A professor gives two types of quizzes, objective and recall. He is planning to give at least 15 quizzes this quarter. The student preparation time for an objective quiz is 15 minutes and for a
recall quiz 30 minutes. The professor would like a student to spend at least 5 hours (300 minutes)
preparing for these quizzes above and beyond the normal study time. The average score on an
objective quiz is 7, and on a recall type 5, and the professor would like the students to score at
least 85 points on all quizzes. It takes the professor one minute to grade an objective quiz, and 1.5
minutes to grade a recall type quiz. How many of each type should he give in order to minimize
his grading time?

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )

4+4+2x

or

2x+8

step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.