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miss Akunina [59]
3 years ago
14

The denominator of a fraction is two more than the numerator. If both numerator and denominator are decreased by six, the simpli

fied result is 1718
17


18


. Find the original fraction. (Do NOT simplify.)
Mathematics
1 answer:
ira [324]3 years ago
4 0

Answer:

\dfrac{40}{42}

Step-by-step explanation:

Let the numerator of the fraction=x

Since the denominator of a fraction is two more than the numerator.

Denominator=x+2

The fraction is therefore:

\dfrac{x}{x+2}

If both numerator and denominator are decreased by six, the fraction becomes:

\dfrac{x-6}{x+2-6}

The simplified result is \dfrac{17}{18}

Therefore:

\dfrac{x-6}{x+2-6}=\dfrac{17}{18}\\$Next, we solve for x\\Cross multiply\\18(x-6)=17(x+2-6)\\18(x-6)=17(x-4)\\Expand the bracket\\18x-108=17x-68\\Collect like terms\\18x-17x=-68+108\\x=40

Substituting x=40 into the initial fraction

\dfrac{x}{x+2}=\dfrac{40}{40+2}=\dfrac{40}{42}

Therefore, the original fraction is \dfrac{40}{42}

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2 years ago
The sum of 5 consecutive odd numbers is 145. What is the third number in this sequence
vredina [299]

Answer: The 3rd number in the sequence is 29.

Step-by-step explanation: What we have is a sequence of “ODD” numbers and they are consecutive, which means they come one after another with regular intervals. We don’t have any of the numbers but we can start by saying ‘let x represent the first number in the sequence’

With this in mind, we can now assume all other four numbers in the sequence. Therefore if the 1st number is x, the 2nd number would be x + 2, and the the 3rd number would be x + 4, 4th number would be x + 6 while the 5th number would be x + 8.

The reason is that, every odd number is an addition of two to the previous odd number. For instance, if you start with 3, the next odd number would be 3+2 (5), and so on.

Therefore we can now write our consecutive odd numbers as follows;

x + (x + 2) + (x + 4) + (x + 6) + (x + 8)

Remember that all the numbers add up to 145. Therefore,

x + x + 2 + x +4 + x + 6 + x + 8 = 145

5x + 20 = 145

Subtract 20 from both sides of the equation

5x = 125

Divide both sides of the equation by 5

x = 25.

The first odd number is 25, which means the 3rd odd number is 25 + 4.

Therefore the 3rd odd number is 29.

5 0
3 years ago
The answer is 3.8 and I CANT FIGURE IT OUT
Alex17521 [72]
3.8 is the answer you already figured it out
8 0
3 years ago
A deposit $400 into an account that pays simple interest ta a rate of 3% per year how much interest will be paid in the first 5
ValentinkaMS [17]

Answer:

$60

Step-by-step explanation:

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6 0
3 years ago
Does the point (4, 0) satisfy the equation y = –5x + 4?
Arlecino [84]

Answer:

no

Step-by-step explanation:

y = –5x + 4

Substitute the point into the equation

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0 = -20+4

0 = -16

This is not true so it is not a solution to the equation

4 0
3 years ago
Read 2 more answers
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