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
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Answer:
m = 5/3
Step-by-step explanation:
<span>Simplifying
7(2e + -1) + -3 = 6 + 6e
Reorder the terms:
7(-1 + 2e) + -3 = 6 + 6e
(-1 * 7 + 2e * 7) + -3 = 6 + 6e
(-7 + 14e) + -3 = 6 + 6e
Reorder the terms:
-7 + -3 + 14e = 6 + 6e
Combine like terms: -7 + -3 = -10
-10 + 14e = 6 + 6e
Solving
-10 + 14e = 6 + 6e
Solving for variable 'e'.
Move all terms containing e to the left, all other terms to the right.
Add '-6e' to each side of the equation.
-10 + 14e + -6e = 6 + 6e + -6e
Combine like terms: 14e + -6e = 8e
-10 + 8e = 6 + 6e + -6e
Combine like terms: 6e + -6e = 0
-10 + 8e = 6 + 0
-10 + 8e = 6
Add '10' to each side of the equation.
-10 + 10 + 8e = 6 + 10
Combine like terms: -10 + 10 = 0
0 + 8e = 6 + 10
8e = 6 + 10
Combine like terms: 6 + 10 = 16
8e = 16
Divide each side by '8'.
e = 2
Simplifying
<span>e=2
</span></span>
(sorry, i went into depth)
128
This question requires us to solve an infinite GP
As we can see the first unit is 16 wide, then 8, then 4 and so on; this can be written as
∞
(64 used as 16*4 = 64 is the area of the first rectangle)
We have 
∞
where a is the first term and r is the common ratio of the GP for summing an infinite GP.
here we have
Therefore
∞
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