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

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<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

7 0

2 years ago

Use the graph of the function. Determine Over what interval(s) the function is positive or negative.

soldier1979 [14.2K]

Answer:

please where is the drawing I mean the graph

6 0

3 years ago

Find the area of the triangle <br> A<br> 47°<br> b<br> 32 ft<br> C<br> 19 ft

Solnce55 [7]

Answer:

222 [ft²].

Step-by-step explanation:

1. the required area can be calculated according to the formula:

A=0.5*b*c*sin(A);

2. after substitution of b=32; c=19 and sin(A)≈0.7313537:

A=0.5*32*19*0.7313537=222.3315248 [ft²].

4 0

1 year ago

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