The second and third terms of a G. P is 6 times the fourth term. Find the possible values of the common ratio.

-1/3 or 1/2.

Step-by-step explanation:

Second term = ar, the third = ar^2 and the fourth = ar^3.

So we have the equation:

ar + ar^2 = 6ar^3

r + r^2 = 6r^3

6r^3 - r^2 - r = 0

r(6r^2 - r - 1) = 0

(3r + 1 )(2r -1) = 0

r = -1/3, 1/2.

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

answer is the third choice:

3x^5+4x^4+x^3+2x^2-10x-7=0

step-by-step explanation: