Allen is on the football team this year but he has poor time management skills. His mother told him that he is off the team if he fails anything. On his first quiz he got a 90, the second he earned an 86, then he earned an 82 on the next two quizzes. Is this sequence arithmetic or geometric? Recursion equation? Function formula? On what quiz will he no longer to play football? How many total points did Allen earn on all the quizzes he has taken up to his removal of the team?

See explanation

Step-by-step explanation:

We can see that the sequence is 90, 86,82,

The common difference is  86 - 90 = -4

                                             82 - 86 = -4

Hence the sequence is arithmetic

The function is;

t(n) = 90 + (n - 1)(-4) = 90 + 4 - 4n

t(n) = 94 - 4n

Since it is AP, we have the sequence as;

90, 86, 82, 78, 74, 70, 66, 62

He will no longer play football after the eighth quiz.

The total points earned is the sum of the first eight terms of the AP

Sn =n/2[2a + (n - 1) d]

Sn = 8/2[2(90) + (8 - 1) (-4)]

Sn = 608 points

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.