I think its c hope this helps sorry if it dont
$14.20 is the cost of each book
(1 - 2x)⁴
(1 - 2x)(1 - 2x)(1 - 2x)(1 - 2x)
[1(1 - 2x) - 2x(1 - 2x)][1(1 - 2x) - 2x(1 - 2x)]
[1(1) - 1(2x) - 2x(1) - 2x(-2x)][1(1) - 1(2x) - 2x(1) - 2x(-2x)]
(1 - 2x - 2x + 4x²)(1 - 2x - 2x + 4x²)
(1 - 4x + 4x²)(1 - 4x + 4x²)
1(1 - 4x + 4x²) - 4x(1 - 4x + 4x²) + 4x²(1 - 4x + 4x²)
1(1) - 1(4x) + 1(4x²) - 4x(1) - 4x(-4x) - 4x(4x²) + 4x²(1) - 4x²(4x) + 4x²(4x²)
1 - 4x + 4x² - 4x + 16x² - 16x³ + 4x² - 16x³ + 16x⁴
1 - 4x - 4x + 4x² + 16x² + 4x² - 16x³ - 16x³ + 16x⁴
1 - 8x + 24x² - 32x³ + 16x⁴
The required number is -3 which when added to the numerator and to the denominator of 5/8 results in a fraction whose value is 0.4.
<h3>What is a fraction?</h3>
Fraction is the ratio of a particular part to the whole parts of an object. A fraction has a numerator and a denominator.
<h3>Calculation:</h3>
The given fraction is 5/8
Consider a number as 'x' which is added to both the numerator and the denominator of the given fraction.
So,
(5 + x)/(8 + x)
Since it is given that the result is 0.4 i.e., 4/10, we can write
(5 + x)/(8 + x) = 4/10
⇒ 10(5 + x) = 4(8 + x)
⇒ 50 + 10x = 32 + 4x
⇒ 10x - 4x = 32 - 50
⇒ 6x = -18
⇒ x = -18/6
∴ x = -3
Therefore, the required number is -3.
Check:
(5 + (-3))/(8 + (-3)) = (5 - 3)/(8 - 3) = 2/5 = 0.4
Learn more about fractions here:
brainly.com/question/17220365
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