If lylah completes the square for f(x)=x squared -12x+7 in order to find the minimum she must write f(x) in the general form f(x)=(x-a)squared +b what is the value of a for f(x)? a. 6 b. -6 c. 12 d. -12

A. 6

Step-by-step explanation:

f(x) = x² − 12x + 7

To complete the square, we first factor the leading coefficient to make it 1 (which it already is).

Then, we take half the second coefficient, square it, and then add to both sides.  So (-12/2)² = (-6)² = 36.

f(x) + 36 = x² − 12x + 36  + 7

Then we factor the perfect square:

f(x) + 36 = (x − 6)² + 7

Then solve for f(x) by subtracting and simplifying:

f(x) = (x − 6)² + 7 − 36

f(x) = (x − 6)² − 29

So the value of a is 6.

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

the answer is 24

step-by-step explanation: