Matthew’s 4th grade science experiment included counting the number of popcorn kernels that popped after 3 minutes in a microwave. If 126 kernels popped and 38 kernels did not pop, what was the percent of kernels popped to the nearest whole percent?

77%

Step-by-step explanation:

step 1

Find out the total kernels

The total kernels is equal to the sum of the kernels popped plus the kernels not popped

so

step 2

Find out the percent of kernels popped

we know that

The 164 total kernels represent the 100%

so

using proportion

Find out what percentage represent 126 kernels popped

The vertex can be found by completing the square:
f(x) = -(x^2 - 50x)
      = - (x^2 + 625 - 625 - 50x)    (take half the coeff of x, square
      = - (x^2 + 625 - 50x ) + 625            it then add and subtract it)
      = - (x^2 - 25x - 25x + 625) + 625
      = - (x(x- 25) -25(x + 25)) + 625
      = - ((x- 25) (x + 25)) + 625
      = - ((x + 25)^2 + 625
so the vertex is (25, 625)
in this context this is the 'optimized' area or the largest possible area with the given perimeter (so it is basically a square, 25 x 4 = 100)