Use the process of completing the square to fill in the blanks.

y = x2 + 8x + 25

16: y = (x^2 + 8x + 16) + 25 - 16

Step-by-step explanation:

To complete the square use (b/2)^2.

Before completing the square, make sure that the a-value is 0. This means that there can be no coefficient to x^2. If there is then factor out this coefficient.

The b-value in this quadratic equation, y = x^2 + 8x + 25, is the coefficient of x. Therefore it is 8. Substitute 8 into the formula to complete the square.

Start by solving inside the parentheses. Divide 8 by 2.

Evaluate the exponent.

Separate the c-value from the a and b values with parentheses like so:

y = (x^2 + 8x) + 25

The blanks should be in the parentheses and outside of the parentheses like so:

y = (x^2 + 8x + __) + 25 - __

You add the answer that you got from (b/2)^2 inside the parentheses and subtract it from the outside of the parentheses.

The number that should fill in the blanks is 16.

y = (x^2 + 8x + 16) + 25 - 16

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;