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3 years ago

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X % of $5 = $4 Please help

1 answer:

ASHA 777 [7]3 years ago

4 0

Answer: 80%

Explanation 4/5=.8

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Step-by-step explanation:

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In this exercise we have to use the knowledge of geometric progression to find three specific numbers, in this way we can say that these numbers correspond to;

$0.16\\ -0.64\\ 2.56$

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now, the differences between the terms must be the same:

$a1*r + 2 - a_1 = a_3 - (a_1*r + 2) = a_1*r^2 - (a_1*r + 2)\\a_1*r^2 - 2*a_1*r + a_1 - 4 = 0$

and now, when we increase the third term by 9,so we have:

$(a_1*r^2 + 9)/(a_1*r + 2) = (a_1*r + 2)/a_1\\(a_1^2*r^2 + 9*a_1)/(a_1*r + 2) = a_1*r + 2\\a_1^2*r^2 + 9*a_1 = (a_1*r + 2)^2 = a_1^2*r^2 + 4*a_1*r + 4\\4*a_1*r - 9*a_1 + 4 = 0\\9*a - 4 = 4*a_1*r\\r = (9*a_1 - 4)/(4*a_1)$

Now we use that identity in the first equation :

$a_1*(9*a_1 - 4)^2/(4×a_1)^2 - 2*a_1*(9*a_1 - 4)/(4*a_1) + a_1 - 4 = 0\\(81*a_1^2 - 72*a_1 + 16)/(16*a_1) - (9*a_1 - 4)/2 + a_1 - 4 = 0\\81*a_1^2 - 72*a_1 + 16 - 8*a_1*(9*a_1 - 4) + 16*a_1^2 - 64*a_1 = 0\\25a_1^2 - 104a_1 + 16 = 0$

The general solution for a quadratic equation is

$(-b + \sqrt{(b^2 - 4ac))/(2a)$

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so, put the numbers in the formula we find:

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See more about geometric progress at brainly.com/question/14320920

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