 + 7/4

Step-by-step explanation:

(x - a)^2 + b = x^2 - 2ax + a^2 + b

equate to your quadratic :

x^2 - 5x + 8 = x^2 - 2ax + (a^2 + b)

equating coefficients (ignoring x^2 as the coefficient is 1 for both)

for x :

-5 = -2a --> a = 5/2

for x^(0) : 8 = a^2 + b , note a = 5/2

thus,

8 = (5/2)^2 + b

8 = 25/4 + b

b = 8 - 25/4 = 32/4 - 25/4 = (32 - 25)/4 = 7/4

hence a = 5/2 , b = 7/4

thus,

x^2 - 5x + 8 = (x - 5/2)^2 + 7/4

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

y=x+9

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step-by-step explanation: