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Aneli [31]
3 years ago
9

the numerator of a fraction is 2 less than its denominator. when both numerator and denominator are increased by 3, the fraction

is increased by 3/20. find the original fraction
Mathematics
2 answers:
Dmitriy789 [7]3 years ago
7 0
First denominator -- x 
<span>first numerator ---- x-2 </span>

<span>new denominator -- x+3 </span>
<span>new numerator ---- x+1 </span>

<span>(x-2)/x + 3/20 = (x+1)/(x+3) </span>
<span>times 20x(x+3) , the LCD </span>
<span>20(x+3)(x+1) + 3x(x+3) = 20x(x+1) </span>
<span>expanding and simplifying gave me </span>
<span>x^2 + 3x - 40 = 0 </span>
<span>(x-5)(x+8) = 0 </span>
<span>x = 5 or x=-8 </span>

<span>if x=5, the original fraction was 3/5 </span>
<span>if x=-8 the original fraction was -10/-8 or 5/4 </span>

<span>check for 3/5 , new fraction would be 6/8 or 3/4 </span>
<span>3/5 + 3/20 = 12/20 + 3/20 = 15/20 = 3/4 </span>

<span>but for 5/4, new fraction would be 8/7 </span>
<span>5/4 + 3/20 = 28/20 = 7/5 ≠ 8/7 </span>
<span>BUT, if we take the unsimplified fraction -10/-8 , new fraction would be -7/-5 = 7/5 </span>

<span>So the original fraction would be 3/5 for sure, but </span>
<span>also the unsimplified fraction -10/-8</span>
creativ13 [48]3 years ago
4 0
The original fraction will be 3/5 and I am positive. :D
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Answer:

width = 1 1/3 inches

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Step-by-step explanation:

let 'w' = width

let '7+2w' = length

P = 2l + 2w

22 = 2w + 2(7+2w)

22 = 2w + 14 + 4w

8 = 6w

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substitute 1 1/3, or 4/3, to find length:

l = 7 + 2(4/3)

l = 7 + 8/3 or 9 2/3

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You are given the system of equations to solve by the elimination method, which is an INCORRECT step that will NOT produce a
SCORPION-xisa [38]

Answer: multiply x by 2 in the first equation and subtract the second equation

Step-by-step explanation:

To solve a system of linear equations by elimination method , our first step is to make its (either x or y) coefficient same.

For that we multiply a number to both sides of the equation not to only one term.

So by checking all the given options it is pretty clear that the last option is not applicable for elimination method because in this 2 is multiplied to only one term, which proceeds to loose the balance of the equation.

Thus , an INCORRECT step that will NOT produce a  system with the same solution is "multiply x by 2 in the first equation and subtract the second equation ".

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A rectangular box which is open at the top can be made from an12-by-18-inch piece of metal by cutting a square from each corner
algol [13]

Answer:

h=2.35in, l=13.3in and w=7.3in

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram that will represent the prolem. (Look at attached picture)

From the diagram we can see that the length ad the width of the box are found by  using the following expressions:

L=18-2x

W= 12-2x

H=x

next, we can make use of the volume formula of a rectangular prism, which is the following:

V=WLH

so we can substitute the expressions we got before on the formula:

V=x(12-2x)(18-2x)

and for ease of calculation, we can multiply the terms, so we get:

V=x(216-24x-36x+4x^{2})

V=x(4x^{2}-60x+216)

V=4x^{3}-60x^{2}+216x

So now we can find the derivative of the volume:

V'=12x^{2}-120x+216

and set it equal to zero, so we get:

12x^{2}-120x+216=0

and now we can solve. We can start by factoring the left side of the equation, so we get:

12(x^{2}-10x+18)=0

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x^{2}-10x+18=0

This one can only be solved by using the quadratic formula:

x=\frac{-b\pm \sqrt{-b^{2}-4ac}}{2a}

so we substitute the corresponding values:

x=\frac{-(-10)\pm \sqrt{-(-10)^{2}-4(1)(18)}}{2(1)}

which yields:

x=7.65in or x=2.35in

we keep the 2.35in only, because the 7.65in returns an impossible box, since that would make the width a negative width.

So the 2.35in height would give us the greatest box. Now we can use it to find the height, the width and the length of the box.

Height=x=2.35

W=12-2x=12-2*2.35=7.3in

L=18-2x=18-2(2.35)=13.3in

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