A teacher can grade 10.5 tests every 30 minutes. How many tests can they grade in two 45 minute prep periods?

31 tests.

Step-by-step explanation:

The rate for the grading is 10.5 every 30 minutes.

Two 45 minute prep periods are 90 minutes.

90 / 30 = 3.

Since three 30 minute periods fit into 90 minutes, we get

3 x 10.5 = 31.5 tests.

Since a teacher did not finish grading the .5 of the test, we don't count it.

Our answer is 31 tests.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

the answer is (-8,-5)

step-by-step explanation:

the endpoint to midpoint is half the length. the length is (-2,-1) so when you are at the midpoint just add it to it to find your answer -6+(-2)= -8 and -4+(-1)=-5 so (-8,-5)