One ordered pair (a, b) satisfies the two equations ab^4 = 384 and a^2 b^5 = 4608. What is the value of a in this ordered pair?

a = 3∛2

Step-by-step explanation:

ab⁴ = 384     --> a = 384/b⁴

Substitute a = 384/b⁴ into the second equation to solve for "b".

   a²b⁵ = 4608

Substitute b = 2∛4 into the first equation to solve for "a".

ab⁴ = 384

a(2∛4)⁴ = 384

        a  = 384/(2∛4)⁴

        a = 24/4∛4

           = 6/∛4

           = 6(∛2)/2

           = 3∛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.

yes

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step-by-step explanation: