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7nadin3 [17]
2 years ago
7

The denominator of a fraction is 3 more than its numerator. If 2 is added to both the numerator and the denominator, the 2 new f

raction is equivalent to Find the 3 original fraction. (Hint: Let the numerator of the original fraction be x)​
Mathematics
1 answer:
Julli [10]2 years ago
7 0

Answer:

  4/7

Step-by-step explanation:

Using the hint, we have an original fraction of x/(x+3). The given manipulations and relations can be used to find the value of x, and the original fraction.

__

<h3>adding 2 to each term</h3>

The new fraction is ...

  \dfrac{x+2}{(x+3)+2}=\dfrac{x+2}{x+5}\\

<h3>new value</h3>

Apparently, the new value of this fraction is 2/3. We can use this to find the value of x.

  \dfrac{x+2}{x+5}=\dfrac{2}{3}\\\\3(x+2)=2(x+5)\qquad\text{multiply by $3(x+5)$}\\\\3x+6=2x+10\qquad\text{eliminate parentheses}\\\\x=4\qquad\text{subtract $2x+6$}

The original fraction is ...

  4/(4+3) = 4/7

_____

<em>Alternate solution</em>

In the ratio 2/3, the numerator is twice the difference between the denominator and numerator. 2 = 2(3 -2)

The problem statement tells us the difference between the numerator and denominator is 3. That is not changed by adding the same number to each. This means the fraction equivalent to 2/3 is (2·3)/(3·3) = 6/9. Subtracting 2 from each of the numerator and denominator gives the original fraction:

  (6-2)/(9-2) = 4/7

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Please do number 3___________________
Alexandra [31]

9514 1404 393

Answer:

  m∠SVW = 80°

Step-by-step explanation:

3. The sum of <em>same-side interior</em> angles SVW (4x°) and VWT (5x°) is 180°. This can be used to solve for x and to find the angle values.

  4x + 5x = 180

  9x = 180 . . . . . . . . collect terms

  x = 20 . . . . . . . . . . divide by 9

m∠SVW = 4x° = 4(20)°

m∠SVW = 80°

_____

4. Then m∠VWT = 180° -80° = 100° = 5x°.

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5. <em>Consecutive interior</em> angles are supplementary. ("Same-side" and "consecutive" are used interchangeably in this context.)

4 0
3 years ago
Some of answers use 3,14 as a substitute for pi.
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2 years ago
ABCD is a quadrilateral <br>Work out angle x<br>​
netineya [11]

First of all, we can work out the length of BD: using the pythagorean theorem, we have

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Now, we can work on triangle BCD and use the sine theorem: we have

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